EEG Journal Vol. XXVII, No. 2

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Oommen, Thomas Board Chair, Michigan Technological University Sasowsky, Ira D. University of Akron

ASSOCIATE EDITORS Ackerman, Frances Ramboll Americas Engineering Solutions, Inc. Bastola, Hridaya Lehigh University Beglund, James Montana Bureau of Mines and Geology Bruckno, Brian Virginia Department of Transportation Clague, John Simon Fraser University, Canada Dee, Seth University of Nevada, Reno Fryar, Alan University of Kentucky Gardner, George Massachusetts Department of Environmental Protection

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Environmental & Engineering Geoscience May 2021 VOLUME XXVII, NUMBER 2 Special Issue on Debris Flows, Part 2 Paul M. Santi and Lauren N. Schaefer, Guest Editors

Submitting a Manuscript Environmental & Engineering Geoscience (E&EG), is a quarterly journal devoted to the publication of original papers that are of potential interest to hydrogeologists, environmental and engineering geologists, and geological engineers working in site selection, feasibility studies, investigations, design or construction of civil engineering projects or in waste management, groundwater, and related environmental fields. All papers are peer reviewed.

The editors invite contributions concerning all aspects of environmental and engineering geology and related disciplines. Recent abstracts can be viewed under “Archive” at the web site, “http://eeg.geoscienceworld.org”.

Articles that report on research, case histories and new methods, and book reviews are welcome. Discussion papers, which are critiques of printed articles and are technical in nature, may be published with replies from the original author(s). Discussion papers and replies should be concise.

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Cover photo A filter barrier for debris flow, clogged with retained material. This barrier is part of an experimental site in the Italian Alps. Each time it is impacted, the deformation of the steel elements is recorded, from which the impact force can be back-calculated. Photo courtesy of Matteo Ceccarelli, Politecnico di Torino. See article on page 195.

Volume XXVII, Number 2, May 2021

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Environmental & Engineering Geoscience Volume 27, Number 2, May 2021 Special Issue on Debris Flows, Part 2 Paul M. Santi and Lauren N. Schaefer, Guest Editors Table of Contents 151

Introduction to Special Issue on Debris Flows-Part 2 Paul M. Santi, Lauren N. Schaefer

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Debris-Flow Hazard Assessments: A Practitioner’s View Matthias Jakob

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Steep Creek Risk Assessment for Pipeline Design : A Case Study From British Columbia, Canada Joseph E. Gartner, Matthias Jakob

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Debris-Flow and Debris-Flood Susceptibility Mapping for Geohazard Risk Prioritization Mattheieu Sturzenegger, Kris Holm, Carie-Ann Lau, Matthias Jakob

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Impact of Debris Flows on Filter Barriers: Analysis Based on Site Monitoring Data Alessandro Leonardi, Marina Pirulli, Monica Barbero, Fabrizio Barpi, Mauro Borri-Brunetto, Oronzo Pallara, Claudio Scavia, Valerio Segor

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Monitoring Debris-Flow Surges and Triggering Rainfall at the Lattenbach Creek, Austria Johannes Huebl, Roland Kaitna

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Monitoring of Rainfall and Soil Moisture at the Rebaixader Catchment (Central Pyrenees) Raül Oorthuis, Marcel Hürlimann, Clàudia Abancó, José Moya, Luigi Carleo

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Mitigation of Debris Flows-Research and Practice in Hong Kong Ken K. S. Ho, Raymond C. H. Koo, Julian S. H. Kwan

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Velocity and Volume Fraction Measurements of Granular Flows in a Steep Flume Luca Sarno, Maria Nicolina Papa, Luigi Carleo, Paolo Villani

Introduction to Special Issue on Debris Flows-Part 2

We hope you enjoy the second of two Special Issues of Environmental and Engineering Geoscience, focusing on the topic of debris flows. These papers were all originally presented at the Seventh International Conference on Debris-Flow Hazards Mitigation (DFHM7), held in Golden, Colorado (USA) from June 10-13, 2019. The conference proceedings were published as AEG Special Publication 28, available at https://mountainscholar.org/handle/11124/173038, and include 134 papers from 17 countries. As guest editors, we selected a subset of these short papers that we thought would be of great interest to E&EG readers in expanded form.

As we noted in the introduction to the first special issue, the DFHM conference covered a huge range of

topics and research tools, and the papers chosen for this special issue represent the spectrum of this research, including three papers on the topics of monitoring and instrumentation, three papers on risk and hazard assessment, a flume study, and a mitigation overview. All of these papers reflect the state of the art in debris flow research and management, and, overall, the content of this issue was designed to provide practical tools and information for both researchers and industry professionals who deal with debris flows.

We offer our thanks to the authors of these Special Issue papers, and hope that you will find them valuable and informative. We are also very grateful to the many reviewers who contributed their time and expertise to improving the papers:

Cláudia Abancó Eric Bilderback Holly Brunkal Chen Cheng Francesco Comiti Kahlil Frederick Cui Liang Gao Nico Gray Marcel Hürlimann Jason Kean Luke McGuire S. Poudyal Francis Rengers Luca Sarno Violchen Sepúlveda Andy Take Ann Youberg

UPC Barcelona TECH Colorado State University Western Colorado University Institute of Mountain Hazards and Environment (China) Libera Universita di Bolzano Institute of Mountain Hazards and Environment (China) Hong Kong University of Science and Technology University of Manchester Universitat Politècnica de Catalunya US Geological Survey University of Arizona Hong Kong University of Science and Technology US Geological Survey University of Salerno Servicio Nacional de Geologia y Mineria (Chile) Queens University Arizona Geological Survey Sincerely, Paul M. Santi, Guest Co-Editor Lauren N. Schaefer, Guest Co-Editor

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Debris-Flow Hazard Assessments: A Practitioner’s View MATTHIAS JAKOB* BGC Engineering, 500–980 Howe Street, Vancouver, BC V6Z OC8, Canada

Key Terms: Debris Flow, Debris Flood, Hazard Assessment, Risk Assessment, Debris-Flow Practice ABSTRACT Substantial advances have been achieved in various aspects of debris-flow hazard assessments over the past decade. These advances include sophisticated ways to date previous events, two- and three-dimensional runout models including multi-phase flows and debris entrainment options, and applications of extreme value statistics to assemble frequency–magnitude analyses. Pertinent questions have remained the same: How often, how big, how fast, how deep, how intense, and how far? Similarly, although major life loss attributable to debris flows can often, but not always, be avoided in developed nations, debris flows remain one of the principal geophysical killers in mountainous terrains. Substantial differences in debris-flow hazard persist between nations.

Some rely on a design magnitude associated with a specific return period; others use relationships between intensity and frequency; and some allow for, but do not mandate, in-depth quantitative risk assessments. Differences exist in the management of debris-flow risks, from highly sophisticated and nation-wide applied protocols to retroaction in which catastrophic debris flows occur before they are considered for mitigation. Two factors conspire to challenge future generations of debrisflow researchers, practitioners, and decision makers: Population growth and climate change, which are increasingly manifested by augmenting hydroclimatic extremes. While researchers will undoubtedly finesse future remote sensing, dating, and runout techniques and models, practitioners will need to focus on translating those advances into practical cost-efficient tools and integrating those tools into long-term debris-flow risk management.

INTRODUCTION Adding 70 million humans to Earth every year leaves a mark not only on ever-expanding urban centers and their suburban fringes, as well as development

*Corresponding author email: mjakob@bgcengineering.ca

of wildland and wilderness interface, but a proportion of that growth also spills directly into mountainous terrain. Mountains consist of peaks and valleys, plateaus and ridges, ice-clad or desert-dry. Irrespective of individual geomorphological or hydrological setting, water, however much or little there may be, drains from zero order and barely noticeable depressions to higher order streams that eventually debouche onto floodplains or peneplains at the piedmont. If sufficiently steep or loose, erodible sediment is available for transport, and debris flows will form whenever rainfall or rain-on-snow runoff exceeds a hydroclimatic threshold. Traditionally, people have built homes and infrastructure on fans because in mountainous terrain these are often areas with the lowest gradients. The threat of debris flow may be recognized, but there can be a perception that riverine floods are the more damaging event because observable bank full flows may occur frequently and major overtopping of the flow channel at higher return periods may have been witnessed. Debris flows, in contrast, may occur at return periods of century scale and are thus outside of the typical memory of residents or infrastructure owners.

The longer the periods between events, the less obvious are the signs of past destruction and geomorphic change. The human trait of thinking that such events are anomalous has led to continued urbanization of fans and cones in areas with high relief. None of this is new, and nations such as Japan, European countries adjoining the Alps, countries straddling the North and South American cordilleras, and other nations have developed systems to map, analyze, and assess hazard and risk and mitigate to specific engineering standards.

Hundreds of thousands of mitigation works have been constructed world-wide, ranging from make-shift log-crib structures or masonry dams built entirely by hand to impressive mega-structures constructed with concrete capable of retaining millions of cubic meters of sediment.

This contribution is not meant as an exhaustive review of debris-flow hazard assessments, of which hundreds have been reported in the literature. Summaries of hazard assessments have been provided elsewhere (Jakob, 2005; Rickenmann, 2016; and Chae et al., 2017). Rather, a few cases and pertinent studies of debris-flow mechanics are highlighted to demonstrate the debris-flow hazard and risk assessments that have

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had a demonstrable effect of reducing risk to populations living with debris-flow hazards.

With humans emitting carbon dioxide at unprecedented levels (at ∼36.8 Gt CO2 in 2019, Global Carbon Project, 2019; Peters et al. 2020), human-caused climate change is now the key existential threat to organized human life on Earth (IPCC, 2018). Pledged national actions are currently a far cry away from reducing global warming to the Paris Agreement targets of 1.5°C above pre-industrial levels (IPCC, 2018; Michaelowa et al., 2018; and Mundaca et al., 2018) and even the fallback target of 2°C looks increasingly unlikely as a tangible target given that after 3 years of flat CO2 emissions, 2017, 2018, and 2019 broke new records (Jackson et al., 2017; Global Carbon Project, 2019). This implies that the higher-end relative concentration paths of 4.5 and greater currently appear more likely (Global Carbon Project, 2019) and thus ought to be used in climate change effects prediction models compared to the lesser radiative forcing scenarios. The hydroclimatic changes associated with a strongly warmer atmosphere will manifest in changing averages, but also notably in extremes, which are particularly relevant for debris-flow initiation (Jakob, 2021). Predictions of changes in precipitation extremes with climate scale at the same rate as atmospheric moisture, which is 7 percent per degree Kelvin following the Clausius–Clapeyron (CC) relation (i.e., Iribarne and Godson, 1981). This hypothesis neglects potential changes in the strengths of atmospheric circulations associated with precipitation extremes. Nie et al. (2018) demonstrate that while increased moisture leads to increased precipitation, the increased latent heating may also lead to stronger large-scale air mass ascent and a super-CC scaling with precipitation extremes well exceeding those predicted by the CC relation. However, any regional simplifications are to be avoided. For example, Tandon et al. (2018) indicate that extreme precipitation events are likely to decrease in the subtropics whereas they may increase everywhere else.

Anecdotal and systematic data point strongly toward drying trends in some locations (Cook et al.

2014), which arguably have led to decreases in available forest floor moisture and increases in the frequency and intensity of forest fires (Abatzoglou and Williams, 2016; Flannigan et al., 2016; and Schoennagel et al., 2017). Climate models are rather clear on that point, predicting increasing heat waves and overall drying in large regions (Flannigan et al., 2016). In conjunction, extreme precipitation events are predicted that are largely attributable to increasing moisture availability in the troposphere as a direct consequence of warming. In tropical and subtropical regions, warmer ocean surface temperatures are currently leading and

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will continue to lead to an intensification of storms (Ma et al., 2017; Jin et al., 2018; and Lin et al., 2009), though a deeper understanding of the dynamic versus thermodynamic components is needed to decipher regional differences (Pfahl et al., 2017). Either way, increasing drought frequencies and severities in temperate forests will have the undesirable effect of more severe wildfires. For example, Krasko (2016) estimated increases in post-fire debris-flow frequency by 40 percent and an increase in magnitude of approximately 50 percent in the western United States. Westerling et al.

(2006) identified a marked increase in wildfire activity in the mid-1980s, with a higher frequency of large fires, fires with longer durations, and fire seasons that last longer. In combination with intensification of extreme rainfall events, this results in an increase in the frequency and sometimes magnitude of post-fire debris flows. One of the most powerful examples of such occurrence is the January 2018 debris flow that affected one of the United States’ most affluent communities in Montecito, California, with 23 confirmed deaths, two missing people, and more than 400 structures damaged or destroyed. This example is particularly worrisome, as California has developed and fostered tremendous skill and expertise in quantifying post-fire hazards and risks (NOAA-USGS Debris Flow Task Force 2005; Staley et al., 2013; and Gartner et al., 2014) and such a disaster was, arguably, avoidable had the hazards been systematically quantified and mapped and evacuations carried out.

However, it is not only wild-fire–prone watersheds that are susceptible to climate change. Increasingly extreme (off the scale) rainfall events are occurring, which trigger catastrophic debris flows that have no historical precedent (Stoffel and Beniston, 2006; Pelfini and Santilli, 2008; Pavlova et al., 2014; and Dietrich and Krautblatter, 2017).

HAZARD ASSESSMENTS Debris-flow hazard assessments form the backbone of any plans to mitigate, whether accompanied by a risk assessment or not. If the hazard assessment is faulty, so will be the risk assessment and, ultimately, the mitigation design to reduce hazard or risk. Of course, this can go both ways: An overestimated hazard will lead to an overestimated risk, which by extension results in overdesign of the mitigation works and the associated burden on funding agencies and/or the taxpayer.

What does a thorough hazard assessment entail?

The list is long but is separated, by and large, by two principal aspects: (1) assessment of the frequency and magnitude of events and (2) assessment of the intensity of the respective debris-flow scenario. Breakthroughs

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have been made in the assessment of frequency analyses with the refinement of, for example, dendrochronological methods (Ballesteros-Cánovas et al., 2015) and radiocarbon dating methods (Chiverrel and Jakob, 2013; Sewell et al., 2015). Magnitude analyses have been greatly enhanced and refined through empirical methods (e.g., Gartner et al., 2014) and numerical modeling that may allow event magnitudes to be reasonably estimated from known source area volumes and user-specified and/or theoretical entrainment rates (e.g., McDougall and Hungr, 2005; Iverson, 2012). Both methods can and ought to be used complimentarily to decipher the “true” frequency–magnitude relationships. It is impossible to characterize every known event; however, statistical science has produced methods that are suited for a magnitude-limited truncation of datasets. Peak over threshold analyses can be applied to this problem set, and statistical distributions such as the generalized Pareto distribution (GPD) are fit for application where fragmentary data exist but where one can be reasonably confident to have captured the biggest events (Jakob et al., 2017).

The degree of sophistication that is being applied to such hazard assessments differs widely from nation to nation, but also within nations with poorly developed or missing guidelines. This results in assessment quality being strongly dependent on the practitioner’s background knowledge and that of their team. Many such assessments are conducted by consulting firms who may have to write competitive proposals. If all or most methods available to the practitioners are proposed, the costs of such studies may become non-competitive and a lower bidder may win the job. This competitive process may put pressure on firms to win jobs with the lowest reasonable effort possible. But what does that mean, and is it truly a problem?

Spectacular failures of debris-flow mitigation works are rarely reported in the scientific literature, presumably for reasons of embarrassment suffered by the design team or potential ensuing legal action.

Particularly in more litigative societies, legal action seems almost predictable and a thorough forensic analysis of a debris-flow mitigation system failure can be obscured through confidentiality clauses. This is lamentable, as the greatest advances in debris-flow mitigation may derive from an analysis of past failures.

In this sense, it is worthwhile to examine a few notable failure modes summarized by Moase et al. (2018).

Regional Debris-Flow Studies Most districts, states, provinces, or even nations have limited funds for geohazard mitigation. This necessitates the allocation of existing funds to those sites

with the highest risk potential. Funds for studies and mitigation often get allocated because of particularly damaging events that result in focused public, media, and political attention. Those sites, however, may not necessarily be the ones with highest risk. High-risk sites are those that occur frequently and with a high economic or life loss potential. Only in the most affluent societies with long histories of debris-flow hazard recognition, quantification, and management is it possible to systematically evaluate hazards and risks and prioritize mitigation accordingly (Kang and Lee, 2018; Sturzenegger et al., 2019). Even if possible, detailed fan and watershed studies for entire nations such as Switzerland, Austria, or Japan take a very long time, and hazard potential changes with land use, extreme events such as major landslides or volcanic eruptions, and direct or indirect consequences of climate change. Therefore, it is advisable to devise methods in which debris-flow susceptibility can be adequately approximated and readily compared to each other. Hazard frequencies can be assessed in classes with class boundaries being systematically defined and aerial photograph analysis allowing class designation.

Debris-flow magnitude can be gleaned from regional debris-flow susceptibility models such as the Flow-R software (“Flow-R” refers to Flow path assessment of gravitational hazards at a Regional scale), a distributed empirical model for regional susceptibility assessments of debris flows developed by Horton et al. (2008, 2013). Flow-R enables identification, at a preliminary level of detail, of potential debris-flow or debris-flood hazard and modeling of their runout susceptibility over large study areas. Unlike other numerical models suitable to simulate debris flows, such as RAMMS, FLO-2D, DAN-3D, and D-Claw, which require substantial computer runtimes depending on the model grid size and modeling domain, Flow-R runs very quickly and can be run on numerous debrisflow susceptible creeks at the same time. Sturzenegger et al. (2020), demonstrate the use of the model for a debris-flow risk-based prioritization study in British Columbia, Canada. Once magnitude and frequency are approximated for many creeks, the consequences can be evaluated either for fixed assets (homes, industries, linear infrastructure), or people in transit (on roads, by rail). Holm et al. (2016, 2017) provide an example of such regional prioritization. Debris-flow hazards and risks are not estimated with any precision with such methods, and the susceptibility maps should not be interpreted as hazard maps. The importance lies in a systematic, replicable, and transparent comparison of risks by using the same methodology for all sites investigated. Such prioritization studies cannot replace detailed fan hazard and risk assessments that would form the basis for mitigation design.

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Future advances in this science could include a linkage between regional frequency–magnitude analysis and susceptibility models. This would allow a higher granularity in regional studies that have design frequency caps. Such added granularity would glean more confidence in risk quantifications as often the highest risk locations are those where the impacts of debris flow lead to loss of life at the lowest return period (highest frequency).

Dating Past Debris Flows In terms of dating past debris-flow events, practitioners have a substantial variety of methods, although environmental conditions and budget are the key constraints. One of the most deeply researched methods, and also one of the most useful due to its precise annual resolution in forested areas with mature trees (i.e., unlogged), is dendrochronology (Stoffel and Bollschweiler, 2008; Stoffel, 2010; Stoffel et al., 2010; Schneuwy-Bollschweiler et al., 2012; and BallesterosCánovas et al., 2015). Some key refinements are still outstanding, such as estimating the individual deposit volumes and intra-seasonal dating precision (Stoffel, 2020). Dendrochronological investigations are also used increasingly to identify possible climate change signals (van den Heuvel et al., 2016). Trees on the fan or along the channel are required to obtain a reasonable dendrochronological record, with the usefulness increasing with tree age. Relative dating methods such as lichenometry (Rapp and Nyberg, 1981; Innes, 1983; Andre, 1990, and Bull, 2018) provide a decent approximation of past events, but without calibration of the lichen growth curve, translation into areas affected by debris flows and their respective date hampers establishment of detailed frequency–magnitude relationships. Radiocarbon dating (i.e., Chiverell and Jakob, 2013) remains a profoundly successful method and can be used not only to date debris flows, but allows approximations of debris-flow volumes of known ages by measuring the thickness of dated deposits. This method requires the excavation of a number of test pits on the fan; costs can quickly escalate, and access can be limited on densely populated fans.

Debris-Flow Magnitude Analysis Empirical relationships between flow volumes and inundated areas are very useful when past debris-flow activity is captured on historic air photographs or from satellite imagery (e.g., Griswold and Iverson, 2008).

However, local coefficients must be established rather than adopting reported ones, as was found in several of the unpublished studies of this author and colleagues.

More work is needed to differentiate hybrid events be-

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tween coarse granular and fine-grained highly mobile events.

One aspect that remains challenging is establishing frequency–magnitude methods on a regional scale. For example, pipelines or other above-ground or buried linear infrastructure are still being built worldwide, some of which cross mountainous terrain. Oil and gas pipeline owners have a particularly low tolerance to pipeline rupture due to the substantial clean-up costs, environmental fines, and very poor publicity, especially in an age in which fossil fuel industries are vilified and investments are increasingly divested from that sector (Rifkin, 2019). Moreover, they wish to know the chance of pipeline impact for a range of return periods; in other words, a frequency–magnitude analysis is needed for tens if not hundreds of fans that their pipeline may cross. However, detailed dendrogeomorphic studies, radiocarbon dating, or even detailed mapping of previous deposits is very time and cost intensive and typically not practical or funded. Jakob et al.

(2020) provide a simple, yet effective regional method to estimate frequency–magnitude relationships. Using well-researched debris-flow frequency–magnitude relationships from nine studies in southwest British Columbia, Canada, Jakob et al. (2020) showed that fan area or fan volume can predict these relationships with quantifiable error. The underlying rationale is that the fan, unless truncated by a higher order stream or obfuscated by a rapidly aggrading floodplain, reflects the sum of all fan-forming events. This method is particularly helpful in areas with late Pleistocene glaciation, where the fan area or volume integrates all debris-flow events that occurred since deglaciation. However, this method is not particularly applicable if a high degree of precision is warranted.

If enough individual frequency–magnitude relationships are known for a particular regional location of study, a similar relationship could be developed in the form of: VS = Af [a ln (T ) − b]

(1)

where T is the event return period, Vs is the normalized total sediment volume in m3 /km2 , Af is the fan area, and a and b are coefficients. The values of the constants depend entirely on the data, and so Eq. 1 has predictive value only for events/locations that would fall within the distribution of the dataset and have similar ancillary properties.

Fan areas are typically simple to measure in Google Earth, from digital terrain models from lidar, or from orthorectified aerial photographs. However, caveats must be identified, such as abnormally large fans for their respective watersheds that may be attributable to previous large landslides that are now overprinted by debris flows. In such cases, the regional method

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previously described may result in overly conservative results. Alternatively, river erosion at the toe of a fan or aggrading floodplains that mask some of the fan area may result in a fan area that is small in relation to the frequency–magnitude of debris flows in the upstream catchment.

The special case of debris-flow magnitude analysis in a post-fire setting has received much attention in the past 10 years, and this paper can hardly do justice of the plethora of literature that has emerged. For the practitioner, general guidelines and simple applications are particularly useful, such as the recovery time for decreasing debris-flow volumes to pre-fire situations (Santi and Morandi, 2013) or estimates of peak discharge in burned and unburned areas from bulked rational formulae and their limitations (Brunkal and Santi, 2017). Other highlights include probabilistic post-wildfire debris-flow modeling (Donovan and Santi, 2017) and studies on the timing of debris flows after fires (De Graff, 2014; De Graff et al., 2015).

These are key in triggering risk assessments, as debris flows may occur very quickly after fires are out (Kean et al., 2019).

Various statistical methods exist that help the practitioner with incomplete datasets that, in our science, are the rule rather than the exception. The application of simple magnitude-cumulative-frequency methods or the GPD can lend credibility to the analysis and its extrapolation to annual probabilities outside the observed record. However, they come with a caveat, namely pronounced confidence bands. As shown by Jakob (2012), their reporting may lead to a confidence loss with one’s client or those potentially affected. The only remedy remains expert judgment, which is based on a thorough understanding of the entire debris-flow system. Only a comprehension of potential point sources, entrainment rates, debris-flow triggering mechanisms, and runout behavior will allow the practitioner or scholar to properly identify and quantify hazard zones.

Debris-Flow Scour and Entrainment It is well known that debris flows in their transport zone are capable of eroding all loose sediments to the bedrock interface (e.g., Jakob, 2005). Installing infrastructure in the sediment fill in debris-flow–prone channels in the transport zone without adequate protection invites damage. In many cases, this can be avoided by burying linear infrastructure passing through mountainous terrain closer to the valley bottom on alluvial fans and colluvial cones. Although fans and cones are generally regarded as depositional landforms (Summerfield, 2014), observations of progressive and catastrophic scour on such landforms indicate that this

view, while perhaps true at century or millennia time scales, is too simplistic. Fan and cone scour have exposed, and in the worst case severed, buried linear infrastructure (e.g., Lau, 2017). Fan scour has also been experimentally researched with the same findings of cyclical scour and fill (de Haas et al., 2018), although experimental studies typically neglect phases of debris flooding that can remove substantial volumes of sediment from fans through exceedance of critical shear stress thresholds (Church and Jakob, 2020). This process is particularly effective in deepening channels in the proximal and medial fans on debris-flow–prone fans with low event frequencies. Continued expansion of buried linear infrastructure, especially hydrocarbons with their particularly high consequences in terms of gas explosions or oil spills, motivates a more detailed examination of fan scour to predict scour depth and manage the risk of buried infrastructure failure. The importance of debris entrainment is also highlighted by Frank et al. (2015), who provide instructive examples from the Swiss Alps.

Several approaches have been presented to examine debris-flow scour (Kang and Chan, 2018). These can be classified broadly into mechanistical, empirical, and experimental. In the mechanistical approach, the governing equations are based on the mechanics of the erosion process and consider shear failure of the erodible material statically or dynamically (Medina et al., 2008; Iverson and Ouyang, 2015; and Pudasaini and Fischer, 2016). Egashira et al. (2001), in contrast, proposed a model reliant on the difference in solid concentration between the debris and the erodible bed. A review by Iverson and Ouyang (2015) suggested that many existing models are not suitable to predict debris entrainment as they incorrectly apply depth-integrated conservation principles. They showed that erosion or deposition rates at the interface between layers must, in general, satisfy three “jump” conditions, which is rarely the case. Kang and Chan (2017) proposed a model that accounts for surface erosional effects through progressive scouring and shear failure on the channel surface. By considering simple geometry and particle configurations, the authors developed equations for progressive scouring and considered rolling and sliding motion. In Kang and Chan’s (2017) model, a probability-density function (PDF) is used to calculate the entrainment rate. The authors compared the model to flume experiments and found that the entrainment rate can be calculated using a normal PDF. Building on their earlier paper, Kang and Chan (2018) developed a progressive entrainment model in which the debris flow is allowed to bulk for each time step. Their model explicitly allows for channel geometry changes. The authors then integrated their entrainment model into a runout model and

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applied it to the 1990 Tsingshan debris flow in Hong Kong. They also compared their progressive entrainment model to a dynamic one and found that the latter substantially underestimated entrainment in the lower one-third of the flow path. To apply the entrainment model successfully, a number of field variables must be measured. These include grain size distribution of samples along the flow path, the initial pivoting angle, the internal friction angle of the colluvium, a swelling factor to account for material dilation, and particle density.

In the empirical approach, erosion rate is correlated with the average velocity and the shear stress based on an empirical coefficient derived from case studies (De Blasio et al., 2011). Theule et al. (2015) developed a functional relationship from a stepwise regression model as an empirical fit for the prediction of channel erosion by debris flows with a critical slope threshold at 0.19. The authors interpreted this slope threshold as the transition between the sediment transport-limited and supply-limited regimes (Bovis and Jakob, 1999), associated with the upstream decreasing erodible bed thickness.

De Haas and van Woerkom (2016) experimentally investigated the effects of debris-flow composition on the amount and spatial patterns of bed scour and erosion downstream of a transition from bedrock to channel colluvium. The debris flows entrained bed particles grain by grain and en masse, and the majority of entrainment was observed to occur during passage of the flow front. The authors found that scour depth was largest slightly downstream of the bedrock to colluvium transition, except for clay-rich debris flows.

The authors also found that basal scour depth increased with channel slope, flow velocity, flow depth, discharge, and shear stress. From a practitioner’s point of view, this result highlights that debris-flow fans with comparatively large watersheds, such as hanging valleys that result in high peak discharges, are particularly susceptible to scour near their apices, where the transition from bedrock to colluvium occurs. This is very much in line with observed scour depths near fan apices and indicates that those locations should be avoided in the design of linear infrastructure.

Using experiments from a 1:30 scale model, Eaton et al. (2017) demonstrated that channel degradation due to floods on alluvial fans is dominated by lateral channel migration rather than vertical incision. However, experiments were conducted on a modeled fan of 4.5 percent gradient, and many debris-flow fans are substantially steeper. Hence, it remains to be determined if the findings from Eaton et al. (2017) can be applied to steeper fans.

Iverson et al. (2011) conducted large-scale experiments at the U.S. Geological Survey’s debris-flow

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flume in Oregon to examine debris entrainment in steep channels. They addressed the pertinent question: How can flows that entrain bed material travel faster and further than those that do not, given that momentum conservation implies flow retardation?

Iverson et al. (2011) found that debris-flow mass and momentum grow simultaneously when rapid debris loading over a wet alluvial channel surface produces large positive pore pressures. These elevated pore pressure fields encourage bed sediment scour, lead to friction reduction, and unleash a positive feedback through further momentum increase. The key question is when the feedback becomes negative either due to deposition, avulsions, or an increasingly dry bed, perhaps due to fan infiltration.

Complementary approaches can be used to assess fan and cone scour. One is centered on the assumption that fan surfaces oscillate around an equilibrium profile along the longitudinal main channel axis on a decadal-to-century time scale, and this equilibrium profile can be approximated by a polynomial fit of the fan surface (Jakob et al., 2018). Deviations from this fit suggest the tendency of a fan to aggrade or degrade and enable probability designations of scour or aggradation in a specific reach based on compute prediction intervals. This method quantifies the probability of scour anywhere along the fan-dissecting streams.

The same principle can be applied across fans to examine the likelihood of fan scour anywhere along the linear infrastructure alignment, if an avulsion carves new channels or travels down existing paleochannels.

These methods, although useful, have limitations inherent in the underlying assumptions and are sensitive to the polynomial profile fit. It is purely statistical and does not inform, or rely on, the physics of scour or material properties of the channel bed.

The potential importance of debris-flow fan scour is demonstrated by an anomalously erosive debris flow that occurred on the fan of Neff Creek, north of Pemberton, BC, Canada, in 2015 (Lau, 2017). Of the total debris-flow volume of 275,000 m3 , 83,000 m3 was eroded from the fan. Passage of the debris flow eroded a small canyon-sized channel into the upper to mid alluvial fan, which at its maximum was 14 m lower than the original fan surface. Similar highly erosive debris flows have been observed in Switzerland (Scheuner et al., 2009; Berger et al. 2011; and Frank et al., 2015) and elsewhere in British Columbia (Jakob et al., 1997; Lau, 2017), but the causes for debrisflow fans to “switch” between deposition and erosion are poorly understood and have only been recently researched (e.g., de Haas et al., 2017). Understanding when such highly erosive events occur on fans is crucial for practitioners tasked with specifying burial depth of pipelines or fiber-optic cables. In the case of

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Neff Creek, it is virtually certain that even a professional with vast knowledge of debris-flow processes would have underdesigned a buried crossing on the mid-to-upper fan due to a severely underestimated scour depth. In addition, clients may exert some pressure on the practitioners not to be overly conservative with the recommended burial depth because costs of construction and maintenance increase substantially with increasing burial depth. Had a pipeline been built, it would have very likely resulted in a fracture and spill of whatever substance the pipeline had carried. It is such events that give us reason to pause and stimulate further research. When examining the current literature on entrainment/scour of debris-flow fans, it is apparent that there is yet no model that can reliably predict catastrophic scour as witnessed at Neff Creek or elsewhere. It appears that the pore pressures generated at the channel base–fluid interface strongly influence how much entrainment can be expected on fans.

The author also speculates that dynamic loading on a saturated cohesionless bed may trigger dynamic liquefaction of the channel bed, further reducing shear strength and aiding entrainment. Once again, the pertinent question for a practitioner is, once a reliable model has been created that may account for the various factors, can the pertinent variables be measured reliably in the field and laboratory with a reasonable amount of effort. If not, then it is unlikely that such a method will find much support by practitioners or the industry. At a minimum, identifying fans that may be susceptible to major scour should be a focus of future research.

Debris-Flow Modeling When debris-flow hazards are identified, runout analyses are usually required to delineate potential impact areas, estimate risks, and finally conceptualize and design risk reduction measures. An ever-increasing number of models and methods have been developed. These range from simple empirical–statistical correlations (e.g., to extract flow velocities or runup; Prochaska et al., 2008), to physical/theoretical (Iverson et al., 2016), to advanced three-dimensional multiphase models (Pudasaini and Mergili, 2019). Other full three-dimensional models have been developed based on smoothed particle hydrodynamics (Han et al., 2019), though not yet introduced in commercially available or free software packages. McDougall (2017) provided an overview of available computer models and discussed some of the challenges being addressed by researchers, including the need for better guidance in the selection of model input parameter values, the challenge of translating model results into vulnerability estimates, the problem with excessive simulation

spreading for specific types of landslides, the challenge of accounting for sudden channel obstructions in the simulation of debris flows, and the sensitivity of models to topographic resolution and filtering methods.

McDougall’s paper is comprehensive, and its details do not need to be repeated herein. Instead, this paper focuses on some of the more recent refinements that were not fully included in McDougall’s (2017) work.

The model D-Claw, developed by Iverson and George (2014), is perhaps the most sophisticated threedimensional model presently available and is based on the physics of landslide and debris-flow motion. It can simulate debris-flow behavior from initiation to deposition using a depth-averaged, two-phase model in which principles of critical-state soil mechanics, grainflow mechanics, and fluid mechanics are combined.

In a follow-up paper, George and Iverson (2014) used D-Claw and compared model output with results from two sets of large-scale debris-flow experiments.

The first experiment investigated debris-flow initiation from landslides triggered by rising pore-water pressures. The second experiment focused on downstream flow dynamics, runout, and deposition. The authors concluded that D-Claw performs well in predicting evolution of flow speeds, thicknesses, and basal porefluid pressures. The generality of D-Claw enables application to almost all landslide or debris-flow environments, requiring geometric input data of a prospective landslide or debris-flow source area as well as debris composition. The model is based on computational routines that solve equations describing the coupled evolution of two components of flow velocity as well as flow depth, debris porosity, and basal pore-fluid pressure. The seamless application in hazard cascades was recently demonstrated for the case of a rock avalanche entering a moraine-dammed lake east of South Sisters volcano in central Oregon, generating a displacement wave and a downstream debris flow in Whychus Creek (George et al., 2019). A cursory review of the literature shows that D-Claw has not been widely adopted by practitioners, though it may simply be a matter of time for a more widespread application. It will also be interesting to see how a fully parameterized model that does not require a priori calibration can be applied cost efficiently. Questions emerge such as whether input variables can readily be measured in the field with standardized methods, even when source areas or debris-flow transport zones are difficult to access. von Boetticher et al. (2015, 2016) developed another three-dimensional model that simulates debris flows as a mixture of two fluids with an additional unmixed phase representing the air and the free surface. Like Iverson and George (2014), von Boetticher et al. (2015) link all rheological parameters to the material composition, and the user must specify only two free model

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parameters. A quasi single-phase mixture volume of fluid method reduces computational time compared to the more computationally intensive drag-force–based multiphase models.

There are potential pitfalls to widespread application of sophisticated debris-flow models by people with little modeling experience or a cursory understanding of the model being applied. For this reason, some key aspects are highlighted for practitioners:

r Understand where the model was developed. It is

r

r

r

r

important to know whether the model is suitable mostly for arid versus humid environments, rock types (weak sedimentary versus competent intrusives), or residual versus moraine and/or colluvial slopes in areas with Quaternary glaciation.

Do not trust any model unless it has been calibrated or at least carefully compared to debris flows observed in the field. The last well-documented debris flow is not necessarily indicative of the full range of flow behavior of future flows. At a minimum, a range of flow magnitudes of past flows ought to be considered. Even then, such calibration does not constitute a systematic test.

Some models do not or do not sufficiently rigorously satisfy nature’s laws, such as physical conservation laws. Such models have been critiqued as “numerical toys” that mimic poorly constrained field observations (Iverson, 2019). The problem faced by many practitioners (including this author) is an insufficient mathematical/physics background to fully comprehend the routines of the model. More effort should be spent on mathematical scrutiny of such models. A shift toward fully tested physics-based mathematical models is desirable, as long as such models are accessible to practitioners and input variables can be measured practically in the field.

Avoid “blind modeling.” With ever-increasing specialization, modelers are at risk of not being involved in the generation of input parameters. This temptation ought to be resisted. While modeling is an integral part of a debris-flow risk assessment, it is only one component. The modeler must be alert that the input parameters dictate modeling outcome and that model sophistication is not a replacement of detailed field investigation.

If possible, compare two or more numerical models and try to reconcile stark discrepancies in inundation area, flow velocities, or flow depths (Rickenmann and Koch, 1997; Rickenmann et al., 2006; Stancanelli and Foti, 2015; Cesca and Agostino, 2018; Palong et al., 2018; and Moase et al., 2018). Multi-model comparison is also the standard in climate change predictions (Emori et al., 2016).

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r Attempt to identify avulsion scenarios that are not part of the raw model output but can be identified as credible scenarios. Such scenarios may require forcing avulsions by numerically adding obstructions to the flow paths (McDougall, 2017). A summary of avulsion scenarios and the associated evolution of debris flows was authored by de Haas et al. (2018). r Be acutely aware of what the numerical models can and cannot do. If a model is unable to simulate runup or super elevation and the modeled topography is susceptible to such phenomena that can strongly influence both the hazard exposure and risk to elements at risk, it should be replaced with a model that can. Runup and super elevation should be hand-calculated to search for obvious discrepancies with model results. r If a continuum model does not allow for channel debris entrainment, question if this could lead to strong model bias. This is less of a problem for cases where the frequency–magnitude relationship has been largely developed from fan field investigation and the model is started at the fan apex in largely depositional environments. However, in situations where the ratio of the point source failure volume and the final debris-flow volume through inchannel entrainment is likely low, neglecting or underestimating entrainment can strongly affect modeling outcome. r Prediction of severe (several meters) fan scour is still under-researched. Several cases of deep fan scour have been reported at least anecdotally or in conference papers or thesis (i.e., Lau, 2017). Most researchers and practitioners would likely have substantially underestimated scour given the textbook wisdom that fans are depositional landforms. However, this topic is hugely important, as misjudged fan scour can lead to catastrophic damage to property and especially the potential impacts to buried linear infrastructures such as oil and gas pipelines.

CONCLUDING REMARKS Debris-flow hazard assessments have considerably improved from times when the design of debris-flow mitigation works was largely based on a practitioner’s gut feel or purely experience-based guidelines. The wealth of methods, be they in dating past events, deciphering their magnitude, numerical models, and measures of debris-flow intensities and vulnerabilities, has been bewildering and illuminating alike. Papers on debris flows appear almost weekly, and only the most motivated can keep up with absorbing the everexpanding information. Rarely can all or even several complimentary methods be applied to a specific problem. This is partially due to geographic constraints

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(i.e., dendrochronology is useless in treeless terrain or radiocarbon dating is impossible in true hyper-arid environments), and partially due to funding limitations in competitive bids for engineering and geoscience studies. Finding the balance of what methods are most cost-effective is key to a successful project completion.

Even in economically and socially advanced nations, steep creek science has not advanced as rapidly as would be desirable. A recent contribution (in German) by Rickenmann and Badoux (2018) identified deficits that are equally applicable to other nations.

They include underfunding of process-based studies of mountain torrents, insufficient documentation of methods used for process characterization, missing transparency in debris-flow hazard assessments, and gaps in the systematic training of debris-flow specialists.

Debris flows will continue to occur in mountainous terrain. Supply-limited watersheds may witness an increase in frequency with a concurrent decrease in magnitude, while supply-unlimited watersheds are likely to witness an increase in frequency and possibly an increase in magnitude, with storms becoming much more frequent and severe due to climate change (Jakob and Lambert, 2009; Jakob, 2021). This, in conjunction with unabated global population increases that push people into increasingly marginal terrains, facilitates an increase in the projected fatalities and economic losses due to debris flows. As with many damaging geophysical phenomena, a chasm has opened between the developed and developing world. In the former, methods for recognition, quantification, and mitigation of debris flows and the financial resources to mitigate debris-flow risks allow deaths from debris flows to be minimalized to nationally insignificant numbers. For example, in 2017, 15,643 people in the United States died by gun violence (Gun Violence Archive, 2018), some 72,000 by drug overdoses (Ahmad et al. 2018), and 40,100 by motor vehicle accidents (National Safety Council, 2018), whereas at most 10s of people (anecdotal data from colleagues) died directly from debris flows. Globally, the total number of debris-flow–related deaths is more significant.

Dowling and Santi (2014) estimated almost 78,000 fatalities recorded in academic publications, newspapers, and personal correspondence between 1950 and 2011, an average of approximately 1,250 fatalities per year.

While insignificant in terms of fatalities, the national economic costs in developed countries are still substantial due to direct impact or infrastructure interruptions (Dowling and Santi, 2014; McCoy et al., 2016). Hence, complacency is certainly not warranted or morally justifiable. As with any science, it is valuable to occasionally take stock of the key accomplishments

and ask the question: What else needs to be achieved until a science has matured to a degree where progress has slowed to a crawl or even stagnates?

One may argue that many of the quantitative methods available for debris-flow hazard quantification are approaching a level of maturity whereby incremental changes do not necessarily translate into safer environments. Similarly, there are little breakthroughs in the methods to mitigate hazard and associated risks. Clearly, refinements in numerical modeling capabilities, such as credible entrainment functions on channels and fans, are still necessary and welcome to the practitioners. Yet, there are potential pitfalls to widespread application of highly sophisticated debris-flow models by people with little modeling experience or a cursory understanding of the underlying physics and supporting mathematics. Similarly, hazard intensity definition and mapping can still be homogenized and improved through existing tools that are well suited to deal with most, if not all, conditions adequately. National or regional databases are certainly needed, as they allow a better statistical treatment of all components of hazard analysis. Setting tolerable risk thresholds or at least guidance will help to fine-tune and custom-tailor mitigation measures while avoiding over-expenditure or underfunding.

Finally, regional or national prioritization is hugely helpful to allocate limited funding to the highest risk situations and to remove the arbitrariness of decisions on mitigation prioritization. None of this will be useful unless a new generation of debris-flow experts is trained in the science and art of debris-flow hazard and risk assessments. This needs to be complemented by the formulation of detailed technical guidelines to homogenize approaches and enhance research efforts, including a systematic process documentation and its testing against existing methods.

Climate change is posing, and will continue to pose, a particular challenge to institutions and practitioners alike, as the expected changes in climate and the associated higher-order effects (glacial and permafrost changes, changes in wildfire activities, beetle infestations and associated tree mortality, all of which influence debris-flow activity) in the ecosystems are becoming unprecedented in human history.

Debris-flow researchers and practitioners will need to respond swiftly by amending their toolboxes in the attempt to predict and possibly manage the effects of climate change as they pertain to debris-flow systems.

Paleoclimate records from the Miocene Thermal Maximum or the Eocene-Paleocene Thermal Maximum, as they pertain to changes in fan aggradation rates, may become increasingly important.

Future changes will require a new generation of experts who are knowledgeable in the ever-increasing

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subfields that feed into successful hazard and risk assessments. It is hoped that this contribution will inspire this next generation and lead to ever more robust tools. It is also a call for funding agencies to provide academia with means to address pertinent outstanding questions so that science can be translated into practice with little delay. In conjunction with wise resource management and an acceptance of researchbased decision making, there is reason for hope that debris-flow risks can be reduced despite an increasing population.

I wish to finish this paper with a mildly philosophical note. The debris-flow practitioner (as other professions) undergoes distinct psychological phases in their careers. Leaving university with a distinct specialty in the form of an honors, master’s, or Ph.D. degree, it is tempting to believe that one is an expert with a good handle on the specific science. Invariably, reality catches up. It may come in the form of assignments that, for budget reasons, do not allow for exhausting all avenues and judgment is required to severely curtail what is the acceptable common denominator. They can also come in very unexpected events. The author has seen debris flows much larger than anticipated, some that flowed much further than thought, and some that went into unimagined directions. This is humbling, but is followed by a phase of mental recovery, further publications and assignments, and the growing external realization of expert judgment, perhaps accentuated by the odd award. A few accurate predictions then lead to growing confidence and often overconfidence. The last phase is the sobering realization that no matter how long one practices, researches, reads, reviews, edits papers or attends conferences, the unexpected will always be lurking in the next watershed, the next fan.

A worrisome tendency is the increasingly litigative environment we find ourselves in. Things will go awry following Murphy’s Law and the fact that the probability of being wrong is proportional to the number of assignments one completes in one’s career. Fewer and fewer people are willing to absolve regulating agencies from permitting construction on debris-flow– prone lands even though there may have been intense lobbying to build in such places. Litigation can result in which practitioners find themselves on the defense in court and possibly with their professional associations that can issue disciplinary notices and hearings that can jeopardize one’s career and leave psychological scars. I hope that future generations of practitioners will not succumb to such pressures, as this would leave a vacuum in a practice that, due to population pressures and ever more severe climate change effects, will be needed more than ever before in the future.

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ACKNOWLEDGMENTS I would like to thank the organizers of the DFHM7 conference who allowed me to share my thoughts at this venue and in a substantially expanded version in this contribution. I am also deeply indebted to all those who have put their minds to pursuing and advancing the knowledge in the broad field of debris-flow science instead of pursuing more lucrative jobs elsewhere.

Their work has inspired me. Many of my colleagues at BGC have substantially contributed to the work presented herein. Specific thanks for reviews, data, references, and thought-provoking comments to Scott McDougall, Carie-Ann Lau, Kris Holm, Markus Stoffel, Dieter Rickenmann, Dick Iverson, Jon Major, Paul Santi, Akhiko Ikeda, Joseph Gartner, and Hamish Weatherly. Thanks also to Lynn Forrest and the BGC library staff for finding many references to which I was oblivious.

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Steep Creek Risk Assessment for Pipeline Design : A Case Study From British Columbia, Canada JOSEPH E. GARTNER* BGC Engineering, Inc., 701 12th Street, Suite 211, Golden, CO, 80401

MATTHIAS JAKOB BGC Engineering, Inc., 500–980 Howe Street, Vancouver, British Columbia, V6Z0C8, Canada

Key Terms: Steep Creek Processes, Debris Flows, Debris Floods, Risk Assessment, Hazard Assessment, Mitigation Design, Pipelines

proposed mitigation measures achieve these threshold criteria.

ABSTRACT

INTRODUCTION

Pipelines in mountainous terrain often cross alluvial fans formed by steep creek processes of debris flows and debris floods and are thus exposed to their associated hazards. The design of new pipeline infrastructure and maintenance of existing pipelines necessitates steep creek risk assessments and appropriate mitigation design. We present methodology for assessing steep creek risk along pipeline routes that evaluates the probability of such processes causing a pipeline loss of containment or disruption in service. The methodology consists of estimating event frequency, scour potential, and the vulnerability of the pipeline to break if impacted by boulders.

The approach can be adapted to other landslide geohazards so that different geohazard locations can be evaluated with a common metric. Steep creek process frequency is estimated based on field observations and review of documented events, historical air photo records, and terrain mapping based on LiDAR-generated topography. Scour potential is estimated based on channel morphology, presence of bedrock, and grain size distribution of channel bed material. Vulnerability is estimated based on flow width and velocity and can be modified for different pipe diameters and wall thicknesses.

Mitigation options for buried pipelines include those intended to decrease the likelihood of the pipeline being exposed and to increase the resiliency of the pipeline to boulder or organic debris impacts, if exposed. The methodology presented is embedded in risk-informed decision making where pipeline owners and regulators can define probability thresholds to pipeline exposure or rupture, and pipeline designers can demonstrate that

Pipelines often travel through a broad range of physiographic terrains that can include prairies, mountain ranges, upland plateaus, and lowlands occupied by floodplains. In western Canada, most fossil fuel reserves lie either in Alberta or northeastern British Columbia (BC) those aiming to reach the ocean need to cross mountainous terrain against its regional north-south grain, a legacy of BC’s tectonic history.

Each of these terrains is characterized by highly variable topography, climate, and geology. As a result, a single pipeline may be exposed to numerous geohazards, including landslides, rock avalanches, debris slides, rock falls, debris flows, debris floods, and scour and bank erosion from clear water floods.

Extreme environmental, economic, and safety consequences can result from a debris flow, debris flood, or other geohazard impacting and breaking a pipeline.

An analysis of pipeline incident data in BC found geohazards to account for approximately 22% of failures (Porter et al., 2016). For example, a Pacific Northern Gas pipeline in BC was ruptured by a rock avalanche that transitioned to a debris flow, resulting in environmental damage to a pristine coastal ecosystem (Jakob et al., 2004; Boultbee et al., 2006). Another recent example is a debris flow in the United States, initiated from the area burned by the Thomas Fire near Montecito, CA, that impacted a high-pressure gas line in a residential area and caused a large explosion that impacted numerous houses (Kean et al., 2019). The potentially catastrophic safety or economic consequences emphasize the importance of accurately characterizing the risks posed to a pipeline traversing rugged terrain so that appropriate mitigation can be designed to minimize pipeline damages, loss of containment, and the attendant consequences.

*Corresponding author email: jgartner@bgcengineering.ca

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This article describes methods for estimating steep creek risks and selecting appropriate mitigation designs that have been applied to various pipelines throughout BC. The focus of this article is on the steep creek processes debris flows and debris floods; however, the methods for risk assessment and mitigation design can be adapted to other geohazard types.

PROBLEM DEFINITION As a result of the presence of existing right-ofways and the logistical and geotechnically motivated desire to construct on shallow slopes, pipelines and other utilities are typically buried along valley bottoms. Where pipelines follow valleys, they will intersect alluvial fans subjected to steep creek processes of debris flows and debris floods. While debris flows have been defined in detail and there is no more misunderstanding in their genesis, debris floods have only recently been defined mechanistically (Church and Jakob, 2020). For practical purposes those authors defined a debris flood as “a flood during which the entire bed, possibly barring the very largest clasts, mobilizes for at least a few minutes and over a length scale of at least ten times the channel width, though commonly much farther.”

Alluvial fans are primarily depositional; however, channel scour is possible on parts of a fan during a debris flow or debris flood. For example, a debris flow near the town of Hope, BC, entrained most of its total volume in the colluvial channel extending through the debris-flow fan (Jakob et al., 1997). A debris flow in Neff Creek near Pemberton, BC, eroded approximately 80,000 m3 of material from its fan (Lau, 2017).

At locations where the pipeline crosses a mountain pass or traverses steep terrain, the pipeline may cross debris-flow channels where massive channel scour is possible. In BC, yield rates in colluvial channels have been reported to range as high as 6 to 28 m3 /m (Hungr et al., 2005). More recent cases have shown yield rates up to 350 m3 /m measured at Neff Creek (Lau, 2017).

As highlighted by Jakob 2020a, incorrect estimates of potential scour on fans prone to debris flow could lead to pipeline ruptures with highly disruptive outcomes to the environment, the pipeline owners, and the design team. The question of when and by how much a debris flow can entrain versus deposit is highly complex, and it appears that the mobilization of channel materials depends in part on pore water pressures (and thus the phreatic surface) of the channel base and banks (Iverson et al., 2011). Entrainment models have been proposed (Kang and Chan, 2018), and several others have been discussed by Jakob et al. (2020), but their practicality and application along pipeline corridors still need to be tested. One of the fundamental prob-

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lems of pipeline crossings is that observers arriving after a major flood, debris flood, or debris flow can only measure the end result of scour or deposition above a pipeline, which is typically achieved via a handheld pipeline locator. This may delude operators and practicing geoscientists and engineers into believing that such measurement is the actual scour; however, deposition that occurs on the falling limb of a flood hydrograph can mask the maximum scour by backfilling recently eroded areas. The maximum potential scour depth during a debris flow or debris flood is critical information for specifying the design burial depth of pipelines. Therefore, empirical or physically-based methods must predict maximum scour rather than net scour.

Pipeline crossings of steep creeks are often characterized as hydrotechnical hazards. However, debris flows and especially debris floods in ephemeral channels pose a different hazard to a pipeline because of their potential to deeply incise channels during a single event, transport large (>2 m diameter) boulders at high velocities, and avulse and travel down paleochannels.

Since debris floods have lower sediment concentrations than debris flows (e.g. Church and Jakob, 2020), they can entrain more channel bed sediment on the fan than debris flows. Debris flows may impart greater shear stress on the channel bed due to higher sediment concentrations than are associated with debris floods. Entrainment of channel bed and bank material is facilitated by high moisture content. Iverson et al. (2011) found that debris-flow mass and momentum grow when rapid debris loading over a wet alluvial channel surface produces large positive pore pressures that encourage bed sediment scour and reduce friction.

Flowing water increases in erosive power with increasing sediment concentration, and hyperconcentrated sediment–water mixtures are especially erosive (Xu, 1999). Stream competency can be theoretically determined by the Shields relation (Church, 2006, 2010), which is an index formed from the ratio of the fluid force acting on the grain to the grain’s inertia.

This describes the propensity of the grain to be transported. Erosion of debris-flow channels is a function of the dimensional shear stress imparted by the flow on the channel bed, which can be expressed as: τ∗ =

ρf gdS , (ρs − ρf )gD

(1)

where τ* is the Shield’s number, d is flow depth, g is the gravitational constant, S is channel slope, ρf is the fluid density, ρs is the sediment density (2.65 g/cm3 ), and D is the grain diameter. Equation 1 can be solved for

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D to become D=

dS . (ρs − ρf )τ∗

(2)

According to Eq. 2, higher sediment concentrations diminish the fluid bulk density differential, which implies higher buoyancy and dispersive stresses (Church and Jakob, 2020). With increases in bulk fluid density, the maximum size of sediment entrained also increases.

Channels on debris-flow fans are shaped by the formative flow, which is defined as the discharge where the flow depth is sufficient to mobilize most stones in the channel bed and bank material precipitating notable channel changes (Eaton et al., 2017). For this to happen, the largest particles in the channel bed (e.g., the 84th or larger percentile of sediment in the channel) need to be mobilized. By definition, this demarks the onset of a “Type 1” debris flood, which is a meteorologically-generated debris flood that mobilizes the channel bed and bank material (Church and Jakob, 2020). Estimating formative flow depths is possible by identifying the flow depth needed to move the 84th or larger particles in the channel bed. Flume studies (Eaton et al., 2017) have shown that exposure probability for buried infrastructure decreased to below detectable levels at burial depths equivalent to 3.6 times the mean formative flow depth. This has not been verified by field observations, which may not identify the maximum scour that occurred during the event as a result of channel infilling particularly on the falling limb of the hydrograph.

Pipeline design for watercourse crossings in BC is guided by the Government of BC’s Guidelines for Management of Flood Protection Works in British Columbia (BC MOE, 1999), which state that the standard design flood is a 200-year return period flood.

Furthermore, a minimum depth of cover (DoC) of 1.2 m across watercourse crossings is typically adopted based on the Canadian Standards Association (CSA, 2015). No such guidelines exist for debris flows or debris floods, which may be able to erode deeper and produce impact forces substantially higher than those exerted by hydrodynamic processes or by bedload mobilized through drag forces at the channel bed in rivers with alluvial beds. This realization necessitates a substantially different design approach for steep creek processes.

Some guidelines for assessing steep creek hazards to pipelines are described in Jakob et al. (2004) and Porter et al. (2004). More recently, as part of the Trans Mountain Expansion Project (TMEP), a controversial pipeline for crude oil extracted from the northern Albertan oil sands has been proposed to connect Edmonton, Alberta, to Vancouver, BC. Trans Moun-

tain Pipeline Unlimited Liability Corporation (ULC) developed a plan to manage and mitigate geohazard sites that exceed specific risk tolerance criteria for the TMEP pipeline (Trans Mountain Pipeline ULC, 2017).

The design basis for protecting pipelines from steep creek hazards can be hazard-based or risk-informed.

In the former case, it consists of a design event scenario (e.g., to protect against a debris flow with a 200-year return period or probability of occurrence of 0.5% in any given year). In the latter case, a level of tolerable risk per site or aggregated over the entire pipeline is identified by the owner or regulator. For example, the National Energy Board (NEB) in Canada required the TMEP to mitigate and manage all geohazard sites with a frequency of a loss of containment (FLoC) greater than 1 × 10−5 (Baumgard et al., 2016; NEB, 2016). This contribution outlines methods to estimate the risk to pipelines posed by steep creek processes and the reduction in risk afforded by mitigation to assist pipeline designers in achieving tolerable risk levels for new and existing pipelines.

RISK ASSESSMENT FRAMEWORK Geohazard risk for pipelines can be calculated as the product of the annual probability of a geohazard, the spatial probability that the geohazard reaches the pipeline, the vulnerability of the pipeline to be damaged or broken by a geohazard, and the consequence (CSA, 1997; AGS, 2000; and Porter et al., 2004, 2017).

While a simple multiplication of factors, it is the estimation of such factors that is challenging.

Total risk includes a systematic evaluation of the consequences of loss of containment, such as health and environmental outcomes, and may go as far as reputational loss to the pipeline operator, the entire industry, and loss in company share value (if publicly traded). Evaluations of such consequences are outside the geotechnical realm, and, thus, we focus on a narrower definition of pipeline risk that treats all pipeline failures as resulting in equal consequences. Pipeline risk is defined here as the FLoC at a debris-flow crossing (Baumgard et al., 2016; NEB, 2016). The FLoC can be expressed as follows: FLOC(i) = I(i) × F(i) × SH(i) × SV(i) × V(i) × M(I,F,SH ,SV ,V (i)) ,

(3)

where

r FLOC(i) is the frequency of loss of containment due to a steep creek process at location i, expressed as an annual frequency;

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r I(i) is the occurrence factor of 0 or 1 expressing

r Grain size distributions in the channel, including

whether a potential steep creek process has credible opportunity to occur at location i; F(i) is the frequency of occurrence of the steep creek process at location i, expressed as an annual frequency; SH(i) is the spatial probability of horizontal impact, expressed as a conditional probability that a steep creek process would horizontally reach the pipeline at location i; SV(i) is the spatial probability of vertical impact, expressed as a conditional probability that a steep creek process would erode to the pipeline at location i; V(i) is the vulnerability of the pipeline, expressed as a conditional probability that a steep creek process would result in loss of containment, given that it occurs and reaches the pipeline at location i. The unmitigated case assumes standard pipeline construction and operation conditions; and M(SH ,SV ,V (i)) is the mitigation reduction factor, ranging from 0 to 1, that is associated with various detailed design measures. This reduction factor accounts for the decreased spatial probability of a hazard reaching the centerline (identified by SH and SV ) or decreased vulnerability due to a specific mitigation applied at location i (identified by V(i) ).

r Channel geometry, including channel width, chan-

r r

r

r

r

The probability of exposure (PoE) is defined as the probability that the pipeline becomes exposed and potentially impacted by a steep creek processes. The PoE is a subset of Eq. 3 and has the form PoE = I(i) × F(i) × SH(i) × SV(i) .

(4)

To fully characterize the steep creek risk at a pipeline crossing, estimates of FLoC should be completed for the active channel on an alluvial fan as well as potential avulsion paths. Multiple estimates of FLoC may be required to evaluate risk at particularly sensitive sites for various event frequencies and magnitudes.

METHODS FOR ESTIMATING FLOC Estimating FLoC can be done by combining desktop analysis, field investigations, and data analyses.

Desktop analyses of a steep creek site may examine the following data sources, if available:

r Air photos and/or Google earth imagery; r Digital elevation models (DEMs) derived from LiDAR data; r Geologic maps; and r Documentation of previous debris flows and debris floods at the site.

Field observations of steep creeks may include

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maximum boulder size;

nel depth, and channel slope;

r Observations of previous deposits on the fan and along the channel;

r Locations of possible avulsion channels; and r The frequency of steep creek processes in the channel, which may include ◦ presence and abundance of boulder impact tree scars; ◦ estimated ages of deposits; and ◦ estimated ages of vegetation in the channel and surrounding area.

While detailed dendrogeomorphic methods or radiocarbon dating of organic sediments in natural outcrops or test trenches can be used to decipher accurate event frequencies, those are often not feasible to over hundreds of kilometers of pipelines within typical project development timelines. However, new methods have emerged to approximate event frequencies and corresponding magnitudes from fan areas or fan volumes alone. Jakob et al. (2020) developed empirical relationships for estimating debris-flow- and debrisflood volumes from fan area or fan volume in the following form: VS = Af [a ln (T ) − b] ,

(5)

where T is the event return period, a and b are coefficients that vary based on region and flow process type (i.e., debris flow versus debris flood), VS is the normalized total sediment volume in m3 /km2 , and Af is the fan area. The approach to estimate frequency and magnitude of steep creek processes in Jakob et al.

(2020) can inform professional judgement on how to estimate the input parameters to the FLoC equation.

For example, a site estimated by the Jakob et al. (2020) models to be subject to frequent, high-magnitude debris flows would have higher estimates for the input parameters to Eq. 3 (F(i) , SV(i) , SH(i) , and V(i) ) than would a site affected by infrequent, small debris flows.

The following sections describe how field and remotely sensed data can be incorporated into estimating each of the variables in the FLoC equation.

Table 1 describes the general approach to estimate each of the variables in the FLoC equation.

Occurrence, I(i) Occurrence (I(i) ) indicates whether a steep creek hazard exists at a given site. A steep creek process is considered a hazard to the pipeline if it has the potential to scour down to at least the top of the pipeline at a given location. If it can be established that erosion by

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F(i) —Events/yr Minimum

Maximum

Debris Flow and Debris Flood

n/a

0.01

0.01

0.1

0.1

1

Little sediment is available for erosion in contributing watershed. Evidence of past flows in channels and on fan is difficult to discern.

Some sediment is available for erosion in contributing watershed. Evidence of past flows on the fan or in the watershed is visible but may be obscured by vegetation.

Sediment is available for erosion in contributing watershed.

Evidence of past flows on the fan and in the watershed is visible.

Abundant sediment available for erosion in contributing watershed, evidence of past flows on the fan and in the channel is easily visible.

1

10

steep creek processes cannot occur, then I(i) = 0. Such sites may be at very distal portions of fans, where fan deposits interfinger with floodplains and their gradients are very low. Alternatively, sites with I(i) = 0 may be those that have been sufficiently armored. At sites where past flows have led to at least some erosion on the fan at the pipeline crossing, I(i) = 1.

Geologic maps may identify alluvial fans that may be dominated by steep creek processes; however, such specialty maps are rare. Air photo analyses may reveal evidence of past debris flows or debris floods as long as they were of sufficient magnitude to be visible through tree canopies or crossing the pipeline rightof-way. Literature searches of debris flows and debris floods in the region may provide site-specific information for the crossing. Field observations of deposits, levees, and tree impact scars can also be used to identify if there is a credible steep creek hazard at the crossing. Watershed morphology can help to identify watersheds dominated by steep creek processes. Typically, small and steep watersheds are most susceptible to debris flows and debris floods. They can be differentiated from watersheds dominated by clearwater floods by plotting the Melton ratio (defined as the watershed relief divided by the square root of the watershed area) (Melton, 1965) against watershed length (Wilford et al., 2004). Figure 1 demonstrates how the Melton ratio and watershed length morphometrics can distinguish dominant hydrogeomorphic processes (e.g., clearwater floods, debris floods, and debris flows) of watersheds located throughout BC and Alberta, Canada.

In summary, the likelihood of occurrence of steep creek processes at a pipeline crossing can be assessed based on a combination of desktop review of geologic maps and air photos, field review of deposits and impact scars, recorded events, and morphometric watershed analysis.

Figure 1. Steep creek processes as a function of the Melton ratio and stream length. Data and process boundaries are from fans in Alberta and BC (Holm et el., 2016; Lau, 2017).

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Gartner and Jakob Table 2. An example of how field evidence on the fan and in the contributing watershed area can be used to estimate F(i) .

Variable

Method to Guide Estimates

I(i)

Site-specific observations of channel and deposited sediment Review of geologic maps and air photos Watershed morphometric analyses (see Figure 1) Site-specific observations of • Sediment availability in the upper watershed • Number and extent of debris-flow or debris-flood deposits in the channel and on the fan • Approximate age of vegetation growing on debris-flow or debris-flood deposits • Interpretation of event frequency and magnitude results provided by methods in Jakob et al. (2020) Site-specific observations of the number and extent of debris-flow or debris-flood deposits at the crossing Numerical modeling of debris-flow or debris-flood runout areas Interpretation of event frequency and magnitude results provided by methods in Jakob et al. (2020) Site-specific observations of • Channel and fan morphology • Erodibility of channel bed material • Presence of abrupt changes in channel slope that could lead to retrogressive scour of a channel knickpoint • Proximity of pipeline crossing to fan apex • Interpretation of event frequency and magnitude results provided by methods in Jakob et al. (2020) Analyses of the yield strength of the pipeline versus the potential dynamic pressure and point load impacts of the debris flow or debris flood Estimates of dynamic pressure as a function of the flow density, channel width, and the flow velocity Estimates of point load impacts as a function of the flow velocity and grain-size distribution of sediment transported by flows Interpretation of event frequency and magnitude results provided by methods in Jakob et al. (2020)

F(i) Figure 2. Conceptual figure demonstrating how observations of fan activity and sediment availability in the upstream watershed influence the frequency of debris flows at a pipeline crossing.

SH(i)

Frequency of Occurrence, F(i) Frequency of occurrence (F(i) ) is defined as the annual probability of occurrence of a steep creek process (hazard probability) at location i. Frequency can be expressed either as a return period or as an annual probability of occurrence. For example, if five debris flows have occurred within a 100-year period, the average return period is 20 years (assuming data stationarity), and the annual probability is the inverse, so 0.05, or a 5% chance that a debris flow may occur in any given year. Given the uncertainty associated with estimating steep creek process frequency at specific sites, frequency classes with minimum and maximum bounds may be used (e.g., 0.03 to 0.1 [10- to 30-year return period], 0.01 to 0.03 [30- to 100-year return period], etc.).

Frequency classification can be based on existing and historical site conditions where air photos are available (Table 2). Figure 2 schematically illustrates how steep creek process activity on a fan and the availability of erodible sediment in the upstream catchment is related to the frequency of a steep creek process that may reach and impact the pipeline. Estimated frequencies based on historical data may differ from frequencies in the future as a result of changes in sediment supply by forestry-related instabilities or forest fires or by changing hydroclimatic environments associated with climate change. The past is no longer a key to the future as it pertains to debris flows and debris floods (Jakob and Lambert, 2009; Jakob, 2020b). Estimates for frequency should be adjusted to account for climate change if science has sufficiently advanced to provide such estimates.

Likewise, observations of existing site conditions may be influenced by a recent, rare event that may bias toward interpreting the site as being subject to frequent steep creek processes. For this reason, documented event histories, field evidence of historical events, and air photo records should supplement fieldbased observations of frequency.

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SV(i)

V(i)

Spatial Probability of Impact, SH(i) and SV(i) The spatial probability of horizontal impact (SH(i) ) is defined as the probability that a given event at location i will reach the pipeline alignment. For input into the FLoC equation, only steep creek processes that would cross the pipeline may be evaluated, which would make SH(i) equal to one. As an alternative, empirical modeling such as Flow-R (e.g., Horton et al., 2013) or numerical modeling such as DAN3D (McDougall and Hungr, 2004), FLO-2D (FLO-2D, 2007), RAMMS (Cesca and Agostino, 2018), or D-Claw (Iverson and George, 2014), or various other models recently summarized by Kang and Chan (2018) may be used to evaluate the spatial probability of horizontal impact along a pipeline crossing of a debris-flow or debris-flood fan.

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Figure 3. A schematic of a pipeline crossing upstream of a fan apex where scour potential is higher than a pipeline crossing of the fan. The pipeline in this example is buried but shown above the ground level for illustrative purposes. Artwork by Jonathan Kroeger.

The spatial probability of vertical impact (SV(i) ) is defined as the probability that a debris flow or debris flood at location i will vertically expose at least the top of the pipeline (termed the “crown”). The pipeline can be exposed by either lateral migration of the channel or by scour of the channel bed sediment. Predicting entrainment of channel material is challenging, and scour depth predictions in steep creek channels are often unreliable. Notwithstanding, the depth to which pipelines are to be buried needs to estimated as accurately as possible. Therefore, estimates for SV(i) should consider a variety of estimates based on field observations, analyses of channel and fan morphology, scour analysis, and professional judgement. The following paragraphs provide guidance for estimating SV(i) and highlight scenarios in which steep creek processes are most likely to deeply scour channels.

Steep creek processes tend to scour channels upstream of the fan apex, oftentimes removing all the colluvium in the channel and possibly exposing bedrock.

As such, pipelines that cross a channel upstream of the fan apex (which is rare, but possible) are particularly prone to be exposed and would be assigned a high (between about 0.7 and 0.9) value for SV(i) . Figure 3 is a schematic of example pipeline crossings of channels upslope of the fan apex.

Although steep creek fans are dominated by depositional processes, pipeline crossings of such fans may be subject to channel scour. Figure 4 shows a pipeline crossing on a fan where material has been both deposited and eroded on the right-of-way. The erosion in this example, however, likely occurred as a result

of sediment reworking by water-dominated flow rather than the debris flow.

Scour depth can vary with respect to position on a fan, with typically higher scour potential near the fan apex, where channel gradients are steeper, than at the distal part of the fan, where flows may be less confined by channel banks and may travel over shallower gradients. Therefore, higher estimates for SV(i) apply to pipeline crossings at the fan apex than at the distal fan.

Local channel geometry can also lead to channel scour on a fan when there is an abrupt increase in channel slope just downstream of the pipeline.

At such locations, knickpoints (sudden changes in

Figure 4. A pipeline crossing of a debris-flow fan near Chilliwack, BC, where debris-flow material was deposited and channels were eroded. Vehicles and road near the bottom of the photo are visible for scale. Photo by BGC Engineering, Inc.

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Figure 5. Illustration of how knickpoint erosion of fill material on a pipeline right-of-way can expose the pipeline.

channel slope) may migrate upstream and expose the pipeline. During construction of a pipeline, it is common for the right-of-way to be constructed in a cut and fill slope. The fill slope may create an over-steepened channel just downslope of the pipeline. As a result, future flows are likely to deposit material in the right-of-way cut and to erode the right-of-way fill material downslope. Figure 5 illustrates the knickpoint erosion scenario, and Figure 6 shows some examples of sites at which knickpoint erosion has occurred. Pipelines constructed upstream of logging roads, highways, and rivers may also have downstream knickpoints that are out of equilibrium with the natural channel slope as a result of cuts into the distal fan deposits. Figure 7 is an example of where a cut slope for a highway has created a knickpoint downstream of a pipeline.

The construction of in-channel sediment control can cause erosion in the downstream channel. After sediment has been removed from a flow by a sediment retention basin, check dam, or debris net, water continues downstream along an erodible bed. The water

is more erodible than a debris flow. Figure 8 demonstrates this scenario.

A real-world example for the above process has been observed by one of the authors (Jakob) at a recent debris flood event on Fairmont Creek, in southeastern BC. Here riprap check dams (Figure 9A) installed in the creek’s transport zone captured a significant volume of a May 31, 2020, debris flood. The sediment starvation from the check dams facilitated substantial downcutting in the downstream channel reaches, which then exposed the buried water lines shown in Figure 9B. In some scenarios, extreme scour (greater than about 10 m in depth) on a fan is possible. An example of extreme scour on a fan was at Neff Creek in BC, where scour near the fan apex was measured to be on the order of 10 m (Figure 10). Identifying fans that are prone to extreme scour is challenging. A watershed with recent deposits near the fan apex may temporarily be susceptible to deep channel scour on the fan due to the over-steepened gradient near the fan apex. Morphometric variables of the average fan gradient and

Figure 6. An example of knickpoint erosion of benched pipeline right-of-way (photo by BGC Engineering, Inc., on April 28, 2018).

Figure 7. An example of knickpoint erosion of a cut slope for a highway (photo by BGC Engineering, Inc.).

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Figure 8. Schematic demonstrating scenario where sediment is removed from a flow, which causes erosion in the downstream channel. Artwork by Jonathan Kroeger.

watershed area have successfully identified some fans where extreme scour has occurred (Lau, 2017), and flume studies have postulated that buried infrastructures on alluvial fans are not likely to exposed if their depth is greater than 3.6 times the mean formative flow depth of a flood (Eaton et al., 2017). Although these studies are not directly applicable to estimating SV(i) , they provide some guidance for identifying fans susceptible to deep channel scour and for evaluating if a pipeline will be exposed at a given burial depth.

The observed depths of active and abandoned channels on a fan can provide an indication of the scour depth of past flows. However, it could be overly conservative to conclude that this incision is attributable to a single event, and it may indeed be the legacy of fluvial reworking rather than attributable to scour by steep creek processes. Regardless, field measurements of channel scour depths and/or LiDAR measurements of channel depths on a fan can be used to evaluate total scour potential at the active or avulsion channels and to arrive at an estimate for SV(i) . This method assumes the presence of at least one deeply incised channel on

Figure 9. Riprap check dam on Fairmont Creek (A) and downstream severe downcutting (B). Photos by Matthias Jakob.

Figure 10. Erosion on the Neff Creek fan in British Columbia, Canada, in 2017 was extraordinary. A person is circled in orange for scale. Photograph by Carie-Ann Lau.

a fan and the inference that other deeply incised channels could form in previously unchannelized areas of the fan. These assumptions are conservative, which is justifiable because of the potentially significant consequences associated with pipeline containment loss.

Pipeline Vulnerability, V(i) Pipeline vulnerability (V(i) ) is the vulnerability of the pipeline to loss of containment, given that the pipeline is exposed at location i. A loss of containment from a steep creek process may be caused by dynamic pressure on the pipeline or impact loading on the pipeline. For dynamic loading to break a pipeline, the dynamic pressure of debris-flow- or debris-flood sediment on a fully exposed pipeline exceeds the yield strength of the pipeline. For a pipeline to break as a result of impact loading, only the top of the pipeline needs to be exposed for a boulder to impact the pipeline with a point load that exceeds its yield strength. Pipeline crossings of rivers wider than about 10 m with flow velocities of 5 to 7 m/s are subject to vortex-induced vibration that can weaken the pipeline and cause it to break. Methods for estimating vulnerability of pipelines to fail by hydrodynamic loading and vortex-induced vibration are provided in Dooley et al. (2014). However, debris flows rarely cause pipelines to fail by this mechanism because they often have unsteady, surging flows in channels with bankfull widths that are often less than 10 m.

Assessment of the vulnerability of a pipeline depends on the yield strength of the pipeline, which varies depending on pipeline wall thickness and pipeline diameter. Vulnerability can be assessed probabilistically using probability distributions of pipeline yield strength, flow velocity, debris-flow- or debris-flood density, and the size of boulders that can be transported by the flow.

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The estimates of steep creek process velocity and bulk density influence the dynamic pressure against a pipeline that has been fully exposed and is spanning a channel. Debris-flow velocities can be estimated using super-elevation of flow around a channel bend (Johnson, 1984) or runup against vertical barriers or adverse slopes (Iverson et al., 2016). However, field evidence for applying these methods may not be available, and methods presented in Prochaska et al. (2008) may be applied with field estimates of debris-flow depth and measurements of channel slope. Debris-flood velocities can be estimated using Manning’s equation with estimates of roughness (Manning’s “n”) based on empirical equations developed for steep creeks (Jarrett, 1984; Zimmerman, 2010).

Bulk density of debris flows in flume studies have ranged from 1,400 to 2,400 kg/m3 , and bulk densities of natural debris flows typically range from 1,800 to 2,300 kg/m3 (Iverson, 1997). Little is known about debris-flood bulk densities, but Type 1 debris floods are likely below 1,300 kg/m3 (Church and Jakob, 2020).

Debris-flow- and debris-flood velocity and grain size distribution influence the magnitude of the point load impacts that are possible on a pipeline that has been partially or fully exposed. The size of boulders that could be transported by a flow can be interpreted from field investigations of the grain-size distributions of steep creek process deposits.

Mitigation Reduction Factor, M(SH ,SV ,V (i)) Mitigation measures to protect the pipeline can reduce FLoC to a tolerable level or to a level that is “as low as reasonably practicable.” The mitigation reduction factor (M(SH ,SV ,V (i)) ) is included to characterize the reduction in FloC at a specific site afforded by mitigation measures. Values for M(SH ,SV ,V (i)) range from 0 to 1 and represent the reduction in the FLoC at a specific site due to a mitigation measure. A M(SH ,SV ,V (i)) value closer to zero represents a mitigation measure with a significant level of protection, and a M(SH ,SV ,V (i)) value closer to one represents a mitigation measure that provides minimal protection for the pipeline.

Different mitigation measures could provide varying degrees of protection from impacts by changing SH(i) , SV(i) , or V(i) at location i. Mitigation measures that decrease SH(i) include debris retention basins and deflection berms. Mitigation measures that can decrease SV(i) include increasing the depth of cover, riprap, or grouted riprap channel protection and grade control structures. Mitigation measures that decrease V(i) include using heavy wall pipeline (i.e., increasing pipeline wall thickness) and concrete pipeline coating.

Values for M(SH ,SV ,V (i)) depend on the degree of risk reduction the mitigation offers. For example, rerouting

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a pipeline or construction of a debris retention basin or deflection berm may have a significant reduction in the SH(i) variable, and the associated mitigation reduction factor, MSH (i) , may be low (e.g., approaching 0.01).

Increasing depth of cover may have varying effects on risk reduction depending on how deep the pipeline is buried, and the associated mitigation reduction factor, MSV(i) , may have a broad range (e.g., from 0.1 to 0.9).

Increasing pipeline wall thickness may have a marginal benefit to reducing risk at the pipeline, and the associated mitigation reduction factor, MV(i) , may be higher (e.g., approaching 0.9).

Accurate characterization of the mitigation reduction factors associated with different mitigation techniques allows for risk-informed design. A pipeline operator or regulatory body may choose a specific risk tolerance threshold. At sites where the risk, as characterized by the estimated FLoC, exceeds this threshold, the amount of risk reduction afforded by various mitigations can be quantified to demonstrate that risk has been reduced below that threshold. Alternatively, a PoE criterion may be chosen for which the pipeline can have a given maximum annual probability of being exposed. Appropriate mitigations to reduce SH(i) and/or SV(i) could be applied until the PoE decreases to a level below this probability threshold.

Typical mitigation approaches for hydrotechnical crossings are minimally applicable to crossings affected by steep creek processes. For example, methods for estimating riprap gradations that will not be transported at hydrotechnical crossings are based on estimates of shear stress and the diameter of sediment that could be transported by a flow with a specific return period.

The return period flow for a hydrotechnical crossing can be estimated using rainfall runoff modeling or regional flood frequency analyses; however, the peak discharges based on these methods are not representative of steep creek processes, which may have much higher peak discharges. Furthermore, sediment transport equations for clearwater flows do not account for the higher sediment concentrations of a debris flow or debris flood. As a result, large boulders exceeding 1 m in diameter can be transported by even modest-sized debris flows or extreme debris floods. Therefore, riprap sizes that are not susceptible to erosion and transport by debris flows often exceed those that are available from nearby sources. Using boulder diameters similar to or smaller than what has been transported by debris flows or debris floods for pipeline protection invites that those will be entrained in future events, thus annulling their design intent. As a result, alternative methods, such as grouted stone pitching or grouted riprap, may be employed (Figure 11).

An alternative to channel bed protection is to decrease the pipeline vulnerability by strengthening its

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Figure 11. Grouted riprap channel erosion protection is designed to decrease the likelihood of channel scour that could expose the pipeline.

Figure 12. Example of a combination of channel grade control and riprap erosion protection and increased depth of cover at a pipeline crossing of an active debris-flow channel. Photo by BGC Engineering, Inc.

SUMMARY materials. The use of heavy wall pipeline and/or concrete coating can decrease the likelihood that a steep creek process will rupture a pipeline. However, these measures are not solely relied upon to protect pipeline crossings, but rather to supplement increased depth of cover. Other approaches decreasing pipeline risk of steep creek process impacts include:

r Routing new pipelines to avoid steep creeks and fans;

r Constructing pipeline crossings of channels and fans with adequate depth of cover so that pipelines are not exposed to steep creek process impacts; and r Placing the pipeline in areas where steep creek processes are most likely to be depositional rather than erosive.

Several mitigation techniques may be required to achieve the tolerable FLoC or PoE value. Figure 12 shows a site at which channel erosion protection, grade control structures, and increased depth of cover are present to protect the pipeline against an active steep creek. Where several mitigation methods are applied, multiple mitigation reduction factors can be integrated into the FLoC equation. Although complimentary mitigation measures provide greater risk reduction, engineering and geoscientific judgement is required to avoid an overly conservative level of risk reduction.

Detailed design of mitigation should incorporate detailed site-specific analysis of potential event magnitudes so that the pipeline is protected against impacts from both the most frequent scenario that could result in a pipeline rupture as well against impacts from larger, less frequent events.

We present a risk assessment methodology suitable for quantifying risk posed by steep creek processes to buried pipelines. Risk is defined as the FLoC and does not incorporate other consequences, such as environmental impact, regulatory fines, cleanup costs of spills, legal fees for claim defenses, service interruptions, share price decrease, and adverse impacts to a company’s reputation. The method can also be applied to identify appropriate design measures to reduce FLoC or PoE to below a tolerable threshold set by either the pipeline owner or regulatory authority. Research is continuing to help define best practices for quantifying debris-flow- and debris-flood frequencymagnitude relationships, runout, scour, and rheology as applicable to linear infrastructure corridors. The methodology provided here provides a framework that can be implemented with existing methods for steep creek hazard and risk assessment and that integrates scientific advancements in steep creek research.

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Debris-Flow and Debris-Flood Susceptibility Mapping for Geohazard Risk Prioritization MATTHIEU STURZENEGGER* KRIS HOLM CARIE-ANN LAU MATTHIAS JAKOB BGC Engineering, 500-980 Howe Street, Vancouver, BC V6Z OC8, Canada

Key Terms: Debris-Flow Susceptibility, Debris-Flood Susceptibility, Flow-R, Risk Prioritization ABSTRACT Regional-scale assessments for debris-flow and debris-flood propagation and avulsion on fans can be challenging. Geomorphological mapping based on aerial or satellite imagery requires substantial field verification effort. Surface evidence of past events may be obfuscated by development or obscured by repeat erosion or debris inundation, and trenching may be required to record the sedimentary architecture and date past events. This paper evaluates a methodology for debrisflow and debris-flood susceptibility mapping at regional scale based on a combination of digital elevation model (DEM) metrics to identify potential debris source zones and flow propagation modeling using the Flow-R code that is calibrated through comparison to mapped alluvial fans. The DEM metrics enable semi-automated identification and preliminary, process-based classification of streams prone to debris flow and debris flood. Flow-R is a susceptibility mapping tool that models potential flow inundation based on a combination of spreading and runout algorithms considering DEM topography and empirical propagation parameters. The methodology is first evaluated at locations where debris-flow and debrisflood hazards have been previously assessed based on field mapping and detailed numerical modeling. It is then applied over a 125,000 km2 area in southern British Columbia, Canada. The motivation for the application of this methodology is that it represents an objective and repeatable approach to susceptibility mapping, which can be integrated in a debris-flow and debris-flood risk prioritization framework at regional scale to support risk management decisions.

*Corresponding author email: msturzenegger@bgcengineering.ca

INTRODUCTION Debris flows and debris floods occur abundantly world-wide and are often responsible for property damage, business interruptions, and sometimes fatalities (e.g., Dowling and Santi, 2014; Jakob et al., 2017).

Climate change is likely to exacerbate this trend directly through more frequent and increasingly intense precipitation events or as a result of secondary effects such as wildfires (e.g., Jakob, 2020a). Debris-flow and debris-flood hazard assessment covering areas on the order of hundreds of square kilometers can be challenging due to the effort required to analyze and map such extensive areas. In addition, hazard mapping requires objective and repeatable criteria to characterize hundreds or thousands of watersheds/fans, where surface evidence for past events is either obfuscated by development or obscured by cycles of erosion or debris inundation.

This paper evaluates a methodology for debris-flow and debris-flood susceptibility mapping at regional scale, based on a combination of digital elevation model (DEM) metrics to identify zones prone to landslide initiation in a semi-automated manner and the Flow-R software to assess the area that can potentially be inundated by flow propagation. This methodology represents an improvement that can be integrated into a regional-scale debris-flow and debris-flood risk prioritization framework presented in Holm et al. (2019), whose objective is to identify, characterize, and rank steep creek geohazard risks. The results support government planning, policy, and regulation, including decisions to fund further assessment of the highestranking creeks.

The risk prioritization framework by Holm et al.

(2019) is illustrated in Figure 1. Prioritization is achieved by combining both a geohazard rating and a consequence rating. The geohazard rating considers the combined likelihood that steep creek geohazards will occur (geohazard likelihood rating) with the likelihood that flows will impact elements at risk as a result of avulsion or high-magnitude events causing erosion of channel banks on the fan

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Figure 1. Summary of the regional-scale steep creek geohazard risk prioritization method (Holm et al., 2019). Channel Confinement, which has been previously estimated from lidar and imagery interpretation, is the parameter to be replaced by susceptibility maps.

(impact likelihood rating). The consequence rating considers the destructive potential (hazard intensity) of steep creek geohazards and the level of exposure of elements at risk (hazard exposure). The improvements in the current study focus on channel confinement, which is used to estimate the impact likelihood rating. We recognized that this parameter is difficult to estimate consistently at regional scale based on geomorphological mapping, especially where airborne lidar data are unavailable.

Susceptibility mapping is a common approach to characterize the relative propensity of slopes to fail at a regional scale. The term “landslide susceptibility” is defined by Fell et al. (2008) as “a quantitative or qualitative assessment of the classification, volume (or area), and spatial distribution of landslides which exist or potentially may occur in an area.” Flow-R (Horton et al., 2013), which stands for “flow path assessment of gravitational hazards at regional scale,” is a software tool that can be used for debris-flow and debris-flood susceptibility mapping. Unlike empirical methods or numerical runout models, which require input parameters not available at regional scale or which may be computationally prohibitive, Flow-R is designed for regional-scale studies (Fischer et al., 2012; Blais-Stevens and Behnia, 2016; Pastorello et al., 2017; and Kang and Lee, 2018). Flow-R is not suited for detailed hazard assessments or the design of mitigation structures because it does not compute debris-flow or debris-flood volume, mass, depth, velocity, peak discharge, or impact forces.

Some authors have integrated Flow-R into preliminary hazard assessments, which typically require definition of landslide magnitude and frequency. Based on the assumption that larger debris flows are less frequent and able to travel for longer distances than smaller, more frequent ones (e.g., Corominas and

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Moya, 2008), Blahut et al. (2010) and Kappes et al.

(2011) defined three magnitude–frequency runout scenarios corresponding to “low,” “moderate,” and “high” hazard by utilizing different sets of propagation parameters. Blahut et al.’s (2010) simulations were coupled with ratings for debris-flow hazard initiation probability. Calibration of these different sets of propagation parameters and associated hazard levels can be challenging at regional scale, as they typically require field investigation of fans, which cannot be completed for regional-scale studies. Therefore, the integration of Flow-R susceptibility maps into hazard assessments should be done with caution.

Some definitions and the details about the methodology are provided in the next two sections, respectively. The section “Pilot Study and Method Evaluation” presents a pilot study to test and compare the methodology with the results of previous detailed debris-flow and debris-flood assessments and mapping. The section “Regional-Scale Susceptibility” shows the application of the methodology at regional scale over a 125,000 km2 area in southern British Columbia. The performance and limitations of the methodology are discussed in the “Discussion,” and a conceptual model for its integration into the risk prioritization framework by Holm et al. (2019) is presented.

DEFINITIONS Steep creek geohazards: Steep creek geohazards include both debris flows and debris floods. A debris flow is defined as a very rapid to extremely rapid surging flow of saturated debris in a steep channel, with strong entrainment of material and water from the flow path (Hungr et al., 2014). Debris floods are floods during which the entire channel bed, barring the very largest

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clasts, becomes mobile for at least a few minutes and over a length scale of at least 10 times the channel width (Church and Jakob, 2020). Three types of debris floods are defined by these authors: Type 1 debris floods are defined when exceedance of a critical shear stress threshold for D84 mobilization occurs; Type 2 debris floods are transitional processes produced by progressive dilution of debris flows; and Type 3 debris floods result from outbreak floods.

Watershed and fan systems: A steep creek watershed consists of hillslopes, small feeder channels, a principal channel, and a fan composed of deposited sediments at the lower end of the watershed. Stream channels on the fan are subject to erosion and scour. In addition, they are prone to avulsion, which are rapid changes in channel location, due to natural cycles in fan development and from the loss of channel confinement during hydrogeomorphological events (de Haas et al., 2017).

Susceptibility mapping: In this paper, susceptibility mapping focuses on the spatial extent and classification of inundation zones within fans, which are typically the developed areas requiring assessment. Unlike hazard mapping that models separate steep creek scenarios with associated return periods, susceptibility mapping considers a range of possible outcomes (Horton et al., 2013). From a geomorphological standpoint, a fan reflects the range of all possible flow outcomes because it includes the deposits of many events of various magnitudes accumulated over a period of time. Some areas of a fan may be inactive or are paleofans developed in the early post-glacial period, or have been abandoned due to substantial base-level lowering. In those cases, susceptibility zones may not cover the entire fan. In some cases (e.g., afterflows or exceptional high-magnitude or high-mobility events), susceptibility zones may extend beyond a fan.

METHODOLOGY This section provides details on the regional-scale steep creek geohazard risk prioritization framework

by Holm et al. (2019), which provides the context for the application of the susceptibility mapping methodology. We then describe the methodology, which has two components: a semi-automated identification and classification of zones susceptible to debris-flow and debris-flood initiation and the Flow-R software for propagation assessments.

Regional-Scale Steep Creek Geohazard Risk Prioritization Framework The regional-scale steep creek geohazard risk prioritization framework (Holm et al., 2019) focuses on alluvial fans, as they are the features subject to steep

creek geohazards. The fans are mapped manually from lidar and aerial imagery and classified based on their dominant process (debris flow or debris flood) using geomorphological characteristics and past records, if available. After alluvial fan mapping and systematic elements-at-risk characterization, the framework combines qualitative geohazard and consequence ratings into priority rankings of the fans. A single priority ranking is attributed to each fan. Approximately 2,000 fans are mapped and prioritized across the study area.

Given that the studies support government planning, policy, and regulation, the focus is on fans containing buildings and infrastructure. The framework is illustrated in Figure 1.

The two components of the geohazard rating, geohazard likelihood and impact likelihood, are based on geomorphological mapping using historical aerial photographs, satellite imagery, airborne lidar, and historical records. The geohazard likelihood rating is obtained by combining a parameter describing “basin activity” and another one characterizing “fan activity.” The “basin activity” parameter considers criteria such as identifiable sediment sources and whether watersheds are supply-limited or unlimited (Jakob, 1996; Jakob, 2020b). The “fan activity” parameter refers to the frequency of debris-flow or debris-flood events mappable on the fans. These two parameters are rated qualitatively between very low and very high and combined in a matrix.

The impact likelihood rating is obtained by combining two parameters: “evidence for previous avulsion” on fans and “channel confinement” on fans. The two parameters are rated qualitatively between very low and very high and combined in a matrix. The “evidence for previous avulsion” parameter considers the frequency of avulsion events on the fans. The “channel confinement” parameter considers channel incision, bends, gradient, and constrictions.

Susceptibility Mapping Susceptibility modeling requires estimation of debris-flow and debris-flood initiation susceptibility and estimation of flow propagation.

Semi-Automated Identification of Zones Susceptible to Debris-Flow and Debris-Flood Initiation Zones susceptible to debris-flow and debris-flood initiation are identified semi-automatically based on stream segments in a two-step process: stream segment delineation and classification. Stream segments are delineated from original data sources, which in this study were based on the National Hydro Network in British Columbia (Government of Canada, 2020). Once

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Sturzenegger, Holm, Lau, and Jakob Table 1. Steep creek process type thresholds using Melton ratio and total stream network length (after Holm et al., 2016).

Process Type Clear-water flood Debris flood Debris flow

Melton Ratio

Stream Length (km)

<0.2 0.2 to 0.5 >0.5 >0.5

All All >3 ࣘ3

delineated, the stream segments are classified to differentiate the ones most likely to generate debris flows from the ones most likely to generate debris floods (Holm et al., 2019). These process types are differentiated using two geomorphometric metrics, the Melton ratio and watershed length, using thresholds defined by Holm et al. (2016) and shown in Table 1. The Melton ratio corresponds to the ratio between watershed relief and the square root of watershed area (Melton, 1957). The watershed length is calculated as the total channel length upstream of a given stream segment to the stream segment farthest from the fan apex. These terrain metrics are appropriate screening level indicators of the propensity of a creek to dominantly produce debris floods or debris flows (Wilford et al., 2004), although the two process types should be viewed as a continuum and can occur within the same watersheds at different return periods and in different stream channel segments.

Stream segments not classified as debris flow or debris flood are associated with clear-water flood (Table 1) and are considered separately in the risk prioritization framework.

After filtering based on slope angle to avoid source zones with slope angles below 15°, the classified stream segments are used as proxy for zones susceptible to steep creek geohazard initiation. This simplification reflects that the risk prioritization, and therefore Flow-R calibration, focuses on the fans. The stream segments classified as debris flow are used as source zones for the debris-flow propagation model. The stream segments classified as debris-flood segments cannot be used as debris-flood source, because some of them are located within or downstream of alluvial fans. To avoid this problem, we use stream segments located upstream of debris-flood segments as debris-floods sources. From a geohazard perspective, this criterion for the selection of debris-flood sources is consistent with a Type 2 debris flood.

The main drivers for using stream segments as flow source zones are that these segments can readily be obtained or generated from DEMs and using stream segments is computationally more efficient across large regions than using wider source zones.

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Propagation Susceptibility Using Flow-R Flow-R models debris-flow and debris-flood propagation susceptibility through a DEM (Horton et al., 2013). In our study, source zones are defined as stream segments using the semi-automated method described previously. Propagation is modeled using Flow-R spreading algorithms (direction and inertial algorithms) and friction loss functions. The direction algorithm determines the probability that simulated flows propagate from one DEM cell to neighboring cells.

The modified Holmgren (1994) algorithm is the recommended direction algorithm, which includes both a factor “dh” allowing smoothing of DEM roughness and an exponent “x” to control flow divergence. The inertial algorithm reproduces the behavior of inertia by weighting flow direction to a neighboring cell based on the change of direction with respect to the direction from the incoming cell. The friction loss function constrains propagation distance based on a friction model, such as the travel angle, corresponding to the angle of the line connecting the source zone to the most distant point reached by debris flow along its path (Corominas, 1996). Simulated flow velocity can be user-capped at a specified value to avoid unreasonable values. Both spreading algorithms and friction parameters need to be calibrated by back-analysis of observed events or based on geomorphological observations, such as by matching Flow-R propagation to the distal boundary of alluvial fans. Flow-R simulations may not inundate the entire area of fans, as some areas may not be or may be very unlikely to be subject to avulsion under present climate and geomorphological conditions.

Flow-R can generate the maximum probability that a DEM cell will be inundated by flows or the sum of probabilities from all upslope sources. The former is calculated using the “quick” calculation method, which propagates probability from the highest source and iteratively checks the remaining source pixels to determine if a higher energy or probability value will be modeled. The latter is calculated in Flow-R using the “complete” method and can be used to identify areas of highest relative regional susceptibility. The complete method analyzes propagation probability from every cell in the source zone and can also calculate the sum of probabilities at each cell of the DEM. The summed probabilities account for watershed size and associated cumulative potential source zones. It should be noted that the sum of probabilities has no physical meaning; rather, it is used in Flow-R as a regional comparison between sites to determine areas with higher hazard potential.

In the regional-scale assessment, we apply the FlowR “complete” method with sum of susceptibilities.

The summed probability values follow a negative

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Figure 2. Map showing the extent of the regional-scale studies and main physiographic regions (labeled in white capital letters). The circled acronyms indicate the four distinct domains defined for calibration of Flow-R parameters; the roadway corridor and Canmore area are also shown. C = Cheekye Creek fan, Ca = Catiline fan, H = Hummingbird Creek fan, J = Johnsons Landing, L = Lillooet Middle fan, M = Mount Currie fans, N = Neff Creek fan, R = Rubble Creek fan.

exponential distribution. They are classified into zones of “very low,” “low” “moderate,” and “high” relative susceptibility. Zones of the DEM with summed probability values lower than a threshold corresponding to the 70th percentile of the probabilities are attributed “very low” regional susceptibility (i.e., “very low” susceptibility includes the majority of areas covered by Flow-R simulations). Zones of “low” regional susceptibility are defined as between the 70th and 85th percentile; “moderate” and “high” susceptibility are defined as between the 85th and 95th percentile and greater than the 95th percentile, respectively. These statistically based thresholds objectively and consistently define susceptibility classes in a study area.

A difficulty with the calibration and evaluation of Flow-R susceptibility maps is comparing debris-flow events associated to specific return periods with susceptibility maps that are not associated with any specific return period, but instead represent a range of possible outcomes. Because the outcome range is reflected in a single output, it is aggregated and, therefore, resembles rare and hence large events. At regional scale, we calibrate Flow-R parameters to best match the mapped distal extent of alluvial fans, which would include unusually large events. For evaluation purposes, due to the lack of records or evidence of events with such return periods, we can only check if events of smaller magnitude are included within the modeled susceptibility zones.

PILOT STUDY AND METHOD EVALUATION

Canmore Area

Before applying the previously presented methodology for susceptibility mapping at regional scale, we compare it against a series of watershed studies previously done at a high level of detail. We first apply it in the Canmore area, Alberta, Canada, where 11 debris-flood fans were studied by BGC Engineering (Holm et al., 2018). We then use it along a 30-km-long roadway corridor near Hope, in Southwestern British Columbia, Canada, that has also been studied in depth

by BGC Engineering.

Canmore is located approximately 90 km west of Calgary, in the Front Range of the Canadian Rocky Mountains (Figure 2), characterized by rugged linear ranges of resistant Paleozoic carbonate rock separated by valleys carved in weaker Mesozoic shales and sandstones (Price and Mountjoy, 1970). In 2013, large debris floods occurred on several fans in this area.

We compared Flow-R debris-flood susceptibility results with detailed numerical modeling results (Jakob et al., 2017; Holm et al., 2018). The detailed numeri-

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Figure 3. Comparison between Flow-R propagation calibrated to the distal extent of the fan, the 2013 debris-flood event outline, and FLO2D modeling results (flow depth and impact intensity) for an estimated 1,000–3,000-year return period event at Cougar Creek, Canmore (see Figure 2). Figure shows 20-m contours.

cal modeling was completed for detailed geohazard assessments based on a spectrum of debris-flood scenarios on 11 creeks, using the software FLO-2D (2018), and provides estimates of flow depth on and beyond alluvial fan boundaries.

Debris-flood sources were identified using the method described previously. We used the freely available Canadian Digital Elevation Model (CDEM) at 20-m resolution in the Flow-R propagation computation. This resolution was selected because it is the highest resolution available covering the entire study area.

Figure 3 shows an example of the Cougar Creek fan, where a 200–400-year return period event occurred in 2013 (Jakob et al., 2017), and demonstrates that FlowR can reproduce the general inundation extent on the southeastern part of the fan generated by FLO-2D modeling for a 1,000–3,000-year return period event.

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The Flow-R extent does not include the full extent of the FLO-2D simulation beyond the fan boundary, because Flow-R parameters are calibrated so that inundation reaches the distal margin of the fan and does not proceed any further. The FLO-2D simulation extending beyond the fan limits has low-impact intensity with an average flow depth lower than, on average, 1 m and velocity less than 2 m/s. This provides confidence in the delineation of potential areas susceptible to debris floods at regional scale. Although it is appropriate to compare the extent of the steep creek propagation susceptibility with the runout extent modeled with FLO-2D, the two models serve separate purposes. FLO-2D is a physics-based, single-phase hydraulic model that simplifies debris-flow rheology to calculate debris-flow and debris-flood intensity (flood depth and velocity), whereas Flow-R is a susceptibility

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Debris-Flow and Debris-Flood Susceptibility Mapping Table 2. Range of tested values and preferred values of the parameters for debris-flood Flow-R propagation based on comparison with FLO-2D and the mapped fans for the 11 fans of the Canmore area.

Selection Directions algorithm Inertial algorithm Friction loss function Energy limitation

Flow-R Parameters and Range of Values Tested

Preferred Value(s)

Holmgren (1994) modified; dh = [1–2]; exponent = [1–4] Weights = default, cosinus, Gamma (2000) Travel angle = [1–9°] Velocity <15 m/s

dh = 2, exponent = 1 Gamma (2000) or Cosinus 2° <15 m/s

model as defined previously. The range of Flow-R parameter values and the preferred values based on comparison with FLO-2D and the mapped fans of the 11 fans of the Canmore area are shown in Table 2.

Flow-R cannot model avulsions at culverts, as shown on Figure 3. Flow-R also cannot simulate bank erosion, channel scour, and aggradation, all of which affect flow behavior. These factors are difficult to include at regional scale because they require review of bridge and culvert designs and maintenance plans and fieldwork to characterize channel bank materials. Consequently, they are typically accounted in more detailed assessments than are feasible at regional scale.

Corridor-Scale Roadway Study The methodology was applied along a roadway located at the toe of several steep creeks in southwestern British Columbia (Figure 2). The goal of this creek prioritization study is to facilitate sciencebased allocation of resources for mitigation along the roadway, without requiring detailed and costly hazard frequency–magnitude analysis and scenario modeling at each creek.

In this study, debris-flow and debris-flood hazards were assessed based on both relative likelihood of initiation and their propagation susceptibility. Source zones were identified based on the stream segments.

The relative likelihood of initiation was evaluated based on past events observed in historical aerial photographs and evidence of erodible deposits in the channel. Propagation susceptibility was modeled using the Flow-R “complete method” with sum of probabilities.

Figure 4 compares the susceptibility map with the extent of debris-flow deposits from a 2017 event at one fan within the corridor. The debris-flow event is estimated to have a 10–30-year return period. This comparison shows that the mapped event is mostly included within zones of moderate and high susceptibility. Since the mapped event does not correspond to the largest credible event on this fan, it is not possible to demonstrate that the susceptibility map includes all potential outcomes. However, the result provides confidence that the selection of susceptibility classes is reasonable.

REGIONAL-SCALE SUSCEPTIBILITY MAPPING This section describes the application and evaluation of the susceptibility mapping methodology at regional scale.

Regional-Scale Application Steep creek susceptibility was mapped in four regional-scale steep creek geohazard risk prioritization projects in southern British Columbia. The study areas cover the Regional District of Central Kootenay (RDCK: 22,200 km2 ), the Columbia Shuswap Regional District (CSRD: 30,100 km2 ), the Thompson River Watershed (TRW: 55,800 km2 ), and the Squamish Lillooet Regional District (SLRD: 16,700 km2 ).

The study areas are in various physiographic regions (Figure 2; Demarchi, 2011). To the west are the Coast Mountains, characterized by northwest–southeasttrending mountain ranges dissected by narrow and 10s–of-kilometers-long, structurally controlled, and glacially modified valleys that host large, elongated lakes and British Columbia’s major rivers. The highest peaks reach elevations above 2,500 m and are covered by rapidly retreating glaciers and some icefields. Precipitation is dominated by Pacific frontal systems traveling with the prevailing west wind and accentuated with heavy rain and snow during late fall and winter.

East of the Coast Mountains lies the Interior Plateau, which is an upland undulating to rolling plateau dissected by creeks and large rivers such as the Fraser and Thompson rivers. Located in the rain shadow of the Coast Mountains, the Interior Plateau is characterized by semi-arid conditions with warm, dry summers and cool winters. To the east, the plateau transitions to mountainous highlands once again intersected by steep-sided valleys and large lakes and eventually to the north–south-trending Columbia Mountains. Narrow and broader structurally dominated valleys in the Columbia Mountains contain elongated lakes drained southward by the Columbia River and its tributaries.

Rugged peaks and glacial cirques in the northern part of the Columbia Mountains contrast with more sub-

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Figure 4. Map comparing the extent of recent debris-flow deposits (black, dashed lines) on an alluvial fan of the roadway corridor with the debris-flow susceptibility map. Figure shows 20-m contours.

dued landscapes and more subtle peaks in the southern ranges.

Debris-flow and debris-flood source zones were identified and classified using the method presented previously. Debris-flow and debris-flood propagation were modeled separately. Debris-flow propagation was calibrated using fans where the debris flow is the predominant steep creek process, and vice versa.

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Classification of fans was previously introduced in “Regional-Scale Steep Creek Geohazard Risk Prioritization Framework.”

Flow-R propagation parameters were calibrated based on comparison to the distal extent of mapped alluvial fans as explained in Section Propagation susceptibility using Flow-R. We delineated four different physiographic domains, and the propagation param-

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Debris-Flow and Debris-Flood Susceptibility Mapping Table 3. Calibrated debris-flow parameters used in Flow-R in each domain of the regional-scale studies. The domains are shown on Figure 2.

Selection Directions algorithm Inertial algorithm Friction loss function Energy limitation

Flow-R Parameter Holmgren (1994) modified Weights Travel angle Velocity

SLRD

TRW

CSRD

RDCK

dh = 2; exponent = 1

dh = 2; exponent = 1

dh = 2; exponent = 2

dh = 2; exponent = 1

Default 7° <15 m/s

Gamma (2000) 9° <15 m/s

Gamma (2000) 7° <15 m/s

Gamma (2000) 5° <15 m/s

SLRD = Squamish Lillooet Regional District; TRW = Thompson River Watershed; CSRD = Columbia Shuswap Regional District; RDCK = Regional District of Central Kootenay.

eters were calibrated separately in each of them. The domain-specific calibration parameters account for different geological, physiographic, and climatic environments. Within each domain, the calibrated propagation parameters do not allow Flow-R propagation to match the distal extent of all fans, and consequently, propagation may extend past fan boundaries for some fans. Tables 3 and 4 show the calibrated debris-flow and debris-flood parameters, respectively, for each domain. Figure 5 shows a map illustrating a section of the RDCK susceptibility map.

Debris-Flow and Debris-Flood Susceptibility Map Evaluation We evaluate the performance of susceptibility mapping by overlying debris-flow and debris-flood susceptibility maps generated based on the methodology with the manually mapped fans introduced in “Regional-Scale Steep Creek Geohazard Risk Prioritization Framework.” We observe that:

r It is important to recognize limitations of statistically based approaches to classify the dominant process type (debris flow, debris flood), as emphasized by Wilford et al. (2004) and Holm et al.

(2016). Where geomorphological mapping identifies a different dominant process than statistically based classification (about 9 percent of cases), the manu-

ally assigned process is used for susceptibility mapping. r Approximately 2 percent of the mapped fans do not have stream segments associated to them because the watersheds fall below the threshold used to delineate the stream network or because the stream segments shallower than 15° have been filtered as part of the semi-automated process described in “Semi-Automated Identification of Zones Susceptible to Debris-Flow and Debris-Flood Initiation.”

Because Flow-R modeling relies on stream segments to define source zones, these fans are consequently not modeled in Flow-R as being susceptible to steep creek geohazards. These cases generally correspond to small (<0.45 km2 ) watersheds with poorly defined channels. r For 2 percent of the fans, Flow-R does not propagate flows to the respective fan. Explanations for these discrepancies include the following: (1) The fans are conservatively classified, based on geomorphological mapping, as debris flood-prone, although the dominant process may be clearwater flood; (2) the fans are located at the outlet of atypical watersheds with flatter sections/terraces alternating with steeper reaches: in these cases, we expect that most debris flows or debris floods will to come to rest or dissipate within the flatter sections; (3) the fans are associated with atypical processes, such as debris flows initiating in volcanic complexes (Jakob

Table 4. Calibrated debris-flood parameters used in Flow-R in each domain of the regional-scale studies. The domains are shown on Figure 2.

Selection Directions algorithm Inertial algorithm Friction loss function Energy limitation

Flow-R Parameter Holmgren (1994) modified Weights Travel angle Velocity

SLRD

TRW

CSRD

RDCK

dh = 2; exponent = 1

dh = 2; exponent = 1

dh = 2; exponent = 1

dh = 2; exponent = 1

Default 2° <15 m/s

Gamma (2000) 5° <15 m/s

Default 3° <15 m/s

Cosinus 4° <15 m/s

SLRD = Squamish Lillooet Regional District; TRW = Thompson River Watershed; CSRD = Columbia Shuswap Regional District; RDCK = Regional District of Central Kootenay.

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Figure 5. Debris-flood susceptibility map for a section of the RDCK domain (see Figure 2) showing the spatial distribution of “low,” “moderate,” and “high” debris-flood susceptibility classes derived from Flow-R modeling.

et al., 2020); or the fan (or portion of it) consists of a rock avalanche deposit. These are further discussed below.

The susceptibility maps were visually compared with 22 previous debris-flow/flood case studies documented in the literature. Figure 6 shows four examples of fans in the SLRD region, where several debris-flow events were mapped; the outlines of these events shown on Figure 6 include several debris-flow events per fan mapped using a combination of historical aerial photographs, satellite imagery, lidar data, and field mapping. For the Mount Currie fans (Figure 6a), debris-flow events were mapped between 1946 and 2019 (Zubrycky, 2020); at the East Middle Lillooet fan (Figure 6b), mapped debris-flow events occurred between 1962 and 2016 (Zubrycky, 2020); at Neff Creek fan (Figure 6c), a large debris flow occurred on September 20, 2015 (Lau, 2017); and, for Catiline Creek fan (Figure 6d), several debris-flow events were mapped for the period between 1967 and 2013 (Zubrycky, 2020) and a debris-flow hazard outline was

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modeled considering an event with a return period greater than 3,000 years (BGC, 2015).

The mapped debris-flow events on the fans illustrated in Figure 6 are consistent with the susceptibility maps. Two events on the Mount Currie fans (Figure 6a) ran out beyond the fan distal extent and are consequently not covered by the debris-flow susceptibility map. Interestingly, the debris-flood susceptibility map covers the distal part of these events, which consist of muddy “afterflows.” Although debris flow is the dominant process at the Mount Currie fans, the combination of debris-flow susceptibility maps with debrisflood susceptibility maps captures the afterflows beyond the fan limit.

The combination of regionally calibrated debrisflow and debris-flood susceptibility maps on the same fan is also of interest at Hummingbird Creek, where an unusually large debris-flow event occurred in 1997 (Jakob et al., 2000). In this example, Flow-R propagation using calibrated debris-flow parameters only reaches the zone near the apex of the fan (Figure 7a).

This reflects unusually low gradients in the creek (10°).

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Figure 6. Maps showing comparisons between the extent of recorded debris-flow events and susceptibility maps: (a) Mount Currie fans; (b) East Middle Lillooet fan; (c) Neff Creek fan; (d) Catiline Creek. The hazard zone in (d) corresponds to the extent of modeled debris flow in BGC (2015).

During this event, the part of the fan downstream of the apex zone was inundated by the afterflow, which consisted of the finer fraction of the debris and which could be classified as a Type 2 debris flood (Church and Jakob, 2020). This zone inundated by the afterflow matches approximately the Flow-R propagation with the regionally calibrated debris-flood parameters, although Flow-R propagation does not extend to the distal part of the fan. This example suggests that for cases where there is evidence of infrequent debris flows due to large side slope failures, but where otherwise the low gradient of the channel and fan suggests that debris flood is the dominant process, it may be beneficial

to combine Flow-R modeling using both debris-flow and debris-flood parameters.

The following are examples where the regionally calibrated susceptibility maps do not cover the inundation zone of recorded debris-flow or debris-flood events. These include the Johnson Landing event, where a debris flow resulted in four fatalities in July 2012, and Cheekye River and Rubble Creek (Figures 3 and 6). Details on these exceptions include:

r Flow-R propagation does not replicate the special case of the Johnsons Landing debris flow, where the main channel is characterized by a sharp bend and

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Figure 7. Maps showing comparisons between the extent of recorded debris-flow or debris-flood events and susceptibility maps: (a) Hummingbird Creek fan, showing debris-flow susceptibility near the fan apex and debris-flow susceptibility throughout the fan; (b) Johnsons Landing, not inundated by Flow-R debris-flow propagation; (c) Cheekye Fan, where debris-flow susceptibility is limited to the upper watershed outlined by a yellow line; (d) Rubble Creek fan, where the fan is indicative of high-mobility rock avalanches. Figure shows 20-m contours.

previous debris-flow events overtopped the channel (Nicol et al., 2013). The susceptibility map does not capture the overtopping of the channel and subsequent avulsion because Flow-R is not a physicsbased model that can account for superelevation, runup or sediment buildup, and overrunning by subsequent flow surges (Figure 7b). r Although debris flow is the dominant steep creek process along Cheekye River, application of the regionally calibrated debris-flow parameters does not allow the susceptibility map to include the fan, and the regionally calibrated debris-flood parameters are used instead (Figure 7c). This result may be explained by the specific runout charac-

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teristics of lahars initiating from rock avalanches in weak and clay-rich pyroclastic rock units on the western flank of the Quaternary Mount Garibaldi volcano, the headwaters of the Cheekye River. r Similarly, application of the regionally calibrated debris-flow parameters does not allow the susceptibility map to cover the fan of Rubble Creek. (Figure 7d). A significant volume of the fan at Rubble Creek is associated with rock avalanches. The most recent one occurred in the fall or winter of 1855– 1856 (Moore and Mathews, 1978). Hence, the “fan” landform is not indicative of debris-flow processes, but rather of high-mobility rock avalanches.

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DISCUSSION This section discusses the results and some limitations of the study for both the identification and classification of stream segments and the production of susceptibility maps based on Flow-R propagation modeling. It also includes considerations about the integration of the susceptibility maps in the risk prioritization framework by Holm et al. (2019).

Stream Segments Identification and Classification Steep creek geohazard source zones are identified as stream segments. One limitation is that stream segments may not be defined for small watersheds (<0.45 km2 ) with poorly defined channels, which would be missed in susceptibility mapping unless separately identified during geomorphological mapping.

The geomorphometric parameters (Melton ratio and watershed length) used for steep creek process type classification systematically identify stream segments as debris-flow or debris-flood sources. Steep creeks may produce debris flows and debris floods or transition from one to the other process in space and time. In the methodology, both debris-flow and debrisflood stream segments can exist within the same watershed and, consequently, alluvial fans may be covered by Flow-R propagation from both debris-flow and debris-flood segments. In such cases, the semiautomated method needs to be supplemented by expert judgment based on geomorphological mapping to determine the dominant process type controlling risk management decisions for an alluvial fan.

The generation of stream segments as source zones for Flow-R modeling is based on topographic criteria, including slope angle, upslope contributing area (flow accumulation), and proximity of stream channels. These are typical debris-flow initiation conditioning factors reported in the literature. Other conditioning factors such as availability of debris material, ground permeability, and vegetation cover have also been shown to be important (Jakob et al., 2005; Carrara et al., 2008; Lawley et al., 2009; Blais-Stevens et al., 2012; Horton et al., 2013; Loye et al., 2016; Baum et al., 2019; and Bee et al., 2019). The latter are important because they control the level of activity within watersheds, but are not considered by the methodology. Consequently, watersheds can exist where debris-flow source zones are mapped but few debris sources exist (e.g., bare competent rock channels with insufficient sediment supply) or where limited debris source zones result in lower runout susceptibility. Although the methodology does not consider sediment availability in the watershed, this parameter is included in the “geohazard likelihood rating” of

Figure 1. Consequently, the integration of the methodology in the risk prioritization framework addresses this limitation.

Propagation Susceptibility With Flow-R The evaluation of the methodology in regional-scale studies shows that it generally provides reasonable estimates of debris-flow and debris-flood susceptibility, but there are some limitations.

Propagation parameters in Flow-R are empirical and require calibration. In the case studies presented in this paper, debris-flow and debris-flood propagation parameters are calibrated so that the simulations closely reproduce the distal extent of mapped alluvial fans. In terms of frequency–magnitude relationships, this calibration approach produces susceptibility maps that include the affected fan areas of rare and large events, and in many cases the modeled extent comprises the largest credible event. Although FlowR modeling can both supplement geomorphologic interpretations and extend mapping more broadly than can be manually examined, Flow-R modeling that is not supported by geomorphic interpretation should be used cautiously in decision-making. For example, it can help regulators define areas requiring further assessment for development approval but is not sufficient on its own to implement hazard acceptance criteria (i.e., criteria based on hazard likelihood).

The calibrated exponent of the modified Holmgren parameter (Tables 2 –4) is lower than documented by other authors, who often report values between 4 and 7 (Claessens et al., 2005; Horton et al., 2013; and Pastorello et al., 2017). The calibrated parameters are considered appropriate and conservative for the specificity of the large-scale regional studies because FlowR propagation includes zones of fan expected to have a low and very low likelihood of being inundated.

Flow-R propagation is controlled by present-day fan topography to estimate runout susceptibility and consequently does not explicitly consider past and recent avulsions and bank erosion. The “evidence for previous avulsion” parameter of Figure 1 accounts for this and, consequently, integration of the methodology into the risk prioritization framework addresses this limitation.

For large study areas, and for each process type (debris flow and debris flood), application of a single set of calibrated Flow-R propagation parameters does not account for local or site-specific characteristics. To minimize this effect, the study areas should be subdivided into domains based on their physiographic, geological and/or climatic conditions, and model parameters calibrated independently for each domain. However, even within a specific domain, one set of debris-

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flow parameters and one set of debris-flood parameters do not always result in the susceptibility maps matching the distal extent of all debris-flow fans and all debris-flood fans, respectively. Individual calibration of each fan is not possible, as it would render the application of the approach unpractical and contradict the very purpose of rapid regional modeling. For this reason, the propagation parameters are calibrated conservatively in that, at some fans, propagation extends past the mapped fan boundary. This is indeed realistic, especially for debris floods whose sediment load may be low at the fan margin but whose water discharge continues beyond the fan boundary. When subdivided into susceptibility classes, debris-flow and debris-flood inundation zones extending beyond the boundaries of debris-flow and debris-flood fan, respectively, often correspond to very low susceptibility zones. Low- to high-susceptibility classes are generally within the fan boundaries and provide an objective and repeatable way to map channel confinement. The subdivision into susceptibility classes therefore avoids excessive conservatism such that up to the 70 percent percentile of the sum of susceptibilities is considered as “very low” susceptibility. We suggest that, when integrating susceptibility maps in the risk prioritization framework, higher weights should be attributed to the fan areas classified as low to high susceptibility, as illustrated in Figure 5.

One specificity of the methodology is that it differentiates debris-flow from debris-flood processes and, therefore, produces both debris-flow and debrisflood susceptibility maps for a given domain. Where both debris-flow and debris-flood source segments are present within a watershed, and both debris-flow and debris-flood susceptibility maps inundate the fan, a dominant process is selected based on geomorphological mapping, because the risk prioritization framework requires a single process per fan. The results illustrated in Figures 6a and 7a suggest that, at some fans, the combination of susceptibility maps produced based on both regionally calibrated debris-flow and debris-flood parameters may be beneficial. This may be appropriate where debris flow is the dominant process, but afterflows propagate past the fan limits. Alternatively, this can be useful where debris flood is the dominant process, but rare debris flow events occur.

CONCLUSION AND PERSPECTIVES We present the application of a semi-automated methodology for debris-flow and debris-flood susceptibility mapping at regional scale, based on a combination of stream and watershed morphometrics to identify zones prone to landslide initiation and Flow-R to assess the area that can potentially be reached by flow propagation. Our evaluation of the method through a

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pilot study and a series of regional-scale assessments suggests that is it objective and repeatable.

In the Canmore example and regional-scale assessments, segments susceptible to steep creek geohazard initiation were identified but we did not attempt to rate them according to their likelihood of generating steep creek geohazards. This was done qualitatively for the corridor-scale study, because the area has been studied in greater detail in previous work. Further research may aim at studying other metrics that can be measured at regional scale, which could be used as proxies for landslide activity and integrated into the susceptibility mapping workflow, thus providing a notion of frequency to the susceptibility map (Michoud et al., 2012). This may further reduce subjectivity and minimize the need for manual mapping over extended regions at the preliminary stage of prioritization studies.

An example of metrics could be the fan area-watershed area ratio. While some authors have associated anomalous fans (those with a high fan area-watershed area ratio) with large landslides (e.g., De Finis et al., 2018), these conditions could also reflect large availability of loose debris within basins, controlled by structural or lithological conditions (Marchi et al., 2002; Loye et al., 2012; Comiti et al., 2014; and De Finis et al., 2018).

The correlation between basin or fan area is a topic of ongoing research (Lau, 2017; Jakob et al., 2020).

We highlighted anomalies at two fans (Cheekye River, Rubble Creek), where the susceptibility maps using regionally calibrated debris-flow parameters do not match detailed investigations and runout models and provided reasons for the respective deviation. These anomalous cases reflect specific characteristics of the watershed sediments (volcanic material for Cheekye River) or the presence of rock avalanche deposits in the fan (Rubble Creek). Further understanding of such anomalous cases represents an opportunity to refine the susceptibility mapping methodology.

ACKNOWLEDGMENTS We thank the Town of Canmore, the Regional District of Central Kootenay, the Squamish Lillooet Regional District, the Columbia Shuswap Regional District, the Fraser Basin Council, and the British Columbia Ministry of Transportation and Infrastructure for the opportunity to use project data in this paper. Thank you to Sophia Zubrycky and Andrew Mitchell for sharing outlines of mapped steep creek events in the SLRD. REFERENCES Baum, R. L.; Scheevel, C. R.; and Jones, E. S., 2019, Constraining parameter uncertainty in modeling debris-flow initiation during the September 2013 Colorado Front Range storm. In

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Impact of Debris Flows on Filter Barriers: Analysis Based on Site Monitoring Data ALESSANDRO LEONARDI* MARINA PIRULLI MONICA BARBERO FABRIZIO BARPI MAURO BORRI-BRUNETTO ORONZO PALLARA CLAUDIO SCAVIA Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy

VALERIO SEGOR Direzione Assetto Idrogeologico dei Bacini Montani, Aosta Valley Autonomous Region, Loc. Amerique 33, 11020 Quart, Italy

Key Terms: Debris Flows, Structural Mitigation Measures, Impact Forces, Site Monitoring System, Numerical Modeling ABSTRACT Debris flows are one of the most complex and devastating natural phenomena, and they affect mountainous areas throughout the world. Structural measures are currently adopted to mitigate the related hazard in urbanized areas. However, their design requires an estimate of the impact force, which is an open issue. The numerous formulae proposed in the literature require the assignment of empirical coefficients and an evaluation of the kinematic characteristics of the incoming flow. Both are generally not known a priori. In this article, we present the Grand Valey torrent site (Italian Alps). A monitoring system made up of strain gauges was installed on a filter barrier at the site, allowing the evaluation of impact forces. The system provides pivotal information for calibrating impact formulae. Two debris flows occurred during the monitoring period. We present the interpretation of videos, impact measurements, and the results of numerical analyses. The combined analysis allows a back calculation of the events in terms of forces, flow depth, and velocity. Thus, we investigate the applicability of the impact formulae suggested in the literature and of the recommended empirical coefficients. The results highlight that hydrostatic effects dominated the impact during the first event, while hydrodynamic effects prevailed in the second one.

*Corresponding author email: alessandro.leonardi@polito.it

INTRODUCTION Debris flows are extremely rapid flow-like landslides that involve a mixture of fine (clay, silt and sand) and coarse (gravel, cobbles and boulders) materials with a variable quantity of water. Their high velocity, impact force, and long runout, combined with poor temporal predictability, make them a major source of hazard for human life and activities in mountainous regions. They cause severe damage and casualties throughout the world each year (Guzzetti et al., 2005; Hilker et al., 2009; Jakob et al., 2012; and Dowling and Santi, 2014). As a consequence, countermeasures are usually adopted to mitigate the related risk.

Concrete dams are among the possible interventions. These are often complemented with drainage filters (filter barriers). The filters are used for the retention of large boulders (which have a high destructive potential) while allowing water and smaller-sized particles to flow through (Marchelli et al., 2020). However, an estimate of impact forces is needed for a reliable design of these structures.

Typically, the impact force is estimated either as a function of the hydrodynamic pressure exerted by the fluid, assumed in steady conditions (e.g., Armanini and Scotton, 1993; Daido, 1993; and Canelli et al., 2012), or as a function of the hydrostatic load (e.g., Lichtenhan, 1973; Armanini, 1997). Both these formulations require the selection of empirical coefficients and knowledge of the flow dynamics at impact (i.e., flow depth and front velocity). The determination of empirical coefficients is particularly critical: multiple sets of recommendations, often conflicting, can be found in the literature (e.g., Huang et al., 2007).

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A contribution to the knowledge of the debris flow dynamics before impact may be obtained, to a certain extent, through numerical modelling (e.g., Iverson and Denlinger, 2001; Pitman and Le, 2005; Pirulli, 2005; and Pudasaini et al., 2005). However, the accuracy of the results depends on the quality of the rheological parameters plugged into the model (Pirulli, 2010a), whose calibration can be achieved only through measurement and observation of events.

Physical modeling of flows in laboratory small- or medium-scale channels (e.g., Armanini and Scotton, 1992; Iverson et al., 2004, 2010; Canelli et al., 2012; and Hürlimann et al., 2015) allows the phenomenon to be investigated under controlled conditions. However, the obtained results are affected by scaling issues, and problems arise concerning the representativeness of the flow composition with respect to site conditions.

Data from real events would allow this limitation to be overcome. However, the number of monitored sites is still limited, especially due to the cost and complexity of the logistics.

Examples of instrumented sites are those of China (Okuda et al., 1980; Zhang 1993; and Suwa et al., 2011), the United States (Pierson 1986; Coe et al., 2008; and McCoy et al., 2010), Taiwan (Yin et al., 2011), France (Navratil et al., 2012, 2013), Austria (Kogelnig et al., 2014), Italy (Arattano et al., 1997; Berti et al., 1999; Marchi et al., 2002; and Comiti et al., 2014), Spain (Hürlimann et al., 2011), and Switzerland (Hurlimann et al., 2003; McArdell et al., 2007; and Berger et al., 2011). Unfortunately, only few of these sites monitor the flow dynamics and measure the impact on a mitigation structure at the same time. An example of such a case is the Illgraben monitoring site in Switzerland (Wendeler et al., 2006), where a flexible ring net barrier is monitored by means of load cells, or that of Erill in the Spanish Pyrenees (LuisFonseca et al., 2011). Strain sensors have been installed on a 2.5-m-high steel pile foundation located in the middle of the Jiangjia Ravine channel in China (Hu et al., 2011). An experimental setup that integrates a video camera, radar, ultrasonic, and load cells in a 1.6m-high target has been installed in the middle of the Schesatobel watershed in Austria (Kaitna et al., 2007).

Nevertheless, to the best of our knowledge, no instrumented site exists where impact forces of debris flows are measured directly on the elements of a real rigid barrier and a video of the flow dynamics is contemporaneously recorded.

In this work, we present a monitored site where a video of the flow dynamics and the interaction with a monitored barrier is available together with a direct measurement of impact forces. This is the Grand Valey torrent site (northwestern Italian Alps, the Aosta Valley Autonomous Region). There, a monitoring sys-

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tem, made up of strain gauges, is installed on the filter elements of a barrier. The measured strain gauge deformations are converted into forces, assuming linear elastic behavior of the barrier filter elements. The site is characterized by an annual frequency of events and by the existence of a set of debris flow control structures.

Two debris flows occurred during the monitoring period considered here.

The flow dynamics before impact are reconstructed by means of RASH3D , a code based on a continuummechanics approach. The back analysis of the first event allows the rheological parameters of the model to be calibrated on the basis of the available video information. The parameters are then used to simulate the second event, for which less information is available. While the code is not suited to simulate threedimensional fluid–structure interaction accurately, it allows quantitatively estimating values of flow height and velocity before impact, which can be plugged into a set of formulae that estimate impact forces. Thus, we are able to back calculate the empirical coefficients.

The obtained results are then compared with the range of values suggested in literature, and we comment on their applicability to the Grand Valey study case.

DESCRIPTION OF THE GRAND VALEY TEST SITE The Grand Valey site is located in the municipality of Saint-Vincent, a small town in the central part of the Aosta Valley Autonomous Region, northwestern Italy (Figure 1a).

Morphology and Geology The basin, which is delimited in the upper part by Mount Zerbion (2,730 m above sea level [a.s.l.]) and Mount Je Tire (2,141 m a.s.l.), has a drainage area of 5.22 km2 and extends from 2,681 to 680 m a.s.l., with a mean slope of 82 percent. The alluvial fan instead extends for 1.47 km2 , from 680 to 445 m a.s.l.

(Figure 1a; Table 1).

The middle-upper part of the basin consists of subvertical slopes of schists, characterized by a high degree of fracturing and poor vegetation, with subordinate phyllitic layers, serpentinite, and greenschist metagabbros. In the lower part, toward the apex area of the alluvial fan, these rock types are interbedded with layers of Austroalpine nappe, both on the left and on the right banks.

In this context, the Grand Valey torrent extends for 5.71 km from its origin at 2,681 m a.s.l. to the confluence with the Dora Baltea River, the main river in the Aosta Valley, at 445 m a.s.l.. The torrent flows for 3.76 km in the aforementioned basin with a mean slope

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Figure 1. (a) Location and main characteristics of the Grand Valey basin. (b) Details of the two most actives sub-branches (A2, B1), with indication of their confluence upstream of the filter barriers at Pèrriere. Area 1 and Area 2 identify the main areas prone to originating flow instabilities. Modified after Leonardi and Pirulli (2020).

of 38 percent, which decreases to 12 percent along the 1.95 km of the fan (Figure 1a).

The upper part of the torrent divides into two main branches, which have an estimated total length of Table 1. Main morphological features.

Grand Valey Parameters

Value

Basin Maximum altitude (m) 2,681 Minimum altitude (m) 680 Mean altitude (m) 1,466 Area (km2 ) 5.22 Mean slope (%) 82 Fan Maximum altitude (m) 680 Minimum altitude (m) 445 Area (km2 ) 1.47 Torrent Length of the main channel (km) 5.71 Length of the main channel in the drainage basin (km) 3.76 Length of the main channel on the fan (km) 1.95 Total length of secondary channels (km) 14.76 Mean slope of the main channel (%) 38 Mean slope of the main channel on the fan (%) 12 Mean slope of the channel (%) 29

14.76 km: the first one comes from southern slopes (A in Figure 1) of Mount Zerbion (2,730 m a.s.l.), while the second one (B in Figure 1) originates from Mount Je Tire (2,141 m a.s.l.). These two branches are in turn composed of two sub-branches (A1, A2, B1, and B2 in Figure 1), which are oriented according to the main discontinuities of the rock mass. All the flow directions merge into a single channel at 1,075 m a.s.l. at Pèrriere (Figure 1), which is located upstream of the experimental site and of the urbanized area of Saint Vincent. The morphological features are summarized in Table 1.

Debris Flow Activity and Undertaken Mitigation Countermeasures The upper part of the Grand Valey basin is affected by large and continuous rockfall phenomena due to the steep slopes and to the high fracturing of the overhanging rock mountain faces. Site surveys identified branch A2 from the Mount Zerbion and branch B1 from Mount Je Tire as the main sources of rock debris (Figure 1b). Each year, during heavy rains in spring and summer, debris is transported downstream by

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Leonardi, Pirulli, Barbero, Barpi, Borri-Brunetto, Pallara, Scavia, and Segor Table 2. List of the main documented debris flow events at Grand Valey.

Date 2004 August 7 2008 May 28 July 12 September 6 November 3 2009 May 26 2011 June 6 June 16 June 17 June 22 July 13 August 26 2012 August 29 2013 July 17 July 29 2014 June 6 June 12 July 7 July 20 July 23 August 3 2015 March 19 June 8 August 14 2016 June 9 July 11

Volume (m3 ) 3,000 6,400 3,500 5,000 3,000 10,000 3,975 200 300 500 4,500 4,500 3,975 3,550 3,810 2,790 2,090 4,670 4,625 2,565 725 800 5,000 2,000 1,875 4,420

debris flows (Table 2). The B1 channel is activated only during the most intense rainfall events.

The regional government has improved and increased the number of defensive structures located along the torrent to reduce consequences on the urbanized area below. However, no countermeasures have been set up in the upper part of the basin because of the difficulty in reaching and stabilizing the coarse material on the steepest slopes.

At present, the protection system, from upstream to downstream, consists of two filter barriers, positioned about 46.5 m from each other, at the Pèrriere hamlet (1,075 m a.s.l.) (indicated as 1 in Figure 1 and detailed in Figure 2a), which together can retain up to 5,000 m3 of material; two steel-net barriers (indicated as 2 in Figure 1 and detailed in Figure 2b); and one slitfilter barrier (indicated as 3 in Figure 1 and detailed in Figure 2c) located at the Tromen hamlet (700 m a.s.l.).

After each debris flow event, the material retained by the filter barriers is rapidly removed by maintenance

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workers in order to restore the complete functionality of the mitigation system.

In the event on July 20, 2014 (Table 2), the first filter barrier at Pèrriere (Figure 2a in the white rectangle), located immediately downstream of the confluence of branches A and B, collapsed (Figure 2d). This barrier was the first to be impacted during events. The barrier was reconstructed at the same position in 2015 (Figure 2a, white box). The lower part of the new barrier is a 17-m-long, 1.15-m-thick, and 2.55-m-high reinforced concrete wall. A 12-m width rack, made up of 18 IPE 270 steel beams (Euronorm 19-57) with a nominal spacing of 0.6 m, is placed on the upper side of the concrete wall to form a filter (Figure 3a and b). The steel beams are 3.0 m long and are embedded into the concrete structure for a length of 1.0 m (Figure 3c).

The debris flow activity is very frequent (Table 2), and the area has easy access. For these reasons, the site was selected in 2012 for the installation of a monitoring station. The monitoring system quantifies the deformation of the steel beams that constitute the filter. On the barrier that was reconstructed in 2015, the monitoring system was reinstalled and upgraded (Pirulli et al., 2014).

Configuration of the Monitoring System The monitoring system consists of several Hottinger Baldwin HBM SLB-700A strain sensors. These devices are designed to measure the deformations of the structural parts on which they are mounted (Figure 3d).

They consist of a metallic box that contains four electric strain gauges, connected to form a Wheatstone bridge, which reacts to the axial dilation or contraction of the instrument by varying their electrical resistance.

The transducers operate effectively across a temperature range of −20°C to 60°C and automatically compensate for thermal expansion. When properly powered and controlled, the devices provide the local axial strain of the structure up to a nominal strain of ±500 μm/m, which is proportional to the measurement of the voltage variation of the Wheatstone bridge (nominal sensitivity 1.5 ± 0.15 mV/V). The presence of these transducers slightly affects the strain at the installation point, but the perturbation of the measurements can be accurately evaluated to obtain the correct strain value (Borri-Brunetto et al., 2016).

In the Pèrriere site, 20 strain sensors (indicated as “E + strain gauge number” in Figure 3a) are installed on the downstream flange of the IPE270 steel beams: 18 of them are positioned at the lower right corner of each steel beam, and two additional are located at mid-height of the two central steel beams (Figure 3a).

Each transducer is mounted at an average distance of 140 mm from the concrete wall on which the beams are

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Figure 2. The structural mitigation works along the Grand Valey torrent. (a) The two filter barriers at the Pèrriere hamlet. (b) The steel net barriers, (c) The slit-filter barrier at Tromen. (d) The barrier at Pèrriere (white rectangle in Fig. 2a) that collapsed in 2014. The position of each of these structures is indicated in Fig. 1 (photos courtesy of the Aosta Valley Autonomous Region).

embedded. Each strain transducer is protected against water and the impact of solid material by a steel box (Figure 3d). Each steel box is welded to the beam but only along its upper side to exclude local stiffening effects due to the box itself and is waterproofed by silicone sealing and a two-component sealant gel filling.

The strain transducers are connected to a Compact FieldPoint (National Instruments cFP-2220) programmable controller equipped with three different eight-channel input modules with 16-bit resolution (National Instrument cFP-SG-140) (Figure 3e). The controller acquires the strain measurements from the transducers at time intervals of 1.15 seconds (0.87 Hz) and stores data every 10 minutes on a removable solid-state drive. The software controlling the Compact FieldPoint was developed within the National Instruments LabVIEW programming environment.

The controller is placed, near the barrier, inside a waterproof container protected with a stainless-steel locker (Figure 3f). Electric power is supplied by an underground cable that runs from the monitoring site to the Pèrriere hamlet, but an uninterruptible power supply is installed to cope with power cuts. A grounding wire protects from damage caused by thunderstorms (Figure 3e).

THE 2016 DEBRIS FLOWS Two main debris flows occurred in the Grand Valey after the monitoring system was installed on the reconstructed barrier: on June 9 (Figure 9a) and July 11 (Figure 10a). The mass mobilized in both events was retained almost completely by the two filter barriers at Perrière. For this reason, the estimation of the involved volumes was made on the basis of the material removed from the basins after each event.

Figure 4 shows the rainfall data recorded by the weather station located in Saint-Vincent Terme (Figure 1a). The two events were triggered by rainfall events that had different characteristics in terms of both intensity and duration. The first and second events were triggered by precipitations with a 1-year and 2-year return period, respectively. In both cases, the recorded rainfall is lower than the typical threshold for this region (around 20 mm/hr; see Tiranti et al., 2018). However, the weather station is located about 2,900 m away from the site and at a lower elevation (626 m a.s.l.) and is only a poor indicator of the actual hydrological conditions on the upper catchment.

The debris flow on June 9 occurred at about 12:38 (UTC). In addition to strain sensors, a set of amateur videos of this event is available since technicians

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Figure 3. The monitored filter barrier. Front (a) and (b) plan (b) views from below, with indications of the positions of the strain gauges (E) (not to scale). (c) The cross section (dimensions in meters). (d) Open protective steel box, with the positions of the transducers. (e) Controller system components. (f) Waterproof container protected by a stainless-steel locker.

were working at the Pèrriere barrier at that time. Eyewitness reports and post-event site surveys confirm that the event consisted of one surge that originated from branch A2 (Figure 1a and b). The mass deposited principally upstream of the monitored barrier and assumed an approximately trapezoidal shape in plan view, the main dimensions of which are summarized in Table 3. Operation for removal of the deposit allowed (1) estimation of the retained volume to about 1,875 m3 and (2) excavation of a longitudinal trench through the deposit that highlighted a grain-size distribution with inverse grading of the clasts with respect to maximum clast size (Figure 5) and the average depth distribution as summarized in Table 3 and Figure 11e.

The debris flow on July 11 occurred at about 16:00.

Although no videos or detailed measurement of the

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deposit are available for this event, an on-site survey indicated that flows traveled down branches A and B (Figure 1). Both the upstream and the downstream retention basins at Pèrriere filled completely, but a Table 3. Debris flow on June 9. Dimensions of the main deposit.

Main Deposit Parameter Plan view Maximum front width Minimum rear width Average length Average area Longitudinal profile Front average depth Centre average depth Rear average depth

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Value (m) 18 10 80 1,100 m2 2 1.6 0.8

Impact of Debris Flows on Filter Barriers

Figure 6. The deposit of the event of July 11.

Figure 4. Rainfall data recorded at the Saint-Vincent Terme weather station referring to when the debris flow on (a) June 9 and (b) July 11 occurred. The red markers point to the exact time when the debris flows occurred.

different type of material caused clogging of the two barriers: rock blocks clogged the upstream barrier, while woody debris (driftwood) clogged the downstream one (Figure 6). The technical staff of the Aosta Valley Autonomous Region, which is in charge of reg-

ular on-site inspection of the area, reported that driftwood usually comes from branch B, which is active only during major rainfall events (Figure 4b).

A first interpretation of the flow dynamics is as follows. A first surge came from branch A and probably caused the clogging of the first barrier, while a second surge, transporting woody debris from branch B, occurred within a few hours from the first one. The second surge flowed over the deposit left by the first surge on the first retention basin. It then deposited in the second retention basin, before the second barrier.

During the debris removal operations, the total volume of debris deposited in the Pèrriere basins was estimated to be about 4,420 m3 . A visual analysis of the deposit notes that the clasts entrained and transported during the event on July 11 were on average larger than those mobilized during the event on June 9. With the exception of the largest clasts, the grain-size distribution with inverse grading was approximately the same for the two events.

Dynamics of the Event on June 9, 2016, Based on Video Analysis

Figure 5. A portion of the vertical longitudinal trench through the central part of the deposit of the event on June 9.

Although the available videos of the event on June 9 are amateur, they are sufficient to reconstruct the process dynamics. The flow can be tracked from the moment the front reaches the confluence between branches A and B to when it stops moving. The main process of debris displacement lasted about 3 minutes (from 12:38 to 12:41), while the water flow lasted longer.

The flow front, at an early stage, featured a large number of coarse grains that were pushed upward and forward by a finer-grained matrix (Figure 7a).

The left side of the flux then rapidly assumed a more fluid-like behavior with coarse particles in suspension.

The blocks concentrated mainly on the right side and

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Figure 7. Event on June 9. (a) The frontal part of the debris flow at the confluence between branches A and B. (b) The asymmetric dynamics of the flow. The bold line defines the limit between the fluid and the coarse part of the flowing mass. (c) and (d) The interaction of the mass with the monitored barrier at two consecutive moments.

advanced more slowly (Figure 7b). At the interaction with the first barrier at Perrière, the asymmetric front caused a rapid obstruction of the right part of the barrier filter, while the left part was loaded dynamically by the passage of the fluid for a longer time (Figure 7c).

In the final stage, the whole process was characterized by a diluted flow that caused the deposition of a thin muddy veneer (Figure 7d).

The video analysis of the time necessary for the front to cover the distance between the confluence between branches A and B and the first impacted barrier gives an estimated average front velocity of about to 2 m/s.

Furthermore, frame extraction and particle tracking from the available videos allow an estimate of the flow velocity at impact, as illustrated in Figure 8. A systematic use of particle-tracking velocimetry is possible. However, because of the low quality of the video, obtaining a consistent velocity field is difficult. Therefore, we focus on estimating the velocity from a set of clearly visible particles distributed on the flow surface (Table 4). From these, an average velocity of about 2 m/s is estimated.

In the following sections, we interpret the measurements from the strain transducers. We also conduct a numerical modeling of the two events that occurred to carry out an in-depth analysis of the flow dynamics and gather all the information necessary to evaluate the applicability of literature impact formulae. We

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Figure 8. Event on June 9. Example of particle-motion tracking as the video advances frame by frame. Note that before hitting the barrier, the front submerges into a pool of water accumulated behind the barrier, becoming undetectable. Therefore, we use the last available frames with a visible front for the particle tracking procedure.

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Impact of Debris Flows on Filter Barriers Table 4. Event on June 9. Particle tracking of some debris selected for the front velocity estimation before impact.

Particle Reference 1 2 3 4 5 6 7 8

Time Interval (s)

Distance (m)

Estimated Velocity (m/s)

4.3 5.6 5.3 4.2 5.0 4.1 4.1 4.7

8.3 14.8 11.4 10.0 12.2 9.1 9.5 10.4

2.0 2.6 2.2 2.4 2.5 2.2 2.3 2.3

finally test whether the back-calculated empirical coefficients are within the range suggested in literature.

Analysis and Interpretation of the Strain Measurements The 20 strain transducers installed on the steel beams measure the axial deformation induced by flow impact. Due to the position of the instruments, a negative strain indicates a compressed gauge, while a positive strain indicates a tensed gauge. Negative values can also be induced by a lateral bending of the beam.

This can happen when the outlet between two beams is clogged by rock blocks, which then load the two beams transversely with respect to the flow direction. Since the strain gauges are in the lower right corner of the steel beams (Figure 3a), in this situation one transducer will be compressed (negative strain), and the other will be tensed (positive strain). This scenario has been tested and successfully back-calculated though discrete-element simulations by Leonardi and Pirulli (2020).

The Event on June 9, 2016 The interpretation of the strain transducer recordings is supported by the amateur videos of the event on June 9. During this event, strain gauges E14 and E18 were unresponsive. By comparing video and strain recordings, we observe four signal patterns, grouped in different panels in Figure 9. Panels (b) and (d) group the majority of the signals coming from the right (E01– E10) and from the left (E11–E20) sides of the barrier, respectively. The signals from the left (panel b) show no evidence of an impulsive signal. From the video recordings, we see that in this area, the flow reached the barrier at low velocity and progressively loaded the barrier (black horizontal arrow). Conversely, the signals from the right side (panel d) reflect a more fluidlike and turbulent behavior (as in Leonardi et al., 2019)

due to the flow transiting for a longer time on this side with more energy.

Panels (c) and (e) show instruments that recorded strong signals, which are induced by large blocks that clogged the outlets, loading transversely the beams.

The Event on July 11, 2016 The measurements of the strain transducers confirmed the multi-surge nature of the event on July 11 and the impulsive behavior of these surges (Figure 10).

Although no video recordings are available, the high values of the strain peaks in the recordings of this event indicate a higher-energy process compared to the event on June 9.

As for the event on June 9, signals that report similar patterns are grouped together and shown in panels in Figure 10. Three main perturbations (surges) are recorded at about 16:00:46, 16:02:18, and 16:06:08.

With few exceptions, the surges can be identified in all recordings reported in the figure. Each surge is characterized by a sudden strain increment (impulsive behavior) and is preceded by a variable time interval in which strains remain roughly constant (shaded areas in the figure). A rough indication of the initiation of each surge is shown by the horizontal numbered arrows in panel (c). The strains are generally larger than those recorded on June 9.

NUMERICAL MODELING OF THE FLOW DYNAMICS An indication of flow depth (h) and velocity (v) is a necessary input for using impact force formulae. As a consequence, their knowledge is needed to evaluate the applicability of the formulae to this case study.

The aim of the numerical analysis is to calibrate the rheological parameters of the model through a back analysis of the event on June 9. The propagation analysis is carried out with RASH3D , a numerical code based on a single-phase integrated solution of the St. Venant equations using the shallow-water assumption. The equations are solved with a finite-volume approach, where the CFL condition has been imposed to define the time discretization. An unstructured triangular mesh is used to discretize the equations. Full details concerning the code formulation and implementation are presented in Audusse et al. (2000) and Pirulli (2010b). The calibration is achieved through a trialand-error process by systematically modifying the parameters until the characteristics of the simulated phenomenon match those of the real event.

The numerical code, being based on a depthintegrated version of the balance equations, can only roughly simulate fluid–structure interaction. To ob-

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Figure 9. Strain measurements recordings for the event on June 9. (a) Distribution of the deposit upstream of the monitored barrier. (b) and (c) Data collected from E01 to E10 (i.e., the right side of the barrier); (d) and (e) concern data from E11 to E20 (i.e., the left side of the barrier).

The horizontal black arrow indicates the time interval in which compression (negative strain) increases.

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Figure 10. Strain measurements for the event on July 11. (a) Distribution of the deposit. (b) and (c) Data collected from E01 to E10 (i.e., the right side of the barrier); (d) and (e) concern data from E11 to E20 (i.e., the left side of the barrier). The black arrows in (c) give a rough indication of the initiation of each flow surge. The shaded areas indicate the time interval in which the measured strain remain roughly constant.

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tain a clear representation of interaction and of the complex three-dimensional flow that develops at impact, more sophisticated methods are required (possibly grain-resolving, as in Leonardi and Pirulli, 2020).

However, RASH3D can reasonably reproduce the main flow features until a few instants before impact. This is in terms of average flow depth and velocity before the impact with the Pèrriere barrier (obtained from the video analysis) and depth distribution of the deposited mass upstream of the barrier (observed along the longitudinal trench excavated during the deposit removal works). Under the hypothesis of the two events having a similar rheological behavior, the calibrated rheological parameters for the event on June 9 are used to model the event on July 11 and interpret its dynamics since no videos are available.

Scenario and Rheological Law Definition

Table 5. Debris flow on June 9. Comparison between data of the observed and simulated velocity and flow depth. v̄ = mean velocity of the mass front between the confluence of branches A and B to the barrier; h̄ = mean depth of the frontal part of the deposit; l¯ = mean length of the main deposit.

Simulation Results Voellmy Rheology µ (−) ξ (m/s2 ) 0.1

0.2

1,000 500 300 200 1,000 500 400

v̄ (m/s)

h̄ (m)

l¯ (m)

5.3 4.0 3.2 2.7 2.7 2.0 1.6

2.3 2.4 2.7 2.8 2.7 2.4 2.2

30 31 36 36 85 82 81

2012). Thus, the basal resistance T can be written as T = ρghμ + ρg

3D

In order to run an analysis, RASH requires (1) a digital elevation model (DEM), (2) the geometry of the initiation volume, and (3) a rheological law.

A pre-event DEM with a 5-m grid spacing in both directions (based on 1:5,000 maps) is available for the considered study site. The mesh grid is locally refined at the location of the barrier, down to a mesh spacing of 0.1 m. The filter barrier is included in the topography by locally modifying the DEM albeit with a few simplifications (e.g., the I-shape of the beam section is not represented). For the event on June 9, it is assumed that the debris was released only from Area 1. For the event on July 11, a simultaneous release from both areas (i.e., Area 1 + Area 2) is considered.

RASH3D can simulate entrainment with the model of McDougall and Hungr (2005). However, in St. Vincent, the debris are mobilized from the steep slopes of the upper catchment (Area 1 and Area 2), and no significant entrainment is observed during the early runout on branches A and B. For this reason, no entrainment along the runout path is considered in the numerical analysis. The initiation volume of each scenario is therefore assumed equal to the volume removed during the works conducted to restore the functionality of the Pérriere mitigation barriers: 1,875 m3 for the event on June 9 and 4,420 m3 for the event on July 11.

Different rheological parameters have to be defined as a function of the selected rheological law.

In this work, we employ the Voellmy rheology. This law assumes that dissipation of kinetic energy is due to a combination of frictional resistance and of a turbulent-viscous drag term (Rickenmann and Koch, 1997; Revellino et al., 2004, Rickenmann, 2005; Pirulli, 2010c; Pirulli and Marco, 2010; and Pirulli and Pastor,

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v2 , ξ

(1)

where, μ is the friction coefficient, ρ is the material density, g is gravity, and ξ is the turbulence coefficient. The two dependent variables are the depth-averaged flow velocity v and the flow height h. The first term on the right side of Eq. 1 accounts for any frictional component of resistance. The second term is analogous to the Chezy formula for turbulent flows in open channels.

In this case, it is included to empirically account for all possible sources of velocity-dependent resistance.

RESULTS The event on June 9 is back analyzed to calibrate the two Voellmy parameters: the friction coefficient, μ, and the turbulence coefficient, ξ. The starting values were obtained from technical literature (e.g., Revellino et al., 2004; Rickenmann et al., 2006). The investigated range is as follows: friction coefficient between 0.1 and 0.2 and turbulence coefficient between 100 and 1,000 m/s2 . Comparison of numerical results with average observed data are summarized in Table 5. Note that simulations with a higher friction coefficient tend to produce longer deposits because the angle of repose of the material increases as well. The best-fit results were obtained for μ = 0.2 and ξ = 500 m/s2 and are illustrated in Figure 11.

The best-fit numerical results and the data obtained from the video recordings exhibit a good correlation on the runout reach above the monitored barrier. The front travels a distance of about 80 me (from the confluence between branches A and B to the monitored barrier) in about 40 seconds. In this area, the computed mean velocity of the flow front, obtained averaging over the first 10 m of moving debris, is about

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Figure 11. Numerical modeling of the event on June 9 with the calibrated Voellmy rheology. Flow height (a) at impact, (b) when the barrier is first overtop, and (c) when the flow filters through the openings. The depth-averaged speed at the same instants is shown in panels (d)–(f).

Final deposit: (g) longitudinal profile from the barrier toward upstream with respect to the on-site surveyed profile. See Fig. 5.

2 m/s. This is close to the value obtained from the video analysis (Table 4).

Numerically, the flow depth at initial impact ranges from 0.2 to 0.4 m (Figure 11a). However, this was immediately followed by the arrival of more debris, leading to a flow height of about 0.6–0.8 m. This does not exactly match the video, although a flow depth of about 0.6 m was observed in the video. After impact, the debris accumulate behind the barrier (Figure 11b).

Once the accumulated debris reach the top of the concrete basement, some material filters through the gaps between the vertical bars, further traveling along the channel (Figure 11f). With respect to the final deposit,

the computed configuration shows an average depth of about 2.5 m for the portion close to the barrier (Figure 11g). The depth decreases progressively upstream.

Under the hypothesis of the two debris flows having similar rheological behavior, the calibrated rheological parameters are used to simulate also the event on July 11, for which no video is available. In this case, the numerical analyses yield a front speed of about 4 m/s before impact. An interesting aspect that emerges is that, even though the material is released simultaneously from Area 1 and Area 2, the flow from Area 2 is delayed compared to that from Area 1. This behavior is in agreement with the interpretation from

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Figure 12. Modeling of the event on July 11 with the calibrated Voellmy rheology: (a) 195 seconds. (b) 500 seconds.

the site surveys. A first surge from Area 1 probably caused the clogging of the first barrier. After about 300 seconds, a successive surge, transporting woody debris, arrived from Area 2 soon after the first event and flowed over the deposit in the retention basin (Figure 12).

Estimation of the Impact Force Since the monitored barrier is almost perfectly orthogonal to the Grand Valey channel and the flowing mass is confined by the channel, it is reasonable to assume (as confirmed from the video recordings) that the impact of the flowing mass is orthogonal to the barrier.

Thus, we assume here that the impact induces a simple uniaxial bending of the filter beams. While this simplification allows capturing the key aspects of the problem, the actual interaction mechanism is likely more complex. For example, the beams can also potentially bend laterally due to grains interlocking at the outlets, as shown by Leonardi and Pirulli (2020).

Assuming that deformations are within the elastic limit, a cantilever beam model with a uniform distributed load (q) over the beam length (l) can be

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used to determine the actual bending moment Mx induced in the cross section a-a of the beam. The cantilever beam is 2 m long. Its section is an IPE270 profile with a deflection resistance modulus Wx equal to 428.900 mm3 and a Young modulus (E) of 200.000 MPa. The length (l) of the distributed load can be assumed to be the depth of the flow front. The a-a cross section on which Mx is computed is centered on the strain transducer, which is at a known distance a from the beam fixed constraint. Under this load configuration, the axial strain (εz ) of the beam measured by the strain transducer results in εz =

Mx σz q(l − a)2 = = , E EWx 2EWx

(2)

which, solved with respect to q, yields an impact force F of 2EWx εz F =q·l = · l.

(3) (l − a)2 However, the solution of the above equation requires a knowledge of the impact depth of the flow (l), which can come either from the video recordings or from the calibrated simulations. By comparing videos and

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Figure 13. Impact force calculated from the strain measurements (a) for the event on June 9 and (b) for the event on July 11. Estimation of values of the empirical coefficients: (c) static coefficient k and (d) dynamic coefficient α.

strain recordings, it is possible to define the flow depth that led to the peak deformations of the event on June 9; this value was found to be about 1.0 m and was recorded at about 12:39. The same flow depth of 1.0 m is assumed for the event on July 11 since no videos are available. This value is clearly an approximation, but it can be used to compare the maximum impact force induced by the two events under similar conditions.

The forces derived from the strain measurements are then expressed dimensionally as a force per unit width.

Obtained results are summarized in Figure 13 for the two events. It emerges that the maximum impact force is due to compression of the transducers. The tension value is usually small except for the steel beams located at the dam side for the event on July 11.

The mean impact force recorded for the event on July 11 (365.38 kN/m) (Figure 13b) is as much as 5.5 times greater than that of the event on June 9 (66.40 kN/m) (Figure 13a). It can be observed that there is a narrow distribution of values for the June 9 event and a wide distribution for the July 11 event.

Comparison with Literature Impact Formulae Several formulae exist in the literature to estimate the impact force on a rigid barrier. These can be

grouped into two main families. The first is typical of slow flows and is based on a pressure term (hydrostatic models), while the second type is characteristic of rapid flows and is computed on the basis of the incoming flow momentum (hydrodynamic models).

Generally, hydrostatic formulae have the appearance 1 (4) kρgh2 , 2 where Fs is the hydrostatic impact force, with k the empirical static coefficient. Lichtenhahn (1973) proposes k-values between 7 and 11, and Armanini (1997) proposes a value of 9.

Hydrodynamic formulae usually take the form Fs =

Fd = αρhv 2 ,

(5)

where Fd is the hydrodynamic impact force and α is the empirical dynamic coefficient. The range of values for the dynamic coefficient is in general larger than for the static coefficient. Armanini and Scotton (1993) propose values of α between 0.7 and 2. Canelli et al. (2012) define α in a range between 1 and 5. Daido (1993) suggests values between 5 and 12.

The estimation of k and α remains an open issue.

For this reason, these formulae have been used here to verify whether the literature coefficients are suitable for

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Leonardi, Pirulli, Barbero, Barpi, Borri-Brunetto, Pallara, Scavia, and Segor

reproducing the impact forces of the Grand Valey debris flows and in particular the values computed in the previous section (Figure 13). In any case, the results are not to be interpreted as general recommendations because they rely on multiple assumptions both on the flow features and on the structural behavior of the barrier.

To back calculate the coefficients, we use the flow depth (h) and velocity (v) obtained from the video analysis (h = 1 m; v = 2 m/s) for the event on June 9. For the event on July 11, the velocity obtained from the numerical analysis is used (v = 4 m/s), while the flow depth is assumed equal to 1 m. The bulk density is assumed equal to 1,900 kg/m3 . The results are shown in Figure 13c and d, respectively, both for the single beam and as an average for both events. For the static coefficient k, a mean value equal to 10.6 was obtained for the event on June 9 and equal to 39.0 for the event on July 11. Only the first of these values falls inside the range proposed in the literature, which seems to confirm that the hydrostatic approach is more appropriate for slower impacts, such as those measured on June 9.

There is a small dispersion of results for the event on June 9 and a wide dispersion for the event on July 11 (Figure 13c).

For the dynamic coefficient α, a mean value equal to 9.8 was obtained for the event on June 9 and equal to 11.5 for the event on July 11. Both the values fall only in the range proposed by Daido (1993). In this regard, it should be pointed out that Daido is the only author among those selected who uses real cases and not laboratory experiments. Moreover, even if the two mean values are close, the dynamic coefficient shows a wider dispersion for the event on July 11 than for the event on June 9 (Figure 13d).

It is generally observed in the literature that hydrodynamic models do√not perform well for low Froude numbers (FR = v/ gh). Hydrostatic models are instead appropriate for low Froude numbers (FR < 1) but underestimate forces for higher Froude numbers (Hübl et al., 2009). The results obtained in this section appear to conform to this rule. A Froude number of about 0.7 was obtained for the event on June 9 and of about 1.4 for the event on July 11. Accordingly, the event on June 9 is well described by a hydrostatic formula, while the event on July 11 is better described by the hydrodynamic formula.

CONCLUSIONS The correct estimation of the impact force of a debris flow front against a mitigation structure is a key aspect in the structural design process, but it still remains an open issue. While numerous formulae are available for the evaluation of the impact force, these

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require the definition of empirical coefficients and a knowledge of the flow dynamics.

In this respect, the monitoring and measurement of real events is fundamental to gather reliable data concerning both flow dynamics and impact forces. To this end, a monitoring system equipped with strain transducers has been installed on the filter elements at the Grand Valey torrent study site. In this article, we presented two debris flow events that occurred during the considered monitoring period. A video of the flow dynamics showing the interaction with the monitored barrier is available for the first of these two events.

The interpretation of the strain measurements in terms of the flow impact force requires the assumption of an impact load perpendicular to the barrier.

This assumption is justified in the Grand Valey study site because of the existence of a narrow channel that forces the flow to impact orthogonally the monitored barrier, as was also observed in the video recordings.

However, any upgrade of the system should include the installation of a second strain gauge at the lower left corner of the downstream side of each beam flange (i.e., in a symmetrical position to the existing instruments) in order to check the exact direction of the impact force of the debris flow. The lateral load, as shown in Leonardi and Pirulli (2020), can be significant if the outlets clog. Alternatively, load cells could be added to improve the characteristics of the existing monitoring system. A mounted camera that turns on during the event would also significantly improve the site potential.

The video recordings give an important contribution to interpret both the debris flow dynamics and the strain gauge recordings but also for the calibration of the rheological parameters used in numerical models.

In the Grand Valey study site, the lack of a video for the second event made it necessary to resort to the numerical modeling to obtain at least a rough estimation of the dynamics of the second event, using the rheological parameters obtained through the back analysis of the event on July 9.

As far as the flow impact is concerned, forces, flow depth, and velocity have been used to evaluate the applicability of the ranges of the empirical coefficients suggested in the literature. The obtained results highlight that hydrostatic effects dominated in the first event, while hydrodynamic effects dominated impact in the second event. For the Grand Valey site, both the static and the dynamic models should be applied: either of them can be more conservative, depending on the flow conditions. The maximum force obtained using the formulae in Eq. 4 and Eq. 5 should be selected as the design value. In order to be able to reproduce the force signal recorded on-site, an empirical coefficient of at least 12 should be applied to both the static and

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the dynamic formulas. However, the strains measured on-site might be induced by a deformation pattern of the barrier that is more complex than the one assumed in our analysis. Thus, the derived empirical coefficient should be interpreted as conservative estimations.

ACKNOWLEDGMENTS This work was supported by the RISKNAT project–Operational programme Italy–France (Alps– ALCOTRA) 2007–2013 and the “Mhymesis— Modelling Hazard of hYperconcentrated Mountain flows: A wEbgis SImulation System” project 2015– 2017. The authors wish to thank P. Gaia and L. Pitet (Aosta Valley Autonomous Region) as well as M. Ceccarelli and A. Lombrino (Politecnico di Torino) for the configuration of the monitoring system and for suggestions for the interpretation of some of the monitoring data.

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Monitoring Debris-Flow Surges and Triggering Rainfall at the Lattenbach Creek, Austria JOHANNES HUEBL ROLAND KAITNA* University of Natural Resources and Life Sciences, Vienna, Peter Jordan Strasse 82, 1190 Vienna, Austria

Key Terms: Debris-Flow Surges, Triggering Rainfall, Roll Waves, 2-D Laser ABSTRACT Debris-flow events often comprise a sequence of surges, sometimes termed “roll waves.” The reason for this surging behavior is still a matter of debate. Explanations include the growth of hydraulic instabilities, periodic sediment deposition and release, or grain size sorting. High-resolution field measurements together with triggering rainfall characteristics are rare. We present results for 3 years of monitoring debris-flow events at Lattenbach Creek in the western part of Austria. The monitoring system includes a weather station in the headwaters of the creek, radar sensors for measuring flow depth at different locations along the channel, as well as a two-dimensional rotational laser sensor installed over a fixed cross section that yields a threedimensional surface model of the passing debris-flow event. We find that the debris flows at Lattenbach Creek were all triggered by rainstorms of less than 2 hours and exhibited surges for each observed event. The velocities of the surges were up to twice as high as the front velocity. Often, the first surges that included boulders and woody debris had the highest flow depth and discharge and showed an irregular geometry. The shape of the surges in the second half of the flow, which carried smaller grain sizes and less woody debris, were rather regular and showed a striking geometric similarity, but still high velocities. The results of our monitoring efforts aim to improve our understanding of the surging behavior of debris flows and provide data for model testing for the scientific community.

INTRODUCTION Debris flows are commonly described as one or more surges of unsorted sediment and water, sometimes having a steep, granular front followed by a more dilute body (e.g., Stiny, 1910; Pierson, 1986; Marchi *Corresponding author email: roland.kaitna@boku.ac.at

et al., 2002; McArdell et al., 2007; Okano et al., 2012; McCoy et al., 2013; and Comiti et al., 2014). A hydraulic approach to explain the development of several surges is based on the observation that in steady uniform flows, small perturbations can amplify without external forcing to create “roll waves” when a certain flow intensity threshold is exceeded (Dressler, 1949).

Concepts based on hydraulic theory have been applied to Newtonian, non-Newtonian (e.g., Ng and Mei, 1994; Zanuttigh and Lamberti, 2007; Longo, 2011; and Arai et al., 2013), and granular flows (e.g., Forterre and Pouliquen, 2003; Di Cristo et al., 2009). Experiments show that roll waves traveling downstream typically show distinct shapes and non-equal velocities (“celerities”). Roll waves are often faster than the mean velocity of the flow, which is close to the front velocity. Therefore, fast surges may cannibalize slow ones and eventually may overtake the front of the flow. This leads to a continuous change of the hydrograph.

Another explanation for the development of surges in flowing debris is connected to the two-phase nature of debris flows. Through dynamic grain size segregation (Johnson et al., 2012) patches of coarse sediment might develop. These regions of higher flow resistance progressively grow to form wave fronts, which ultimately might decouple from the preceding flow.

Iverson et al. (2010) described this mechanism for roll waves developing during large-scale debris-flow experiments. Surges in natural flows that develop as a result of segregation processes supposedly do not show distinct shapes.

In natural channels, surge development might also be connected to discrete sediment input from landslides or bank failure and/or channel bed erosion.

In a study combining high-resolution hydrologic and geomorphic monitoring data in a recently burned watershed, McGuire et al. (2017) concluded that the mechanism for debris-flow surge initiation is likely connected to en-masse failure of sediment stores that were periodically deposited and remobilized in the channel during a storm event (cf. the sediment capacitor model of Kean et al., 2013).

Field data on surge development, surge celerities, and shapes are rare (cf. review by Zanuttigh and

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Huebl and Kaitna

Figure 1. (A) Overview and location of the study site Lattenbach in Tyrol, Austria; (B) photo of two pylons carrying the flow depth sensors at the monitoring site Grins.

Lamberti, 2007), and there are also only a few approaches to model the downstream deformation of single waves (Edwards and Gray, 2015). The aim of this study was to document surges in natural debris flows. The research questions can be summarized as follows:

r What are the characteristics of debris-flow stage hydrographs at Lattenbach Creek? Do surges have distinct shapes? r Is the first surge always the one with the highest discharge? r Are celerities of single surges higher than mean/front velocity of the flow? r Is there a relationship between rainfall and event characteristics, such as peak discharge, volume, or number of surges?

In the following sections, monitoring data of observed debris flows from 2015 to 2017 at Lattenbach Creek, Austria, are presented and analyzed.

STUDY AREA Lattenbach Creek is a tributary to the Sanna River in the western part of Austria (Tyrol Province). The

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Lattenbach drains an area of about 5.3 km², flows through the village of Grins, and confluences with the Sanna River at the community Pians (Figure 1A). The watershed is located at the transition between the socalled “crystalline Alps” and the limestone formation of the northern Alpine chain. As a result of a geological fault there is a complicated sequence of weak rock (e.g., phyllite) and more competent material such as limestone. The rugged terrain shows deep-seated landslides, which constantly feed the channel with fresh sediment. This geomorphological activity is expected to be connected to the frequent occurrence of debris flows in the watershed.

METHODS Site Dawinalpe A meteorological station is located around 300 m west of the Lattenbach catchment at an altitude of 1,820 m a.s.l. The measured parameters at site Dawinalpe include temperature, humidity, radiation, snow height, and rainfall. Rainfall data were recorded at an interval of 10 minutes. Debris-flow triggering rainfalls were derived manually. Non-triggering rainfalls

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were detected automatically based on the condition of rainfall “P: within 10 minutes > 0 and a subsequent 30-minute rainfall sum of >0.5 mm. Note that the definition of non-triggering rainfall events is crucial for the calculation the conditional probabilities (cf.

Berti et al., 2012); however, in this study we expect no ramifications.

Site Grins A channel monitoring system was installed at two locations at the lower reach of the channel. Over the years several modifications were made to improve the system. Here we describe the most recent configuration. Site Grins (Figure 1B) is located about 1.3 km upstream of the confluence with the Sanna River at the end of a reach of check dams and consists of two radar distance sensors (S1 and S2) for measuring flow height (type Vegapuls WL 61, accuracy ±2 mm), a rotational laser scanner (type Sick LMS511-20190, accuracy ±3 percent), and a digital video camera (type Mobotix M16). The measurement frequency of the radar sensors is 2 Hz and that of the rotational laser scanner is 36 kHz, with a rotation rate of 25 per second. The laser scanner data were binned at 0.25° intervals and averaged over five consecutive rotations, yielding five data points per bin per second. After transformation into Cartesian coordinates, mean values over 1 second were computed for better visualization. The distance between S1 and S2 is 47 m. Since all sensors are located at the overflow section of a check-dam, channel erosion is limited to the height of temporary deposits from fluvial bedload transport. The laser sensor is installed at the same location as the upstream sensor S1.

Additional seismic sensors were installed at the channel banks.

The front velocity and the velocity of single surges were estimated by manually determining the travel time of the front and the peaks of the surges between sensors S1 and S2. For the assessment of surface velocity distribution, a high-frequency Doppler radar system (HF radar, IBTP Koschuch, Leutschach, Austria) described in Huebl et al. (2018) was used.

Figure 2. Sketch of the definition of an effective flow height for calculation of a debris-flow discharge.

The monitoring system is triggered when one of three conditions are met: a voltage signal from a ripcord upstream of the station Grins, a seismic threshold at Grins, or a flow depth threshold of 0.5 m at S1.

Calculation of Discharge At location Grins S1 we calculated discharge Q(t) with Q (t) = f (H (t)) × v (t) , where f(H(t)) is a second-order polynomial function between flow depth H(t) and the cross-sectional area occupied by the flow, and v(t) is the mode of the surface velocity distribution at time t derived from the highfrequency Doppler radar system (Huebl et al., 2018).

In case of substantial deposition at the check dam before the debris flow arrived or deposition after the passage of the flow, we calculated an effective flow height H’, assuming a logarithmic decrease of erosion rate along the surge (Figure 2). The assumption of highest erosion rates at the front were motivated by field measurements of debris-flow erosion by Berger et al.

(2011).

RESULTS AND DISCUSSION 2015–2017 Debris Flows

Site Pians To record the travel time and wave deformation over an extended distance, site Pians was installed 1.14 km downstream of station Grins, at a location 0.15 km upstream of the confluence with the Sanna River. Here, only one flow depth sensor S3 (type Sommer UPM-10, accuracy ±10 mm) with a measurement frequency of 2 Hz and a digital video camera (type Mobotix M16) was installed.

Between 2015 and 2017, six debris-flow events were registered (Figure 3), with two events occurring on the same day (08/09/15). The total flow volumes ranged between 5,000 and 47,000 m³ (Table 1). All of the events displayed several surges, with a maximum of more than 50 surges for the event on September 10, 2016 (09/10/16). For three out of six events, the maximum peak discharge was associated with the first surge, estimated at 47, 60, and 65 m³/s. A maximum

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Figure 3. Overview of calculated discharges and cumulative volumes of the debris-flow events as well as recorded rainfall sums at Lattenbach Creek for the 2015–2017 period.

observed peak discharge of 143 m3 /s was registered for the event in 2016, exceeding the engineering design discharge of the 150-year flood event (∼30 m³/s) more than four times. We find that the peak discharge increased with flow volume (Table 1), as expected from empirical relationships (Rickenmann, 1999).

The front velocity of the debris flows observed at site Grins varied between 1.5 and 5.9 m/s. The average velocities between site Gins and site Pians (1.14 km

downstream of Grins) were in a similar range, between 1.9 and 4.5 m/s (Table 1).

Debris-Flow Event on September 10, 2016 For the debris-flow event in 2016 we counted more than 50 surges. The combined information of crosssectional flow depth variations (three-dimensional hydrograph, Figure 4) and surface velocity with time

Table 1. Arrival times of debris-flow front and mean front velocities of the debris flows observed between 2015 and 2017.

Date 08/09/15 08/09/15 08/16/15 09/10/16 07/29/17 07/30/17

Arrival at Grins, All p.m. Times

Front Velocity (m/s-)

Qpeak at Grins (m³/s)

Total Volume (m³)

S1

S2

Arrival Pians S3

S1–S2 (47 m)

S1–S3 (1,140 m)

47 65 12 143 60 87

12,000 18,500 5,000 46,000 14,000 41,000

8:03:23 11:01:05 3:48:35 6:53:53 6:29:29 5:25:35

8:03:32 11:01:13 3:49:07 6:54:05 6:29:39 5:25:46

8:10:26 11:05:20 No data 6:58:11 6:39:43 17:30:46

5.2 5.9 1.5 3.6 4.7 4.3

2.7 4.5 — 4.4 1.9 3.7

Qpeak is the peak discharge of the debris flow event.

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Figure 4. Three-dimensional hydrograph and surface velocity of surges of the debris-flow event at Lattenbach on September 10, 2016.

shows that a sequence of very irregular surges with a wide variety of surface velocities (t ∼ 3,250–3,900 seconds) is followed by a period of relative regular surges with velocities around 8 m/s and inter-surge velocities of <1 m/s (t ∼ 3,900–4,330). The time refers to the start of data recording at around 6:00 pm. The de-

bris flow lasted another 30 minutes, with some minor surges and generally a more uniform flow depth and surface velocity, as shown in Figure 4.

In Figure 5 we compare the hydrographs measured at site Grins (S1) with the hydrograph measured at site Pians (S3), which is 1.14 km downstream of Grins.

Figure 5. Hydrographs of the debris-flow event at Lattenbach on September 10, 2016, at the site Grins and the site Pians, including average normalized surges, as indicated.

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Figure 6. Intensity and duration of rainfall events (blue circles) and debris-flow triggering rainfall events (red circles) measured at station Dawinalpe between 2015 and 2017. The size of the blue circles indicates the frequency of rainfall events. The size of the red circles represents the maximum discharge of observed debris-flow events.

The mean travel time of the front was about 4 minutes and 16 seconds, yielding a mean front velocity of 4.4 m/s. The manually derived velocity of the surges at site Grins varied between 4 and 12 m/s. It is interesting to see that on its way to site Pians, the fast-moving surges eventually merged with preceding slower ones, leading to one big first surge that seemed to be slightly detached from the rest of the flow. The tail of the flow again displays rather regular surges, but with a reduced number. Note that between sites Grins and Pians there is a ∼10-m-high check dam, which may significantly influence the deformation of the hydrographs. The generally high flow height at site Pians can be explained by the bedrock reach at Pians, which is much narrower compared to the cross section at site Grins. To test the self-similarity of the shapes of surges we overlaid the regular, undisturbed surges in the back of the flows at both sites. We find that surges after a longer travel

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distance are more similar than the ones at the upper station. We speculate that this might be connected to internal flow dynamics of the very fine-grained flows rather than to external forcing (e.g., from lateral or basal sediment input).

Triggering Rainfall Between 2015 and 2017, all debris flows at Lattenbach Creek were triggered by intensive storm events with a minimum duration of 30 minutes and a maximum duration of 2 hours (Figure 6). The precipitation sums measured at station Dawinalpe ranged from around 4 mm to 42 mm, yielding average intensities between 2 and 32 mm/hr. Most triggering rainfalls were significantly higher than the automatically detected non-triggering rainfalls (blue circles in Figure 6). As a result of the limited number of debris-flow events, we

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refrain from deriving an intensity-duration threshold relation (see review by Guzzetti et al., 2008) or applying Bayesian statistics, as demonstrated by Berti et al.

(2012). There is an indication that the peak discharge increases with average rainfall intensity. However, we do not find a relation between rainfall and other characteristics, such as total event volume or number of surges.

CONCLUSIONS In this contribution monitoring data from debris flows occurring from 2015 to 2017 at Lattenbach Creek, Austria, are presented. In total, six events were recorded, with a maximum event volume of ∼47,000 m². A rotational laser scanner, together with a high-frequency Doppler radar, were successfully tested and provide data for model development and model testing. Though there was significant variation in terms of event volumes, velocities, and water content (visually assessed from videos), the events showed some common features.

r All events occurred as a sequence of surges. The events with large volumes showed irregular surges at the front of the flow, which were associated with large boulders and woody debris. At a later stage, the surges appeared more regular. r All surges had higher velocities (“celerities”) than did the front. r Five out of six events exceeded the engineering design discharge of a flood event with a return period of 150 years. r All events were triggered by short, intensive rainfalls, lasting from 30 minutes to 2 hours.

For the largest event in 2016, a significant transformation of the hydrograph over a distance of more than 1 km was observed, resulting in a very large frontal surge and a reduced number of smaller ones.

Likely as a result of a limited number of events and the lack of spatial information of rainfall, we do not find a clear relationship between rainfall metrics and debris-flow characteristics. Ongoing monitoring and analysis of weather radar measurements will improve the assessment of a coupling between rainfall and surging behavior of debris flows at Lattenbach Creek.

ACKNOWLEDGMENTS The authors thank Fritz Zott for realizing and maintaining the monitoring site, Georg Nagl for field support, David Prenner for supporting rainfall analysis, and Andreas Schimmel for processing the laser data. This project received financial support from the

Austrian Climate and Energy Fund within the framework of the ACRP Programme.

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Huebl, J.; Schimmel, A.; and Koschuch, R., 2018, Evaluation of different methods for debris flow velocity measurements at the Lattenbach Creek. In Yamada, T. (Editor), Interpraevent 2018 in the Pacific Rim Symposium Proceedings, Research Society Interpraevent, Klagenfurth, Austria, pp. 2–8.

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Monitoring of Rainfall and Soil Moisture at the Rebaixader Catchment (Central Pyrenees) RAÜL OORTHUIS* MARCEL HÜRLIMANN Department of Civil and Environmental Engineering, UPC BarcelonaTECH, Jordi Girona 1-3, 08034 Barcelona, Spain

CLÀUDIA ABANCÓ Department of Civil and Environmental Engineering, UPC BarcelonaTECH, Jordi Girona 1-3, 08034 Barcelona, Spain; and College of Life and Environmental Sciences, University of Exeter, Amory Building, Rennes Drive, EX44RJ Exeter, U.K.

JOSÉ MOYA Department of Civil and Environmental Engineering, UPC BarcelonaTECH, Jordi Girona 1-3, 08034 Barcelona, Spain

LUIGI CARLEO Department of Civil Engineering, University of Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Italy

Key Terms: Monitoring, Rainfall Infiltration, Torrential Flows, Soil Moisture, Threshold, Pyrenees ABSTRACT The instrumental monitoring of torrential catchments is a fundamental research task that provides necessary information to improve our understanding of the mechanisms of debris flows. While most monitoring sites include meteorological sensors and analyze the critical rainfall conditions, very few contain soil moisture measurements. In our monitoring site, the Rebaixader catchment, 11 debris flows and 24 debris floods were detected during the last 9 years. Herein, the initiation mechanisms of these torrential flows were analyzed, focusing on the critical rainfall conditions and the soil water dynamics. Comparing the temporal distribution of both rainfall episodes and torrential flows, the Kernel density plots showed maximum values for rainfalls at the beginning of June, while the peak for torrential flows is on July 20. Thus, the antecedent rainfall, and especially the soil moisture conditions, may influence the triggering of torrential flows. In a second step, a new updated rainfall threshold was proposed that included total rainfall duration and mean intensity. The analysis of soil moisture data was more complicated, and no clear trends were observed in the data set. Therefore, additional data have to

*Corresponding author e-mail: raul.oorthuis@upc.edu

be recorded in order to quantitatively analyze the role of soil moisture on the triggering of torrential flows and for the definition of thresholds. Some preliminary results show that the soil moisture at the beginning of a rainfall event affects the maximum increase of soil moisture, while a slight trend was visible comparing the initial soil moisture with the necessary rainfall amount to trigger a torrential flow.

INTRODUCTION Torrential flows like debris flows and debris floods represent an important natural hazard for society and infrastructures in mountainous regions as a result of their high velocities, long runout distances, and great impact forces (Hilker et al., 2009). Detailed data recorded at catchments with monitoring systems are necessary to improve our knowledge about the triggering mechanisms of debris flows and other torrential processes. Understanding the triggering mechanisms is a complex task since it depends on several variables; the slope angle, sediment availability, and water input play the most important roles (Takahashi, 1981, 2019; Iverson, 1997; Jakob and Hungr, 2005; and Brayshaw and Hassan, 2009). Herein, we present data recorded at the Rebaixader torrent, where torrential activity is high and for which a comprehensive time series on the initiation of debris flows and debris floods is available. In this study we distinguish between the torren-

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tial flows using the classification of Hungr et al. (2001, 2014).

There are three principal approaches with which to monitor and analyze debris-flow triggering (Hürlimann et al., 2019). The most common approach focuses on rainfall measurements, the main triggering factor of torrential flows (Wieczorek and Glade, 2005) and generally defines thresholds for debris-flow triggering (Deganutti et al., 2000; Gregoretti and Dalla Fontana, 2007; Coe et al., 2008; Abancó et al., 2016; and Bel et al., 2017). Debris flows are commonly triggered by intense convective rainfalls (Hürlimann et al., 2003; Underwood et al., 2016; Prenner et al., 2019), which are known to have strong spatial and temporal variations. Therefore, the location of the rain gauge should be as close as possible to the initiation area to better assess the triggering rainfalls. The second approach analyzes the soil water dynamics by recording soil moisture and/or pore water pressure in natural slopes of the catchment (Comiti et al., 2014; Hürlimann et al., 2014) or in the channel bed (McArdell et al., 2007; Gregoretti, 2012; and McCoy et al., 2012). Soil moisture and pore water pressure are strongly related to soil infiltration capacity and consequently runoff generation, which is known to trigger debris flows or other torrential flows. The third approach investigates the channel discharge and the mobilization of sediments in the channel (Coe et al., 2003; Gregoretti and Dalla Fontana, 2008; and Gregoretti et al., 2016). However, initiation mechanisms are still not totally resolved because of the complexity of debris flow phenomenon and the harsh mountainous conditions under which torrential flows develop (steep slopes, possible rockfalls, difficult accessibility, …), which complicate the task of installing and maintaining the monitoring system (Imaizumi et al., 2005).

The present investigation focuses on the rainfall and the soil moisture measured at the Rebaixader catchment. The rainfall time-series covers the last 10 debris flow seasons (2009 to 2018), while the soil moisture records started in 2012. The main objective of the study was to improve our understanding of the initiation mechanisms of debris flows and debris floods.

A secondary goal included establishing the definition of critical values or thresholds that provide necessary information for the launch of early warning or alarm systems.

THE REBAIXADER MONITORING SITE Settings The Rebaixader monitoring site is located in a small first-order basin at the Southern Central Pyrenees, which shows a typical morphology of a torrential

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catchment (Figure 1) developed in an old glacial valley. The catchment drains an area of 0.53 km2 ; the altitude ranges from 1,350 m a.s.l. at the fan apex up to 2,475 m a.s.l. at the highest peak. The debris flows and debris floods initiate in a steep bare scarp of about 32º with a badland-like morphology and then progress to the channel zone. This latter is 150 m long, 8–10 m in width, and has a mean slope of 21º. At the bottom of the slope, the fan or deposition zone has an area of 8.4 Ha and an average slope of 18º.

The bedrock consists of Palaeozoic slates and phyllites formed during Hercyanian orogeny (Muñoz, 1992), while the soils include colluvium and glacial deposits. The main scarp is located in a thick lateral moraine till, which consists of sandy gravels and provides almost unlimited sediment availability. The main reasons to locate a monitoring system in this catchment include the steep gradient and the fact that it has almost no restriction in sediment supply, which promotes high torrential activity. Therefore, water input due to rainfall events is the main factor triggering torrential flows in the Rebaixader catchment. Since the installation of the monitoring network more than 30 torrential flows have been detected, with one debris flow and two debris flood events per year as an average.

The climate conditions are affected by three principal factors: 1) the west winds from the North Atlantic, 2) the vicinity of the Mediterranean Sea, and 3) the orographic effects of the Pyrenean mountain range. The mean annual precipitation ranges from 800 to 1,200 mm (Abancó et al., 2016). In the Pyrenees, the most common triggering rainfalls are on one side short-duration and high-intensity convective summer storms and on the other side long-lasting rainfalls with moderate intensity, during autumn (Hürlimann et al., 2003).

Monitoring Description The monitoring in the Rebaixader torrent started in summer 2009 with the aim of detecting debris flows and other torrential processes. Since that time the monitoring system has been improved and includes, at the moment, five different stations: four stations monitor the initiation mechanisms, including two meteorological stations (METEO-CHA and METEO-TOP, installed in 2009 and 2012 respectively) and two infiltration stations (INF-SCARP1 and INF-SCARP2, installed in 2012 and 2015 respectively), and the FLOWWR station (installed in 2009), which detects and identifies the different torrential flows (Figure 1). In this study, records at the INF-SCARP2 station are not included.

The principal rain gauge is METEO-CHA, which is installed in the lower part of the catchment. It is a stan-

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Figure 1. The Rebaixader monitoring site. (a) General view of the catchment with the open scarp where the debris flows and debris floods initiate, the channel zone where the torrential flows develop, and the fan or deposition zone. The red rectangle specifies the channel reach, where the sensors of the flow detection station are installed (FLOW-WR); the green dot indicates the principal rain gauge (METEO-CHA); the yellow dot designates the secondary rain gauge (METEO-TOP); and the light blue squares represent the infiltration stations (INF-SCARP1 and INF-SCARP2). (b) Topographic map showing the location of the monitoring stations and principal geomorphological features. (c) Close-up of the open scarp, which provides significant sediment availability.

dard tipping bucket rain gauge with a resolution of 0.2 mm (until 2015 the resolution was 0.1 mm). The rain gauge METEO-TOP was temporarily installed just above the main scarp and was removed in November 2016. The infiltration stations are built in a steep

(30°–40º) bare slope at the highest part of the open scarp, which is actually stable but very close to the most active portion of the initiation zone. The stations consist of eight moisture sensors (Decagon 10HS), which measure volumetric water content (VWC) at

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Figure 2. Video frame of a debris flow passing the channel zone and detected at FLOW-WR station (July 17, 2013, 13:18 hours UTC).

Flow is moving from top right to bottom left.

different depths between 5 and 50 cm, and two water potential sensors (Decagon MPS-2) recording matric suction at 15 and 50 cm in depth. This set-up is totally different from that of other sites described in the literature, in which soil moisture and pore water pressure are measured in the channel bed (McCoy et al., 2012).

All of the meteorological and infiltration stations have a sampling rate of 5 minutes.

The most important part of the monitoring system forms the FLOW-WR station, which detects and allows classification of the torrential flows. The sensors in this station include five geophones, which trigger one radar device and one ultrasonic sensor to measure the depth of the flow, and one video camera, which is activated if a certain ground-vibration threshold is exceeded (Abancó et al., 2012, 2014; Hürlimann et al., 2014). All of these devices are located in the channel reach or at the highest part of the fan (Figure 1) and record the data at 1 Hz when the ground-vibration threshold is exceeded; otherwise the recording rate is every 2 hours. More detailed information on the monitoring system is available in Hürlimann et al. (2014, 2019). Figure 2 shows a video frame of a debris flow of about 10,500 m3 passing through the channel zone on July 17, 2013 (13:18 hours UTC) detected at the FLOW-WR station.

ANALYSIS OF THE RAINFALL DATA Between July 2009 and September 2018 a total of 11 debris flows and 24 debris floods were observed.

Rainfall data from METEO-CHA are available for all torrential events except one debris flow, which was measured by METEO-TOP. Moreover, 446 rainfall

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Figure 3. Temporal distribution of rainfall and torrential activity. Kernel density plots of 481 rainfall episodes (a) and 35 debris flow or debris flood events (b). Note: days 357–78: winter; 79–172: spring; 173–265: summer; and 266–356: autumn.

episodes that did not trigger any important torrential flow were selected. Rainfall parameters, such as duration (D), total rainfall (Ptot ), mean intensity (I), and maximum intensity for different durations (e.g., Imax_5min for 5 minutes), were evaluated. An important and critical task during the rainfall analysis is the definition of the total rainfall duration. Herein, this parameter was determined by the condition that no rainfall was observed 1 hour before and after the episode (Abancó et al., 2016).

In the first step of the analysis, the rainfall events were analyzed by searching for seasonal or cyclic patterns using Kernel density plots. The Kernel density is a method to estimate the density of a sample smoothly by removing the dependence of the end points of histogram bins centering the blocks at each data point (Duong, 2001). The temporal distribution of all of the 481 rainfall episodes (both triggering torrential flows or not) is plotted in Figure 3a. The results show that

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the highest density for the rainfall episodes is at 14:00 UTC and between April and July, with a maximum on June 5. If this density plot is compared with the one of debris flow and debris flood occurrence (Figure 3b), some interesting facts can be observed. First of all, the maximum Kernel density for the triggering of torrential flows is shifted 45 days to July 20, and the range of high-density values is between June and August. In terms of time of day, the maximum density of a trigger is approximately at the same hour as for the rainfall episodes (13:00 UTC).

The difference of the temporal occurrence between rainfall and triggering of torrential flows (about 1.5 months) may be associated with the effects of antecedent rainfall and the soil moisture evolution during late spring and early summer. Similar results were observed by other authors, which found that antecedent rainfall, up to 45 days, increased the soil moisture conditions and debris flow occurrence (Eyles, 1979; Govi and Sorzana, 1980; Wieczorek and Glade, 2005).

The importance of antecedent rainfall and the corresponding increase of soil moisture have been reported many times in debris-flow and landslide research (Wieczorek and Glade, 2005; Gregoretti and Dalla Fontana, 2007), but until now no clear relation between antecedent rainfall and debris-flow triggering was observed at Rebaixader (Abancó et al., 2016).

Nevertheless, a possible effect of snowmelt cannot be neglected for debris flows that occur in late spring or early summer (Hürlimann et al., 2010; Abancó et al., 2016). It must be stated that additional information of rainfall (intensity, duration, or total rainfall) was not incorporated into the density plot. However, the measurements gathered at Rebaixader confirm the hypothesis that debris flows are generally triggered in summer by convective rainstorms of short duration and high intensity, while long-lasting rainfalls during spring normally do not provoke events (Hürlimann et al., 2014).

In the second step of the analysis, the rainfall threshold for the triggering of torrential flows was assessed.

Abancó et al. (2016) had already proposed two thresholds for the data registered during the 2009–2014 period. The present data set includes additional records from the last 4 years (the new data set spans from 2009 to 2018). Therefore, the threshold for the relation between total duration and mean intensity was reconsidered and updated (Figure 4). The new threshold line was defined by applying the following procedure: first, a power-law trend line was fitted using the data from the 11 debris-flow triggering rainfalls. Then, the scale parameter defined in the previous step was reduced, keeping constant the exponent, until all the debris flows were located above the threshold line. The new updated threshold can be expressed by the follow-

Figure 4. Relationship between total rainfall duration and mean intensity for debris flows/debris floods triggering and non-triggering (no-trig) events. The resulting threshold is illustrated by the green line and expressed in Eq. 1.

ing equation: I = 11D−0.74 ,

(1)

where I is the mean intensity (in mm/hr) and D is the duration (in hours) of the rainfall events. Although the rainfall events, which triggered debris floods, were not used to define the threshold, it is noteworthy that most of them are located above the threshold. Indeed, only four debris floods (usually of small volume) did not fulfill the threshold condition.

ANALYSIS OF THE SOIL MOISTURE DATA The analysis of the soil moisture due to rainfall infiltration focuses on the station INF-SCARP1, which has the longest time series (2012–2019). In a first step, time series of VWC measurements at three different depths are compared with the corresponding daily rainfall from March until October 2013 (Figure 5).

This period covers all the torrential flows detected during 2013: one debris flow at mid-July and five debris floods between June and September. Vertical dashed lines indicate the moment of their peak discharge at the FLOW-WR station. The main meteorological station METEO-CHA was clogged during July 2013, and the corresponding missing data were collected with recordings from the METEO-TOP station. The VWC time series at 15 and 30 cm in depth present some missing data due to technical problems. Despite this temporal lack of data, all the torrential flows detected at the FLOW-WR station, except the last debris flood

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Figure 5. Volumetric water content (VWC) and daily rainfall time series from March until October 2013. (a) VWC measured at three different depths at infiltration station INF-SCARP1. (b) Daily rainfall of METEO-CHA and METEO-TOP meteorological stations. Vertical dashed lines indicate the moment of torrential flow peak discharge observed at the FLOW-WR station.

in September 2013, present VWC measurements at all depths. Note that the June 17 event corresponds to a small debris flood of about 100 m3 which was triggered by a short and low-intensity rainfall (Ptot = 4.4 mm, D = 0.6 h, Imax_5min = 12 mm/h). The other torrential flows volumes ranges between 600 and 10,500 m3 .

Results show that torrential flows at the Rebaixader catchment are mainly triggered during summer and are not necessarily due to the heaviest rainfalls in terms of total rainfall amount, as it can be observed during months of July and early September in Figure 5.

Regarding VWC measurements, results demonstrate that higher rainfall amounts are necessary to trigger torrential flows when the soil is initially dryer before the rainfall event, while if the initial water content at 15 and 30 cm in depth is higher (close to the highest VWC values), less rainfall is needed. This can be noted when comparing the event that occurred in June 5, where the soil at 15 and 30 cm in depth was initially dryer and the necessary rainfall amount to trigger torrential flows was high, or during July, with an initial wetter soil condition and lower triggering rainfalls. This suggests that as soil saturates, higher runoff rates are developed, which implies a higher erosion and

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transport energy that may trigger torrential flows. As a result of this link between soil moisture, runoff and transport energy, the proposed hypothesis is that torrential flows at Rebaixader may develop from continuous erosion due to intensive runoff. Thus, it can be stated that the initial soil moisture content affects the values of the necessary triggering rainfalls.

Figure 6 shows two examples of the soil moisture response during rainfalls that triggered torrential flows.

The soil moisture is given by the VWC and is measured at three different depths (15, 30, and 50 cm).

The first case shows the fast response and sharp increase of the VWC at the three depths due to a short and intense rainstorm (Ptot = 15.8 mm, D = 3.25 hours, Imax_5min = 96 mm/hr) that triggered a large debris flow of about 10,000 m3 . The second example illustrates the soil moisture response during a rainfall with a longer duration and smaller maximum intensity (Ptot = 54.5 mm, D = 7 hours, Imax_5min = 49.2 mm/hr), which triggered two debris floods with a total volume of about 2,000 m3 . In the second case, the VWC slowly increased during a period of about 2 to 3 hours and, maximum values were generally lower than in the first example, although the total rainfall is more

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Figure 6. Relationship between hourly rainfall and soil volumetric water content (VWC) during the triggering of torrential flows. Examples of July 17, 2013, debris flow (a) and June 5, 2013, debris flood (b). VWC is measured at the three different depths of station INF-SCARP1.

Vertical dashed lines indicate the moment of peak discharge observed at the FLOW-WR monitoring station.

Figure 7. Comparison between rainfall and soil moisture corresponding to debris flows/debris floods triggering and non-triggering (no-trig). (a) Relationship between initial volumetric water content (VWCi ) and the increment in volumetric water content ( VWC). (b) Relationship between initial VWC and maximum rainfall intensity for 5-minute duration (Imax_5min ). VWC values correspond to the sensor installed at 30 cm in depth at the INF-SCARP1 monitoring station.

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than three times higher. A significant time lag occurred between the start of the rainfall and the increase in VWC. Unfortunately, soil moisture measurements are not available for all the debris flows and debris floods that occurred at the site. Technical problems have occurred many times, since maintenance is complicated in such a remote high-mountain environment and because processes like soil thawing and freezing, rock falls, and other slope instabilities are very common. Nevertheless, a complete record of rainfall and soil moisture is available for 10 of the torrential events (four debris flows and six debris floods). Figure 7 shows the soil moisture values measured at 30 cm in depth at INF-SCARP1. The 10 torrential events are compared with soil moisture data from non-triggering rainfalls, which were selected for Imax_5min values larger than 12 mm/hr.

The relationship between the initial VWC before the rainfall and the increment of VWC due to the rainfall is presented in Figure 7a. A tentative trend is observed for the rainfalls that triggered torrential flows: a larger increase of soil moisture was measured when the soil was dryer at the beginning of the rainfall. In addition, maximum rainfall intensity recorded in 5 minutes was compared with the initial VWC (Figure 7b). A slight trend might be identified, which shows that a smaller rainfall is needed to trigger debris flows when the initial VWC is higher, although many more data would be needed to verify this correlation. Such a pattern was already observed during a rainfall analysis in Italy (Gregoretti and Dalla Fontana, 2007). Note that the debris flood triggered by the low-intensity rainfall of 12 mm/hr mobilized a small volume of about 100 m3 .

CONCLUSIONS Monitoring data on debris-flow triggering has been recorded at the Rebaixader catchment since 2009. A total of 11 debris flows and 24 debris floods were detected during this period. In this work we focused on the initiation mechanisms of these torrential flows by analyzing the critical rainfall conditions and the soil moisture related to water infiltration into the soil.

The results show that most of the torrential flows at the test site occurred in summer (between June and August) and at around 13:00 UTC. In contrast, the highest probability of rainstorms is about 1.5 months earlier (between April and July), which supports the hypothesis that antecedent rainfall, snowmelt, and/or soil moisture conditions are important for debris-flow triggering. The intensity and duration of rainfall are not included in this analysis, but previous studies at Rebaixader showed that most debris flows are provoked by short and intense rainstorms in summer,

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while spring rainfalls of lower intensity and longer duration normally do not trigger debris flows. In addition, a new updated threshold was defined that included total duration and mean intensity of the rainfalls.

Regarding the soil water dynamics, the VWC changes during rainstorms were analyzed. Results show that a higher soil moisture increment is produced when the soil is dryer at the beginning of a rainstorm.

Comparing rainfall and soil moisture measurements, the data indicate that the maximum 5-minute rainfall intensities required for the triggering of torrential flows are generally larger than the non-triggering rainfalls, as could be expected. Moreover, it seems that the initial soil moisture content affects the values of the triggering rainfalls, and smaller 5-minute rainfall intensities are necessary to trigger a torrential flow when soil moisture content is higher at the beginning of the rainstorm. However, a complete data set is available only for a small number of events. Therefore, additional data are necessary to confirm the former hypothesis and to define threshold values of soil moisture causing torrential flows.

ACKNOWLEDGMENTS The study was funded by the national research project called “Slope Mass-Wasting Under Climate Change (SMuCPhy),” granted by the Government of Spain (project reference number BIA 2015-67500-R) and co-funded by AEI/FEDER, UE. We thank the reviewers for their comments, which significantly improved the quality of the manuscript.

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Mitigation of Debris Flows—Research and Practice in Hong Kong KEN K. S. HO RAYMOND C. H. KOO JULIAN S. H. KWAN Geotechnical Engineering Office, Civil Engineering and Development Department, Hong Kong SAR Government, Civil Engineering and Development Building, 101 Princess Margaret Road, Ho Man Tin, Hong Kong, China

Key Terms: Geotechnical, Landslides, Modelling ABSTRACT Dense urban development on a hilly terrain coupled with intense seasonal rainfall and heterogeneous weathering profiles give rise to acute debris-flow problems in Hong Kong. The Geotechnical Engineering Office (GEO) of the Hong Kong SAR Government has launched a holistic research and development (R&D) programme and collaborated with various tertiary institutes and professional bodies to support the development of a comprehensive technical framework for managing landslide risk and designing debris-flow mitigation measures. The scope of the technical development work includes compilation of landslide inventories, field studies of debris flows, development and calibration of tools for landslide run-out modelling, back analysis of notable debris flows, physical and numerical modelling of the interaction between debris flows and mitigation measures, formulation of a technical framework for evaluating debris-flow hazards, and development of pragmatic mitigation strategies and design methodologies for debris-flow countermeasures. The work has advanced the technical understanding of debris-flow hazards and transformed the natural terrain landslide risk management practice in Hong Kong. New analytical tools and improved design methodologies are being applied in routine geotechnical engineering practice.

INTRODUCTION Natural hillsides cover over 60 percent of the land area of Hong Kong. Dense urban development on a hilly terrain coupled with intense seasonal rainfall and heterogeneous weathering profiles give rise to acute debris-flow problems in Hong Kong. The locations and timing of debris flow on natural hillsides cannot be predicted with precision. The severe rainstorm of 7 June 2008 highlights the potential vulnerability of developments located close to natural terrain in Hong Kong. This rainstorm caused several hundred land-

slides, including many debris flows that affected developed areas. Starting in 2010, systematic study and mitigation of natural terrain landslide risk have become core components of the Hong Kong Government’s Landslip Prevention and Mitigation Programme (LPMitP), which is managed by the Geotechnical Engineering Office (GEO), Civil Engineering and Development Department, Hong Kong SAR Government.

In order to tackle natural terrain landslide hazards, technical development work has been in progress by GEO through systematic mapping and studies of notable landslides. Advances have been also made in the understanding of the mechanisms and classification of natural terrain landslides and debris run-out modes, together with the formulation of risk management and hazard mitigation strategies.

Based on the state-of-the-art knowledge, GEO developed a technical framework for evaluating landslide hazards (Ho et al., 2015) and implemented research and development (R&D) studies to advance the strategy and design of mitigation measures in order to reduce landslide risk to a level as low as reasonably practicable (ALARP). The GEO adopted a “react-toknown-hazard” principle in dealing with natural terrain hazards affecting existing developments, i.e. to carry out studies and mitigation actions where significant hazards become evident. Under the LPMitP, which commenced in 2010, about 30 natural terrain catchments with known hazards to existing buildings or important transport corridors are systematically dealt with annually.

This paper presents the progressive development of the natural terrain risk mitigation practice in Hong Kong, and the advances made by the R&D work. The practical challenges in relation to the design, construction, and maintenance of landslide mitigation measures are discussed.

NATURE OF NATURAL TERRAIN LANDSLIDES Hong Kong has a population of over 7 million and a small land area of 1,100 km2 , only 15 percent of

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Figure 1. Landslide-prone natural terrain of Hong Kong.

which is developed land. The terrain is hilly, with 75 percent of the land being steeper than 15° and 30 percent being steeper than 30°. Rainfall intensities exceeding 70 mm/hr and 300 mm/d are not uncommon. The encroachment of urban development on hilly terrain together with intense seasonal rainfall and variable weathering profiles give rise to acute slope safety issues in Hong Kong. This is reflected by a death toll of over 470 fatalities due to landslides since the 1940s (Ho et al., 2016).

Hong Kong comprises a hilly terrain with dense urban development close to steep hillsides. The natural terrain is typically mantled by weak and heterogeneous saprolite or colluvium, which is susceptible to shallow, small- to medium-scale landslides (see Figure 1), usually several hundred cubic meters in size, or occasionally more sizeable landslides, due to loss of suction or buildup of local perched water pressure as a result of intense rainstorms. This can be further complicated by ongoing progressive deterioration of the condition of the natural hillside due to successive heavy rainstorms.

These landslides can develop into debris flows where debris reaches drainage lines, with surface water flow resulting in increased mobility (i.e., larger velocity and greater run-out distance). Based on the landslide inventory, on average about one landslide occurs each year for every 2 km2 of natural hillside in Hong Kong.

Occasionally, larger-scale debris flows (see Figure 2) can occur given adverse site settings and intense rainfall. The inventory, compiled using aerial photographs, contains records of more than 100,000 past failures on the natural hillsides in Hong Kong (MFJV, 2007).

Apart from structural, geological, and hydrogeological factors, unfavorable topographical factors can also contribute to increased susceptibility to landslide initiation, such as a break in slope, topographic depres-

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Figure 2. The 1990 channelized debris flow at Tsing Shan.

sion, head (i.e. the highest point) of a drainage line, and presence of regolith downslope of a rock outcrop (GEO, 2004). The design of landslide mitigation measures in Hong Kong makes reference to the findings of the natural terrain landslide hazard study with due consideration of geological and geomorphological factors pursuant to the guideline given in GEO Report No. 138 by Ho and Roberts (2016). Channelized debris flows along incised drainage lines or pronounced topographic depressions with concentrated surface water flow tend to be more mobile (as compared to landslides on a planar hillslope) with notable velocities (in the order of 10 m/s or more). Due cognizance needs to be taken of the nature of channelized debris flows in the design of mitigation measures. Debris flows can occur in pulses and may entrain loose materials due to erosion along the flow path. They can also engulf large boulders, which can be isolated or in clusters occurring as a bouldery front, typically with an inverse grading due to reverse segregation (see Figure 3). The complex and transient nature of such surge two-phase flows can be further complicated by the presence of large broken tree trunks. Additionally, there is the possibility of dam break pulses occurring along the drainage line due to buildup of a temporary debris dam.

NATURAL TERRAIN LANDSLIDE RISK MANAGEMENT The GEO has launched a holistic R&D program and collaborated with various tertiary institutes and professional bodies to support the development of a comprehensive technical framework for managing landslide risk and designing debris-flow mitigation measures with more scientific rigor, which incorporates the application of fundamental risk manage-

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Figure 3. Bouldery front of channelized debris flows observed in June 2008 in Hong Kong.

ment concepts at the policy administration level in LPMitP. It has now evolved into a comprehensive regime which embraces a range of initiatives that serve to manage the landslide risk through an explicit riskbased strategy and approach in a holistic manner. The scope of the technical development work, focusing on hazard identification and risk mitigation, includes compilation of landslide inventories, field studies of debris flows, development and calibration of tools for landslide mobility modelling, back analysis of notable debris flows, physical and numerical modelling of the interaction of debris flows and design of mitigation measures, formulation of a technical framework for evaluating debris-flow hazards, and development of pragmatic mitigation strategies and design methodologies for debris-flow countermeasures. The work, which spans the last two decades, has advanced the technical understanding of debris-flow hazards and transformed the natural terrain landslide risk management practice in Hong Kong. The principal goals of the holistic slope safety system are to reduce landslide risk to the community through a policy of priority and partnership, and to manage public perception and tolerability of landslide risk in order to avoid unrealistic expectations. New analytical tools and improved design methodologies are also being applied in routine geotechnical engineering practice by local practitioners, including geotechnical engineers and engineering geologists.

Risk-based priority ranking systems, which consider both the likelihood and consequence of slope failure, have been developed to ensure that the most deserving catchment areas are selected for priority action under LPMitP. The ranking systems incorporate extensive local experience and insights in failure mechanisms for identifying vulnerable natural hillside catchments, including consideration of different types of facilities and infrastructures.

The GEO has also pioneered the development of quantitative risk assessment techniques to manage landslide risk as well as to evaluate the performance and cost-effectiveness of the government’s efforts in reducing landslide risk using engineering

works. Territory-wide quantitative risk assessments carried out by GEO serve to define the scale of the respective landslide hazards, evaluate the risk portfolio and distribution, provide a basis for formulating appropriate risk reduction strategies, and setting of realistic slope safety goals for the systematic program to mitigate hazardous catchments.

Landslide risk can be quantified as follows: Risk = P × C,

(1)

where P is probability of occurrence of landslide hazard, and C is landslide consequence.

The risk posed to a given facility can be managed by reducing P by means of stabilization works or by reducing C through mitigation measures, or by doing both. For existing facilities such as buildings or roads subjected to natural terrain hazards, slope stabilization on the steep hillside is often neither practically nor economically and environmentally justifiable.

Instead, defensive mitigation strategy involving the implementation of mitigation measures (such as debris-resisting rigid barriers, steel flexible barriers, or boulder fences) is generally more practicable (Ho et al., 2015). In view of the complexities and uncertainties associated with debris flows, emphasis has been given by GEO in developing and adopting pragmatic and suitably simplified barrier design methods. An overview of the advances in geotechnology for slope stabilization and landslide risk mitigation was given by Ho (2005) and Ho (2019).

EVOLUTION OF BARRIER DESIGN PRACTICE IN HONG KONG Phase 1—Development of Barrier Design Guidelines Traditionally, the assessment of natural terrain landslide hazards was undertaken by engineering geologists through an engineering geology approach, with a qualitative risk assessment and the necessary risk mitigation measures determined largely by experience and judgement. The process was typically not transparent.

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Starting in the late 1990s, significant advances have been made by GEO in developing practical numerical tools for debris mobility assessment and calibrating the rheological models and input parameters through systematic back analysis of local case histories of the more mobile landslides (Kwan and Sun, 2007). The GEO developed two in-house numerical models, namely 2dDMM and 3dDMM, for landslide debris mobility analysis. These algorithms have been used to back analyze channelized debris flows and open hillside failures in Hong Kong as well as published case studies in other countries. Advances in numerical modelling of landslide debris movement have greatly enhanced the capability of assessing debris influence zones and the rational design of risk mitigation works. GEO also promulgated guidance on the assessment of debris discharge, flow velocity and thickness, debris run-up, retention capacity of barriers, and surface drainage provisions (GEO, 2014).

Design retention volume for debris-resisting barriers duly considered the total discharge of landslide source volume and the volume of entrainment in the landslide run-out path. The barrier height was designed with consideration given to debris run-up against the barrier. Debris mobility analysis and field mapped debris deposition profiles of landslide case histories have been reviewed. Based on the results of the review, guidance on design good practice and key considerations to be made for assessing the design retention volume and surface drainage provisions were recommended.

Based on the findings of back analyses of past natural terrain landslides, guidelines on the assessment of debris mobility of future natural terrain landslides for design purposes were promulgated by GEO for reference by the practitioners. The technical guidance on mitigation measures promulgated by GEO at that time covered primarily the design of rigid barriers against debris and boulder impact. In developing the guidance, a holistic approach was adopted, including benchmarking against international practice and reviewing relevant laboratory and field studies, back analysis of instrumented field data, performance review of barriers upon impact by landslides, etc. (Kwan, 2012). In essence, the basis of the guidance promulgated at this early stage was largely empirical, supported by literature review, limited field studies, and scarce instrumented data.

Phase 2—Rationalization and Enhancement of Barrier Design Guidelines From about 2010 onwards, GEO initiated further R&D work focusing on the use of flexible and rigid barriers to arrest natural terrain landslides.

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The advances have led to an improved understanding, which enables the guidance on barrier design to be rationalized and expanded. The basis of the enhanced design approaches is multipronged, including back analysis of field observations, use of physical models (laboratory flume), numerical techniques, analytical solutions, etc. A key consideration is to build in sufficient robustness to cater for the uncertainties in the field associated with the complex characteristics and variable compositions of debris flows. The work culminated in the promulgation of new or improved design guidance covering the following areas: (1) a design methodology for the impact of debris and boulders on rigid and flexible barriers using a force approach (Kwan and Cheung, 2012); (2) a design methodology for debris impact on flexible barriers using the energy approach based on insight from Discrete Element analysis and a simplified analytical framework (Sun and Law, 2015); (3) a design methodology for debris impact on rigid or flexible barriers using the force approach, including a multiple-phase debris impact model, which accounts for dynamic impact pressure and static earth pressure of the deposited debris, with due allowance made for the variation in debris velocities at different phases of debris impact as computed from debris mobility analysis (GEO, 2015; Koo et al., 2016), together with allowance for the additional drag force in the event the debris overtops the barrier; (4) an analytical framework for the design of multiple barriers (with the upstream barriers acting as check dams) based on a newly developed staged mobility analysis (Kwan et al., 2015); and (5) a design framework for the use of prescribed flexible barriers in mitigating open hillslope landslides in order to streamline the design process (GEO, 2014).

The current design approaches adopted in Hong Kong are summarized in Figures 4, 5, and 6, and the multiple-phase debris impact model is developed from observation of the results of centrifuge tests and laboratory flume tests estimating deposition volume of each phase using maximum frontal thickness (hmax ) and discretized debris-flow impact velocity.

The concepts of a composite structure comprising a rigid barrier with baffles to dissipate the energy of landslide debris and arrest some of the boulders, together with a cushioning layer on the rigid barrier front face to help reduce boulder impact load, are promoted to enhance robustness.

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Figure 4. Summary of the energy approach for design of flexible barriers (Sun and Law, 2015).

Figure 5. Summary of the force approach and key design checks for flexible and rigid barriers (Kwan, 2012).

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minimizing the cut-and-fill balance for site formation works. The configuration of rigid debris-resisting barriers can be altered in design more efficiently to minimize earthwork costs, as well as environmental and visual impact. Figure 7 shows the rigid barrier modelling with cut-and-fill volumetric analysis in BIM. Phase 3—Optimization of Barrier Design To validate or calibrate the various design approaches and improve the understanding of barrier behavior with a view to optimizing barrier design, GEO has continued to undertake in-house development work and collaborate with practitioners and with local tertiary institutes and overseas experts in pursuing various R&D initiatives. These include the use of state-of-the-art physical modelling (centrifuge as well as laboratory and field flume tests) to study mechanisms, application of advanced numerical modelling, and development of new analytical approaches as detailed below.

Figure 6. Simplified multiple-phase impact model for force approach (GEO, 2015). Assessment of geotechnical stability of barriers is undertaken for successive impacts. The impact velocity is estimated based on the debris velocity hydrograph and volume of debris deposition involved.

Apart from the promulgation of technical design guidelines, GEO has also published guidance on other related design and construction issues as follows: (1) suitable detailing of rigid and flexible barriers (e.g., avoiding damage to posts in flexible barriers due to boulder impacts, improving drainage provisions, enhancing resilience against scouring of the substrate of the barrier foundation, and detailing of a deflector at the crest of a rigid barrier to avoid spillage of debris due to debris run-up upon impact, etc.); (2) improvement of contract specification for new flexible barriers to enhance durability based on a performance review of about 100 local barriers, together with retrofitting of deteriorated steel components of existing barriers; and (3) guidance on slope landscaping and use of bioengineering techniques to improve the aesthetics and biodiversity of the plants on or close to the barriers (GEO, 2011).

GEO is currently also using a Building Information Modelling (BIM) tools to examine buildability issues and construction sequencing in order to optimize the design layout of barriers and minimize cut-andfill operations. BIM is used to optimize the layout by

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Displacement-Based Approach for Assessing Geotechnical Stability and Flexural Response of Rigid Barriers Conventional force-based design approaches for geotechnical stability assessments often result in overdesign of rigid barriers subject to debris impact, which is transient in nature. The newly proposed displacement-based approach could provide a more realistic evaluation of the performance of rigid barriers subject to boulder impact. Based on fundamental principles of dynamic analysis, Lam and Kwan (2016) developed closed-form formulae for estimating the translational and rotational movements, as well as the flexural deflection and tensile reinforcement strain of rigid barriers, due to boulder impact (see Figure 8). A series of small-scale impact tests were carried out to verify the predictions using this displacement-based approach (Lam et al., 2017), and good agreements between analytical results and experimental data were obtained. A comparison was made between the displacement-based approach and the conventional limit equilibrium analysis. Based on the impact scenarios that are typically encountered in routine design (i.e., a 1-m-diameter boulder with a velocity of 10 m/s impacting onto a typical 6-m-high, 10-m-long rigid barrier), the predicted translational and rotational movements of the barrier were found to be insignificant based on the displacement-based approach.

Large-scale tests were also carried out to investigate the structural response of a rigid barrier subject to impact by a solid steel impactor, which successfully

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Figure 7. BIM modelling for rigid debris-resisting barriers.

validated the enhanced flexural stiffness method. The above have demonstrated that substantial cost savings in structural design could potentially be achieved in barrier designs by accounting for the inertia effect of a rigid barrier.

Field Testing of Cushioning Materials for Reducing Boulder Impact Load on Rigid Barriers Field monitoring and observations together with recent centrifuge tests indicate that impacts due to hard inclusions (i.e., boulder front) of a debris flow can re-

sult in high-magnitude and transient loads on a rigid barrier. With a view to damping out these force spikes, a systematic study on the use of different cushioning materials to shield the barrier was initiated by the GEO. In general, the cushioning materials are deformable and thus capable of prolonging the impact process and attenuating the impulsive forces due to the hard inclusions. A large-scale instrumented pendulum impact test facility involving a 1.16-m-diameter concrete ball (2,000 kg in weight) with a maximum impact velocity of 8.4 m/s and a kinetic energy of up to 70 kJ suspended by a 6-m-high steel frame was set up. Four types of cushioning materials, namely,

Figure 8. Design framework for displacement approach (Lam and Kwan, 2016). Translational and rotational displacements of barriers induced by boulder impact are calculated based on the principle of energy conservation with consideration of boulder impact energy (KE) and energy dissipations due to basal friction and rise in centre of gravity.

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Figure 9. Large-scale physical impact test on rigid barrier with cushioning materials (Lam et al., 2018).

rock-filled gabions, recycled glass cullet, ethylene-vinyl acetate (EVA) foam, and cellular glass, were tested (see Figure 9). The results showed that the cushion layer could effectively reduce the maximum impact forces, although it would become less effective after successive impacts (Lam et al., 2018; Ng et al., 2018). The test data were also used to calibrate numerical models for further parametric studies.

Recent large-scale impact tests have also shown the effectiveness of a gabion cushioning layer in preventing localized structural damage (such as cracking, penetration, perforation, and scabbing) in a reinforced concrete barrier, and in substantially reducing the flexural deflection at the barrier crest (by 67 percent to 90 percent).

Study on Use of Baffles to Dissipate Energy of Debris Flows Baffles are flow-impeding structures installed along the flow path to dissipate the energy of debris flows and screen out large boulders. A series of instrumented flume tests and back analyses were carried out to investigate dry sand flow impact on an array of baffles (Choi et al., 2014). The influence of baffle height, number of rows, and transverse and longitudinal spacing of baffles was systematically examined. These small-scale tests with dry sand indicated that increasing the baffle height from 0.75 to 1.5 times the approaching flow depth would lead to a more effective development of subcritical flow conditions, which promote energy dissipation of the debris. Increasing the number of rows

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from a single row to a staggered three-row array resulted in about 70 percent additional energy loss. Energy loss is attributed to the deflection of granular jets and back-water effects.

In addition, a large-scale instrumented pendulum impact test facility, which is similar to the setup as shown in Figure 9, was used for investigating the dynamic performance of boulder impact on baffles with a maximum impact velocity of 5 m/s and a kinetic energy of up to 50 kJ. Different types and sizes of baffles, such as steel square hollow column with grouting (SC) (200 × 200 SC) and steel square hollow column without infill grouting (SH) (200 × 200 SH), steel H universal column (UC) (305 × 305 UC) and steel frame with a height of 1.5 m, were tested. The results show that the structures of baffles could stop large boulder impact and effectively dissipate the impact energy by structural yielding with limited deformation (see Figure 10), especially the hollow section (CMW, 2019).

Parametric Study of Varied Debris Composition and Different Barrier Configurations Using Physical Tests Centrifuge and/or flume tests were conducted for various types of mitigation structures (e.g., flexible barrier, curved rigid barrier, slit barrier, etc.) to examine the effects of impact mechanisms and influence of different debris compositions under controlled conditions (Choi et al., 2016; Ng et al., 2016; and Song et al., 2017). During the frontal impact of a two-phase debris flow without hard inclusions, the measured dynamic pressure coefficient in the hydrodynamic approach is

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Figure 10. Field testing of boulder impact on baffle structures (CMW, 2019).

close to unity (which confirms the principle of conservation of momentum) for both rigid and flexible barriers that are upright. Increasing the solid fraction of a debris flow was found to promote transition from runup mechanism to pile-up mechanism. These two mechanisms are illustrated in Figure 4. A viscous fluid-like debris flow will involve a pile-up mechanism upon impacting on a barrier. The debris is deflected and shoots up along the barrier wall stem until the kinetic energy of the debris is fully dissipated. For a frictional debris flow, the frontal debris is deposited behind the barrier wall and forms a wedge-like stationary mass. Debris material from further behind will travel onto the back of the wedge, which is referred to as a run-up mechanism. Furthermore, test results indicated that the presence of large hard inclusions (boulders) in the debris flow is liable to induce transient force spikes reflecting significant impulse loading on a rigid barrier (Kwan et al., 2018).

Advanced Coupled Interaction

Analysis

of

Debris-Barrier

Advanced numerical modelling has been adopted to simulate debris-barrier interaction using the computer program LS-DYNA. Various researchers (e.g., Kwan et al., 2015, 2019; Koo et al., 2018) have demonstrated that the arbitrary Lagrangian-Eulerian method in LS-DYNA appears to be a promising tool for modelling debris flow and debris-barrier interaction. Such modelling has been benchmarked against laboratory flume tests and actual landslide cases in terms of debris run-out characteristics. In the conventional approach, landslide mobility analyses and structural analyses of the barrier are carried out separately. The landslide mobility is first simulated under a free-field condition to obtain design parameters such as flow velocity and

depth (e.g., 3d-DMM by Kwan and Sun, 2007), which are then converted into a pseudo-static impact force as input to a separate structural model (e.g., computer program NIDA-MNN by Sze et al., 2018). This latter approach, however, neglects the dynamics of debrisbarrier interaction.

Coupled analyses can be carried out using LSDYNA, with the landslide mass modelled as a continuum in a finite element formulation. The results successfully reproduce the deformation and forces in various structural components as observed in instrumented case studies (Cheung et al., 2018). The coupled analyses also provide insight on the energy dissipation of landslide debris in the debris-barrier interaction process. The preliminary findings are that the overall strain energy absorbed by the flexible barrier upon debris impact only amounts to a fairly small portion (generally less than 35 percent based on parametric studies) of the total debris impact energy, due to internal distortion of the debris and changes in momentum flux direction under a debris run-up mechanism upon impact.

To further optimize the design of flexible barriers, the GEO in-house design team adopted the advanced coupled analysis in LS-DYNA to account for the dynamic effects of debris-barrier interaction. The LS-DYNA model can simulate the whole process of debris-flow mobility from the source to impact on the flexible barriers at the downstream end (see example in Figure 11). The structural components also can be explicitly modelled, including force-displacement characteristics of brake elements, and detailed connections between shackles, ring nets, and cable ropes.

It is noteworthy that the continuum model adopted in LS-DYNA has certain limitations as it may not fully simulate particle-fluid interaction and the presence of hard inclusions at the debris front. Other

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Figure 11. LS-DYNA simulation of debris impact on flexible barrier.

research tools such as coupled analysis using discrete element models and computational fluid dynamics models are being used to examine the potential effects of particle-fluid interaction (Li and Zhao, 2018).

WAY FORWARD The above studies have provided useful yardsticks for calibrating or bracketing existing design approaches. They further highlight the potential scope for further rationalizing and optimizing the design of landslide mitigation measures; e.g., the numerical coupled analyses suggest that the impact energy transmitted to a flexible barrier could be much lower than that assessed by the current design approach because of internal distortion of the debris and changes in momentum flux direction. Similarly, the displacement approach, corroborated by laboratory model tests, suggests that the dynamic force exerted on a rigid barrier is much lower than conventional elastic theory describes if the inertia effect is duly considered.

Notwithstanding the above, it should be borne in mind that the physical models are constrained by the use of idealized materials as compared to real-life debris flows, and potentially by uncertainties involved in scaling up the observed behavior.

ONGOING CHALLENGES Some ongoing challenges and pertinent issues faced by the practitioners are highlighted below: (1) Behavior of energy dissipation (or brake) elements: Brake elements are an essential component of a flexible barrier in dissipating the impact en-

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ergy. However, there is as yet no internationally recognized testing standard with which to check their stress-strain characteristics at an appropriate strain rate and assess their degree of variability.

Based on limited site observations following debris impact (e.g., Kwan et al., 2014), there is an element of uncertainty regarding the actual behavior of different types of brake elements, particularly when they become buried by landslide debris (as some of them apparently were not activated following debris impact and barrier deformation).

(2) Potential for escalated level of landslide hazards due to climate change: Recent local experience with extreme rainfall events has shown that the response of natural hillsides in Hong Kong is highly sensitive to more severe rainfall in that the number, scale, and mobility of landslides are considerably elevated. The assessment of the landslide hazard to be managed during the design life of the mitigation measure is fraught with considerable uncertainty, given that the relatively short time window available for compiling the landslide inventory may not have captured the extreme rainfall events. This is exacerbated by the increased likelihood of occurrence of more frequent and intense rainfall events associated with potential climate change. The possibility of the barriers being under-designed and overwhelmed by more sizeable and/or more mobile landslide hazards than those anticipated by the designers based on prior knowledge and experience calls for a paradigm shift in the strategy for managing the associated landslide risk. A recent initiative by the GEO is the development of smart barriers (see Figure 12) incorporating the use of real-time wireless sensors and Internet

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Figure 12. Smart rigid barrier system (incorporating the use of real-time wireless sensors, Internet of Things [IoT], and cloud computing technology to provide early warning of landslide impact).

of Things (IoT) and cloud computing technology to provide early warning of landslide impact and facilitate timely emergency response. Other recent advances in the management of landslide risk associated with extreme weather events in Hong Kong entail improvement of the landslide warning system to incorporate an alert system specifically for debris flows on natural terrain (Ho et al., 2017), development of rainfall-based landslide susceptibility zoning (Ko and Lo, 2018), and innovative approaches in enhanced public education.

These are some of the non-structural measures of landslide risk management under a systems approach in addressing landslide risk in a holistic manner.

(3) Durability and long-term maintenance of flexible barriers: A cost-effective long-term strategy for maintenance of flexible barriers is needed, given that the steel components are subject to progressive deterioration in hot and humid climates like Hong Kong. It is also necessary to have improved knowledge on the rate of corrosion of steel components and various forms of treatment in corrosive environments.

CONCLUSIONS The design of landslide risk mitigation measures for debris flows and other flow-like landslides is highly challenging in light of the many uncertainties involved.

A holistic and progressive approach has been adopted in Hong Kong to improve our fundamental knowledge of debris flows and to provide scientific insight into the behavior of debris-resisting landslide barriers as a result of debris-structure interaction (e.g., effect of Froude number of debris flows on impact behavior, influence of debris impact mechanisms, presence of a dead zone associated with debris deposition upon initial impact, effect of varied debris composition, including the solid fraction, postulated effect of suction on debris mobility and impact behavior, influence of compressibility of debris flow on impact behavior, etc.). The systematic technical development work carried out on landslide mitigation measures has led to an improved understanding of the related mechanisms and the controlling parameters. Nevertheless, it is important to remain pragmatic and to strike a suitable balance in translating research findings into practice with due account taken of the simplifications made

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in the model testing and computational analyses as opposed to the complex and random nature of real debris flows in the field. Due allowance should also be made in the design for enhanced robustness and redundancy in managing the uncertainties.

Apart from the consideration of appropriate technical standards and improved design methodologies, there are other pertinent issues that are of relevance to practitioners, including guidance on proper detailing of the works, consideration of buildability, the structural form to be adopted (e.g., re-supported flexible barrier versus side-anchored flexible barriers), an appropriate acceptance system for flexible barrier products for quality assurance and quality control, landscaping works, etc.

ACKNOWLEDGMENTS This paper is published with the permission of the Head of Geotechnical Engineering Office and Director of Civil Engineering and Development, Hong Kong SAR Government, China.

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Velocity and Volume Fraction Measurements of Granular Flows in a Steep Flume LUCA SARNO* Department of Civil Engineering, University of Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy, and Institute of Fluid Dynamics (FDY), Technische Universität Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany

MARIA NICOLINA PAPA LUIGI CARLEO Department of Civil Engineering, University of Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy

PAOLO VILLANI Department of Civil Engineering, University of Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy, and University Consortium for Research on Major Hazards (CUGRI), Salerno, Italy Via Giovanni Paolo II, 132 - 84084 - Fisciano, Italy

Key Terms: Debris Flows, Granular Flows, Volume Fraction, Particle Image Velocimetry (PIV), Stochastic-Optical Method (SOM), Rheological Stratification ABSTRACT Laboratory experiments on granular flows remain essential tools for gaining insight into several aspects of granular dynamics that are inaccessible from field-scale investigations. Here, we report an experimental campaign on steady dry granular flows in a flume with inclination of 35°. Different flow rates are investigated by adjusting an inflow gate, while various kinematic boundary conditions are observed by varying the basal roughness. The flume is instrumented with high-speed cameras and a no-flicker LED lamp to get reliable particle image velocimetry measurements in terms of both time averages and second-order statistics (i.e., granular temperature). The same measuring instruments are also used to obtain concurrent estimations of the solid volume fraction at the sidewall by employing the stochastic-optical method (SOM). This innovative approach uses a measurable quantity, called two-dimensional volume fraction, which is correlated with the near-wall volume fraction and is obtainable from digital images under controlled illumination conditions. The knowledge of this quantity allows the indirect measurement of the nearwall volume fraction thanks to a stochastic transfer function previously obtained from numerical simulations of

*Corresponding author email: sarno@fdy.tu-darmstadt.de; lsarno@unisa.it

distributions of randomly dispersed spheres. The combined measurements of velocity and volume fraction allow a better understanding of the flow dynamics and reveal the superposition of different flow regimes along the flow depth, where frictional and collisional mechanisms exhibit varying relative magnitudes.

INTRODUCTION Granular materials and liquid-granular mixtures are involved in several hazardous geophysical flows, such as debris flows, secondary pyroclastic flows, and avalanches. However, many aspects of their dynamics are not completely understood. In addition to numerous numerical and field-scale investigations (e.g., Iverson and Vallance, 2001; Medina et al., 2008; Kuo et al., 2009; Iverson and George, 2014; Sarno et al., 2017; Papa et al., 2018; Tai et al., 2019; and Amicarelli et al., 2020), laboratory experiments on granular media are a useful tool to get insight into the granular dynamics (e.g., Capart et al., 2002; G.D.R. MiDi, 2004; Pudasaini et al., 2005; Sarno et al., 2011a, 2018a; and Carleo et al., 2019). Granular flows may exhibit a rich variety of flow regimes, ranging from a solid-like behavior corresponding to slow deformations and mainly frictional dissipation mechanisms to a gas-like behavior with strong collisions among the grains. An intermediate regime, very frequent in nature and known as dense-collisional, is characterized by the coexistence of collisional and frictional mechanisms. To date, a constitutive law, capable of reliably describing all these regimes, is still lacking. Moreover, some peculiarities of the granular dynamics, such as the effects of fixed boundaries (e.g., Jop et al., 2005;

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Sarno et al., 2011b, 2018a), the occurrence of a rheological stratification (e.g., Armanini et al., 2005; Sarno et al., 2014), and the existence of non-local momentum exchange mechanisms (e.g., Mills et al., 1999; Pouliquen and Forterre, 2009), still require some effort to be totally understood. The rheophysical classification of real debris flows is even more complex due to the polydispersity of the grain size distribution and the interplay between solid and liquid phases (e.g., Bardou et al., 2003). Moreover, it should be noted that different rheological behaviors may also occur during the same debris-flow event due to the time-space evolution of the debris flow wave and the consequent local variations of the grain size distribution and water content.

In this regard, it is worth mentioning that a very large variability of debris flow regimes has been reported in a few field-scale investigations on the Rio Gadria catchment (Italy, BZ) (Theule et al., 2018; Coviello et al., 2019; Hürlimann et al., 2019; and Nagl et al., 2020), where collisional and viscoplastic behaviors were observed even in the same debris-flow event.

Considering the aforementioned difficulties, the flow velocity and solid volume fraction fields represent relevant quantities to be investigated in a laboratory setting. It is well known that the volume fraction is strongly coupled with the rheological behavior of the granular medium in free-surface flows, where a stressfree boundary condition takes place at the free surface. Yet, while optical techniques for measuring the flow velocity (e.g., particle image velocimetry [PIV] and particle tracking velocimetry [PTV]) have reached a certain maturity (e.g., Pudasaini et al., 2005; Jesuthasan et al., 2006; and Sarno et al., 2018b, 2019a), the estimation of the volume fraction by optical noninvasive methods is much more challenging and arduous (e.g., Capart et al., 2002; Spinewine et al., 2003; Sheng et al., 2011; and Sarno et al., 2016).

Here we present an extensive laboratory campaign on steady dry granular flows carried out in a rectangular flume with various basal surfaces. For obtaining reliable velocity measurements and also information about second-order statistics of the velocity field, such as the granular temperature, we chose a window deformation multi-pass PIV approach (Sarno et al., 2018b), and we specifically employed the open-source code PIVlab (Thielicke, 2014; Thielicke and Stamhuis, 2014). Additionally, in order to estimate the volume fraction profiles at the flume sidewall, we employed the stochastic-optical method (SOM) proposed by Sarno et al. (2016, 2019b). Sarno et al. (2018a) reported an investigation on similar chute flows with chute inclination angle of 30°, where they observed a rich variety of velocity profiles, depending on the roughness of the basal surface and on the sidewall resistances, also in turn depending on the flow depth. More recently,

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Table 1. Properties of the granular material.

Parameter Chemical composition Grain color Grain density, ρs Mean diameter, d Relative standard deviation of d Young’s modulus Poisson ratio Random loose volume fraction Internal angle of friction, ϕ Coefficient of restitution, e

Value Polyoxymethylene acetal plastic Matte white 1,410 kg/m3 3.3 mm 5% 2,700 MPa 0.35 0.6 27° 0.85

Carleo et al. (2019) presented a complementary laboratory study where the SOM method proposed by Sarno et al. (2016) was used for the first time for the estimation of the sidewall volume fraction profiles in steady granular flows. Yet the study was limited to flows on a smooth bed. As an extension of the works

by Sarno et al. (2018a) and Carleo et al. (2019), here we present a new data set, obtained with the same apparatus but with a slightly higher chute inclination angle of 35°. The employment of several bed surfaces allowed us to investigate different basal kinematic boundary conditions (KBC), namely, slip KBC, no-slip KBC, and also an intermediate no-slip KBC where grain rolling and saltations are made possible by the relatively low bed roughness and high inclination of the flume. Due to the larger mass forces, the shapes of the velocity profiles previously observed by Sarno et al.

(2018a) are only partially observed in the present campaign. Hence, these new experimental findings allowed us to better understand and ascertain the limits of the flow regimes identified in our previous works.

THE EXPERIMENTAL APPARATUS AND THE MEASURING METHODS The experimental apparatus, identical to that employed by Sarno et al. (2018a), consists of a 2-m-long transparent Plexiglas flume with a rectangular cross section of width equal to 8 cm, corresponding to 24 grain diameters. All the experiments hereafter reported were carried out with a flume inclination, α, of 35°. Additionally, the granular medium employed in this study is the same previously employed by Sarno et al. (2018a) and Carleo et al. (2019) and is composed of acetal-polymeric (polyoxymethylene [POM]) spheroidal beads with mean diameter d = 3.3 mm.

Other relevant properties of the granular medium are listed in Table 1.

A reservoir for the granular medium, equipped with an external hopper (total capacity 40l), was located in the upper part of the channel (Figure 1a). In order

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Figure 1. (a) Sketch of the laboratory equipment (x-z view). (b) y-z view. (c) Locations of the high-speed camera and of the LED lamp.

to observe different flow rates, the granular material was allowed to flow down through an adjustable gate located close to the basal surface of the flume. The investigated range of gate openings is 5–14 cm. For each gate opening, after a transient phase, an intermediate steady state lasting several seconds was observed. A good experimental repeatability was achieved by controlling the relative humidity of air to values greater than 60 percent, to limit the electrostatic forces among POM grains and the flume boundaries as much as possible.

The main geometrical property characterizing the roughness of the flume basal surface is represented by the characteristic length of roughness, that is, the average length of bumps/asperities in the surface. Different flume basal surfaces with various roughness were investigated: 1. Smooth Bakelite surface (hereafter denoted by the symbol S) with a characteristic length of the roughness 10 μm 2. Sandpaper linings with characteristic lengths of the roughness of 162 μm (corresponding to grit P100 FEPA/ISO 6344, hereafter denoted by P100), 269 μm (P60), and 425 μm (P40) 3. Grain-type basal surface (hereafter denoted by G) made up by randomly gluing the POM grains on a smooth surface, so that the characteristic length of roughness was d/2 = 1.65 mm The laboratory flume was equipped with the following instrumentation devices: a load cell (model Laumas AZL-50 kg with accuracy of 8 g) placed at the outlet of the flume for the estimation of the mass flow rate, two digital high-speed cameras (by AOS Technologies Corporation), and a planar no-flicker LED lamp (model PhotoSonics MultiLED-LT). The camera model AOS S-PRI was placed aside the chan-

nel to concurrently measure the sidewall velocity and the volume fraction profiles at the cross section under study, located 40 cm downstream of the inflow gate (Figure 1). A second camera (model AOS Q-PRI) was positioned above the channel to measure the velocity profile at the free surface in the same cross section (x = 40 cm). For reliable PIV analyses and consistent volume fraction estimations, the cameras’ sampling rates were set equal to 1 kHz. The LED lamp was located 32 cm away from the side of the channel. The angle of incidence of light, ζ , with respect to the normal to the sidewall was precisely set equal to 25° (Figure 1c).

The position of the lamp and, especially, the precise regulation of ζ are crucial for accurate volume fraction measurements, as will be described in more detail below.

Using the open-source code PIVlab (Thielicke and Stamhuis, 2014), a window deformation multi-pass PIV approach was employed for obtaining velocity measurements at the sidewall and at the free surface.

The PIV is a well-established technique in fluid mechanics and is based on the maximization of the crosscorrelation function between two frames delayed by a short time interval (e.g., Adrian, 2005). When digital images are used, the cross-correlation task is carried out in a discretized fashion. In order to reliably extend the PIV approach to granular flows, some modifications of the classical PIV should be considered (e.g., Eckart et al., 2003; Sanvitale and Bowman, 2016; and Sarno et al., 2018b, 2019a). The use of the window deformation approach is practical to reduce gradientbias errors, especially in the case of highly sheared granular flows, which are frequent in nature. In addition, the multi-pass approach, which is based on a progressive refinement of the interrogation window, is particularly appropriate for granular flow applications so as to obtain a high spatial resolution without

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loss-of-pairs errors (Sarno et al., 2018b). In the present application, we employed the same PIV settings of Sarno et al. (2018a), to which we refer the reader for further details. Considering the theoretical accuracy of PIVlab reported to be of the order of 0.02 pixel/frame (Thielicke, 2014; Thielicke and Stamhuis, 2014) and taking into account the specific image scales of our video recordings, the accuracy of the velocity measurements in the present application is 0.004 m/s.

The measurement of the volume fraction was obtained by using the stochastic-optical method (SOM) proposed by Sarno et al. (2016, 2019b, 2020) and recently employed for estimating the sidewall volume fraction profiles in chute granular flows by Carleo et al.

(2019). This method, thanks to a highly controlled steady illumination coming from a given angle of incidence ζ , allows the estimation of the near-wall volume fraction, c3D , by means of a measurable quantity named two-dimensional volume fraction c2D and defined as follows. With reference to a given interrogation window lying on the transparent wall, c2D is defined as the ratio between the area of the projections on of all illuminated and visible grain portions and the total area of . A stochastic transfer function between c2D and c3D was found by extensive numerical investigation based on Monte Carlo simulations of randomly dispersed spheres at different volume fractions. The transfer function of exponential type is reported as follows: c3D = f (c2D , ζ ) = a (ζ ) exp (b (ζ ) c2D ) ,

(1)

where a and b are parameters depending solely on ζ (Sarno et al., 2016). A local binarization formula requiring the calibration of one threshold parameter was proposed for the estimation of c2D from grayscale digital images. The SOM method was extensively validated

by Sarno et al. (2016, 2019b) on random dispersions of POM beads immersed in a water/sucrose solution and by using interrogation windows of different sizes and shapes. The best accuracy was found with angles of incidence, ζ , between 20° and 40°. Considering these previous results, in the present investigation, we chose ζ = 25°. The tilt of the lamp with respect to the z direction was set equal to zero. Similar to Carleo et al.

(2019), elongated rectangular interrogation windows of size 1d and 16d in the z and x directions, respectively, are employed here. Such interrogation windows are also designed to have a 50 percent overlap along z so as to get a spatial resolution of d/2 along the flow depth. Sarno et al. (2019b) showed that the accuracy obtainable with elongated interrogation windows is comparable to that achieved with squared interrogation windows of the same area. The accuracy of the method was verified by validation on random granular dispersions of known volume fraction, and a root mean square error on c3D of 0.025 was observed. Ad248

Table 2. List of the experiments carried out with chute inclination angle of 35°.

Experiment ID

Gate Opening (m)

Basal Surface

Exp-5S Exp-6S Exp-7S Exp-8S Exp-10S Exp-12S Exp-14S Exp-5P40 Exp-6P40 Exp-7P40 Exp-8P40 Exp-10P40 Exp-12P40 Exp-14P40 Exp-5G Exp-6G Exp-7G Exp-8G Exp-10G Exp-12G Exp-14G

0.05 0.06 0.07 0.08 0.10 0.12 0.14 0.05 0.06 0.07 0.08 0.10 0.12 0.14 0.05 0.06 0.07 0.08 0.10 0.12 0.14

Bakelite (S) Bakelite (S) Bakelite (S) Bakelite (S) Bakelite (S) Bakelite (S) Bakelite (S) Sandpaper (P40) Sandpaper (P40) Sandpaper (P40) Sandpaper (P40) Sandpaper (P40) Sandpaper (P40) Sandpaper (P40) Grain (G) Grain (G) Grain (G) Grain (G) Grain (G) Grain (G) Grain (G)

Qm (g/s) h (m) 1,084 1,417 1,725 2,124 2,717 3,332 4,243 858 1,146 1,440 1,799 2,353 2,819 3,399 773 1,038 1,297 1,555 2,263 2,635 3,066

0.009 0.012 0.016 0.020 0.027 0.034 0.044 0.018 0.021 0.023 0.027 0.035 0.042 0.050 0.019 0.023 0.027 0.031 0.040 0.050 0.059

ditional inaccuracies might arise near the free surface, as the binarization algorithm might struggle to identify illuminated elements when a reflecting background is visible. To reduce such errors, a white-noise sheet of paper was positioned as background on the outer side of opposite wall of the flume. The key details of this application of the SOM approach are sketched in Figure 2.

RESULTS AND DISCUSSION The results of the experimental campaign are presented and discussed here. For reference and ease of comparison, in Figure 3, we also report the longitudinal velocity profiles, ux , previously obtained by Sarno et al. (2018a) with a flume inclination angle α = 30° and analogous bed surfaces of those employed in the present experimental campaign.

First, by comparing the experiments with the same gate opening, we preliminarily observed that the granular flows on different sandpaper linings exhibit the same no-slip basal KBC and very similar velocity and volume fraction profiles. It indicates that the flow dynamics are weakly influenced by variations of the basal roughness within the investigated range (162 μm, 425 μm) of sandpapers. The list of the experiments is shown in Table 2. To maximize the robustness of data, the mass flow rates, Qm , and the flow depths, h, as well as the velocity and volume fraction profiles hereafter reported, are obtained by carrying out two

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Figure 2. (a) Basic setup of the stochastic-optical method. (b) Monte Carlo numerical sample of randomly dispersed spheres for determining the stochastic relationship between c2D and c3D . (c) Elongated interrogation window of size 16d × 1d employed for estimating the sidewall volume fraction profiles at the cross section under study (x = 0.40 m).

averages. The first one consists of time averaging the instantaneous measurements in a time interval within the steady state of length 1 second. Subsequently, these time-averaged values have been additionally averaged by considering four different repetitions of the same experiment.

Consistent with other works in the literature with frictional sidewalls (e.g., Baker et al., 2016; Sarno et al., 2018a; and Meninno et al., 2018), the velocity measurements at the free surface are found to exhibit approximately parabolic profiles with maximum value at the middle point of the cross section and minima near the sidewalls.

The runs on smooth Bakelite bed (S) show a slip basal KBC with negligible grain rolling. The longitudinal velocity, ux , and the volume fraction, c3D , profiles at the sidewall are reported in Figure 4. Due to large slip, the ux profiles are much blunter than the profiles observed on the same S bed with α = 30°

(Figure 3a). By exploiting the additional information of the c3D profiles (Figure 4b), three regions are identified in the flow domain: 1. A 1d-thick region (hereafter called basal layer) near the basal surface, characterized by a shear band where c3D is relatively small ( 0.3–0.5) and increases with z: in this region, the shear rate, z ux , is larger than in the rest of the flow domain.

2. An intermediate region (denoted as core layer), noticeable only if h is high enough, where c3D shows an approximately constant value (close to the loose random packing c3D 0.6) and ux is approximately linear.

3. A 2d–4d-thick upper region (hereafter called surface layer) where c3D rapidly decreases and ux increases less than linearly with z.

These findings, which agree with data reported by Carleo et al. (2019) for granular flows on smooth bed

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Figure 3. Sidewall ux velocity profiles observed by Sarno et al. (2018a) with a flume inclination angle, α = 30°. (a) Smooth Bakelite bed (S). (b) Sandpaper bed (P40). (c) Grain-type bed (G). The unit of the y-axis is z normalized by the grain diameter, d. Different colors of the lines correspond to different gate opening values.

and inclination of 30°, indicate the occurrence of a rheological stratification along the flow depth (Armanini et al., 2005; Sarno et al., 2014; and Meninno et al., 2018). Specifically, in the case of small flow depths, the ux profile clearly exhibits a Bagnold-like scaling corresponding to the grain-inertia regime (Bagnold, 1954), that is, a 3/2-power law with z (Sarno et al., 2018a; Carleo et al., 2019). When h increases, the increasing effects of the sidewall friction (Jop et al., 2005) and, possibly, the onset of non-local momentum exchanges (e.g., Mills et al., 1999) cause a progressive linearization of the velocity profiles (core layer), and the concave Bagnold-like shape ( zz ux < 0) can be recovered only in the surface layer, where the effect of sidewall resistances becomes negligible. Due to the increasing collisionality, in this surface layer, c3D is considerably smaller with values between 0.3 and 0.5.

Noticeably different kinematic boundary conditions at the bed were observed by increasing the basal roughness. Figure 5 shows the experimental profiles of ux and c3D obtained on the sandpaper bed (P40). In this

case, different from the smooth Bakelite bed, the basal roughness is large enough to inhibit grain sliding so that a no-slip KBC occurs. Yet, since the characteristic length of roughness (425 μm) is still significantly smaller than the grain size, noticeable grain rolling and saltations are observed, especially for experiments with low h, where the relatively small sidewall resistances are incapable of enforcing the formation of a lower static wedge (e.g., Jop et al., 2005). Such phenomena are progressively inhibited by increasing h.

A regime stratification slightly different from the smooth bed can be observed in Figure 5. In the basal layer ( 1d thick), c3D is very small, and the shear rate, z ux , is higher than the S-bed case. Similar to the S bed, also in this case for all experiments, c3D increases from the basal to the central zone. Yet c3D becomes approximately constant at 0.6 only for the experiments with high enough h (i.e., Exp-10P40, Exp-12P40, and Exp-14P40). In the core layer, the ux profiles exhibit a weakly concave Bagnold shape instead of the linear one observed in the case of the S bed. An ap-

Figure 4. Experimental profiles obtained on the smooth Bakelite bed (S). (a) Longitudinal velocity, ux . (b) Volume fraction, c3D .

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Figure 5. Experimental profiles obtained on the sandpaper bed (P40). (a) Longitudinal velocity, ux . (b) Volume fraction, c3D .

proximately linear behavior of ux can be barely identified only in the three experiments with the highest h. This finding can be explained by the fact that the basal roughness causes stronger-velocity fluctuations that propagate in the core layer. By comparing the experiments on sandpaper with those on smooth bed and similar h, it emerges that such a high grain collisionality seems to cause a more persistent Bagnold shape of the ux profiles. Moreover, it should be noted that the velocity profiles are notably different also from those observed with α = 30° and the same bed surface (P40), which are either linear or even weakly convex ( zz ux > 0) in their mid- to lower zone (Figure 3b). This discrepancy is clearly due to the different basal KBC induced by the higher slope. Only if h becomes significantly high so that the increasing sidewall friction inhibits the basal grain saltations, the character of the velocity profiles shifts from Bagnold concave ( zz ux < 0) to approximately linear ( zz ux 0). This phenomenon reflects the increasing magnitude of the frictional mechanisms in the core layer. Analogous to the S bed (Figure 4), a more collision-dominated regime, characterized by zz ux < 0 and a rapidly decreasing c3D , takes place in the uppermost surface layer of thickness of 2d–4d.

The experimental results on the grain-type bed (G) are reported in Figure 6. Similar to the P40 bed, a noslip KBC is enforced by the basal roughness. Yet in this case, the roughness is high enough that the grain rolling and saltations are almost completely inhibited.

In fact, the grains tend to interlock with the bumpy layer of glued grains. As a consequence, a weak rolling is observed only in the case of small flow depths (i.e., runs Exp-5G and Exp-6G), while in all other experiments, a no-slip KBC with no rolling occurs.

By comparing Figure 6a with Figure 3c, it is clear that the increased chute slope hinders the formation

of a friction-dominated lower creep flow, characterized by an exponential velocity tail (Komatsu et al., 2001) and systematically observed by Sarno et al. (2018a).

For all experiments, the volume fraction c3D reaches the loose random packing ( 0.6) soon above the bed.

Further above, the c3D profiles are almost constant along the entire flow depth, except in the surface layer.

For small enough values of h (i.e., Exp-5G, Exp-6G, and Exp-7G), the shape of the ux profile once again resembles the Bagnold shape. When h increases and, consequently, also the pressures and the sidewall resistances become larger (e.g., runs Exp-12G and Exp14G), the ux profile exhibits a progressive convex shape ( zz ux > 0) in the lower part of the flow and an approximately linear shape ( zz ux 0) in the core layer.

In these cases, the behavior in the lower region can be regarded as the onset of the friction-dominated creep flow layer (Figure 3c), which, however, cannot fully develop due to the higher slope of the flume. Analogous to that already observed with other basal surfaces, a surface layer with a thickness of a few grain diameters where zz ux < 0 and c3D rapidly decreases with z occurs in all experiments on the G bed.

The experimental profiles of the shear rates, z ux , observed for the different basal surfaces are reported in Figure 7. From this figure, the main regions of the velocity profiles already discussed above can be more clearly identified.

The strong similarities about the surface layer, also evident by comparing the shear rates reported in Figure 7, indicate that the flow dynamics near the free surface is scarcely influenced by the basal surface. Additionally, it is worth noting that the shape of the c3D profiles has several similarities for all the investigated beds (Figures 4b, 5b, and 6b); in particular, we systematically observed z c3D > 0 in the basal layer, z c3D 0 in the middle region of the flow, and

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Figure 6. Experimental profiles obtained on the grain basal surface (G). (a) Longitudinal velocity, ux . (b) Volume fraction, c3D .

z c3D < 0 in the uppermost surface layer. This behavior is in generally good agreement with several pre-existing experimental and numerical works on dry granular flows (e.g., Ancey, 2001; Brodu et al., 2013; and Meninno et al., 2018). Yet it is worth mentioning that it differs from a few investigations on liquidgranular mixtures where z c3D > 0 was observed along a larger portion of the flow depth, probably due to additional dissipation mechanisms of the interstitial fluid or due to the occurrence of faster flow regimes (e.g., Egashira et al., 2001; Capart et al., 2002).

fluctuating velocities, is useful to better understand the granular flow dynamics and to better investigate the type of momentum exchange mechanisms occurring in the flow domain. A synthetic indicator of the magnitude of the fluctuation velocities is represented by the so-called granular temperature, T, a quantity proportional to the fluctuation kinetic energy of the granular medium per unit mass (e.g., Jenkins and Savage, 1983).

By neglecting the rotational and vibrational terms, T can be defined as 2 1 3 u i (t) , (2) T (z) = i=1 3

GRANULAR TEMPERATURES

where u i is the ith of the fluctuation velocity, u i (t) = ui (t) − ui , with ui (t) and ui being the instantaneous and the ensemble-averaged velocities in the i direction. The ensemble average operator in Eq. 2 can be substituted by a time average provided that the system ergodicity is met (Sarno et al., 2018b). Thus, T was estimated by using the instantaneous measurements within a single experiment. Additionally, the y-component of the fluc-

In this section, the granular temperature profiles, estimated from multi-pass PIV measurements, are reported and briefly discussed. Similar to turbulent flows, granular currents can be considered only steady on average since velocity fluctuations due to grain collisions and grain rearrangements occur in all flow regimes. A knowledge of second-order statistics of the velocity field, namely, the standard deviations of the

Figure 7. Experimental profiles of the shear rate, z ux . (a) Smooth Bakelite (S). (b) Sandpaper (P40). (c) Grain basal surface (G).

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Figure 8. Experimental profiles of the granular temperature (smooth Bakelite basal surface, S).

tuation velocity, which is inaccessible by optical measurements, was assumed to be of the same order of the z-component (Sarno et al., 2018a). The resulting T profiles were subsequently averaged over four repetitions, analogous to what is reported on all measurements above. For details about the employment of the multi-pass PIV approach for estimating the granular temperature, we refer the reader to Sarno et al. (2018b, 2019a). The granular temperature profiles of the experiments on S-, P40-, and G-type beds are shown in Figures 8–10, respectively.

Regarding the runs on smooth bed (S type), the T profiles (Figure 8) exhibit a C-shape along z, analogous to that observed by Sarno et al. (2018a) in the case of a smaller chute inclination and identical bed.

The highest values of T occur near the basal surface because of the slip KBC and the subsequent formation of a shear band. A smaller relative maximum is located in the surface layer, where the flow regime is more collisional. This is also consistent with the lower values of

Figure 9. Experimental profiles of the granular temperature (sandpaper basal surface, P40).

Figure 10. Experimental profiles of the granular temperature (graintype basal surface, G).

the volume fraction there (Figure 4b). Conversely, in the core layer, corresponding to the region where c3D 0.6 (Figure 4b), T exhibit significantly smaller values (of order of 0.8 m2 /s2 ).

Moving to Figures 9 and 10, it can be noted that for P40- and G-type beds, some new interesting peculiarities of the T profiles appear. The granular temperature profiles on sandpaper exhibit non-zero values at the bed, and its maximum is located at 1d above it.

Then, for increasing values of z, T rapidly decreases and reaches a plateau at z 5d. This finding is consistent with the already mentioned grain rolling and saltation phenomena observed by the naked eye. Indeed, these phenomena indicate a source of fluctuation kinetic energy at the bed that, similar to a heat transfer phenomenon, diffuses from z = 0 toward the flow domain and consequently increases the magnitude of T not only in the basal layer but also in the lower part of the core layer. It is noteworthy that in this case of noslip KBC with rolling and saltations, the magnitude of T at the bed is considerably higher also than the case of pure slip KBC, obtained with the S bed. Moreover, it is worth recalling that the T profiles, previously obtained

by Sarno et al. (2018a) with the same P40 bed surface and smaller chute inclination (30°) were noticeably different, since they were monotonically increasing with z and exhibited an approximately zero value at the bed.

It is striking that these counterintuitive discrepancies arise by just slightly increasing the flume inclination from 30° to 35°. It is probably due to the fact that at α = 35°, the basal roughness is high enough to promote the grains’ saltations and rolling, but, because of the higher active forces, it is insufficient to keep the lower layer of grains at rest.

A similar behavior can be observed in Figure 10 (G-type bed), where, however, the maximum of T is reached farther from the bed at z 2d–5d. Moreover,

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in this case, we observed T 0 at the bed because of the effects of grains interlocking with the lowermost glued layer. This is in agreement with the sensibly zero flow velocity measurement at the bed (Figure 6a). Also in this case, the T profiles are markedly different from the ones observed by Sarno et al. (2018a) with the same G bed, which exhibited a strictly increasing trend with an approximately exponential shape. With α = 35°, despite the fact that the first layer of grains is interlocked on the glued layer, a source of fluctuation kinetic energy arises from the bumpy bed and diffuses upward in the flow domain. In this case, the magnitudes of the granular temperatures are slightly smaller than those observed on the P40 bed, probably due to the complex interplay between the basal geometry and the higher normal pressures. Indeed, it can be noted that the flow depths of the data set with G bed are on average higher than those with the P40 bed. Furthermore, we believe that some influence to the fluctuation velocities near the bed could be also due to the specific shape of the roughness (i.e., the roundness of the bumpy G-type bed compared to the sharp sandpaper lining).

INSIGHTS ON THE DEBRIS FLOW DYNAMICS The present laboratory results, obtained under controlled and simplified conditions, shed some light on the complex dynamical behavior of geophysical granular flows and debris flows. Specifically, the collisional and friction-collisional regimes observed in the laboratory are also expected to occur in the presence of a dense interstitial fluid provided that the grain size is large enough to avoid the onset of a viscoplastic regime (e.g., Bardou et al., 2003). In the case of a polydisperse solid phase, which is common in natural debris flow events, a chiefly collisional regime typically occurs in the main front of the debris flow surge, while a viscoplastic regime is usually observed in the tail of the debris flow, where the finest solid components accumulate (Coviello et al., 2019; Nagl et al., 2020). The various basal roughnesses investigated in the present work encompass the main cases of real debris flows, where the basal sliding surface either is made of the same granular material or corresponds to a less frictional bed rock. The laboratory results also highlight the importance of the sidewall friction, which together with the basal kinematic boundary conditions, in turn influenced by the channel slope, determines the occurrence of various velocity profiles, such as the Bagnold-type, the linear and the convex ones. These combined effects are also expected to take place in real debris flows if the flow geometry is of a channelized type. In this regard, our experimental investigation highlights the crucial influence of the bed slope on

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the shape of the velocity profiles and on the granular temperature distribution, further enriching the complex picture of the debris flow dynamics. The observed variety of velocity profiles is in qualitative agreement with the in-field velocity measurements reported by Nagl et al. (2020). In addition, our laboratory-scale results suggest that such a rich variety of velocity profiles and the consequent longitudinal heterogeneity of real debris flows are influenced not only by the grain size distribution and volume fraction variations but also by the geometrical properties of the cross section, especially the bed slope. The bed slope typically varies along the debris flow path. Hence, a Bagnold or a stratified linear-Bagnold velocity profile is expected to develop in the steep headwater streams, typically characterized by a bed slope significantly higher than the angle of friction of the solid phase. Conversely, when the basal slope decreases, such as in the downstream reaches or on an alluvial fan, the stratified linearBagnold profile with the lower exponential tail is expected to appear. The measurements of the volume fraction and granular temperature profiles are also useful for better understanding the essential features of real granular flows and debris flows, especially considering that reliable measurements of these quantities can hardly be obtained in the field or are limited to averaged estimations in the cross section (Nagl et al., 2020).

A limitation of the present study is represented by the fact that a sole mono-disperse case has been reported, while in real debris flows and rock avalanches a poly-disperse granular phase is typically involved. In this regard, further laboratory studies on poly-disperse granular flows are advisable, especially for studying other essential features of the granular dynamics, such as the grain segregation.

CONCLUSIONS In this work, we studied the effects of the basal surface on the dynamics of dry granular flows in a steep laboratory flume. Specifically, as an extension of the work by Sarno et al. (2018a), a higher chute inclination angle of 35° was investigated in order to ascertain the influence of larger active forces on different basal KBC. Moreover, in this experimental campaign, we provided not only the flow velocity measurements but also estimations of the volume fraction profiles obtained using the SOM method (Sarno et al., 2016).

The comparisons of the velocity and volume fraction profiles clearly indicate that different flow regimes develop along the flow depth. For all investigated basal surfaces, a Bagnold-like shape of the velocity profile, together with a volume fraction decreasing with z, is typically observed if the flow depth is small enough.

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Velocity and Volume Fraction Measurements of Granular Flows

When the flow depth increases, the Bagnold scaling remains visible only in the uppermost region of the flow domain (surface layer), while in the lower zones, various flow regimes take place. Specifically, the velocity profiles are found to gradually shift from concave to approximately linear in an intermediate region (core layer), characterized by a roughly constant volume fraction profile (c3D 0.6), and, for the case of Gtype bed, they become even weakly convex in the lower region. These phenomena, promoted by the effects of the sidewall friction, are compatible with the occurrence of a rheological stratification along the flow depth, where the magnitude of the frictional mechanisms increases inversely with the grains’ collisions from upwards to downwards. In the lowermost region (basal layer), with thickness of around 1–2 particle diameters and typically characterized by a lower volume fraction, the effects of different basal roughnesses become evident. The aforementioned findings only partially overlap with the experimental results

by Sarno et al. (2018a) carried out on analogous bed surfaces but with a smaller slope (30°). Specifically, due to the larger active forces, no fully developed lower creep flow with exponential velocity tail could be observed here, not even on the coarsest Gtype bed. Moreover, for all experiments on sandpaper, a weakly concave Bagnold-like velocity profile was found to persist also in the presence of relatively high flow depths. This behavior is made possible thanks to the non-negligible grain rolling and saltations at the bed, in turn allowed by the slightly larger acting forces.

The reported granular temperature profiles further support these observations. In particular, the basal roughness was found to deeply influence the magnitude of the fluctuation velocities not only near the bed but also in the lower region of the core layer, that is, within a distance of 2d–5d from the bed. In the case of sandpaper (P40) and granular (G) beds, the granular temperature profiles noticeably differ from the monotonically increasing ones previously observed with the same basal surfaces and smaller slope (Sarno et al., 2018a). Once again, this discrepancy is caused by sustained grain saltations and bed rolling, in turn promoted by the basal roughness and larger active forces.

From these experimental findings, it clearly emerged that the granular dynamics and the occurrence of stratified flow regimes is not only governed by the bed roughness and sidewall resistances but also strongly influenced by the magnitude of the active forces, namely, by the flume slope, which is capable of modifying the character of the flow. Understanding the aforementioned behavior is also crucial for a reliable mathematical modeling of granular flows and for predicting the

rich variety of flow regimes occurring in real cases and in complex topographies.

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Cover photo A filter barrier for debris flow, clogged with retained material. This barrier is part of an experimental site in the Italian Alps. Each time it is impacted, the deformation of the steel elements is recorded, from which the impact force can be back-calculated. Photo courtesy of Matteo Ceccarelli, Politecnico di Torino. See article on page 195.

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