Environmental & Engineering Geoscience NOVEMBER 2016
VOLUME XXII, NUMBER 4
THE JOINT PUBLICATION OF THE ASSOCIATION OF ENVIRONMENTAL AND ENGINEERING GEOLOGISTS AND THE GEOLOGICAL SOCIETY OF AMERICA SERVING PROFESSIONALS IN ENGINEERING GEOLOGY, ENVIRONMENTAL GEOLOGY, AND HYDROGEOLOGY
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EDITORIAL BOARD ROBERT H. SYDNOR JEROME V. DEGRAFF USDA Forest Service Consulant THOMAS J. BURBEY CHESTER F. WATTS (SKIP) Virginia Polytechnic Institute Radford University SYED E. HASAN University of Missouri, Kansas City ASSOCIATE EDITORS JOHN W. BELL PAUL M. SANTI Nevada Bureau of Mines and Colorado School of Mines Geology ROBERT L. SCHUSTER U.S. Geological Survey RICHARD E. JACKSON (Book Reviews Editor) ROY J. SHLEMON R. J. Shlemon Geofirma Engineering, Ltd. & Associates, Inc. JEFFREY R. KEATON AMEC Americas GREG M. STOCK National Park Service PAUL G. MARINOS National Technical University RESAT ULUSAY Hacettepe University, Turkey of Athens, Greece CHESTER F. “SKIP” WATTS JUNE E. MIRECKI U.S. Army Corps of Radford University Engineers TERRY R. WEST Purdue University PETER PEHME Waterloo Geophysics, Inc NICHOLAS PINTER Southern Illinois University SUBMISSION OF MANUSCRIPTS 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. To submit a manuscript go to http://eeg.allentrack.net. If you have not used the system before, follow the link at the bottom of the page that says New users should register for an account. Choose your own login and password. Further instructions will be available upon logging into the system. Please carefully read the “Instructions for Authors”. Authors do not pay any charge for color figures that are essential to the manuscript. Manuscripts of fewer than 10 pages may be published as Technical Notes. For further information, you may contact Dr. Abdul Shakoor at the editorial office.
THIS PUBLICATION IS PRINTED ON ACID-FREE PAPER EDITORS ABDUL SHAKOOR Department of Geology Kent State University Kent, OH 44242 330-672-2968 ashakoor@kent.edu
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Cover photo Overview of the Jiweishan landslide, China. See article on page 341. Photo courtesy of Li Bin, Chinese Academy of Geological Sciences.
Environmental & Engineering Geoscience Volume 22, Number 4, November 2016 Table of Contents
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A Durability-Based Approach for Designing Cut Slopes in Weak Rock Units in Ohio Abdul Shakoor and Yonathan Admassu
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Landslide Susceptibility Screening Using Wind-Driven Rainfall J. David Rogers, M. Farooq Ahmed, Elamin H. Ismail
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Empirical Methods and Estimation of Hydraulic Conductivity of Fluvial Aquifiers Sudarsan Sahu and Dipankar Saha
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Initiation Mechanism of the Jiweishan Landslide in Chongqing, Southwestern China Feng Zhen, Li Bin, Cai Qi Peng, Cao Jia Wen
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Study of the Damage Mechanics and Dewatering Recover Programs for the Shield Tunnel under the Yangtze River Baotian Xu, Jianfei Qiu, Qian Sun, Changhong Yan, Bu Xu, Shi Liu, Canhui Che
A Durability-Based Approach for Designing Cut Slopes in Weak Rock Units in Ohio ABDUL SHAKOOR1 Department of Geology, Kent State University, Kent, OH 44242, ashakoor@kent.edu
YONATHAN ADMASSU Department of Geology and Environmental Science, James Madison University, Harrisonburg, VA 22807, admassyx@jmu.edu
Key Terms: Weak Rock, Redbeds, Raveling, Gully Erosion, Cut Slope Design, Durability, Drainage
ABSTRACT Seven cut slope sites along Ohio highways containing thick (.10 ft/3.3 m) units of weak rocks (shales, claystones, and mudstones) were selected for investigating slope stability problems and developing design recommendations. Stability problems affecting weak rock slopes in Ohio include raveling, gully erosion, mudflows, and, occasionally, deep-seated rotational failures. Field data regarding slope height, slope angle, slope stratigraphy, catchment ditch dimensions, natural slope angle, and talus slope angle were collected for the seven sites. Laboratory data pertaining to the sites included point load strength index, second-cycle slake durability index (Id2), plasticity index (IP), and geologic strength index. The Franklin shale rating system, global stability analysis using SLIDE software, natural slope angle, and talus slope angle were used to determine safe cut slope angles for weak rock units. Based on the correlation between Id2 and stable slope angles, as indicated by the shale rating system, we propose cut slope angles for weak rock units as follows: Id2 ,20 percent— flatter than 2H:1V (,276); Id2 5 20–60 percent— 2H:1V (276); Id2 5 60–85 percent—1.5H:1V (346); Id2 5 85–95%—1H:1V (456); and Id2 .95 percent— 0.5H:1V (636). These angles are corroborated by talus slope angles, the natural angles attained by talus material covering cut slopes in weak rocks. Redbeds, consisting of very weak claystones and mudstones, should be analyzed on a case-by-case basis. Additionally, surface drainage, including backslope, midslope, and downslope drains; jute matting to promote vegetation growth, and adequate catchment ditches should be provided for all weak rock slopes. 1
Corresponding author email: ashakoor@kent.edu
INTRODUCTION Types of Cut Slopes in Ohio Most cut slopes in Ohio are in the eastern and southeastern parts of the state, where bedrock consists of inter-layered limestone, sandstone, shale, claystone, mudstone, and coal belonging to the Pennsylvanian and Permian groups (Pottsville, Allegheny, Conemaugh, Monongahela, and Dunkard groups). These rocks were deposited as cyclothems in nonmarine, deltaic or estuarine environments (Chesnut, 1981; Bennington, 2002; and Camp, 2006). Based on bedrock lithology, cut slopes in Ohio can be divided into three broad types: (1) those that consist mostly of hard rock units (limestone, dolomite, sandstone, and siltstone); (2) those that consist mostly of weak rock units (shale, claystone, and mudstone); and (3) those that consist of inter-layered strong and weak rock units. Cut slopes consisting of hard rock units make up approximately 20–25 percent of all cut slopes, and those consisting mostly of weak rock units make up less than 10 percent of all slopes. The majority of the cut slopes in Ohio consist of inter-layered strong and weak rock units. Figure 1 shows the three types of cut slopes present in Ohio. Site designation in the caption for Figure 1a and the rest of this article, follows the Ohio Department of Transportation (ODOT) standard notation that uses the three-letter county code, the numerical name of the road, and the mile marker measured from the county line, separated by hyphens. For example, LIC-16-28 in the caption for Figure 1 refers to a site in Licking County, along state route 16, at mile marker 28. Types of Failure Affecting Cut Slopes in Ohio The types of failure affecting a cut slope in Ohio depend on the geology of the slope. The slope failures affecting strong rocks include plane, wedge, and toppling (Cruden and Varnes, 1996). Wedge failures are rare in Ohio because of the steeply dipping nature of
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discontinuities that prevents their lines of intersection from daylighting on the slope face. However, where thick units of strong rock are inter-layered with weak rock, undercutting of strong units by weak units, due to differential weathering, promotes all three types of failure (Shakoor and Weber, 1988; Shakoor, 1995). Although plane, wedge, and toppling failures commonly occur in strong rocks, slopes consisting of silty shales, containing jointing and having second-cycle slake durability index (Id2) values of .80 percent, can also exhibit these failures (Krinitzsky and Kolb, 1969; Franklin and Gruspier, 1983; Wu et al., 1987; Young and Shakoor, 1987; and Rauber and Shakoor, 2009). Claystones and mudstones may fail as rotational slides along circular surfaces or, more commonly, quasi-circular surfaces that develop as a result of lateral pressure of water in sub-vertical valley stress relief joints (Bjerrum, 1967; Ferguson and Hamel, 1981). In addition, a common problem with cut slopes consisting of weak rock units is degradation due to weathering. Weathering causes raveling (fragmentation) of weak rock, with the raveled material accumulating at the base of the slope (Franklin and Gruspier, 1983). In Ohio, raveling, mudflows, and gully erosion are the main problems affecting cut slopes consisting of weak rocks (Figure 2). Slopes with inter-layered stratigraphy experience failures that are typical of both strong rock units (plane, wedge, and toppling failures) and weak rock units (raveling, mudflows, erosion gullies). However, the most frequent failures affecting these slopes are undercutting-induced failures. Undercutting-induced failures require at least three sets of intersecting discontinuities for a rock block to move freely when the depth of undercutting exceeds the spacing between the discontinuities. The three common types of discontinuities present in Ohio are bedding, orthogonal joints, and valley stress relief joints. The initial movement of the undercut blocks can be in the form of a plane failure, a wedge failure, or a toppling failure. Regardless of the initial mode of failure, all undercutting-induced failures descend as rockfalls (Shakoor and Weber, 1988).
Purpose of the Study
Figure 1. Examples of types of cut slopes in Ohio: (a) a slope comprising mostly sandstone (LIC-16-28); (b) a slope comprising mostly shale (JAC-33-12); and (c) a slope comprising alternating thin units of strong and weak rock (ATH-50-22).
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This article is part of a comprehensive study on the design of cut slopes in Ohio that was conducted for and funded by ODOT. We have previously published design recommendations for slopes cut in strong rock units (Admassu and Shakoor, 2013) and in interlayered sequences of strong and weak rock units (Admassu and Shakoor, 2015). The purpose of this article is to develop design approaches for slopes cut
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Figure 2. Examples of types of failure affecting weak rock slopes in Ohio: (a) raveling of a shale slope (FRA-270-23); (b) mudow on a shale slope caused by groundwater seepage (CLE-275-5.2); and (c) gully erosion on a slope consisting of claystone/mudstone (redbeds) (ATH-33-23).
in weak rock units, including shales, claystones, and mudstones. RESEARCH METHODS Site Selection Twenty-six sites were selected for the overall study on designing cut slopes in Ohio. Seven of the 26 sites contained significantly thick (.10 ft/3.3 m) units of weak rock that required independent design. Figure 3 shows the location of the 26 sites, with the seven sites containing thick units of weak rock (the focus of this study) shown in red. Table 1 provides a geologic summary of the seven sites.
Field Investigations Field investigations for the weak-rock cut slopes, conducted during spring and summer of 2008, consisted of collecting data regarding slope geometry (slope angle, slope height, slope aspect, and bench width), slope stratigraphy, hydrologic conditions, and ditch dimensions. Additionally, samples of various lithologic units were collected for laboratory testing. Slope-geometry data were obtained from slope profiles drawn for the sites using a laser range finder and ArcGIS. A stratigraphic cross section was prepared for each site incorporating the stratigraphic details into a previously prepared slope profile. Groundwater flow conditions for each site were evaluated qualitatively.
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Figure 3. Location map of the 26 project sites. The seven sites containing signiďŹ cantly thick (.10 ft/3.3 m) units of weak rock are shown in red. The bedrock geology map is from the Ohio Department of Natural Resources (ODNR, 2006). Note: 1 mile = 1.6 km.
A measuring tape was used to collect width and depth data for catchment ditches. Three samples of each lithologic unit, each weighing approximately 30 lbs (13.6 kg), were collected from the sites containing weak rock units. Samples were dug out from 1 to 2 ft (0.3 to 0.6 m) deep to ensure that they were obtained from fresh bedrock. In all, 69 samples of weak rock were collected during the field investigation stage. The samples were wrapped in plastic bags and stored
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in 5-gallon plastic buckets to preserve natural water content and prevent disintegration. ODOT drilled 15 of the 26 sites during spring 2008, providing additional core samples of weak rock. Laboratory Investigations Laboratory tests were performed on weak-rock samples to determine unconfined compressive strength,
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Designing Cut Slopes in Weak Rock Table 1. Geologic summary of the seven cut slope sites containing thick (.10 ft/3.3 m) units of weak rock.
Site
Lithology
ADA-32-12 COL-7-5
Limestone underlain by claystone/mudstone Sandstone inter-layered with shale
Upper and Lower Silurian Middle and Lower Pennsylvanian
FRA-270-23 GUE-22-6.9
Shale Sandstone inter-layered with shale
Upper Devonian Middle and Lower Pennsylvanian
JEF-CR77-0.38 MUS-70-11
Sandstone inter-layered with shale Sandstone inter-layered with shale
Upper Pennsylvanian Middle and Lower Pennsylvanian
WAS-7-18
Red claystone/mudstone inter-layered with sandstone
Lower Permian and Upper Pennsylvanian
slake durability index, density, and Atterberg limits. These properties were used in stability analysis using various methods. The point load test, conducted in accordance with the specifications of the International Society for Rock Mechanics (ISRM) (ISRM, 1985), was used to determine unconfined compressive strength. Approximately 10–20 pieces of rock from each sample were failed by the point load tester to determine the point load index, corrected for 50-mm sample size (Is50). Based on the research conducted by Greene (2001), a conversion factor of 10 was used to convert point load index to unconfined compressive strength. Slake durability index, which represents the resistance of a rock to weathering and disintegration upon exposure to moisture, was determined for outcrop samples by performing the slake durability index test in accordance with American Society for Testing and Materials (ASTM) method D 4644 (ASTM, 1996). Two cycles of the test were run for each sample to determine the Id2. Density was determined for 21 core samples of weak rock (13 shale samples, 8 claystone/mudstone samples). Five measurements each of core diameter and length were taken to determine the average core volume in cubic centimeters. The weight of each core sample, oven-dried for 24 hours at 105uC, was measured to the nearest tenth of a gram. These measurements were used to calculate density values in g/cm3 that were then converted to lb/ft3 (Mg/m3). Atterberg limits (liquid limit, plastic limit, and plasticity index) were determined for all samples of weak rock that had Id2 values of less than 80 percent using ASTM method D 4318 (ASTM, 1996). Plastic limit (PL) is the minimum water content at which a soil changes from a solid state to a plastic state, and liquid limit (LL) is the minimum water content at which a soil-water mixture changes from a plastic to a viscous liquid state. Plasticity index (IP) is the numerical difference between LL and PL (Holtz et al., 2011). We used multiple wetting and drying cycles to break down
Formation or Group Name
Geologic Age
Peebles Dolomite Allegheny and Pottsville groups Ohio Shale Allegheny and Pottsville groups Conemaugh group Allegheny and Pottsville groups Dunkard group
weak rocks to prepare samples (125 g of material passing the No. 40 sieve) for Atterberg limits test. Stability Analysis In order to perform slope stability analysis and develop design criteria, weak rocks were considered as an independent design unit. For this research, we defined a design unit as a portion of a slope, or the entire slope, that could be cut at a unique stable angle. When a lithologic unit consisted of .90 percent of weak rock (shale, claystone, mudstone), with strong rock (limestone, sandstone, siltstone) occurring evenly as thin (,3 ft/1 m) layers, we considered it a weak-rock design unit. The anticipated slope stability problems in this design unit include raveling, mudflows, gully erosion, and, occasionally, rotational slides. We used the Franklin shale rating system (Franklin and Gruspier, 1983), SLIDE software (Rocscience, Inc., 2010), angle of repose of talus material, and natural slope angle to analyze the stability of slopes consisting of weak-rock design units. Stability analysis and design of such slopes need to consider durability characteristics of the weak rocks in addition to strength properties. The Franklin shale rating system considers both durability and strength characteristics to select stable slope angles. Applying the Franklin shale rating system involves two steps: (1) rating the weak rock on the basis of Is50, Id2, and IP, using the chart provided in Figure 4a, and (2) determining stable slope angles against rotational failures using the graphs in Figure 4b. The upper curve in Figure 4b represents probable maximum stable slope angles in which jointing is either absent or at favorable orientations so that failure, if it occurs, would be through intact shale material. The lower curve represents stable slope angles in which stability is controlled by unfavorably oriented discontinuities daylighting on the slope face, not by the intact strength of the shale. Franklin
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Figure 4. (a) Franklin shale rating chart; (b) range of cut slope angles for weak rock as a function of shale rating (Franklin and Gruspier, 1983).
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The angles of talus material accumulating at the base of cut slopes consisting of weak rock units and the slope angles of adjacent natural slopes were measured for selected sites. The talus angles represent the angles of repose of talus (raveled) material, whereas the natural angles represent the final stable angles that slopes consisting of weak rock units, adjacent to the cut slopes, have attained after undergoing weathering and erosion. The talus angles were measured during the field investigation stage using a transit compass. The natural slope angles adjacent to cut slopes consisting of weak rock units were determined using raster GIS techniques. Digital elevation models, 10 m 6 10 m, were downloaded from http://seamless. usgs.gov/index.php, and ArcGIS was used to calculate the natural slope angles. Figure 5. Frequency distribution of slope angle for weak rock units.
FIELD AND LABORATORY DATA and Gruspier (1983) state that the trends shown in Figure 4b are only approximate and that slopes in weak shales or those with adverse jointing should be checked using the limiting equilibrium analysis and laboratory-determined strength values. As an example of the application of the Franklin shale rating system, a shale rock with Is50 5 1.9 MPa, Id2 5 70 percent, and IP 5 14 will have a rating of 4.1 according to the shale rating chart (Figure 4a), which, according to Figure 4b, yields upper and lower stable angles of 35u and 19u, respectively. The SLIDE software program (Rocscience, Inc., 2010) calculates the factor of safety against rotational failures due to low rock mass strength of weak rocks in accordance with the Hoek and Brown failure criterion (Hoek and Brown, 1980, 1997). In order to use the SLIDE program, a slope profile was drawn and the required input parameters, such as the geologic strength index (GSI) value taken from the chart provided in Marinos and Hoek (2000, 2001); compressive strength of intact rock, as determined from laboratory tests; and disturbance factor and mi values taken from tables provided in Marinos and Hoek (2000, 2001), were entered to determine the factor of safety values for a number of failure circles, selected by the SLIDE program. The disturbance factor (D) is a measure of rock mass disturbance during excavation, where D 5 0 indicates an excellent quality of controlled blasting and D 5 1 indicates a poor quality of production blasting. The mi parameter is a curve-fitting parameter derived from triaxial testing of intact rock, with a range of 4 to 8 for weak, clay-bearing rocks. The SLIDE software computes the factor of safety based on Bishop’s (Bishop, 1955) and Janbu’s (Janbu, 1968) methods. The analysis provides the location of the failure circle with the smallest factor of safety value.
Microsoft Excel was used to draw histograms and to obtain descriptive statistics (range, mean, standard deviation, skewness, and kurtosis) for all field and laboratory data suitable for such analysis. The class sizes in the histograms were chosen so that they clearly showed data distribution. The upper bound of each class in the histograms was labeled in the middle of each bar. For each histogram, the range, mean, and population count, as computed by descriptive statistics, were given below the histogram. Field Data Slope Angle Slope angle for weak rock units ranges from 27u to 80u, with a mean of 45u. The frequency distribution of slope angle for weak rocks is left-skewed (Figure 5), indicating generally lower slope angles (,50u) for weak rock units. Stratigraphic Cross Sections Figure 6 shows an example of a stratigraphic cross section for a weak-rock slope. Weak rock units in the stratigraphic cross sections were described as shales or claystones/mudstones. These rocks were differentiated on the basis of the presence or absence of fissility, with shales being fissile and claystones and mudstones being non-fissile. According to Potter et al. (1980), the distinction between claystones and mudstones depends on clay content. Since clay content was not determined in the laboratory, claystones and mudstones were treated as one rock type in stratigraphic descriptions, referred to as claystones/ mudstones. Based on field observations and previous
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Figure 6. Example of a stratigraphic cross section for a slope consisting entirely of weak rock unit (FRA-270-23 site). Note: 1 ft 5 0.3 m.
research (Dick and Shakoor, 1992; Hajdarwish et al., 2013), most shales in the study area are silty in nature and gray to dark gray in color. Upon weathering, shales produce sheet-like fragments, whereas claystones and mudstones tend to turn into soil-like material. Shale outcrops belonging to the Ohio Shale Formation (upper Devonian) are common in the study area. Shales are also associated with the sandstones belonging to the Allegheny, Pottsville, Conemaugh, Monongahela, and Dunkard groups (Lower Permian–Upper Pennsylvanian). The claystone/mudstone units include the gray, green, and red varieties. The gray claystones/mudstones are mostly associated with the upper Ordovician age fossiliferous limestones. The green claystones/mudstones are commonly found with limestone units belonging to the Monongahela group. Red claystones/mudstones, often termed redbeds, are associated with limestones and sandstones belonging to the Allegheny, Pottsville, Conemaugh, Monongahela, and Dunkard groups. Catchment Ditches Catchment ditches are an integral part of slope design in Ohio. They are used to retain failed material, preventing it from reaching the roadway and posing hazards to traffic. The width of catchment ditches in
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the study area ranges from 7–70 ft (2.1–21.2 m), and the depth varies between 0.5 ft (0.2 m) and 3 ft (1 m). The catchment ditch slopes are either 3H:1V or 6H:1V. Laboratory Data Unconfined Compressive Strength Unconfined compressive strength values for shale samples from outcrops range from 545–7,094 psi (4–49 MPa), with a mean value of 2,904 psi (20 MPa). The frequency distribution of compressive strength for shale samples is left-skewed (Figure 7a), indicating that most strength values are in the range of 2900–4,350 psi (20–30 MPa). Unconfined compressive strength values for claystone/mudstone samples from outcrops range from 107–5,618 psi (0.7–39 MPa), with a mean value of 854 psi (6 MPa). The frequency distribution for claystones/ mudstones is also left-skewed (Figure 7b), indicating the prevalence of lower strength values (1,450 psi/ 10 MPa). Slake Durability Index Id2 values for outcrop samples of shales range from 72–99 percent, with a mean value of 91 percent. The
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population range from 18 to 98 percent, with a mean of 54 percent. Dry Density Dry density was measured for 13 shale and 8 claystone/mudstone samples from drilled core. Mean values of density for shales and claystones/mudstones are 166 lb/ft3 (2.66 Mg/m3) and 164 lb/ft3 (2.63 Mg/m3), respectively. Atterberg Limits Atterberg limits were determined to find plasticity index values for outcrop samples with Id2 values ,80 percent (mostly claystones/mudstones). Plasticity indices of weak rock units, having Id2 values of ,80 percent, are needed for application of the Franklin shale rating system (Franklin and Gruspier, 1983). The plasticity index values range from 2–21, with an average value of 11. Figure 9 shows the nearly normal frequency distribution of plasticity index for outcrop samples. It should be noted that the numbers of data points (“Count”) in Figures 5, 7, 8, and 9 are different because of the type of property measured or the number of samples available for testing. STABILITY ANALYSIS RESULTS The Franklin shale rating system (Franklin and Gruspier, 1983) and rock mass strength parameters were used to conduct stability analysis of the seven sites with thick (.10 ft/3.3 m) units of weak rock. Additionally, talus slope angles and natural slope angles were used to supplement the results of the stability analysis.
Figure 7. Frequency distribution of unconfined compressive strength for outcrop samples of (a) shale and (b) claystone/ mudstone. Note: 145 psi 5 1 MPa.
frequency distribution of slake durability index for shales is right-skewed (Figure 8a), indicating the predominance of greater than 90 percent values. This is attributed to the silty nature of most shale units (Dick and Shakoor, 1992; Hajdarwish et al., 2013). Slake durability index values for claystone/mudstone samples from outcrops show possibly two populations (Figure 8b). Descriptive statistics show that the values for the first population range from 0 to 10 percent, with a mean of 4 percent, and that those for the second
Stability Analysis Using the Franklin Shale Rating System Franklin and Gruspier (1983) developed a shale rating chart (Figure 4a) and a relationship between stable slope angle and shale rating (Figure 4b). The shale rating is based on Id2, Is50, and IP. Using the shale rating (Table 2), two slope angles, an upper angle (if unfavorable discontinuities do not exist) and a lower angle (if unfavorable discontinuities exist) were obtained from Figure 4b. These angles are considered to be stable slope angles against an overall (global) rotational failure. The method does not apply to failures caused by surficial weathering (Franklin and Gruspier, 1983). Table 2 shows the results of stability analysis, using the Franklin shale rating system, for the seven sites. The mean upper and lower angles are 48u and 25u,
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Figure 9. Frequency distribution of plasticity index for outcrop samples.
too conservatively for the dry state. The upper-angle values given by the Franklin shale rating system appear to be more reasonable for this study because the weak rock units at the seven sites analyzed do not have unfavorably oriented discontinuities. Therefore, four of the seven sites can be considered stable, two marginally stable, and one potentially unstable with respect to a global rotational failure.
Stability Analysis Using Rock Mass Strength
Figure 8. Frequency distribution of slake durability index for outcrop samples of (a) shale and (b) claystone/mudstone.
respectively. Four of the seven sites (COL-7-5, FRA270-23, GUE-22-6, and JEF-CR77-0.38) have existing slope angles that are less than the upper angles suggested by the shale rating system, indicating that the weak rock units at these sites are stable against global rotational failures. Two of the sites (ADA-32-12 and MUS-70-11) have slope angles that are 5u to 6u higher than the upper slope angles, indicating that the weak rock units at these sites are marginally stable. One site (WAS-7-18) has an existing slope angle that is 22u higher than the upper angle slope angle, indicating that the slope at this site is potentially unstable. JEFCR77-0.38 is the only site that has an existing slope angle that is less than the lower angle given by the shale rating system, indicating that it was designed
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The GSI method, as described in Hoek and Brown (1997) and Marinos and Hoek (2000, 2001), was used for rock mass strength–based stability analysis (global stability analysis) for the seven sites. The SLIDE software program was used to perform the analysis. Input data for the SLIDE program included unconfined compressive strength, density, mi, D, and GSI. Laboratory data were used to obtain unconfined compressive strength and density values. A mi value of 4 was assigned for claystone/mudstone, a value of 6 for shale, and a value of 7 for shale inter-layered with thin siltstone units, as suggested by the SLIDE program. A D value of 0.3 was assigned to slopes that were mechanically excavated, and a value of 0.5 was assigned for slopes that were pre-split. A very low GSI value of 20 (the range being 10 to 70), as recommended by Marinos and Hoek (2000) for undisturbed silty or clayey shale with or without a few very thin layers of sandstone, was chosen for all weak rock units. Table 3 summarizes the results of the stability analysis. Three sites (ADA-32-12, COL-7-5, and JEF-CR77-0.38) resulted in factor of safety values of less than 2.0. These three sites were further analyzed for saturated conditions (water table assumed to be
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Designing Cut Slopes in Weak Rock Table 2. Stability analysis results for weak rock units using the Franklin shale rating system.
Site No. ADA-32-12 COL-7-5 FRA-270-23 GUE-22-6 JEF-CR77-0.38 MUS-70-11 WAS-7-18 *NA
Rock Unit
Existing Slope Angle (u)
Mean Is50 (MPa)
Gray claystone/mudstone Shale/siltstone Shale Shale Shale Shale Claystone/mudstone (redbeds)
27 57 35 45 27 40 45
0.4 2.0 2.7 2.3 2.0 1.9 0.3
Mean Id2, (%)
Mean Plasticity Index of Weak Units
Franklin Shale Rating
3 96 99 96 96 70 3
16 NA* NA* NA* NA* 14 12
2.1 7.4 7.8 7.4 7.4 4.1 2.3
Upper and Lower Slope Angles by Shale Rating (u) 21 64 66 64 64 35 23
11 34 35 34 34 19 13
represents rocks whose average second-cycle slake durability index is .80 percent.
at the ground surface) by SLIDE software, which resulted in factor of safety values of 1.0, 0.3, and 0.3, respectively. Note that the JEF-CR77-0.38 site had the existing slope angle (27u) that was less than the lower slope angle given by the shale rating system (34u) and was considered to have been designed too conservatively for the dry state. However, under completely saturated conditions, even a gentle slope angle of 27u is unstable. The remaining sites (FRA-270-23, GUE-22-6, MUS-70-11, and WAS-7-18) showed factor of safety values that were greater than 2.0, suggesting that they would also be stable under saturated conditions. If the factor of safety for a rock slope under dry conditions happens to be greater than 2.0, it is common to assume that the slope will also be stable under saturated conditions (Hoek and Bray, 1981). If the factor of safety for dry conditions turns out to be less than 2.0, the slope is further analyzed for saturated conditions to evaluate its stability. It should be noted, however, that for the WAS-7-18 site the SLIDE analysis results are contradictory to the results obtained using the shale rating system, which indicated this site to be potentially unstable. A possible explanation for this discrepancy could be that the shale rating system is based on durability, point load strength index, and plasticity index of intact rock, whereas slide analysis is based on rock mass strength. Although the three sites analyzed for stability under saturated conditions are unstable (factor of safety equal to or less than 1.0), we believe it is unlikely that completely saturated conditions, with a water table at the ground surface, will develop during the service life of these cut slopes because of the low permeability of weak rock units and because of the fact that the groundwater table was not encountered at any of the 15 drilled sites. However, a significant decrease in factor of safety upon saturation does suggest the need for the provision of surface drains to minimize infiltration.
Stability Evaluation Using Natural Slope Angle and Talus Angle The stability problems observed on slopes consisting of weak rock units are due mainly to surficial weathering. Raveling is the most common form of slope degradation in weak rocks, accompanied by mudflows, in some cases. Stability analyses based on the Franklin shale rating system and rock mass strength are applicable to rotational failures, which were not observed at the seven sites containing weak rocks. Therefore, we considered it prudent to examine the natural angles of repose that slopes consisting of weak rock units reach after undergoing years of weathering and erosion. The methods used to determine the natural angles of repose were (1) measuring natural slope angles adjacent to cut slopes of the study sites and (2) measuring the angles of raveled material that accumulated as talus material at the base of the slopes. We selected 10 sites, consisting of either entirely weak rock units or weak rock units with a minor proportion of strong rock units, for these slope angle determinations. Except for the FRA-270-23 site, the other nine sites were different than the seven study sites shown in Figure 3. The reason for selecting different sites was their greater suitability for measuring the two types of angle. Multiple measurements of natural slope angle and talus angle were made at each site, and the mean values were computed. Table 4 shows the mean and the maximum natural slope angle values for each site. The mean value of the maximum natural angle is 17u, which is too gentle to use for design purposes. The maximum natural slope angle values for the five sites consisting of red and gray claystone/mudstone show a narrow range of 10u–12u, which is also too gentle for design of slopes in these rocks. The narrow range of low slope angles for red and gray clay claystone/mudstone does, however, suggest that slopes in claystone/mudstone need to be cut at significantly gentler angles than do those in shales, especially silty
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290
1.0 0.3 — — 0.3 — — 1.6 1.3 3.3 2.7 1.6 3.4 2.3 0.3 0.5 0.3 0.3 0.5 0.3 0.3 4 7 6 6 6 6 4 20 20 20 20 20 20 20
Geologic Strength Index (GSI)
164/[2.63) 156/[2.50] 166/[2.66] 166/[2.66] 166/[2,659] 166/[2.66] 164/[2.63]
Existing Slope Angle (u)
27 57 35 45 27 40 45
626/[4.3] 2,878/[19.8] 3,854/[26.5] 3,302/[22.8] 2,906/[20.0] 3,125/[21.5] 428/[2.9]
Factor of Safety (Saturated) Factor of Safety (Dry) Disturbance Factor, D (Based on Hoek and Brown, 1997) Hoek and Brown Intact Rock Constant (mi) Average Unconfined Compressive Strength [UCS] (psi/[Mpa]) Average Dry Density (lb/ft3/ [Mg/m3])
shales. A plot of natural slope angle versus slake durability index did not show any relationship. Table 4 also shows the talus angle values for the 10 sites. The talus angle ranges from 25u to 40u, with a mean value of 35u. The talus angles are steeper than the natural slope angles because of the steeper inclination of the cut slopes on which the talus accumulates. It can be assumed that if slopes are cut at angles close to the talus angle, the raveled material would drape the slope face, reducing further degradation and allowing vegetation growth. Field observations of weak rock units show that shales, which exhibit higher slake durability index values, have higher talus angles than do claystones/mudstones, which have lower slake durability index values. Therefore, we performed a regression analysis to investigate further the relationship between the talus-slope angles and the corresponding Id2 values (Figure 10). Although a moderately strong correlation (R2 5 0.793) is observed, the data are not normally distributed (Davis, 2001), having three clusters around Id2 values of ,10 percent, 70 percent, and .90 percent, which limits the usefulness of the exercise. However, the relationship between lithology and talus angles (Table 5) shows that the red claystone/mudstone units (redbeds) have the lowest angle of 25.5u, as compared to the gray claystones/mudstones and shales, which have talus angles of 39u and 37u, respectively. The slightly higher talus angle value for gray claystones/mudstones compared to shales may be due to some cohesion, in addition to friction, in gray claystone/mudstone–derived talus. The talus angle data suggest that cut slope angles of approximately 25u or less for redbeds and of 35u–40u for other weak rocks can help reduce the amount of degradation and improve stability.
Gray claystone/mudstone Shale/siltstone Shale Shale Shale Shale Claystone/mudstone (redbeds) ADA-32-12 COL-7-5 FRA-270-23 GUE-22-6 JEF-CR77-0.38 MUS-70-11 WAS-7-18
Rock Unit
Comparison of Methods
Site No.
Table 3. Stability analysis results for weak rock units using SLIDE software. Note that factor of safety values for saturated conditions were determined for only those cases in which the factor of safety values for dry conditions were found to be less than 2.0.
Shakoor and Admassu
The Franklin shale rating system indicates mean values of 45u and 24u, respectively, for the upper and lower bounds of stable slope angles for weak rocks. The talus angle approach suggests cut slope angles of 37u for shales, 39u for gray claystones/mudstones, and 25.5u for red claystones/mudstones (redbeds) (Table 5). The natural angle approach is too conservative to be feasible for design purposes. Based on a comparison of the approaches discussed above, it can be stated that a 1H:1V slope (45u) can generally be used for shales (especially those that are silty in nature), a 1.5H:1V (34u) slope is needed for gray claystones/mudstones, and a 2H:1V (27u) or gentler slope is required for redbeds.
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Designing Cut Slopes in Weak Rock Table 4. Natural slope angle and natural talus angle values for the 10 sites consisting predominantly of weak rock units.
Site ATH-33-23 ATH-50-28 COL-11-16 COL-30-30 FRA-270-23 GUE-77-21 GUE-70-12.9 HAM-74-8.9 HAM-74-12 HAM74-16.6
Rock Unit
Second-Cycle Slake Durability Index, Id2 (%)
Mean Natural Slope Angle (u)
Maximum Natural Slope Angle (u)
Mean Talus Slope Angle (u)
Red claystone/mudstone (redbeds) Red claystone/mudstone (redbeds) Shale Shale Shale Shale Shale Gray claystone/mudstone Gray claystone/mudstone Gray claystone/mudstone
3.2 2.8 90.8 96.7 99.3 93.8 96.3 65.9 67.0 68.0
4 4 20 14 15 5 4 6 6 6
12 12 36 29 23 10 13 11 10 11
25 26 40 40 36 35 37 37 39 39
DISCUSSION AND SLOPE DESIGN CONSIDERATIONS Discussion The main slope problems associated with weak rock units are raveling and mudflows. Mudflows are uncommon and were observed at only two sites (ADA-32-12 and CLE-275-5) consisting of claystone/ mudstone units, with a few layers of limestone, whereas raveling was observed at all seven sites consisting of weak rock units. Both raveling and mudflows are related to surface weathering and require only routine maintenance. The mean maximum natural slope angles for red claystones/mudstones (redbeds), gray claystones/ mudstones, and shales were found to be 12u, 11u, and 22u, respectively (Table 5). The mean talus angles
for these rock units were 25.5u, 39u, and 37u, respectively (Table 5). Skempton (1964) and Bjerrum (1967) found the natural slope angles for clay-shale slopes, several thousand years old, to be as low as 8u–10u. The relatively higher values of talus angle compared to natural slope angle represent the younger age of cut slopes and the associated talus. Over time, the cut slopes in weak rock are expected to weather down to their natural slope angles of 10u–20u. For the purposes of cut slope design, within the anticipated service life of five to six decades, the average talus angle can be used as a reasonable guideline for cut slope angle. In addition to weathering-related degradation, water is an important agent of erosion of slopes consisting of weak rock units. Even where slope angles are gentle, surface water degrades cut slopes through
Figure 10. Relationship between talus slope angle and 2nd-cycle slake durability index (Id2).
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Shakoor and Admassu Table 5. Maximum natural slope angle and mean talus angle values for various lithologies.
Lithology Red claystones/mudstones (redbeds) Shales Gray claystones/mudstones All weak rock units
Maximum Natural Slope Angle (u)
Mean Talus Angle (u)
12 22 11 17
25.5 37 39 34
gully erosion (Figure 2c). Gully erosion is very common in claystone/mudstone units, but not in shales. The red claystones/mudstones are more prone to gully erosion compared to the gray claystone/mudstone units. A global or deep-seated rotational failure in weak rock units could cause closure of a roadway, leading to expensive maintenance (Franklin and Gruspier, 1983). Although evidence of a global failure was not observed at any of the project sites during the course of this study, the Franklin shale rating system and the GSI methods were used to check the potential for global (rotational) failure. Based on a comparison of the existing slope angles with the upper angle values obtained from the Franklin shale rating system (Figure 4b, upper curve), the study sites consisting of weak rock units are stable to marginally stable to potentially unstable. On the other hand, a comparison of the existing slope angles with the lower angle values given by the shale rating system (Figure 4b, lower curve) indicates that only two of the study sites are stable. Since unfavorably oriented discontinuities were not observed at the study sites, use of the lower angle will be too conservative. GSI-based analysis showed that all sites except one have factor of safety values greater than 1.5 under dry conditions. For saturated conditions, one site has a factor of safety equal to 1.0, and two sites have values less than 1.0. Although it is unlikely that cut slopes in weak rocks will become completely saturated because of their low permeability, relatively unfractured nature, and deep water table, the results of the Franklin shale rating and GSI analyses suggest that flatter slope angles need to be used for those slopes found to be marginally stable or unstable. Slope Design Considerations for Weak Rock Units Slope design considerations for weak rock units include cut slope angles, drainage control, and catchment ditches. The main objective of selecting appropriate cut slope angles for weak rock units should be to minimize the natural degradation of slopes by
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weathering and erosion processes. This can be accomplished by employing the following considerations: 1. Weathering of slopes in weak rocks is greatly influenced by their durability, as indicated by Id2 values. Thus, slope design for weak rock units should be based on Id2 values. The Franklin shale rating system (Franklin and Gruspier, 1983), used for determining stable slope angles for the seven sites in this study, is based on Id2, Is50, and IP. However, one of the limitations of the Franklin shale rating system is the use of Is50 and IP in addition to Id2. Previous research (Sarman, 1991; Greene, 2001) shows that point load test data for weak rocks can be quite inconsistent and unreliable. Furthermore, disintegrating weak rocks to prepare samples suitable to determine IP is a timeconsuming process. To overcome these limitations, we established the relationship between Id2 values and slope angles suggested by the Franklin shale rating system (Table 2), as shown in Figure 11. This figure provides a very useful guide for selecting appropriate slope angles for the weak-rock design units. The relationship shown in Figure 11 is based on 43 data points, including data from the seven study sites consisting of weak rock units (shown in bold). The remaining 36 data points are based on a previous study by Sarman (1991), who tested shale, claystone, and mudstone samples from across the United States to investigate their swelling potential. The relationship between Id2 and slope angle (Figure 11) shows two distinct trends, with the change occurring at an Id2 value of about 80 percent. This is because the shale rating system uses Id2 and IP values for rating when Id2 is ,80 percent and Id2 and Is50 values when Id2 is .80 percent. This distinction also accounts for soil-like versus rock-like behavior of weak rocks, depending upon their Id2 values. Based on Figure 11, the slope angles shown in Table 6 appear appropriate for designing cut slopes in weak rock. The slope angles based on Figure 11 are also in agreement with the talus angles observed in this study (25.5u–39u) as long as the Id2 values are less than 80 percent. Using angles suggested by Figure 11 would allow the raveled material to stay on the slope face, protecting it from further weathering. It should be noted, however, that slope angles selected on the basis of Id2 (Figure 11) may require more detailed analysis, such as global stability analysis or kinematic analysis, especially for weak rocks with Id2 values . 80 percent, which are likely to contain jointing. 2. Selecting slope angles for redbeds, which usually have Id2 values less than 20 percent and are
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Figure 11. Relationship between second-cycle slake durability index and shale rating slope angle for weak rock units. The data points from the seven study sites are shown in bold. The remaining data are from Sarman (1991).
characterized by their very weak and highly erodible nature, should be addressed on case-by-case basis. Slopes as gentle as 3H:1V (18u) may be required in some cases. 3. Using erosion control matting over a slope face may be considered to hold raveled material and facilitate vegetation growth, especially where slopes flatter than 2H:1V (27u) are used. This was done at the JEF-7-14 site (Figure 12a), a site not included in this study. At this site, the lower shale unit was draped with a jute mat that held weathered material and promoted vegetation growth. 4. Providing a backslope drain (a ditch behind the crest of the cut slope) may be considered to reduce surface water erosion. A backslope drain was provided at GUE-22-6 during its rehabilitation work (Figure 12b). Backslope drains can be seen on cut slopes in shale all along the Pennsylvania Turnpike. Most of these shale slopes do not show active raveling and are covered with grass. For long, high slopes, providing mid-slope and down-slope drains Table 6. Relationship between second cycle slake durability index (Id2) and suggested slope angles, based on Figure 11. Second-Cycle Slake Durability Index [Id2] (%) ,20 20–60 60–85 85–95 .95
Suggested Slope Angles [(u)] ,2H:1V 2H:1V 1.5H:1V 1H:1V 0.5H:1V
[,27] [27] [34] [45] [63]
may be necessary. Figure 12c shows the field application of various types of drains. 5. Catchment ditches should be designed according to the guidelines provided in Pierson et al. (2001) and should be wide enough to accommodate raveled material and any rockfalls resulting from the presence of minor strong rock units.
CUT SLOPE DESIGN RECOMMENDATIONS FOR WEAK ROCKS We recommend a six-step approach for designing cut slopes in weak rocks: 1. Use Id2 and Figure 11 to select an appropriate slope angle, as discussed above under “Slope Design Considerations.” 2. Provide a backslope drain (Figure 13), lined with rip rap and underlain by an impermeable geofabric, to reduce surface runoff. Connect the backslope drain to the toe drain. For a long slope cut (.1,500 ft/455 m), consider both providing downslope drains and connecting the backslope drain to the toe drain. For a high but gentle (,1H:1V) cut slope (e.g., slopes in redbeds), a midslope drain, lined with rip rap and connected to the backslope drain, may be necessary. 3. Consider using erosion control matting for weak rocks with Id2 values of ,80 percent. 4. Provide an adequate catchment ditch (Pierson et al., 2001) to contain raveled material and any rockfalls.
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6. Monitor cut slopes in weak rocks regularly. The monitoring program should focus on documenting surficial changes. Photographs and LIDAR scans are excellent tools for monitoring temporal changes occurring on the slope surfaces. Photographs taken annually and LIDAR scans taken every 3 to 4 years should be adequate. Although the design recommendations listed above are based on a study of the seven sites in Ohio, they should be applicable to weak rock sites in other areas with similar geologic and climatic conditions. Degradation of cut slopes in weak rocks in Ohio occurs as a result of the combined effect of all three climatic cycles: heating and cooling, wetting and drying, and freezing and thawing. However, the Id2-based slope angles should not be used where weak rock units are jointed without ascertaining the suitability of selected angles by a global stability analysis or a kinematic analysis, or both.
CONCLUSIONS Based on the results of this study, the following conclusions can be drawn:
Figure 12. (a) Vegetation growth over weak rock unit facilitated by placement of jute matting (JEF-7-14 site); (b) backslope drain, connected to toe drain, lined with riprap and underlain by an impermeable geofabric at the rehabilitated GUE-22-6 site; and (c) field application of various types of surface drains for a weak rock slope.
5. Treat redbeds, characterized by very low durability (Id2 usually ,20 percent), as special units and design on a case-by-case basis. Consider past experience of slope performance in redbeds in selecting the final slope angle.
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1. Slope stability problems in Ohio are closely related to stratigraphy, which consists of stronger, durable rocks (limestones, dolomites, sandstones, siltstones) alternating with weaker, non-durable rocks (shales, claystones, mudstones). 2. Raveling, mudflows, gully erosion, and occasional development of deep-seated rotational failures are the main problems affecting the stability of cut slopes in weak rocks. 3. The relationship between Id2 and the stable cut slope angles, as suggested by the Franklin shale rating system, can be used to select appropriate slope angles for weak rock design units, as follows: Id2 ,20 percent—flatter than 2H:1V (,27u); Id2 5 20–60 percent—2H:1V (27u); Id2 5 60–85 percent —1.5H:1V (34u); Id2 5 85–95 percent—1H:1V (45u); and Id2 .95 percent—0.5H:1V (63u). Redbeds should be treated on a case-by-case basis. 4. Providing adequate drainage should be an integral part of cut slope design in weak rocks. In order to minimize erosion and promote vegetation, use of jute matting may be considered. 5. Adequate catchment ditches should be provided for all cut slopes in weak rock. ACKNOWLEDGMENTS The authors would like to thank the Ohio Department of Transportation and the Federal Highway
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Figure 13. Recommended cross section of a slope design for weak-rock design units. Backslope and midslope drains are lined with riprap and are connected to the toe drain in 3 dimensions. Note: The backslope and midslope drains are not drawn to scale.
Administration for the financial support of this research project. The authors would also like to acknowledge the constructive and useful comments by the three reviewers, which greatly helped improve the quality of this article. Disclaimer The authors are solely responsible for the contents of this article, including the accuracy of the data. The contents do not reflect the official views or policies of the Ohio Department of Transportation or the Federal Highway Administration. REFERENCES ADMASSU, Y. and SHAKOOR, A., 2013, Cut slope design recommendations for sub-horizontal hard sedimentary rock units in Ohio, USA: Geotechnical Geological Engineering, Vol. 31, No. 4, pp. 1207–1219. ADMASSU, Y. and SHAKOOR, A., 2015, Cut slope design for stratigraphic sequences subject to differential weathering: Environmental Engineering Geoscience, Vol. 21, No. 4, pp. 311–324. AMERICAN SOCIETY FOR TESTING AND MATERIALS (ASTM), 1996, Annual Book of ASTM Standards, Soil and Rock (1), Vol. 4.08, Section 4: West Conshohocken, PA 1000 p. BENNINGTON, J. B., 2002, Eustacy in cyclothems is masked by loss of marine biofacies with increasing proximity to detrital source: An example of central Appalachian Basin, U.S.A. In Hills, L. V.; Henderson, C. M.; and Bamber, E. W. (Editors), Carboniferous and Permian of the World: Canadian Society of Petroleum Geologists, Memoir 19, Ontario, Canada, pp. 12–21. BISHOP, A. W., 1955, The use of slip circle in the stability analysis of slopes: Geotechnique, Vol. 5, No. 1, pp. 7–17.
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Landslide Susceptibility Screening Using Wind-Driven Rainfall J. DAVID ROGERS Department of Geosciences and Geological and Petroleum Engineering, Missouri University of Science & Technology, Rolla, MO email:rogersda@mst.edu
M. FAROOQ AHMED1 Department of Geosciences and Geological and Petroleum Engineering, Missouri University of Science & Technology, Rolla, MO email:mfanr5@mst.edu
ELAMIN H. ISMAIL Department of Geosciences and Geological and Petroleum Engineering, Missouri University of Science & Technology, Rolla, MO, USA
Key Terms: Wind-Driven Rainfall, Landslide, Slope Aspect, GIS, Susceptibility Mapping
this method were found to be more reasonable than others yet produced of such a large study area (~75,000 km2).
ABSTRACT
INTRODUCTION
Rainfall is one of the most significant triggering factors for shallow landslides, raveling, and erosion of over-steepened slopes, especially in steeply inclined mountainous regions, such as the western Greater Himalayan Mountains of northern Pakistan. The influence of wind-driven rainfall is usually neglected in comparisons between rainfall and mass wasting. Winddriven rain falls with an angle of incidence influenced by prevailing wind direction and velocity. The need to include considerations of incident rainfall distribution with respect to mass wasting processes is long overdue. The idea of coupling “wind-driven” rainfall based on directional monsoon with regional topography (slope aspect) was analyzed to ascertain the actual distribution of rainfall upon slopes exhibiting varying inclinations and slope aspect. Regional-level landslide susceptibility maps were prepared for the entire Indus River watershed using widely accepted methods including GIS heuristic weighted overlay and fuzzy logic techniques by including traditional rainfall distribution maps as one of the triggering factors. The results of that analysis were then compared with current research to examine whether an oblique/ inclined rainfall correction map would aid in assessing landslide susceptibility by considering the impacts of slope inclination and aspect on the effective rainfall being “caught” by those slopes facing the prevailing wind directions. The susceptibility maps produced by
Rainfall-triggered mass wasting is an ongoing process of landscape evolution, especially on steeply inclined slopes without significant vegetation. Rainfall-induced erosion and mass wasting exert significant impacts on societal infrastructure each year. In developing countries, large landslides can affect people, property, and the sustaining lifelines for hundreds of kilometers downstream for years or even decades afterward. Many countries lack the economic resources to assess the risk of landslide-induced calamities, and even fewer nations can afford to mitigate such problems. The actual pattern of rainfall is markedly influenced by horizontal wind speeds and topography (Hobbs et al., 1973), especially during severe events, such as typhoons or subtropical storms, which, in turn, affect the rate of erosion (Helming, 2001; Tarolli et al., 2011). The amount of rainfall varies considerably on slopes with different aspect, even causing rain shadows over significant areas (De Lima, 1990). The horizontal wind speed and wind azimuth (direction) are the two most significant variables to compute the actual rainfall distribution on slopes (De Lima, 1990; Helming, 1999; and Liu and Shih, 2013). The topographic effect of wind-driven rainfall varies considerably on steeply inclined hill slopes (Geiger, 1965; Stout et al., 1993; and Blocken et al., 2005). This effect is even more pronounced across mountain ranges with extreme elevation, such as the Himalayas (Anders et al., 2006). The small-scale topographic effects of
1 On leave from the University of Engineering and Technology, Lahore, 3 Pakistan.
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wind-driven rainfall have not been widely studied in the past. A large body of knowledge exists asserting topographic influence on wind-driven rainfall as a significant factor in catchment hydrology, runoff, and mass wasting (Reid, 1973; Craig, 1980; Sharon et al., 1988; Lentz et al., 1995; Goossens et al., 2000; and Erpul et al., 2003). This is because captured precipitation is a function of rainfall incidence, slope inclination, and slope aspect (orientation), with respect to the wind-driven rain vector. In conventional landslide susceptibility mapping rainfall raster maps have traditionally been employed without considering topographic effects, such as orographic lifting and rainfall incidence (Hobbs et al., 1973). When vertical rainfall rasters are applied to landslide susceptibility mapping they may overestimate landslide hazards by assuming equally distributed rainfall. The rainfall intercepted by slopes of varying shape and height facing the prevailing wind can be quite different (Struzer, 1972; Wakimizu et al., 1988; and De Lima, 1990). Similarly, the rate of erosion triggered by rainfall/runoff could also be expected to vary with slope aspect and the prevailing wind velocity and vector (direction). In other words, the assumption of vertically inclined rainfall on every slope, regardless of slope aspect, could be erroneous. For these reasons, modern evaluations of landslide susceptibility should include some means of incorporating the topographic effects of wind-driven rainfall, variability of rainfall intensity, incident rainfall, and the dominant slope aspect. Landslides, especially debris flows, are a major source of sediment in the un-glaciated portions of the Greater Himalayan Mountains system (Singh et al., 1995; Shroder and Bishop 1998; Awan, 2002; and Gabet et al., 2004). The steeply inclined, perversely fractured, and highly weathered slopes are subject to high rates of tectonic uplift and intense (monsoon) precipitation. The prevailing weather and geologic setting of northern Pakistan create an almost “perfect storm” scenario for landslides. In order to create susceptibility maps that include rainfall as a significant triggering factor, the actual volume of precipitation received by hillslopes should be ascertained with as much reliability as the existing data justify. This assessment should include the impacts of horizontal wind speed, terminal velocity of the rain drops, the type of rainfall, and other topographic factors, such as slope curvature and slope aspect (De Lima, 1990; Liu and Shih, 2013). Monsoon is a seasonal wind reversal rainfall system between southwest and southeast Asia, as well as portions of West Africa and Asia-Australia (Trenberth et al., 2000). The Asian monsoon has two annual cycles: winter monsoon (October to November) and summer monsoon (May to September) (Shamshad,
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2011). The southwest summer monsoon cycle typically generates heavy rain-bearing wind from the Bay of Bengal and the Arabian Sea that engender intense precipitation in parts of India, Pakistan, Nepal, and neighboring countries (Wake, 1987; Ahasan et al., 2014). The significant temperature difference between the ocean and continental land masses is the major driving force for the monsoon phenomenon. Monsoons generate between 65 percent and 70 percent of the total annual rainfall in the uplands of Pakistan, including the Himalayas (Sarfraz, 2007). This intense and persistent rainfall often triggers mass movements, such as landslides, debris flows, and rock avalanches. These events often flush large volumes of sediment into channels, which can temporarily block flows, resulting in devastating flash floods in the Greater Himalayas and surrounding areas (Singh et al., 1995; Archer, 2001; and Awan, 2002). In 2010, exceptionally torrential rainfall was recorded (during summer monsoon spell) across much of Pakistan, including the Upper Indus River Basin. Though of only a few days’ duration, these intense storms inundated one-fifth of the entire country and triggered numerous landslides, causing loss of billions of dollars (Hicks and Burton, 2010). The sudden ferocity and detrimental impacts of this storm sequence testify to the impact rainfall can exert in the Upper Indus River Basin (northern Pakistan). If a moderate to major earthquake were to have occurred during the same storm sequence, it is difficult to imagine the crippling damage that might have been sustained, setting Pakistan back for decades to come. Regional-level landslide susceptibility maps were recently prepared for the entire Indus River Watershed by incorporating a conventional rainfall isohyet (rainfall intensity) map as one of the triggering factors (Ahmed et al., 2014). The current susceptibility study was the first to include the potential de-stabilizing impacts of “wind-driven/effective” rainfall across this region. The effective rainfall, or wind-driven rainfall, is the actual amount of precipitation felt by a sloping surface. It depends on the falling rainfall incidence, slope inclination, and slope aspect. This procedure modified the monthly averaged monsoon rainfall intensity and coupled it with the directional monsoon (slope aspect) to provide a more realistic estimate of the incident rainfall distribution over slopes of varying inclination and aspect. All of the various combinations utilized in constructing the landslide susceptibility maps (generated from heuristic overlay index and susceptibility techniques) that had utilized conventional rainfall data (monthly averaged rainfall intensity) were repeated by incorporating the effective (wind-driven) rainfall distributions, resulting in a noticeable
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Figure 1. Map showing the location of the upper Indus River Basin study area in northern Pakistan.
improvement in the susceptibility mapping, as compared to previous studies. REGIONAL SETTING OF THE STUDY AREA Northern Pakistan is surrounded by the Karakoram, western Himalaya, and Pamir Mountains along its northern borders and by the Hindu Kush Ranges on the west. The upper Indus River Basin, with an area of more than 75,000 km2 (Figure 1), was selected for landslide susceptibility mapping that incorporated wind-driven rainfall. The Indus River and its tributaries tend to follow longitudinal valleys in the steepest areas and then flow across the structural grain of the mountains, until they join the main stem of the Indus River in northern Pakistan (Kazmi and Jan, 1997; Leland et al., 1998). The Indus River Basin supports a number of large alpine glaciers, including the Batura Glacier, Biafo Glacier, and Baltoro Glacier in the Gilgit Baltistan area. The Indus River exhibits slight meandering or braided flow in the flatter segments of the mountain valleys that increases markedly where the river passes through steep and/or constricted gorges, until it emerges from the hills above Tarbela Reservoir. The principal formations exposed within the Upper Indus River Watershed include Tkk, Tkb, MPzm, PCb, Jk, KJc, and JPzd, map units of different geologic ages (Figure 2). The Tkk unit chiefly comprises Miocene to Cretaceous rocks of the Karakoram
batholith and associated plutons (including granites, granodiorites, tonalite, granite gneiss, and hornblenderich amphibolite rocks) (Kazmi and Rana, 1982). MPzm formations are derived from units of Mesozoic to Paleozoic age within the Northern Suture mélange, along the Main Karakoram Thrust (MKT). This unit is intensely deformed and characterized by a chaotic assemblage of volcanic rocks, limestone, red shale, conglomerate, and quartzite. The JPzd map unit includes the Darkot-Karakoram metamorphic complex of Jurassic to Paleozoic age, comprising slates, phyllites, quartzite, ultramafic units, and marble. All of the other rock units along with their abbreviations are defined in Table 3B of Appendix B. These rocks predominate in the Shyok River Basin, Skardu, Nanga Parbat Haramosh Massif, Hunza, and Gilgit areas of northern Pakistan. There also exists a significant variation in the seasonal temperatures (monthly averages: −17uC at Khunjerab in January and 33uC at Chilas in June), as well as in day and night temperatures in northern Pakistan (Awan, 2002). These variations frequently promote frost-induced heave, which aids in the rapid disintegration of exposed rock surfaces. The preliminary landslide inventory and susceptibility maps (Ahmed and Rogers, 2012, 2014a, 2014b; Ahmed et al., 2014) suggest that the majority of the slopes on both sides of the Upper Indus River channel are prone to mass wasting. A large number of bedrock rockslides/rock avalanches (.350 long, with the majority exhibiting an area of .10 km2) have been
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Figure 2. Geological map of the study area, modified from the Geological Survey of Pakistan (1994); the rock units are explained in Table 3B of Appendix B.
identified along the main Indus River and its principal tributaries (Hewitt, 1998, 2002; Shroder and Bishop, 1998; Korup et al., 2010; and Hewitt et al., 2011). Those events include landslide dams at Gol-Ghone, Katzarah, and Lichar Gah areas along the main stem of the Indus River; at Masher-brum, Saltoro, and Khaplo areas along the Shyok River; at Boultar Glacier, Shakejareb, Ganesh-Saukien, and Attabad (2010) areas along the Hunza River; and at Bhurt, Gupis, Chillingi Glacier, and Karambar (Lake Ishkoman) along the Gilgit River (Gardner and Hewitt, 1991; Hewitt, 1998, 2002; and Korup et al., 2010). In addition to these, hundreds of smaller to medium-sized (a few tens to few hundreds of cubic meter) landslides and debris flows frequently occur during the monsoon season (Singh et al., 1995; Awan, 2002; etc.) DATA The input data used for this landslide susceptibility study included the following: Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Digital Elevation Model (DEM), 30-m resolution, to generate elevation, slope, slope aspect, and curvature raster layers (see Figure A1, Appendix A) and the Landsat Thematic Mapper (TM5) data (collected between 2008 and 2011 of the monsoon rainfall season of mid-June to mid-September) to extract Normalized Difference Vegetation Index (NDVI) information. Other physical factor maps included bedrock lithology; areal distance from the surface traces of active faults; areal distance to major
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river channels; and the predominant triggering factors, which included seismicity (see Figure A2, Appendix A) and the rainfall intensity map. Monthly average rainfall intensity data for the monsoon season (mid-June to mid-September) were obtained from a free online open-source Global Climate Data source for ecological and GIS studies (www.worldclim.org and http://www.pakmet.com. pk). The data were gleaned from records collected between 1950 and 2000 (Figure 3). According to conventional rainfall intensity maps employing isohyets (lines of equal precipitation), uniform rainfall is assumed to occur along those lines without any variation in volume or intensity with respect to the underlying topography. The use of conventional rainfall intensity data in landslide susceptibility mapping often leads to overestimation of landslide hazards on some slopes while significantly underestimating the actual, or “effective precipitation,” on slopes facing different directions (Blocken et al., 2005; Liu and Shih, 2013). This is especially true in tropical and subtropical areas that receive intense precipitation, like the study area described here, which receives 700–850 mm of annual precipitation at elevations between 3,000 m and 4,325 m (Awan, 2002). METHODOLOGY The steps taken to generate wind-driven rainfall and the landslide susceptibility maps are summarized below.
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Figure 3. Conventional rainfall intensity map for the upper Indus River Basin (monthly monsoon rainfall intensity averages, 1950–2000).
Preparation of Inclined Rainfall Raster Map from Conventional Rainfall Intensity Map The horizontal wind speed and wind direction are the two most significant variables with which to compute the actual rainfall distribution on slopes (De Lima, 1990; Helming, 2001; and Liu and Shih, 2013). Wind-driven rain falls with an angle of incidence under the influence of prevailing wind direction and wind speed (velocity). Figure 4 presents an example in which a theoretical hillslope is inclined at 55u (from horizontal) and facing directly into the prevailing storm track (normal to its azimuth), with rain falling at an incidence angle of 45u. Such a slope would receive about 230 percent more rainfall than the same horizontal planimetric area above or below the slope. If runoff is directed toward the slope, this would be expected to exacerbate erosion by overland flow, as well as near-surface seepage. The retaining walls and cut slopes along coastlines often exacerbate local erosion because they receive more rainfall. De Lima (1990) prepared a nomograph depicting correction factors that can be applied to rain gauge– collected precipitation data to compensate for the obliquity of the rainfall on sloping surfaces. By this simple method, one can compute the respective correction factors for the average precipitation based on its prevailing azimuth, average wind velocity, type of rainfall, terminal speed of the raindrops, slope (surface inclination), and slope aspect (azimuth).
In this study the incident rainfall vector for the monsoon season was computed and the conventional rainfall intensity map was reproduced by computing the incident rainfall angle using De Lima’s nomograph (1990). For the average annual monsoon rainfall in northern Pakistan, the horizontal wind speed (coming from the Arabian Sea) varies from 6 to 15 m/s during the months of June through September (Rashid, 2004; Ahasan et al., 2014). The monsoon rainfall type likely comes under the category of “rain showers” or “torrential” showers (Awan, 2002; Ahasan et al., 2014). The incident rainfall vector (h) (see Figures 5 and 6) was obtained from De Lima’s nomograph
Figure 4. Schematic diagram illustrating the concept of how rainfall inclined at 45u affects a hillslope inclined at 55u and normal to the wind direction (storm track).
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Figure 5. De Lima nomograph (1990) for rain-gauge correction factors (Cgau), which is also useful to determine the rainfall’s angle of incidence, given the wind speed (Vw), terminal raindrop speed (VT), and type of rainfall. The colored lines with arrows illustrate how the angles of incidence (h) were determined at different wind speeds.
(1990), assuming constant wind speeds (Vw) of 6, 10, and 15 m/s and terminal raindrop velocities (VT) of between 8 and 10 m/s (more suitable for the type of rainfall as ‘showers’ and ‘torrents’). With De Lima’s nomograph, the incident rainfall angle was found to be 33u, 45u, and 57u, respectively (shown in Figure 5). Several combinations of input rainfall data (i.e., rainfall type, wind speed, and terminal velocity) can be applied to ascertain the more reasonable angle of rainfall incidence under the given conditions. With variation of the angle of incidence, the effective precipitation falling on the slopes varies considerably. Figure 6 presents the basic vector force diagram used to compute the inclined rainfall vector. If the incidence is found to be 45u, the actual rainfall vector can be computed as OB (rainfall vector) 5 OA/cos (h) (where h 5 45). For example, if the maximum monthly monsoon rainfall intensity value for the study area was 700 mm (OA component), by applying this correction the actual rainfall intensity would be adjusted upward, to 990 mm, an increase of 41 percent. By applying this concept, the rainfall intensities at h 5 33u, 45u, and 57u for the study area were adjusted by dividing the
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rainfall raster by the cos (h) value, using the Raster Calculator in ArcGIS. The new map shows maximum rainfall intensities as high as 990 mm (instead of the original 700 mm) for a rainfall incidence of 45u. The variation in the amount of rainfall at other incident angles is summarized in Table 1. Coupling of Inclined Rainfall Intensity Map and Slope Aspect The influence of topography on rainfall direction and intensity has traditionally been neglected in published correlations between rainfall and landslide
Figure 6. Schematic diagram illustrating how to compute the true rainfall vector from the vertical rainfall intensity map.
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Landslide Susceptibility Screening Table 1. Variation in the amount of monthly averaged rainfall intensity at different angles of incidence (obtained from the De Lima nomograph, 1990). Increased Incident Rainfall (mm) at Different ‘θ’ Values Rainfall Intensity (mm) 0 50 100 150 200 250 300 400 500 600 700
θ 5 33u
θ 5 45u
θ 5 57u
0 60 119 179 238 298 358 477 596 715 834
0 71 141 212 283 354 424 566 707 848 990
0 92 184 275 367 459 551 734 918 1,101 1,285
recurrence (e.g., Nilsen and Turner, 1975; Nilsen et al., 1976a, 1976b; Cannon and Ellen, 1985; and Wieczorek, 1987). The need to adjust incident rainfall distribution with respect to the topographic effects is long overdue. It has been noted that those slopes facing the prevailing wind direction receive more rainfall compared to leeward slopes and semi-horizontal ground (Blocken et al., 2005), as shown in Figure 7. This is one reason why slopes receiving wind-driven rainfall should be more susceptible to surficial erosion and mass wasting. The actual amount of received rainfall depends upon the rainfall incidence, wind direction, and slope aspect. For this regional study (area ~75,000 km2) the amount of rainfall was computed assuming the average incidence of 45u, with the average velocity of 10 m/s. When combined with changing slope aspect directions, the effective rainfall (in millimeters) was then computed for all of the slopes in the Upper Indus River Basin. The predominant aspect direction lies along azimuths facing southwest (180–270u), which
Table 2. Distribution of landslides and different aspect faces. Inventory Slides Aspect (u) 0–45 46–90 91–135 136–180 181–225 226–270 271–315 316–360
Total Slides 171 263 249 286 332 442 324 187
%
7.6 11.7 11.0 12.7 14.7 19.6 14.4 8.3 Total 5 2,254
Documented Slides Total Slides
%
Rating
45
12.6
0.4
71
19.9
0.7
161
45.2
1
79
22.2
0.8
Total 5 356
face into the predominant storm tracks (Sarfraz, 2007; Ahasan et al., 2014). The maximum rating of 1 (“the most significant”), on a scale of 0 to 1, was assigned to this azimuth quartile (southwest) because it experiences the greatest increase in effective precipitation. Interestingly, higher densities of landslides were mapped on the southwest-facing slopes in this area (Ahmed et al., 2014) (see Table 2 and Figures A3 and A4 in Appendix A). Other slopes’ aspects were adjusted accordingly, with lower weights. This reclassified slope aspect map was then multiplied with the inclined rainfall raster using the Raster Calculator in ArcGIS, which allowed the computation of effective rainfall distribution across the slopes facing different aspects. The resultant effective/wind-driven rainfall map is shown in Figure 8, which can be compared with the original rainfall map (see Figure 3). The comparison shows that the intensity of rainfall in the study area is redistributed with respect to a differently weighted aspect map. It is also important to note that the locations of the previous minimum and maximum rainfall values were altered significantly after combining the incident rainfall raster with the aspect map. Landslide Susceptibility Mapping Techniques
Figure 7. A schematic presentation of incident rainfall distribution on sloping ground. The windward slopes will generally receive considerably more rainfall than the leeward slopes.
The heuristic/weighted overlay and fuzzy logic methods are well suited for regional studies seeking to construct reconnaissance-level susceptibility maps (Schernthanner, 2005; Erener and Uzgeun, 2008; Bachri and Shresta, 2010; Intarawichian and Dasananda, 2010; and Sharifi et al., 2011). Figure 9 presents a flow chart describing the stepwise procedure adopted for this study. The most important step in crafting a susceptibility map is the selection of indicator map units. The next step is to allocate different weights to the individual map layer attributes and rank them according to their anticipated
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Figure 8. Map illustrating the effective rainfall across the Upper Indus River Basin, generated by combining the inclined monsoon rainfall map (at θ 5 45) (seasonal monsoon rainfall monthly average) with the slope aspect map. Note the “rain shadows” that form on the northeastfacing slopes.
contribution to slope instability. The criteria for assigning the weights and ranking of different input layers were based on expert knowledge of landslides in the study area. The slope aspect exerts a marked
effect on susceptibility of the local topography, often triggering asymmetric deterioration and disintegration of slope surfaces due to solar radiation, prevailing wind directions, and precipitation volume falling on
Figure 9. Flow chart explaining the methodology adopted to compute wind-driven rainfall and landslide susceptibility mapping.
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Landslide Susceptibility Screening Table 3. Various combinations of map layers (%) were used for the weighted overlay landslide susceptibility index mapping, using both the conventional rainfall intensity and wind-driven rainfall raster maps. Run 1 3 4 5 8 9
Relief
Slope
Curvature
10 5 5 5 5 5
10 25 20 20 20 15
10 5 5 5 5 5
Aspect (10 (05 (10 (05 (10 (10
+ 10) + 10) + 05) + 10) + 10) + 10)
Rain
Seismic Hazard
Faults
Drainage
NDVI
Geology
10 10 10 5 5 10
10 10 15 20 15 20
10 10 10 10 5 10
10 5 5 5 5 5
10 15 15 15 20 10
5 20 5 15 5 15 5 15 5 20 5 20
NDVI 5 Normalized Difference Vegetation Index.
different slopes (Tarolli et al., 2011; Liu and Shih, 2013). The slope aspect map was divided into eight different classes of 45u. Each class (slope face) was then compared and overlapped with the available data on landslides. The analysis revealed that the landslide density varies across different slope aspects (slope faces). The maximum number of landslides (~45 percent of the 2,254 slides mapped along the Indus River) were observed on southwest-facing slopes (see Table 2). These observations point to the important role likely played by the wind-driven monsoon in triggering landslides. This analysis also aided the authors in rating different slope faces with respect to their anticipated instability. Similarly, the other map layers, including the lithology, elevation, slope angle, seismic hazard, faults, and drainage networks, were also compared with the spatial distribution of mapped landslides and rated individually, based on expert knowledge (see Table B1–B3 in Appendix B). All of the input map layers exhibiting different numerical attributes and units were reclassified to a common scale of 1 to 9 in ArcGIS, where 1 signifies the lowest susceptibility and 9 the highest with respect to slope instability (see Tables B4 and B5 in Appendix B). In this way the resulting reclassified map layer was transformed into a raster data set in which each individual cell value equates to an anticipated probability of risk. Several combinations of input factor maps were used to perform sensitivity analysis in order to estimate the most reasonable susceptibility maps. The
zones delineate different levels of susceptibility and were obtained by overlapping “controlling factor” map layers, then dividing these into four main groups: low hazard (0–25 percent), moderate hazard (26–45 percent), high hazard (46–65 percent), and very high hazard (.65 percent), according to their respective levels of susceptibility (Ahmed et al., 2014).
RESULTS AND DISCUSSION Landslide susceptibility hazard zones were delineated based on two widely accepted methodologies for regional area studies (.10,000 km2): GIS heuristic weighted overlay and fuzzy logic techniques. Susceptibility Maps Obtained from GIS-Weighted Overlay Index Technique GIS heuristic–weighted overlay is qualitative in nature and depends upon the expert’s judgement. According to this technique the layer maps are reclassified on a common scale and then each individual map layer is weighted differently on a “percent age” scale (total count, 100 percent). For this study, reclassified input map layers (on a scale of 1 to 9) were combined by giving different weights to each individual map layer, with their anticipated significance toward landslide instability. A few combinations of equally and differently weighted layer maps are summarized in Table 3. The first two susceptibility maps were
Table 4. Variation in distribution of the landslide susceptibility hazards zones (%) depending on weighted combinations of different map layers, using conventional rainfall intensity map and its equivalent wind-driven rainfall raster. Low Hazard Combination Run Run Run Run Run Run
1 3 4 5 8 9
Moderate Hazard
High Hazard
Very High Hazard
Run a
Run b
Run a
Run b
Run a
Run b
Run a
Run b
20.3 19.3 20.1 23.1 22.4 24.7
22.5 18.1 19.1 25.0 23.4 27.8
48.0 44.2 37.2 32.4 39.6 41.2
46.1 41.2 40.0 36.0 40.6 39.1
22.7 24.4 28.1 29.2 27.2 23.0
24.0 28.4 27.8 25.2 28.3 24.0
9.0 12.1 14.6 15.3 11.8 11.1
7.4 12.3 13.1 13.8 7.7 9.1
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Figure 10. Landslide susceptibility map derived from equally weighted map layers employing inclined rainfall and slope aspect as separate map layers (Run 1a).
modeled to ascertain whether there was any significant difference generated by combining the incident rainfall map layer with the slope aspect map layer, as compared to a susceptibility map constructed by employing them as separate map layers. The results obtained from the two maps are tabulated in Table 4, in terms of percentage of the respective area for increasing hazard levels. All of the
combinations show a decrease in very high hazard zones, with a corresponding increase in the low hazard, and mixed trends in other zones when incident rainfall and aspect maps were used in combination (effective rainfall raster). In Run 1a (Table 4), all of the map layers were given the same weight (10 percent), including the rainfall and aspect map layers (Figure 10). In Run 1b (Table 4),
Figure 11. Landslide susceptibility map derived from equally weighted map layers, but employing incident rainfall and slope aspect as a combined map layer, weighted 20 percent (Run 1b).
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Figure 12. (A) Enlarged portions of the equally weighted overlay index map, employing inclined rainfall and aspect as separate map layers (employing a 10 percent weight for all 10 map layers, including inclined rainfall and slope aspect, Run 1a); (B) Enlarged portion of the equally weighted overlay index map, but employing inclined rainfall and aspect as a combined map layer weighted at 20 percent (Run 1b). Note how the upper susceptibility map (A) predicts more severe slope instability than does the lower susceptibility map (B).
eight map layers were assigned weights equal to 10 percent, but the rainfall and slope layers were combined and weighted at 20 percent in order to compare the two procedures (Figure 11).The results show that the susceptibility map produced using equally weighted map layers (Run 1a) appears to overestimate the high hazard zone in some aspect directions (i.e., not significant rainfall directions), as compared to the map employing separately weighted rainfall and aspect layers (Run 1b). Overall, there was a 1.6 percent decrease in very high hazard estimation when we employed rainfall and aspect as combined layers (comparable to wind-driven rainfall). Hence, the map from
Figure 13. Schematic pixel values illustrating how different results are obtained when rainfall and slope aspect rasters are employed as separate map layers (above) or as a combined map layer in landslide susceptibility evaluations.
Run1b looks more reasonable and appears to be a more credible spatial prediction of landslide suscepti‐ bility (see Table 4). Figure 12A and B present an enlarged portion of the Indus River channel in its lower elevations, where the anticipated rainfall (600–900 mm monthly average) impact is linked to the predicted landslide hazards. A careful comparison of these two maps suggests that the landslide susceptibility map (Figure 12A) prepared using the equally weighted layers (including rainfall and aspect as separate map layers) results in a more severe prediction of hazardous areas (1.6 percent more very high hazard estimation, see Table 4), as compared with the map that employed rainfall and aspect as a combined map layer, weighted 20 percent (Figure 12B). This difference (particularly shown in highlighted zones on Figure 12A and B) can be explained by considering the schematic pixel values shown in Figure 13, which presents the various pixel combinations that were used. Different results were achieved for the same pixel locations by applying basic math (i.e., the cross multiplication carried out within the matrix) for rainfall and slope aspect layers. Several comparisons presented in Table 4 suggest that it appears more reasonable to incorporate incident rainfall and slope aspect maps as a single raster map for landslide susceptibility mapping in this region, in which the rainfall incidence appears to be a significant factor (overall, the decrease in “high to very high susceptibility” was noticed according to the results presented in Table 4).
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Figure 14. Landslide susceptibility map of the upper Indus River Basin prepared using the fuzzy logic approach, considering inclined rainfall (excluding slope aspect map layer) and excluding areas covered by alpine glaciers.
Susceptibility Maps Obtained Using the GIS Fuzzy Logic Technique Fuzzy logic is a semi-quantitative technique that has been used by numerous researchers to assess landslide susceptibility on a regional scale (e.g., Binaghi et al., 1998; Pistocchi et al., 2002; Saboya et al., 2005; Pradhan, 2010, 2011; Feizizadeh and Blaschke, 2011; and Kayastha et al., 2013). This technique is based on classical fuzzy set theory, which was introduced by Zadeh (1965). In landslide susceptibility mapping fuzzy logic defines the instability factors as members of a set ranging from 1 (expressing the highest susceptibility to landsliding) to 0 (expressing no susceptibility to landsliding) and allows different degrees of membership therein, between these extremes. First the fuzzy memberships were allocated to the reclassified input map layers (Tables B4 and B5 in Appendix B) based on expert knowledge. There are several fuzzy operators (fuzzy AND, fuzzy OR, fuzzy
Table 5. Variation in the distribution of the landslide susceptibility hazards zones (%) for the maps constructed using the fuzzy logic technique.
Combination 1 2
308
Low Hazard
Moderate Hazard
High Hazard
Very High Hazard
15 14
44.5 37
27 33
13.5 16
algebraic sum, fuzzy algebraic product, and fuzzy gamma) available; those could be used to combine the input map layers in order to compute the different levels of susceptibility (Pradhan, 2011; Kayastha et al., 2013). The fuzzy gamma (γ) operator is found to be more suitable for the regional kind of analysis by many researchers (Pradhan, 2011; Feizizadeh and Blaschke, 2011). Figure 14 presents the susceptibility map produced with an inclined rainfall map fuzzification (excluding the aspect map), using a fuzzy overlay (see Table 5, combination 1). Figure 15 shows the susceptibility map produced with incident rainfall and aspect maps combined (shown in Table 5, combination 2). An analysis of the results obtained from the two combinations is summarized in Table 5. These reveal that the fuzzy overlay index method appears to be less sensitive to the assignment of relative weights to each layer because it is semi-quantitative in nature, as compared to the heuristic method, in which the results are more predictive, based on manual inputs of parameter weights and rankings. Figure 16 shows an enlarged portion of the Indus River channel in its lower elevations, in which the anticipated incident rainfall impact is tied to the predicted landslide hazards (600–900-mm monthly averaged monsoon rainfall). The highlighted zones in these two images suggest that the susceptibility map produced with inclined rainfall map (excluding
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Figure 15. Landslide susceptibility map compiled using a fuzzy logic approach, considering incident rainfall and slope aspect as a combined map layer and excluding areas covered by alpine glaciers.
the aspect map) using a fuzzy overlay and the susceptibility map produced with inclined rainfall (see Figure 16A) tend to overrate the high to very high hazard areas, as compared with the map that employed rainfall and aspect as a combined map layer in applying fuzzy membership (Figure 16B).
Validation of Susceptibility Results The idea behind this study was to highlight the significance of wind-driven rainfall in estimating landslide susceptibility. The numerical values summarized in Table 4 and Figures 12 and 16 present a noticeable improvement in the susceptibility obtained using wind-
Figure 16. (A) Enlarged portion of the fuzzy overlay index map, employing rainfall as a separate map layer (excluding slope aspect); (B) Enlarged portion of the fuzzy overlay index map of the same region, with rainfall and aspect as a combined map layer. This portion of the susceptibility map suggests that rainfall (600–900 mm/mo) is a major triggering factor in the lower elevations of the study area. Detailed examination of the map in A shows that the high and very high susceptibility zones are overestimated when the rainfall raster is input as a separate variable, without including the slope aspect raster.
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Figure 17. Landslide inventory overlapped with the landslide susceptibility map.
driven rainfall versus conventional susceptibility mapping employing simple rainfall intensity maps. However, the results obtained from this study were also compared with the previously documented (historic) landslides as well as the landslide inventory data (Figure 17). Zones of high to very high susceptibility were clustered about the tectonically active Nanga Perbat Haramosh region, where numerous active thrusts perturb the Himalaya (the MMT, MKT, and other unnamed thrust faults). The comparison shows that 85 percent of the landslide loca� tions match with the high to very high susceptibility levels, which is quite satisfactory for this regional-level study. CONCLUSIONS The present research emphasizes the importance of using wind-driven rainfall rasters in landslide susceptibility mapping for regional-level studies. Both methods employed for this study were simple and were deemed suitable to produce reconnaissance-level susceptibility maps of a sizable mountainous region. The use of conventional rainfall isohyet (intensity) rasters might exaggerate the landslide susceptibility hazards on some slopes while significantly underestimating the hazards on other slopes. The concept of including incident rainfall, based on the regional rainfall data, and coupling it with slope aspect (directional monsoon) was introduced to generate wind-driven rainfall (effective rainfall). A 41 percent increase in actual rainfall intensity was noted
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using De Lima’s nomograph (1990) for suggested monsoon incidence of 45u with an average wind speed of 10 m/s (see Table 1). The susceptibility predictions obtained using wind-driven rainfall maps by applying the heuristicweighted overlay index and fuzzy logic mapping techniques were compared with previous landslide susceptibility maps generated from conventional rainfall rasters and slope aspect as individual map layers (see Table 3). The map generated from the equally weighted layers, including combined incident rainfall and aspect layers, predicts lower landslide susceptibility hazards than does the map prepared using equally weighted map layers with rainfall and aspect, separately weighted (see Figures 12 and 16). The other combinations also exhibited noticeable refinements in the susceptibility mapping predictions when employing incident rainfall in combination with slope aspect rasters (see Tables 4 and 5). The susceptibility results were also validated with the available data on landslides in the region. As this is a regional study covering ~75,000 km2, the same concept might be applied to smaller areas. With better-resolution data, more refined and accurate landslide susceptibility distribution zones could be expected from similar susceptibility studies. ACKNOWLEDGMENTS The authors wish to thank the Missouri University of Science and Technology, the Geological Survey of Pakistan, and the Pakistan Metrological Department
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for their support of this study. This research was supported by a scholarship grant from the University of Engineering and Technology, Lahore, Pakistan. REFERENCES AHASAN, M. N.; CHOWDHURY, M. A. M.; AND QUADIR, D. A., 2014, The summer monsoon weather system and its relationship with rainfall over South Asia: Open Journal Atmospheric Climate Change, Vol. 1, No. 2, pp. 2374–3808. AHMED, M. F. AND ROGERS, J. D., 2014a, Significance of Wind-Driven Rainfall in Landslide Susceptibility Mapping: AEG 57th Annual Meeting, Scottsdale, AZ, Vol. 57, 41 p. AHMED, M. F. AND ROGERS J. D., 2014b, Creating reliable, firstapproximation landslide inventory maps using ASTER DEM data and geomorphic indicators, an example from the upper Indus River in northern Pakistan: Environmental Engineering Geoscience, Vol. 20, No. 1, pp. 67–83. AHMED, M. F.; ROGERS, J. D.; AND ISMAIL, E. H., 2014, A regional level preliminary landslide hazard study of upper Indus River basin: European Journal Remote Sensing, Vol. 47, pp. 343–373. ANDERS, A. M.; ROE, G. H.; HALLET, B.; MONTGOMERY, D. R.; FINNEGAN, N. J.; AND PUTKONEN, J., 2006, Spatial patterns of precipitation and topography in the Himalaya. In Willett, S. D.; Hovius, N.; Brandon, M. T.; and Fisher, D. (Editors), Tectonics, Climate, and Landscape Evolution: Geological Society of America Special Paper 398, pp. 39–53. AWAN, S. A., 2002, The climate and flood risk potential of northern areas of Pakistan: Science Vision, Vol. 7, Nos. 3–4, pp. 100–109. BACHRI, S. AND SHRESTA, R. P., 2010, Landslide hazard assessment using analytic hierarchy processing (AHP) and geomorphic information system in Kaligesing mountain area of Central Java Province, Banda Ache, Indonesia. In Agussabti, Syamsidik, Nasaruddin, Fatimah, Azmeri, Arnia (Editors), 5th Annual International Workshop and Expo on Sumatra Tsunami Disaster and Recovery: Tsunami and Disaster Mitigation Research Center, Banda Ache, Indonesia, pp. 107–112. BINAGHI, E.; LUZI, L.; MADELL, P.; PERGALANI, F.; AND RAMPINI, A., 1998, Slope instability zonation: A comparison between certainty factor and Fuzzy Dempster-Shafer approaches: Natural Hazards, Vol. 17, pp. 77–97. BLOCKEN, B.; CARMELIETA, J.; AND POESEN, J., 2005, Numerical simulation of the wind-driven rainfall distribution over small-scale topography in space and time: Journal Hydrology, Vol. 315, pp. 252–273. CANNON, S. H. AND ELLEN, S., 1985, Rainfall conditions for abundant debris avalanches in the San Francisco Bay region, California: Geology, Vol. 8, No. 12, pp. 267–272. CRAIG, D., 1980, Two examples of the effect of topography on rainfall distribution patterns: Weather, Vol. 35, No. 10, pp. 301–307. DE LIMA, J., 1990, The effect of oblique rain on inclined surfaces: A nomograph for the rain-gauge correction factor: Journal Hydrology, Vol. 115, pp. 407–412. ERENER, A. AND UZGEUN, H. S. B. D., 2008, Analysis on landslide hazard mapping methods: Regression models versus weight rating: International Archives Photogrammetry, Remote Sensing Spatial Sciences, 37 (Part B8), Beijing. ERPUL, G.; NORTON, L. D.; AND GABRIELS, D., 2003, Sediment transport from interril areas under wind-driven rain: Journal Hydrology, Vol. 276, Nos. 1–4, pp. 184–197. FEIZIZADEH, B. AND BLASCHKE, T., 2011, Landslide risk assessment based on GIS multi-criteria evaluation: A case study in
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APPENDIX A Additional Figures
Figure A1. Input map layers for landslide susceptibility analysis: (A) elevation map, (B) slope angle map, (C) curvature map, and (D) slope aspect map. Note that all of these raster maps were extracted from ASTER DEM 30-m data.
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Figure A2. Input map layers for landslide susceptibility analysis: (E) NDVI map extracted from Landsat TM5 satellite imagery (collected between 2008 and 2011 of the monsoon rainfall season [mid-June to mid-September]), (F) drainage map extracted from ASTER DEM 30-m data, (G) rasterized seismic hazard map (Giardini et al., 1999), and (H) rasterized structure map (Kazmi and Rana, 1982).
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Figure A3. Overlay of landslide inventory map and aspect map layer.
Figure A4. Zoomed-in image showing the overlay of landslide inventory map and aspect map layer in NPHM region.
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APPENDIX B Additional Tables
Table B1. Comparison between slope angles and mapped landslides. Slope Map (u)
No of Slides
% Age
252 746 1,010 214 32
11.2 33.1 44.8 9.5 1.4
Table B2. Comparison between elevation map and mapped landslides. Elevation Map (m)
0–15 16–30 31–45 46–60 .60
304–1,000 1,001–2,000 2,001–4,000 4,001–6,000 .6,000
No. of Slides
% Age
91 541 1,443 158 21
4 24 64 7 .1
Table B3. Normalized relationship between different geologic rock units and mapped landslides. Slide No. 1 6 2 3 4 5 7 8 9 10 12 13 14 15 16 Total
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Rock Unit PsPg, Cb, and CDK KJd Tkk JPzd MPzm MPzs Tkm and Tkb KJc Jk PCb and PCs PCt Eg JPm Eat PCa
Mapped Area (km2)
Area % of the Total
No of Slides/ Unit Area
No of Slides/ 100 km2
—
No of Mapped Slides
Documented Slides
— 112.32 1,511.21 71.19
0.66 8.85 0.42
0.2048 0.1800 0.2528
20 18 25
— — — 23 272 18
4,497.32 4,641.12 2,151.68
26.33 27.17 12.60
0.1054 0.1351 0.1157
11 14 12
474 627 249
5 18 7
2,263.79 519 850.27 262.3 37.9 161.04 17,079.14
13.25 3.04 4.98 1.54 0.22 0.94
0.1361 0.1965 0.1305 0.2249 0.2375 0.1304
14 20 13 22 24 13
308 102 111 59 9 21 2,254
9 — — — — —
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21 18 3 38 31 15
Landslide Susceptibility Screening Table B4. Ranking of different geologic rock units for landslide susceptibility analysis. S. No
Geologic Formation
1 2 3
Cb (Carboniferous rocks) CDK (Carboniferous to Devon. rocks) Eat (Cambrian rocks)
4 5
Eg ( Cambrian igneous rocks) JK (Jurassic rocks)
6
JPm (Jurassic to Permian metasediments)
7 8 9
JPzd (Jurassic to Paleozoic rocks) KJc (Cretaceous to Jurassic rocks [Chilas]) KJcy (Cretaceous to Jurassic)
10 11
MPzm Mesozoic to Paleozoic(Metasedimentary rocks) MPzs (Meso to Paleozoic rocks)
12 13
Mz (Mesozoic rocks) PCa (Permian to Carboniferous igneous rocks
14
PCb n PEb (Pre-Cambrian basement rocks)
15
PEm (Pre-Cambrian low-grade metasedimentary rocks)
16 17 18 19
PEs (Precambrian metamorphic rocks) Pet (Pre-Cambrian metamorphic and sedimentary rocks) Ps-Pg (Permian rocks) Pzm (Paleozoic rocks)
20 21 22 23 24 25
Q1 (surficial deposits) Tkb (Miocene to cretaceous, batholith and plutons) TKk (Miocene to cretaceous, batholith and plutons) Tkm (Mafic and felsic) KJd (Dras volcanic rocks) CpEm (Carboniferous to Pre-Cambrian metasedimentary and sedimentary rocks)
Major Rocks
Rating
Slates, phyllitic slates with subordinate limestone and quartzite Crinoidal limestone, dolomite, and partings of slates Limestone, dolomite, sandstone shales, mudstone, conglomerate, etc. Mostly granite and finely foliated gneisses Intensely deformed, banded amphibolites, hornblende, gabbros, diorite, garnet schist Marble and dolomitic marble, graphitic phyllitic and calcareous schist Slate, phyllite, gneiss, quartzite, limestone, and marble. Norite, pyroxene-gabbros, dunite, and peridotites Volcanoclast sediments, metamorphosed green schist, interbedded slates Sandstone, shale quartzite, limestone, slates, phyllite Volcanic rocks, limestone, red shale, sandstone, quartzite, conglomerate Fossiliferous limestone, shale, marl, and sandstone, etc. Alkaline and tourmaline granite, Syenite with miner carbonates Feldspathic gneiss, graphitic schist, quartzite and marble intruded with granite, diorite Slates, quartzose sandstone, phyllite, algal limestone, quartzite units Schistose to Phyllitic quartzite, schist, slate marble Metaquartzite, Garnet mica schist Dolomite, fossiliferous limestone, and shale sandstone Slate, phyllite and quartzite with gabbro, diorite, and granite intrusions Clays, silt, sands, and gravels Granite, granodiorites, hornblende gabbros, etc. Granite, granodiorites, diorite, and granitic gneiss, etc. Younger tertiary Gabbros, diorite and granite and pegmatites Basalt, andesite, and pillow lava Schist, phyllite, marbles, quartzite, dolomite, limestone slate
7 3 8
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3 5 5 5 3 6 8 5 5 2 6 5 4 5 4 3 1 2 2 3 5 6
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Rogers, Ahmed, and Ismail Table B5. Ranking of different input map layers for landslide susceptibility analysis.
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Empirical Methods and Estimation of Hydraulic Conductivity of Fluvial Aquifers SUDARSAN SAHU1 Central Ground Water Board, South Eastern Region (SER), Bhujal Bhawan, Khandagiri, Bhubaneswar 751030, Odisha, India
DIPANKAR SAHA Central Ground Water Board, Bhujal Bhawan, NH-IV, Faridabad 121001, Haryana, India
Key Terms: Grain Size Analysis, Hydraulic Conductivity, Empirical Equation, Effective Grain Size, Pumping Test
ABSTRACT The present work evaluates a few established empirical equations that calculate the hydraulic conductivity (K) of aquifer materials using grain size parameters. Loose sand samples (N 5 51) of unconsolidated fluvial deposits, obtained from various aquifer zones in boreholes (N 5 4), were used for the purpose. Grain size analyses of the samples were carried out through dry sieving, and different particle size parameters were determined from the size grading curves. The K values were estimated using the empirical equations. The applicability of the methods were assessed by estimating the K of fine to very coarse sand. To appraise the suitability of the methods, the K values were compared with those estimated through conducting pumping tests in the tube wells. The Breyer, Hazen, Terzaghi, and United States Bureau of Reclamation methods maintain consistency in estimating the K values of the fluvial sand with respect to the grain sizes. The Kozeny-Carman method yields moderately underestimated values of K for medium-coarse to very coarse sand. Slitcher and Terzaghi methods often underestimate the K values. While the Alyamani and Sen (A&S) method calculates the K within range for sand populations with Uc , 5, it is sensitively dependent on the shape of the size grading curve and gives underestimated values for materials with Uc . 5. INTRODUCTION The hydraulic conductivity (K) of water-bearing formations determines the ease with which water passes 1 Corresponding author. tel.: +91-9438365741; email: sudarsan_cgwb@ yahoo.co.in.
through the porous media (Darcy, 1857; Hubbert, 1940; Alyamani and Sen, 1993; and Chakraborty et al., 2006). Information about its spatial variation within the aquifer helps to create better groundwater development and management plans, predict contaminant transport mechanisms, and solve a number of geotechnical problems (e.g., Smith and Schwartz, 1980; Sudicky, 1986; Boadu, 2000; Conant et al., 2004; and Saha et al., 2007, 2009, 2011a). Field techniques such as the pumping test, augur hole test, slug test, and tracer test are the most trusted ways to estimate the K of saturated formations (e.g., Taylor et al., 1987; Melville et al., 1991; Jones et al., 1992; Vukovic and Soro, 1992; Meinken and Stobar, 2003; and Todd and Mays, 2005). However, due to lack of precise knowledge of aquifer geometry and hydrogeologic boundaries, the ability to accurately determine K in field conditions is limited (Ishaku et al., 2011; Uma et al., 1989). The field techniques, which involve construction of tube wells for carrying out different tests, are time consuming and expensive. There are laboratory techniques (Todd, 1980; Vukovic and Soro, 1992; Todd and Mays, 2005; and Yeol et al., 2005), which face the problem of collecting undisturbed samples representing aquifer. Further, permeameter tests, involving the downward infiltration of water through the sediment/soil profile, are a function of vertical hydraulic conductivity (Taylor et al., 1987). Empirical methods based on sediment grain size have alternatively been used as laboratory techniques since the 19th century (e.g., Hazen, 1892; Slitcher, 1899) for estimating conductivity of aquifer materials. The methods are less expensive and do not depend on the geometry and hydraulic boundaries of the aquifer (Alyamani and Sen, 1993; Odong, 2007; and Ishaku et al., 2011). Field techniques such as pumping tests no doubt provide the best estimates of K with a greater insight into the conductivity in the aquifer over a larger area. However, during preliminary hydrogeological investigations, it is advantageous to use empirical methods, which can give first approximations regarding the conductivity in the aquifer at the location. A
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carefully chosen method can estimate the K values best approaching the in situ measured values (Taylor et al., 1987). Various researchers on groundwater have tried to find a relation between the grain size of aquifer material and the hydraulic conductivity (e.g., Hazen, 1892; Slitcher, 1899; Kozeny, 1927; Carman, 1937, 1956; Krumbein and Monk, 1942; Breyer, 1964; Terzaghi and Peck, 1964; Masch and Denny, 1966; Ahuja et al., 1989; Shepherd, 1989; and Alyamani and Sen, 1993). However, the equations have their own limits of applications and give only approximate values of the K for point samples (Detmer, 1995; Cheng and Chen, 2007; Odong, 2007; Song et al., 2009; Ishaku et al., 2011; Vienken and Dietrich, 2011; MacDonald et al., 2012; and Takounjou et al., 2012). Oh et al. (2013) observed that, for Quaternary fluvial deposits consisting of fine to coarse sand and sandy gravels, the K values determined by using the empirical equations lie in-between those determined from in situ tests. The K values of the same aquifer material estimated by using different empirical methods may also differ from each other (Vukovic´ and Soro, 1992; Milham and Howes, 1995; Kasenow, 2002; Odong, 2007; Song et al., 2009; and Vienken and Dietrich, 2011). Odong (2007) and Ishaku et al. (2011) got wide ranges of K values from these methods for aquifers consisting of sand and gravels, but they did not verify the K values with in-situ estimates. It is generally observed that the grain size–based empirical equations are best suited for sediments dominated by loose sand and gravel, and they are less suited for deposits dominated by silt and clay (Vukovic and Soro, 1992; Chapuis, 2004). The dilemma when applying the empirical methods lies in the fact that the conductivity they estimate is uncertain. Chen (2000) and Song et al. (2009) argue that the grain-size methods provide neither horizontal conductivity nor vertical conductivity. However, the values of K for clastic sediments demonstrated by the pioneer workers (e.g., Shepherd, 1989; Alyamani and Sen, 1993) approach more towards the horizontal K. In anisotropic media of stratified sand, the horizontal K is higher than the vertical K (at least 3 times; Powers, 1992). Ayers et al. (1998) and Cheng and Chen (2007) found higher K values estimated from the empirical methods than the vertical K of the aquifer determined from pumping tests. The methods yield higher (maximum: 3–6 times) K values for streambed samples in comparison to the vertical conductivity obtained by conducting permeameter tests (Rahn, 1968; Song et al., 2009). This suggests that for the assessment of the empirical methods, the derived K values can be compared with the horizontal K obtained from in situ methods.
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The present study evaluates the conditions of applicability and suitability of several empirical methods for determining the K of fluvial sand. The samples of aquifer materials (N 5 51) used for testing the methods consist of unconsolidated granular formations of fluvial origin obtained from boreholes (N 5 4) in parts of the Gangetic Plains. The strengths and weaknesses of the empirical methods were assessed by comparing their results with those obtained from pumping tests in tube wells (N 5 3) constructed in the boreholes. The results have applicability even beyond the boundaries of the Gangetic Plains. BOREHOLE LOCATION AND DEPOSITIONAL SETTING The boreholes considered for the present study are distributed in an area of approximately 250 km2 in the Sone-Ganga interfluves in the middle reaches of the Gangetic Plains in India (Figure 1). The area forms a part of the mega-fan created by the Sone River in the southern marginal parts of the basin (Geddes, 1960; Sahu, 2012; and Sahu and Saha, 2015). Downstream of the Allahabad, the Ganga River flows very close to the southern Indian craton. Further downstream, the river has been pushed northward by the Sone mega-fan and tectonic activities in the region (Sahu et al., 2010; Sahu and Saha, 2015). The mega-fan forms the widest marginal plain in the entire Ganga Basin. The active Ganga River has incised on to the mega-fan surface at its northern fringes. The craton-derived bed load in the Sone River is oxidized brownish yellow, fine to very coarse in nature with frequent gravel admixtures. The channel avulsions in the Sone have built stacked columns of sand bodies a few hundred meters thick intervened with minor clay layers. The sediment samples obtained from various depths in the mega-fan and those from the channel bed of the active Sone River show similar textural characters of roundness (semi-rounded to well rounded) and size (Misra and Valdiya, 1960; Maitra and Ghose, 1992). Fluvial regimes (discharge and sediment supply) controlled by climate and tectonics have largely been responsible for the geomorphological evolution of the Sone mega-fan during the late Quaternary (Sahu et al., 2010). DATA USED AND METHODOLOGY Borehole Sampling We used drill-cut samples of four boreholes up to a depth of 250 m below ground level (bgl). The boreholes were drilled by a rotary rig using drill bits (rock-roller type) of diameter 216 mm. Bentonite
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Empirical Hydraulic Conductivity Estimation for Fluvial Aquifers
Figure 1. (A) Schematic outline of Ganga Basin in India. (B) Map of Ganga Basin depicting the extent of Marginal Alluvial Plain (MAP) at the distal parts of the basin. (C) The Sone-Ganga interfluves in Middle Ganga Plain, India, showing the location of boreholes, the samples of which have been utilized for grain size analysis. Except the upper 30–40 m of Himalayan-derived (gray color) sediment laid down by the Ganga River, the boreholes display mostly the peninsular (brownish yellow) sediments down to their bottom (refer Figure 2). These sediments might have been brought by the Sone River and deposited in its mega-fan (Geddes, 1960; Sahu, 2012; Sahu et al., 2015).
mud was used as the additive to water for the drilling fluid. The resultant slurry is superior to pure water while drilling in highly porous and water-bearing formations. Its viscosity possesses the ability to suspend relatively coarse and heavy particles. It tends to form a thin, low-permeable cake on wall of the borehole, preventing collapse of formation material. In general, however, borehole sampling while drilling with a mud rotary rig is cumbersome and leads to erroneous sampling if proper attention is not paid. The viscous drill mud hinders the settling of fines along with the coarser materials in the sample catcher, which are lost to the mud pit, and the samples lose their representativeness of true formation materials. It is more troubling if the samples are meant for estimation of aquifer parameters such as hydraulic conductivity. In view of this, the density of the drill mud was checked frequently to ease the settling of fines in the sample catcher. This was done either by adding mud or water, whichever was necessary. Maintaining the density of the fluid also minimizes the mixing of
samples from different zones (Driscoll, 1986). For better sampling purposes, the drilling rate was kept within 8–10 m/hr while penetrating the granular zones in order to have control over the volume of sediment cuttings coming to the sample catcher. At regular intervals of 3 m, the well was washed to clean the hole from the drill-cut materials before progressing for further drilling. Thus, the samples obtained represent largely 3 m intervals unless there was a change in lithology. After crossing every clay zone, in which the drilling rate remained ~1 m/hr, the hole was properly washed, and the fluid density was corrected for the damage done by the mixing of formation clay in it. However, the possibilities of slight mixing up of the samples, particularly in the transitional zones, cannot be completely ruled out. The samples were washed properly in clean water through mild rinsing in a container to remove the remaining drill mud. During this process, care was taken so that even the finest of fine of the aquifer materials would not be lost. The litholog, thus prepared,
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— A&S 7
1
USBR 6
1300[Io + 0.025(d50 − d10)]2
1
d20 1
Kozeny-Carman 5
0.36
Slitcher Terzaghi 3 4
(g/v)Ck f(n)d102
Breyer 2
0.36(d202.3)
d10 n3/(1 – n)2
Coarser than clay d10 , 3 mm Medium-grain sand Uc , 5 Well-graded sand
d10 d10 n 3.287 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n 0:13 3 1 n
0.01 bγ 5 10.7 6 10−3 for smooth grains, 6.1 6 10−3 for large grains. Ck 5 8.3 6 10−3
d10 1 Cb 5 6 6 10−4 log 500/Uc
d10 1 + 10(n − 0.26)
Domain of Applicability
Ch 5 6 6 10 Hazen 1
where Cb is the Breyer empirical coefficient 5 (6 6 10−4) log 500/Uc. It is applicable for 1 , Uc , 20 and 0.06 mm , d10 , 0.6 mm. Thus, it is useful for analyzing heterogeneous porous media with the poorly sorted grains.
322
Effective Grain Diameter
g Cb d10 2 ; v Author
K ¼
d102ffi (g/v) 6 1 6 10−2 n 3.287 pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 (g/v)bc n 0:13 3 1 n d10 2
The Breyer method does not take into account the porosity as a function in the equation to determine the hydraulic conductivity (porosity value taken as unity in Table 1). The equation is given as:
(g/v)Cb d102
Breyer Equation (1964)
(g/v)Ch
where Ch is the Hazen empirical coefficient 5 6 6 10−4, g 5 acceleration due to gravity in m/s2, v 5 kinematic viscosity of water in m2/s, f(n) (function of porosity n) 5 1 + 10(n − 0.26), and d10 (in mm) is the effective grain size, which represents the largest grain diameter of the smallest 10 percent of grains in the samples. The equation is suitable for sediments with Uc , 5 and 0.1 mm , d10 , 3 mm. Uc is the uniformity coefficient of formation samples and is defined as “d60/d10,” where d60 and d10 represent the sieve diameters retaining 40 percent and 90 percent of the samples, respectively.
−4
g Ch f ðnÞd10 2 ; v
Sl. No.
K ¼
Porosity Function
The history of equations relating the hydraulic conductivity to grain size began with Hazen (1892), who initially derived an equation to estimate the K of loose and uniformly graded sand. The most widely accepted and used Hazen equation is:
Coefficients
Hazen Equation (1892)
Empirical Formula
A few empirical formulae (adopted from Vukovic and Soro, 1992; Kresic, 1997; and Kasenow, 2002) used for estimating the K values of aquifer materials are presented in Table 1. The equations are further elaborated in the following:
Table 1. Brief summary of the empirical methods used and their applicability for determination of hydraulic conductivity.
Empirical Equations
f(n)d102
was finally calibrated for correction of depth by reconciling it with the drill time log and the electrical logging report. For the present study, only the sand samples obtained from the granular zones were considered for analysis and determination of the K values.
Uc , 5.0 0.1 mm , d10 , 3 mm 1 , U c , 20 0.06 mm , d10 , 0.6 mm 0.01 mm , d10 , 5 mm for large-grain sand
Sahu and Saha
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Empirical Hydraulic Conductivity Estimation for Fluvial Aquifers
Slitcher Equation (1899) Slitcher devised the following formula while describing quantitatively the steady-state groundwater flow field in response to a discharging well. K¼
g 1 10 2 n3:287 d10 2 : v
This formula is applicable for sand populations with effective grain diameter (d10) between 0.01 and 5 mm. Terzaghi Equation (1964) Terzaghi formulated the following equation using d10 as the effective grain diameter. g bc K ¼ v
n 0:13 2 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi d10 2 ; 3 1 n
where bγ is the empirical coefficient dependent on the grain size and shape: bγ 5 10.7 6 10−3 for smooth grains and 6.1 6 10−3 for large grains. Terzaghi’s formula is most applicable for large-grain sand (Vukovic and Soro, 1992). Kozeny-Carman Equation Initially proposed by Kozeny (1927) and later modified by Carman (1956), the equation is widely referred and used as Kozeny-Carman equation. It relates the hydraulic conductivity with the square of the effective grain diameter, porosity, and the physical properties of the fluid. The equation is given by: K ¼
g Ck f ðnÞd10 2 ; v
where Ck is Kozeny-Carman empirical coefficient 5 8.3 6 10−3, and f ðnÞ ¼
n3 ð1 nÞ2
:
This formula is not appropriate for either soil with effective size (d10) above 3 mm or for clayey soils (Carrier, 2003). United State Bureau of Reclamation (USBR) Equation The USBR formula calculates hydraulic conductivity taking d20 as the effective grain size. K ¼ 0:36 d20 2:3 ;
where the K is in cm/s, and d20 is in mm. It does not depend on porosity (Table 1). The formula is most suitable for medium-grain sand with Uc , 5 (Cheng and Chen, 2007). Alyamani & Sen (A&S) Equation (1993) Alyamani and Sen (1993) proposed an equation that was exceptionally different from the earlier form of equations. Instead of a single grain size parameter, the authors used d10 (effective grain diameter in mm) and d50 (median grain diameter in mm), considering the sorting character in the sediment sample. The equation is as below: K ¼ 1300½Io þ 0:025ðd50 d10 Þ 2 ; where K is the hydraulic conductivity (m/d), and Io is the intercept (in mm) of the line formed by d10 and d50 with the grain-size axis. The method is best suited for a well-graded aquifer sample (Odong, 2007). Sediment Grain Size Analyses Hydrogeological parameters like porosity, hydraulic conductivity, and permeability are greatly dependent on the size of sediment grains and the percentage of various sediment fractions. There are various techniques employed in grain size determination, such as direct measurement, dry and wet sieving, sedimentation, and measurement by laser granulometer, X-ray sedigraph, and coulter counter. However, the most widely used method to determine grain size distribution is by laboratory sieve analysis. For the purpose of sieve analysis, from the borehole lithologs, different water-bearing zones were identified with the help of their physical and textural characters, and the samples from respective zones were mixed together pro‐ perly. Photographs of few representative samples collected from the boreholes are produced in the Figure 2. A sediment sample of 250 g by weight was taken for sieving out of the bulk by a repeated process of coning and quartering. This was then put in the coarsest sieve at the top of a stacked set of sieves with the mesh diameters decreasing downward. The stacked sieves (of sizes 2.0, 1.0, 0.50, 0.25, 0.18, 0.12, and 0.70 mm) were placed in a mechanical shaker for sieving up to 10 minutes. The weight of each sand fraction retained in individual sieve was measured and expressed as percent of the initial (total) weight of the sample. The silt/clay (,0.07 mm) fraction in each sample was found to be ,1.0 percent, and hence only dry sieve analysis of the sand fraction was undertaken
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Figure 2. Photographs showing the representative aquifer samples obtained from the four boreholes at Karnamepur, Bharauli, Nargada Narayanpur, and Paharpur. (A, i–v) The craton-derived medium to very coarse sand, and (B, i–ii) Himalayan-derived fine sand.
(Alyamani and Sen, 1993). Because the samples were collected from a mud rotary rig, and there were chances of missing finer size ranges, it was essential to assess the representativeness of the samples. Earlier study has indicated that the silt/clay fraction is either lacking or constitutes a very minimal part of the samples of the Sone sand obtained from deeper portions of boreholes (Maitra and Ghose, 1992). However, in the present study, the grain size distribution patterns in bed-load samples (N 5 3) of the active Sone River (from pits 0.3 m deep on the channel bed of the river) were compared with the borehole samples. The Sone sand from the active channel is absolutely low in the silt/clay fraction (mostly 0.03 to 0.92 percent, maximum 1.7 percent), which is insignificant to affect the in situ hydraulic conductivity (Alyamani and Sen, 1993). Semi-logarithmic grain size distribution plots of both the active river and the borehole samples (Figure 3A–D) were prepared with the grain size on the X-axis given in the phi (φ) scale (φ 5 −log2d, where d is the grain size in mm). The curves of the river and borehole sediments display similar
324
particle size grading characters. This indicates that the older sand (from boreholes) is also low in clay/ silt content, signifying minimum loss of fines during sampling. From the grain size distribution curves, the median grain diameters (d50) were determined. The sand samples were classified according to the grain size classes given by Wentworth (1922). The grain size parameters, such as d10, d20, d50, d60 (sieve diameters that retain 90 percent, 80 percent, 50 percent, and 40 percent of the sample by weight, respectively), determined from the curves are presented in Table 2. The uniformity coefficients (Uc) of the sand populations (Table 2A–D) were calculated using the relation between the size parameters d10 and d60 as cited earlier. The curves were also utilized in determining the intercept Io taken in the A&S method. All these results were utilized by the formulae as described earlier to estimate the hydraulic conductivity of the aquifer samples. A value of 1.14 6 10−6 m2/s was taken as the kinematic coefficient of viscosity of water at a temperature of 25uC.
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Empirical Hydraulic Conductivity Estimation for Fluvial Aquifers
Figure 3. Grain size distribution curves for borehole sediments obtained from the four borehole locations: (A) Karnamepur, (B) Bharauli, (C) Nargada Narayanpur, and (D) Paharpur. The grain size (in x-axis) is given in phi (φ) scale. The size distribution patterns in borehole sediments have been compared with those in the bed-load sediments (N 5 3) in the active Sone River in the area in order to assess any loss of ďŹ nes during the sampling process (refer text for details).
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325
326
d10
(A) Karnamepur 19–31 0.45 31–38 0.28 38–44 0.60 44–50 0.23 50–68 0.22 68–90 0.33 90–100 0.24 100–115 0.29 130–135 0.33 135–156 0.35 156–159 0.20 159–203 0.33 222–228 0.22 228–234 0.20 234–237 0.30 237–250 0.20 (B) Bharauli 31–37 0.21 37–56 0.28 56–69 0.21 69–103 0.21 130–144 0.19 144–181 0.23 181–206 0.22 206–250 0.18 (C) Nargada Narayanpur 19–25 0.17 25–35 0.20 40–44 0.18 44–50 0.18 50–56 0.28 56–65 0.24 65–78 0.19 92–99 0.43 134–146 0.41 146–178 0.20 178–195 0.22 195–210 0.21 210–247 0.21
Depth Range (m) 1.42 1.12 1.36 0.87 0.65 1.25 1.14 1.40 1.55 1.57 1.22 1.42 1.06 1.24 1.47 1.35 1.05 0.84 0.85 0.65 0.42 0.82 0.75 0.45 0.20 0.45 0.35 0.30 1.00 0.64 0.39 1.15 1.13 0.55 0.91 0.86 0.61
0.31 0.37 0.3 0.27 0.21 0.36 0.32 0.2 0.19 0.22 0.21 0.20 0.38 0.34 0.21 0.63 0.61 0.23 0.34 0.33 0.28
d50
0.81 0.50 0.90 0.39 0.30 0.50 0.37 0.49 0.65 0.68 0.30 0.58 0.35 0.30 0.58 0.31
d20
0.21 0.51 0.43 0.35 1.31 0.72 0.51 1.35 1.28 0.75 1.15 1.10 0.70
1.35 1.09 1.10 0.88 0.55 1.05 0.97 0.62
1.58 1.31 1.50 1.09 0.82 1.55 1.42 1.70 1.80 1.85 1.51 1.70 1.41 1.50 1.75 1.66
d60
Sand Size Parameters (mm)
1.23 2.55 2.38 1.94 4.67 3.00 2.68 3.13 3.11 3.75 5.22 5.24 3.33
6.42 3.89 5.23 4.17 2.89 4.55 4.4 3.46
3.51 4.67 2.50 4.73 3.72 4.69 5.91 5.86 5.45 5.28 7.55 5.15 6.40 7.50 5.83 8.30
Uc
0.16 0.15 0.14 0.14 0.1 0.13 0.14 0.24 0.23 0.11 0.05 0.05 0.11
0.00 0.14 0.05 0.10 0.13 0.08 0.09 0.11
0.21 0.1 0.41 0.05 0.11 0.1 0.03 0.06 0.02 0.05 0.15 0.05 0.02 −0.07 0.01 −0.09
Io
46 41 42 43 36 40 41 40 40 38 35 35 39
33 38 35 37 40 36 37 39
39 36 42 36 38 36 34 34 35 35 32 35 33 32 34 31
N (%)
fs ms ms ms cs cs ms vcs vcs cs cs cs cs
vcs cs cs cs ms cs cs ms
vcs vcs vcs cs cs vcs vcs vcs vcs vcs vcs vcs vcs vcs vcs vcs
Sand Type*
3.6 40.8 34.1 24.4 71.8 65.9 41.1 86.7 85.2 54.4 70.2 69 65.9
69.1 70.9 67.1 58.5 43.5 69.6 67 47.1
82 73.9
83.6 85.2 69.1 83 72.1
88.7 80.4 93.2 74 62.1 79.6 72.1
cvcs
17.8 34.8 34 36 20.8 22.6 27.7 8.5 9.6 22.8 16.4 18 22.6
16.3 21.8 18.3 25 27.8 19.8 20 22.6
7.7 11.2 5.1 13.3 22.9 15.2 17.3 13.5 10.6 9 14.2 10.8 14.8 13.6 9.3 10.2
ms
78.4 24.4 31.8 39.6 7.4 11.6 31.1 4.8 5.2 22.7 13.3 13 11.6
14.6 7.4 14.5 16.5 28.6 10.6 13.0 30.1
8.7 16.4
5.8 5.8 16.8 6.1 13.0
3.6 8.4 1.7 12.6 14.9 5.2 10.6
fvfs
69.7
79.1
cs
16.7
7.4
fs
Various Sand Grades (%) vcs
38 45 37 37 71 59 41 191 178 38 41 37 46
34 76 38 42 39 48 45 33
205 68 409 45 48 95 46 66 88 104 28 91 37 28 73 27
HAZ
34 41 34 33 71 55 37 177 165 36 43 39 42
37 74 39 41 36 48 44 31
194 68 369 46 46 95 49 71 92 108 32 94 41 33 78 32
BREY
16 16 14 14 21 20 15 65 60 12 12 10 15
9 24 11 13 14 14 13 11
67 20 149 13 15 28 12 18 24 29 7 26 10 7 19 6
SLIT
37 36 31 33 45 45 33 144 134 26 25 22 34
19 53 23 28 30 31 29 24
148 44 332 29 34 61 27 38 53 63 14 56 21 15 42 13
TERZ
K (m/d)
58 51 43 47 56 61 45 192 180 34 31 27 44
22 68 28 36 41 39 37 31
194 54 464 36 44 75 32 46 64 77 17 68 25 17 51 15
KOZ
7 10 9 8 34 26 9 107 100 11 26 24 17
21 32 20 15 9 30 23 8
192 63 244 36 20 63 32 60 115 128 20 89 28 20 89 21
USBR
34 31 27 27 18 26 27 87 80 18 6 6 19
1 31 6 16 25 12 13 18
71 19 239 6 19 20 4 10 3 8 40 8 2 3 2 5
A&S
Table 2. Summary of results of the grain size analysis and the conductivity (K) values estimated for the aquifer materials by using the empirical methods at (A) Karnamepur, (B) Bharauli, (C) Nargada Narayanpur, and (D) Paharpur: The size parameters such as d10, d20, d50, d60, Uc, and the porosity, n, have been defined in the text. Io is the slope intercept (on x-axis) of the line formed by joining d10 and d50 in the size grading curve.
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11 17 1 26 38 16 38 129 87 5 23 1 1 0.2 90.1 50.5 8.7 9.1 52.1 12.5 6.2 3.4 4.5 9.1 6.1 10.0 10.9 10.8 4.1 19.5 13.8 20.8 22.5 20.4 4.5 8.4 8.1 8.7 7.2 8.8 10.8 10.2 4.3 29.1 77.3 70 25.1 67 89.2 88.1 87.3 81.8 86.4 80.7 77.9 78.5 fs fs vcs cs fs cs vcs vcs vcs vcs vcs vcs vcs vcs 44 42 33 38 45 38 38 39 39 33 36 32 34 33 0.09 0.110 −0.06 0.13 0.17 0.1 0.14 0.3 0.24 −0.1 0.11 −0.06 −0.05 −0.04 1.70 2.21 6.76 3.72 1.57 3.78 3.97 3.35 3.38 6.28 5.00 7.00 6.52 6.40 0.17 0.31 1.69 0.93 0.30 0.87 1.79 1.51 1.49 1.57 1.75 1.68 1.50 1.60 0.15 0.24 1.42 0.75 0.24 0.73 1.68 1.03 1.21 1.65 1.30 1.40 1.32 1.35 0.11 0.19 0.43 0.43 0.20 0.33 1.00 0.65 0.66 0.80 0.55 0.51 0.52 0.52 0.10 0.14 0.25 0.25 0.19 0.23 0.45 0.45 0.44 0.25 0.35 0.24 0.23 0.25 (D) Paharpur 4–13 13–28 28–50 50–69 69–75 75–82 82–113 131–140 140–147 147–168 168–196 196–206 213–236 236–250
HAZ 5 Hazen; BREY 5 Breyer; SLIT 5 Slitcher; TERZ 5 Terzaghi; KOZ 5 Kozeny-Carman; USBR 5 U.S. Bureau of Reclamation; A&S 5 Alyamani and Sen. *c-vcs 5 coarse to very coarse sand; ms 5 medium sand; f-vfs 5 fine to very fine sand; cs 5 coarse sand; fs5 fine sand; vcs 5 very coarse sand
2 6 45 43 8 24 311 115 106 186 79 66 50 68 17 28 30 57 62 45 172 203 189 32 82 29 26 46 11 19 25 44 41 35 134 153 144 27 66 22 20 27 5 9 12 20 18 16 61 69 65 13 30 11 9 12 11 21 52 59 39 48 190 196 185 53 109 52 43 53 13 23 47 62 44 50 196 209 196 49 107 42 38 48
TERZ fs cs fvfs ms cvcs Sand Type* N (%) Io Depth Range (m)
d10
d20
d50
d60
Uc
Various Sand Grades (%) Sand Size Parameters (mm)
Table 2. Continued.
vcs
HAZ
BREY
SLIT
K (m/d)
KOZ
USBR
A&S
Empirical Hydraulic Conductivity Estimation for Fluvial Aquifers
Figure 4. Borehole lithologs at Karnamepur, Bharauli, Nargada Narayanpur, and Paharpur with the location of the slots in the tube wells constructed in them.
Porosity (n) values of sand for determining hydraulic conductivity were calculated using the following equation given by Vukovic and Soro (1992): n ¼ 0:255 1 þ 0:83Uc : Pumping Test The lithological logs (Figure 4) of the boreholes indicate that the formations beyond ~130 m depth are continuous in space and time, forming a specific aquifer group in the local hydrogeological setup (CGWB, 2008; Saha et al., 2011a; and Sahu, 2013). The aquifer is separated from the overlying shallow aquifer by a (middle) clay/silty-clay layer (thickness: 18–35 m) of limited vertical conductivity (range: 0.0072–0.047 m/d). The confined nature of this aquifer is also supported by the age of groundwater (determined by 14C analyses). The groundwater in the confined aquifer is quite old (~3,000 years), in contrast to the groundwater of recent age (,40 years) in the shallow aquifer (Saha et al., 2011b). Tube wells were constructed tapping the granular zones in the confined aquifer. At Karnamepur, the tube well taps 57 percent
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Sahu and Saha Table 3. Hydrogeological details of pumping tests conducted in the tube wells.
Sl. No. 1 2 3 4
Drawdown (m)
Location of Tube Well
Pre-Pumping Water Level (OW) (m bgl)
Pumping Discharge (m3/d)
Duration of Pumping (min)
MW
OW
Karnamepur Bharauli Nargada Narayanpur Paharpur
6.56 4.40 5.17
4,670 4,387 4,529
700 1,100 760
9.91 8.48 9.51
0.76 0.38 0.47
5.80
4,670
500
4.23
0.54
OW 5 observation well; MW 5 main well; bgl 5 below ground level.
of the zones consisting of up to very coarse sand (Table 2) within the depth range of 136–199 m bgl (136 m to the top of the shallowest slot/bottom of the middle clay, and 199 m to the bottom of the deepest slot). Similarly designed, the tube wells at Nargada Narayanpur and Paharpur tap 37 and 41 percent of the granular zones in the depth ranges of 136–217 m bgl (coarse to very coarse sand) and 134–250 m bgl (very coarse sand), respectively. However, in case of Bharauli, 70 percent of the zones (medium to coarse sand) have been tapped between 162 and 215 m bgl, whereas the bottom of the middle clay lies at a depth of 132 m bgl. Pumping tests were conducted for durations of 700, 760, and 1,100 minutes at Karnamepur, Nargada Narayanpur, and Bharauli, respectively, at a discharge range of 4,387–4,670 m3/d (Table 3). Each tube well was accompanied by one observation well tapping the aquifer at similar depths as in the test wells. Using a steel measuring tape, through hold and cut method, the water-level data from the pre-pumping (static) stage, as well as data during the pumping test, were collected from both the discharging wells and
observation wells. Data from both stages (pumping and pre-pumping) were utilized to calculate the drawdown (water level during pumping − pre-pumping water level) in tube wells during pumping. Time-drawdown data were plotted on semi-logarithmic as well as on logarithmic scales. The log-log plots of pumping test data from Nargada Narayanpur, Karnamepur, and Bharauli wells are produced in Figure 5. For the Paharpur well (pumping duration: 500 minutes), only the reported values of transmissivity and discharge (CGWB, 2008) have been used owing to the nonavailability of the actual pumping test data. A wide variety of formulae are available for the analysis of pumping test data, based on differences in aquifer type and geometry, boundary conditions, and underlying assumptions. For the confined aquifer, widely used methods such as that presented by Theis (1935) and the straight-line method of Cooper-Jacob (1946) were utilized for the analysis of data, considering the tapped confined aquifer to be homogeneous and isotropic with uniform aerial extension. The methods also assume that the rate of discharge from the
Figure 5. Log-log plots of time-drawdown data of pumping tests conducted at Karnamepur, Bharauli, and Nargada Narayanpur wells (data of Paharpur not available). The figure also shows the Theis match points (1, 2, and 3), which have been used for estimating the transmissivity of the aquifers.
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pumping well remains constant and takes place in an unsteady state. This method is expressed through the following equation: T¼
Q W ðuÞ; 4ps
where T 5 transmissivity of the aquifer m2/d, Q 5 pumping discharge in m3/d, W(u) 5 well function of u, and s 5 drawdown in tube wells in m. For smaller values of u (#0.01) in the Cooper-Jacob method, a plot of drawdown against logarithmic time produces a straight line. The method is expressed through the following equation: T¼
2:3 Q ; 4 p Ds
where Δs 5 slope of the straight line in m. It is the difference in drawdown over one log cycle. The hydraulic conductivity values for the aquifer at four borehole locations were calculated from the obtained transmissivity by using the following equation: K¼
T ; b
where b 5 thickness (in m) of aquifer tapped.
RESULTS AND DISCUSSION In total, 51 sand samples from different depth zones of the four boreholes were analyzed for their grain size grading. Most of the samples beyond ~30 m depth are craton-derived Sone sand, which are brownish yellow and coarser in nature in comparison to the finer Himalayan-derived gray sand lying at the top parts of the boreholes (Figure 2). As per the d50, the samples are classified from fine to very coarse sand (Table 2). The effective grain size, d10, used by most of the equations (except USBR and A&S) as cited above, is found to vary between 0.1 and 0.6 mm. The values of uniformity coefficient (Uc) remain within 1.23 and 8.30. Applicability of Empirical Equations and Estimation of Hydraulic Conductivity If the desired application limits in calculating hydraulic conductivity are considered, only the empirical equations given by Breyer, Kozeny-Carman, and Slitcher are applicable to all 51 aquifer point samples.
However, the grain size criterion (d10 as the effective size) given in all the equations, except Terzaghi and USBR for their applicability, is being satisfied by the nature of the particle size distribution in all the samples. The equations of Terzaghi and USBR are applicable to large-grain sand and medium-grain sand, respectively. However, the present work includes few fine to medium sand samples, and most of the samples are coarse to very coarse in nature, which restrict the applicability of the two equations. The equations of Hazen and USBR set the condition of applicability only when Uc , 5, whereas in many of the present cases, Uc exceeds 5. However, for a fresh assessment of the equations, values of conductivities were calculated for the samples from all depth ranges of the four boreholes using all the equations without noticing their desired application limits. The typical ranges of K values for granular formations of different size groups have been suggested by early workers (Todd, 1980; Driscoll, 1986). It is observed that, with few exceptions in the cases of fine to medium sand and poorly sorted coarse sand, the formulae suggested by Kozeny-Carman, Breyer, Hazen, and USBR estimate hydraulic conductivities close to the standard values (Figure 6A–D). The A&S formula, though it gives approximate K values for fine to medium sand (Table 2B–D) with moderate grading, is extremely sensitive to the shape of the grain size distribution curve. In many cases, the method yields underestimated conductivity values. Similarly, the Slitcher method calculates lower values of K in all cases, which is consistent with the observations made by early researchers (Vukovic and Soro, 1992; Cheng and Chen, 2007). This method is a good estimator of K for fine to medium sand, but in cases of coarse sand, the formula mostly gives underestimated values, which may be due to the lower porosity function (n3.287) used in the formula. The Terzaghi method yields good K values in the present exercise for wellsorted coarser sand populations with d10 exceeding ~0.25 mm. For the poorly sorted sand populations with finer admixture, the method gives underestimated K values. Since a fixed empirical coefficient (bγ) of 10.7 6 10−3 (for smooth grains) has been used for all the larger as well as finer sand samples, the properties such as grain size and sorting, with resultant porosity, determine the suitability of the method. In contrast to the earlier conclusion (Vukovic and Soro, 1992), the USBR equation estimates satisfactory values of K for relatively better-sorted coarse to very coarse sand. While the equation leads to better conductivity values for fine sand, also in consonance with Ishaku et al. (2011), in the present exercise, it gives grossly underestimated K values of medium sand, for which it is supposed to be suitable.
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Sahu and Saha
Figure 6. Plotting of depth versus hydraulic conductivity (K) obtained through different empirical equations for four boreholes: (A) Karnamepur, (B) Bharauli, (C) Nargada Narayanpur, and (D) Paharpur.
Grain Size versus Hydraulic Conductivity (K) The methods such as Hazen, Kozeny-Carman, Terzaghi, and Slitcher make use of both the grain size and porosity in predicting the K values, while Breyer takes into account Uc along with grain size for the purpose. The A&S and USBR methods use only the grain size criterion for estimating the value of K. The equations, except A&S, bear a general form, which can be expressed as: K Âź Cde 2 ; where de is the effective grain diameter, taken as d20 in USBR and d10 in the other equations. The coefficient C includes both the fluid properties (such as its temperature, viscosity) and medium properties (such as porosity, sorting, particle shape, and Uc, except the grain size) for calculating the hydraulic conductivities.
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The above equation can be re-written in a more general power equation form as follows (Shepherd, 1989): Y Âź AX B : If the K values (Y) are plotted against the grain size (X) on log-log paper, the coefficient A is the value of Y at X 5 1, and B is the slope of the line that is fitted to the data. The estimated K values have been plotted against d102 and d50 separately for finding out the consistency of the equations in estimating K through a simple power regression technique. The exercise may not imply the applicability of the methods for predicting K. However, it can inform the statistical relevancy of the number of variables used in the methods and the consistency in determining the K values. Since the value of K bears an overall linear relationship with the grain size, the coefficient of determination (R2) of
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Figure 6. Continued.
the plotting of the two variables may indicate the approach to reality by the different methods in the present exercise. The K versus d102 plots (Figure 7) display a stronger R2 (98 percent) for the Breyer method (Table 4), which calculates K by taking into account two grain size (variable) parameters, d10 and Uc. This is followed by the Hazen method (using porosity function and d10 as the parameters), with R2 value of 94 percent. The methods of Kozeny-Carman, Terzaghi, and Slitcher show weak to moderate correlations between 70 and 80 percent (Table 4). The B exponents (slope of the regression line) for the methods with d10 as the effective grain diameter remain in the range of 0.91–0.97, whereas the coefficient of proportionality, A, varies within 234.7–857.6 (Table 4). The Breyer and Hazen methods with B at 0.97 each best approach
the slope of 1.5 suggested by Shepherd (1989) for fluvial sediment. The USBR method, with a slope at 1.49 and the coefficient at 2,066, also gives a consistent set of K values. In the K versus d50 plots (Figure 8), the methods that use d10 as the effective grain diameter exhibit poor coefficient of determination values (R2: 6–39 percent), with the Breyer and Hazen methods showing values at the upper end at 39 and 28 percent, respectively (Table 4). The Kozeny-Carman, Terzaghi, and Slitcher methods display minimum R2 values (6–11 percent), indicating high variation in their K value estimates with respect to the fitted power regression line. This may be happening due to the wide range of porosity functions taken in the equations for different point samples. The slopes of the regression lines vary
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Sahu and Saha Table 4. Summary of power regression analysis (refer Figures 7–8) of grain size versus hydraulic conductivity (K). K vs. d102
K vs. d50 2
Method
A
B
R (%)
A
B
R2 (%)
HAZ BREY SLIT TERZ KOZ USBR A&S
843.4 857.6 234.7 518.4 620.7 2066 82.74
0.97 0.97 0.93 0.94 0.91 1.49 0.68
94 98 80 78 70 84 11
63.7 64.7 18.7 40.8 52.0 43.7 11.0
0.59 0.69 0.39 0.38 0.29 1.58 - 0.66
28 39 11 10 6 75 8
HAZ 5 Hazen; BREY 5 Breyer; SLIT 5 Slitcher; TERZ 5 Terzaghi; KOZ 5 Kozeny-Carman; USBR 5 U.S. Bureau of Reclamation; A&S 5 Alyamani and Sen.
between 0.29 and 0.69, with values of A in the range of 18.7–64.7 (Table 4). The Breyer, Hazen, Kozeny-Carman, and Terzaghi methods meet the minimum coefficient value of 32.6 (unit in m/d) as suggested by Shepherd (1989) for fluvial sediment. The USBR method gives a higher R2 value (75 percent), depicting a higher number of data points agreeing with the regression line. This may be due to the fact that the method uses d20 as the effective grain diameter, and in comparison to d10, it is closer to d50. It is important to note that the method gives consistently high R2 values for both the plots, indicating a better relation of the calculated K values with the grain size parameter used in the equation. In the K versus d50 plot, the method, with a slope at 1.58 and coefficient of proportionality at 43.7, meets both the standards as mentioned in the above lines. In the case of the A&S method, which is based on the shape of the grain size distribution curve, both the correlations (K versus d102 and K versus d50) show weak R2 values (11 percent and 8 percent, respectively; Table 4). This may indicate the high sensitivity of K, due to the wide variation in the value of the factor Io utilized in the formula, depending on the slope of the line through d50 and d10. The K versus d50 plot shows a reverse slope of the trend line (Figure 8), depicting lower K values for coarser sand samples. This may be due to lower Io values for poorly sorted coarser sand samples. Uniformity Coefficient Conductivity (K)
Figure 7. Plot of hydraulic conductivity (K) obtained through different empirical equations versus square of effective grain size (d102) for the four boreholes.
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(Uc)
versus
Hydraulic
Out of the total 51 sand populations, only 10 are fine to medium in nature (Uc 5 1.23–3.46), and the rest (41) are coarse to very coarse (N 5 14, coarse, Uc 5 3.0–5.23; N 5 27, very coarse, Uc 5 2.5–8.3). Twenty sand populations (very coarse sand) bear Uc . 5 (range: 5.23–8.30), and the rest, 31 (N 5 21, coarse to very coarse sand, N = 10, fine to medium sand), possess Uc , 5 (range: 1.30–5.0). Figure 9
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Figure 9. Plot of uniformity coefďŹ cient (Uc) versus hydraulic conductivity (K) obtained through different empirical equations for the four boreholes. Figure 8. Plot of hydraulic conductivity (K) obtained through different empirical equations versus median grain size (d50) for the four boreholes.
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Sahu and Saha Table 5. The transmissivity (T) and hydraulic conductivity (K) values estimated from pumping tests. Karnamepur Method of Calculation Jacob Straight line Theis Arithmetic average
Bharauli
Nargada Narayanpur
Paharpur
T (m /d)
Kx5 T/b (m/d)
T (m /d)
Kx5 T/b (m/d)
T (m /d)
Kx5 T/b (m/d)
T (m /d)
Kx5 T/b (m/d)
5,980 7,724 6,852
94.9 123.60 108.8
4,014 6,653 5,334
48.4 80.2 64.3
5,529 6,010 5,770
68.3 74.2 71.2
8,553 na 8,553
78.5 na 78.5
2
2
2
2
na 5 not available.
depicts the Uc versus K plots for all the methods utilized in the present work. A systematic decline in the K values after Uc of ~5 is discernible in all the methods. The methods of Slitcher, Terzaghi, Kozeny-Carman, and A&S, however, seem to give poor correlation to conductivity values after Uc exceeds 5 and generate lower K values for the sand populations. Barring the sample from the depth range of 38–44 m bgl at Karnamepur (for which all the methods yield abnormally high K values), for the remaining samples, the Slitcher method calculates the K in the range of 5– 69 (average: 26 m/d) for Uc # 5 and significantly lower values in the range of 6–29 (average: 14 m/d) for the very coarse sands with Uc . 5. In the case of Terzaghi method, the K values fall in the range of 11–153 m/d (average: 57 m/d) for Uc # 5 and only 13–63 m/d (average: 29 m/d) for the very coarse sands with Uc . 5. The Kozeny-Carman method gives fairly good conductivity values in the range of 17–203 m/d (average: 75 m/d) for Uc # 5, whereas it estimates lower values in the range of 28–77 m/d (average: 36 m/d) for Uc . 5. Similarly, the K values obtained with A&S fall in the ranges of 6–129 m/d (average: 33 m/d) and 0.2–40 m/d (average: 6 m/d) for the sand populations with Uc # 5 and Uc . 5, respectively. All the other methods (Hazen, Breyer, and USBR) give good approximations of K for sediments with Uc . 5. The Breyer method is the only one that takes Uc as a factor in its equation and proposes its suitability for a wide range of sediment types, with Uc varying between 1 and 20. The K values by this method fall in the range 11–196 m/d (average: 74 m/d) for Uc # 5; for Uc. 5, the estimates are fairly good in the range of 39– 94 m/d (average: 55 m/d). The equations of Hazen and USBR, which have been restricted only for sediments with Uc , 5, provide reasonably good results for the sand populations with higher Uc (up to ~7) also. The K values through Hazen range within 13–209 m/d (average: 78 m/d) for Uc # 5; for Uc . 5, the values vary within 27–91 m/d (average: 51 m/d). However, the USBR method estimates the parameter better for the sand populations with Uc . 5 than for those with Uc # 5: The values range between 20 and 128 m/d (average: 58 m/d) in the former case, while they are within 2–244 m/d (average: 47 m/d) for the latter
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case. The interpretation indicates that the equation is more suitable for aquifer materials with Uc . 3. Field Method versus Empirical Equations Hydraulic Conductivity from Pumping Test The pumping test is considered to be one of the better methods for determining hydraulic conductivity in field conditions (e.g., Taylor et al., 1987; Jones et al., 1992; Vukovic and Soro, 1992; and Todd and Mays, 2005). This indicates how the aquifer responds to groundwater withdrawals. Based on observations of water levels near pumping wells, an integrated K value over a sizeable aquifer section can be obtained. Since the aquifer is not disturbed during pumping, the reliability of this determination is superior to laboratory methods such as the use of empirical methods, which estimate the K values for point samples. The average T values obtained from the Theis and Cooper-Jacob methods for the four borehole sites, (1) Karnamepur (very coarse sand), (2) Bharauli (medium to coarse sand), (3) Nargada Narayanpur (coarse to very coarse sand), and (4) Paharpur (very coarse sand), are 6,852, 5,334, 5,770, and 8,553 m2/d, respectively. The cumulative thicknesses of the zones tapped at the first, third, and the fourth sites are 63 m, 109 m, and 81 m, respectively, where the slotted zones start from the bottom of the middle clay itself. However, in case of the second site at Bharauli, the slotted zones start at 162 m bgl. In this case for estimating K, the thickness of the confined aquifer starting from bottom of the confining bed (at 132 m bgl) up to the bottom of the deepest slot (at 215 m bgl) can be taken (Figure 4), considering the entire aquifer of 83 m thickness lying above the deepest slot to be contributing water to the well during pumping. The average K values through pumping test are worked out to be 108.8, 64.3, 71.2, and 78.5 m/d respectively, (Table 5). Average Hydraulic Conductivity in Tube Well Construction Zones from the Empirical Equations This section aims at determining the average K values of the granular zones tapped for the construction of tube wells. The K values for the different zones
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within the tube well construction column of four boreholes as calculated using the empirical formulae are given in Table 2. Since the aquifers in the boreholes are vertically continuous within the screened zones, it can be considered that during pumping tests, the entire screened lengths might be contributing water to the total discharge of the wells. So in order to calculate the average horizontal K values (Kx) of the aquifer, the individual hydraulic conductivity values of all the layers may be taken. The average Kx values (Table 6) have been calculated using the following formula; Kx ¼
1 ðK1 b1 þ K2 b2 þ K3 b3 :::::::Þ; b
where Kx 5 horizontal hydraulic conductivity; b 5 total thickness of the aquifer (m) 5 b1 + b2 + b3…, where b1, b2, b3… indicate the thickness of each layer (m); and K1, K2, K3… 5 horizontal hydraulic conductivity (m/d) of each layer. For the very coarse sand at the Karnamepur and Paharpur screened zones, except Slitcher and A&S, the other five methods yield good average K values ranging between 49 and 98 m/d (Table 6). As the grain size decreases to coarse to very coarse sand, and medium to coarse sand at Nargada Narayanpur and Bharauli, respectively, the USBR method behaves similar to the Slitcher and A&S methods and gives lower average K values. Only four methods, Kozeny, Hazen, Breyer, and Terzaghi, in this case, produce better average K values, ranging between 29 and 56 m/d for the entire tube well construction zones.
A Comparison between the Two Approaches and Assessment of Suitable Empirical Equations A comparison between the pumping test results and the estimates using the empirical methods reflects the better methods as also indicated by a simple power regression technique (see section on Grain Size versus Hydraulic Conductivity). The Breyer method, which bears the highest coefficient of determination (R2 5 98 percent in K versus d102 plot) among all the methods utilized (Table 4), estimates the K values with overall less deviation (+4 percent to –27 percent) from the field technique results (Figure 10). Similarly, the Hazen method, displaying R2 of 94 percent, yields good K values for coarse to very coarse sand (Karnamepur, Nargada Narayanpur and Paharpur), with deviation ranging between +1 percent and −21 percent from the in situ estimates. However, in the case of medium to coarse sand at Bharauli, the deviation stands at –26 percent (Figure 10B). Both the above methods calculate the conductivity with more
precision (+4 percent to −15 percent variations) for the very coarse sand aquifers at Karnamepur and Paharpur (Figure 10A and D). The Kozeny-Carman method, which bears a low R2 (70 percent; Table 4), estimates K values fairly well (−18 percent to −37 percent). Using this method, workers have also got K values close to in situ measured values for fluvial deposits consisting of fine to coarse sand and open framework gravels (Esselburn, 2011; Ferreira et al., 2011). Earlier works estimating the K of, particularly, the fluvial loose sand and gravels using empirical methods suggest that either or all of the Breyer, Kozeny-Carman, and Hazen methods give largely acceptable values (e.g., Taylor et al., 1987; Wolf et al., 1991; Detmer, 1995; Sperry and Peirce, 1995; Odong, 2007; Ishaku et al., 2011). The USBR method, showing better correlation coefficients (R2 5 84 percent and 75 percent) in both the plots (K versus d102 and K versus d50, respectively), has resulted in reasonably good K values for very coarse sand at Karnamepur and Paharpur, with variation of −10 percent for the former location and +21 percent for the latter one (Figure 10A and D). For the medium to coarse sand and coarse sand aquifers at Bharauli and Nargada Narayanpur, respectively (Figure 10B and C), the method gives highly underestimated values (−55 percent and −61 percent, respectively). Detmer (1995), Odong (2007), and Sezer et al. (2009) have observed that the method largely underestimates the K values. Ishaku et al. (2011) found the method to be suitable for fine sand only. In the present exercise also, the method estimated good approximations of K for finer sand populations (Table 2). Song et al. (2009), while estimating the conductivity values of the streambed sediment of Elkhorn River, NE, observed lower numerical values of K obtained by this method in comparison to the Hazen, Breyer, Kozeny-Carman, and Terzaghi methods. The Terzaghi, Slitcher, and A&S methods, with R2 values of 78 percent, 80 percent, and 11 percent, respectively (in K versus d102; Figure 7), give lower values of K (higher - percent variation in the range of −38 to −91 percent from the in situ estimates) consistently for all four tube well construction zones. Regarding the Terzaghi and Slitcher methods, similar conclusions have also been made earlier by other workers (e.g., Wolf et al., 1991; Odong, 2007; Ishaku et al., 2011). However, in the present exercise, the underestimation is less (−38 to −49 percent) in case of the Terzaghi method, while it is much higher (−65 to −91 percent) in case of Slitcher and A&S methods. Odong (2007) has opined the high sensitiveness of the A&S method to the shape of the grain size grading curve in any sand population. Sezer et al. (2009) observed that the A&S method underestimates the K
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Sahu and Saha
Figure 10. Plot of average hydraulic conductivity (K) obtained through different empirical equations for the well construction zones at (A) Karnamepur, (B) Bharauli, (C) Nargada Narayanpur, and (D) Paharpur. The ďŹ gure also depicts the comparative study with the average K values computed from pumping tests.
values in coarse-grained sand, while it is overestimated in case of fine-grained sand. CONCLUSIONS Empirical equations based on the size grading characteristics of the water-bearing materials either overestimate or underestimate the hydraulic conductivity. However, selection of better methods based on the nature of the particle size distribution of the
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aquifer material minimizes this problem. Based on the present set of samples consisting of loose sand of fluvial origin and the assessment of K values through different approaches, the following conclusions can be made regarding the applicability of the empirical equations: 1. The formulae given by Hazen and Breyer are suitable enough to assess the conductivity of the aquifer in the initial phases of exploration. These methods give good approximate values of K for
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Figure 10. Continued.
very coarse sand or coarse to very coarse sand with minimum deviation of +4 to −15 percent. For the coarse sand and medium to coarse sand, respectively, the formulae give underestimated values of K by −21 percent (Breyer) to −46 percent (Hazen) of the value computed through pumping tests. In consistency with the application conditions given in Breyer equation, the formula is suitable for all kinds of heterogeneous porous materials, irrespective of their sorting. In contrary to the
early condition (Uc , 5), the Hazen equation seems to work well for water-bearing materials of fluvial origin with higher Uc (up to ~7) also. 2. Though the USBR method is supposed to be suitable for medium sand with Uc , 5, the method yields more reliable values of K (variation: −10 to +21 percent) for better-sorted coarse to very coarse sand with Uc even larger than 5. For medium sand, the method gives highly underestimated (up to −61 percent) values of K. The method is suitable for aquifer materials with Uc . 3.
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Sahu and Saha Table 6. Average hydraulic conductivity obtained through different empirical equations for the tube well construction zones in the four boreholes. Average Kx (m/d)
Method Applied
Karnamepur (136–199 m bgl)
Bharauli (132–215 m bgl)
Nargada Narayanpur (136–217 m bgl)
Paharpur (134–250 m bgl)
HAZ BREY SLIT TERZ KOZ USBR A&S
92 95 26 56 68 98 10
44 43 13 29 38 22 15
56 54 18 39 51 28 21
79 82 23 49 64 95 20
HAZ 5 Hazen; BREY 5 Breyer; SLIT 5 Slitcher; TERZ 5 Terzaghi; KOZ 5 Kozeny-Carman; USBR 5 U.S. Bureau of Reclamation; A&S 5 Alyamani and Sen; m bgl 5 m below ground level.
3. The Terzaghi method leads to underestimated values of K (variation: −38 to −49 percent) for medium to coarse to very coarse sand. However, for fine and medium sand, the equation gives reasonably good conductivity values. 4. The Kozeny-Carman method yields moderately (variation: −18 to −37 percent) underestimated values of K for medium to coarse to very coarse sand. However, it seems to lead to overestimated values of K for fine to medium granular materials. 5. The Slitcher method always gives highly underestimated (variation: −66 to −76 percent) values of K for coarser sand. However, for fine sand and medium sand, the equation leads to reliable values of K. 6. Similar to Slitcher method, the A&S method gives highly underestimated values of K (up to −91 percent) for coarse to very coarse sand with Uc . 5. Though, the equation gives quite better values of K for finer sand populations with Uc , 5, the equation is sensitively dependent on the shape of the grain size distribution curve. 7. The methods Terzaghi, Kozeny-Carman, Slitcher, and A&S lose their applicability for fluviatile granular materials with Uc . 5. Though the methods were tested for the middle parts of Gangetic Plains, the results may find applicability in other such sedimentary basins elsewhere in the world with similar depositional environments. ACKNOWLEDGMENTS The authors sincerely thank the Chairman and Member (SAM) of Central Ground Water Board for their constant encouragement to complete the article. Thanks are due to R. R. Shukla, S. N. Dwivedi, and
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S. Upadhyaya for their support and discussion on the subject for understanding. The authors thank‐ fully acknowledge the anonymous reviewers, whose valuable suggestions helped in improving the manuscript. The authors also extend their sincere thanks to all the researchers whose works have been cited in the article.
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Initiation Mechanism of the Jiweishan Landslide in Chongqing, Southwestern China FENG ZHEN LI BIN1 Key Laboratory of Neotectonic Movement and Geohazards of MLR, Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
CAI QI PENG College of Civil Engineering, Huaqiao University, Quanzhou 361021, China
CAO JIA WEN China Geological Survey, Beijing 100037, China
Key Terms: Massive Rock Slope Failure, Landslide, Karst, Centrifuge Modelling
ABSTRACT Plagioclinal slopes in cuesta escarpments are oblique to bedding dips and widely distributed in the mountainous area of southwestern China, and the failure patterns are conventionally assumed to be rockfall or slab collapse, rather than rockslide. The catastrophe of the Jiweishan rockslide on June 5, 2009, illustrates a unique mechanism of plagioclinal slope failure, where the slope failure moves in the direction of apparent dip and is confined by four planes. Geological analysis concluded that the Jiweishan rockslide was a result of the weakinterlayer-controlled geological structure, underground mining, and karst. Modelling tests reproduced the instant failure of key blocks in the apparent dip direction followed by block glide, and they suggested that weakening of the slip surface and the discrete structure contributed to slope failure. Numerical simulation indicated that rear blocks acted on relatively stable key blocks during long-term gravitational creep on the weak interlayer. Strength reduction of the weak interlayer was a key factor in the rockslide occurrence. Ultimately, a three-dimensional limit equilibrium method of stability analysis for apparent dip slide is proposed, along with validation of modelling tests.
1 Corresponding author. Tel.: +86-010-88815022; email: 52572706@qq.com.
INTRODUCTION Massive rock slope failure is the result of timedependent deformation, indicating that signs of instability, such as cracks, recurring small rockfalls, and noise, would occur prior to the failure (Glastonbury and Fell, 2000). This provides engineering geologists with a certain amount of time to estimate the probability of catastrophic failure, and it makes early warning and anticipation of landslides feasible. Successful risk assessment of the hazards of massive rock slope failure depends on the recognition of pre-failure features and, in particular, accurate prediction of the failure mode (Hutchinson, 2006). The Jiweishan landslide has taught a costly lesson on the importance of accurate recognition of the failure mode. Based on empirical analysis and field investigation, previous assessment anticipated a lateral rockfall to the east (Xu et al., 2009; Yin et al., 2010). However, an apparent dip rockslide occurred that became a rock avalanche, which then ran north along the Blacksmith Valley for 1.25 km (Liu, 2010; Feng et al., 2012). Figure 1 illustrates the difference between the estimated and actual rockslide areas. The reasons for the Jiweishan landslide have been discussed by some researchers, and it is considered that poor geological conditions and underground mining were the main causal factors (Xu et al., 2009; Yin et al., 2010; Feng et al., 2012; Deng, 2014; and Zou, 2014). In this study, we present an integrated analysis of the Jiweishan landslide, including numerical simulation and physical modelling, to increase the understanding of the failure mechanisms and behavior of the apparent dip rockslide from plagioclinal slope failure. Furthermore, we propose a three-dimensional limit equilibrium method for stability assessment.
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Figure 1. Jiweishan Escarpment topography 5 hours prior to the large rockslide (view to 340u). The outcrop in the area consists of a thick sequence of Middle Permian limestone and the underlying Lower Silurian shale, which forms a “hard-on-soft” landform. The sliding mass originated from the Middle Permian limestone.
GEOLOGICAL BACKGROUND Calcareous and mountainous areas are highly prone to geo-hazards all around the world (Abele, 1994; Yin, 2004; Parise and Gunn, 2007; Santo et al., 2007; Ruff and Rohn, 2008; Parise, 2010; and Palma et al., 2012). On June 5, 2009, a massive rock slope failure occurred at the crest of the Jiweishan Escarpment in Wulong County, Chongqing, southwestern China. A 5 6 106 m3 rock mass with an average depth of 60 m and run-out length of 1.5 km slid into the Blacksmith Valley. The avalanche covered an area of 0.47 km2 and buried 12 houses and a mining factory, causing 74 deaths. An aerial image of the Jiweishan rockslide shown in Figure 2 presents a complete view of the path of the resulting rock avalanche. Lying in the southeastern limb of the Changba Syncline, strata in the Jiweishan hill dip to N15uW, and an east-facing cuesta escarpment has been formed by river incision. Faults are barely developed in the area. The strata mainly consist of thick-bedded limestone of Middle Permian age, in which karst caves, dissolution pores, and fissures are highly developed. Underlying the limestone is Lower Silurian sandy shale. Between the thick limestone and Silurian shale, there is a measure of iron ore with a thickness of approximately 10 m. Underground mining has occurred since the 1920s, and long-wall panels lie beneath the rockslide source area (Figure 3). The panels are about 130 m below ground surface and 140 m behind the cliff face. Several layers of muddy and carbonaceous shale are sandwiched in the limestone. Two sets of dominant tectonic joints are contained in the rock mass with dip direction and dip angle of 185u ∠ 75u and 77u ∠ 80u. 342
Figure 2. Aerial image of the Jiweishan rockslide. (A) Orthograph of the Jiweishan rockslide (taken on June 12, 2009). The geometry of the sliding mass, comprising proximal hexahedron-shaped blocks and a prism-shaped block, is shown schematically with white lines. The yellow arrows represent the karstic belt where the sliding mass broke through. The red arrows show the directions of sliding mass movement. (B) Oblique view of Jiweishan rockslide (taken on December 29, 2014, by Google Earth). The avalanche buried the adit entrance and former residential site. A dammed lake was formed in the Blacksmith Valley.
The rockslide headscarp and western boundary (T0 and T1, respectively; see Figure 2) are traced along the joints. The headscarp dates back to the 1960s, and its maximum width of approximately 1.5 m was reached in 1999. Striae oriented to the dip direction were observed on the sliding surface in the crest area. These indicate years of creep under gravity. A stereonet plot view of structures in the Jiweishan Escarpment is presented in Figure 4. The strata dip NNW, while the cliff faces to the east. The topographic/bedding-plane intersection angle is 105u. Powell classified these types of slopes that are oblique to the bedding dips as plagioclinal slopes (Cruden and Hu, 1993). Furthermore, the bedding planes dip slightly opposite to the cliff slope. For a plagioclinal slope with hard and jointed limestone resting on a bed of shale, it is conventionally considered that a slab failure or topple is more likely to occur in the direction of the cliff face (Terzaghi, 1950; Dussauge et al., 2002; Rohn et al., 2004; and Poisel et al., 2009). According to a pre-disaster risk assessment, which did not include a geotechnical survey, a total of 0.2 6106 m3 of susceptible rock mass was considered likely to fail as lateral
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The Jiweishan Landslide
Figure 3. Topographic map of the Jiweishan rockslide.
collapse and endanger a region of 100 m to the east under the cliff (Chongqing 136 Geological Mineral Resource Co., Ltd., 2008). However, the actual failure differed from the estimation in terms of the failure mode, direction of movement, run-out, and volume. The upper limestone mass slid northwards on the carbonaceous shale interlayer and sheared through the toe of the karstic belt (indicated by yellow arrows in Figure 2) in the apparent dip direction (N21uE), and then it moved into the valley, transforming into a catastrophic rock avalanche (Hungr et al., 2001). Signs of slope creep in the Jiweishan landslide area were first discovered in the 1960s, and the tensional headscarp indicates long-term dip slide. Creep tests have been carried out on the weak intercalated layers of carbonaceous shale, so as to explain the role of rheological characteristics in slope deformation. Saturated specimens and samples with natural water content were sheared under three different normal stress values of 0.5 MPa, 1.0 MPa, and 1.5 MPa. Figure 5 shows the results of saturated specimen tests under normal stress of 1.5 MPa. The specimen did not undergo creeping behavior until critical shear stress. Three stages of primary creep, steady state creep, and tertiary creep could be observed. The primary creep lasted for
a short time, and the strain rate was relatively high, but it slowed with increasing time at this stage. The strain rate reached a minimum and became near constant during steady creep. In tertiary creep, the strain rate exponentially increased, with great displacement and shear failure occurring in a short time. According to Boltzmann’s superposition principle, isochronal curves under different normal stress had been drawn in terms of time. Curves of 1.5 MPa normal stress are presented in Figure 6. The shear stress corresponding to the inflection point of the isochronal curves is considered to be shear strength. Table 1 lists the critical shear strength under different normal stresses and the rheological strength values of the carbonaceous shale interlayer. It can be seen in Table 1 that the internal friction angle and cohesion of rheological strength under natural water content are 29.63u and 96 kPa, respectively. Values in a saturated state are 27.20u and 88 kPa, respectively, dropping by 8.2 percent and 8.3 percent. The creep tests show that the intercalated layer of carbonaceous shale in the Jiweishan landslide area would soften under the influence of water, and the critical shear strength would decrease with decreasing strength. So, in a specific stress field, strength decrease
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Figure 4. A lower-hemisphere projection of the structures in the Jiweishan hill. The strata dip slightly into the slope and nearly parallel to the escarpment face. Strike of the conjugate joints is approximately parallel to the dip direction and strike of the strata.
would cause creep behavior and eventually shear failure. In the field, intermittent episodes of percolating water led to slope creep until landslide initiation. The reasons for the apparent dip slide in the Jiweishan Escarpment can be summarized as geological structure, underground mining, and karst. A slip surface parallel to the bedding planes is favorable for rockslide, and there are several relatively weak layers of carbonaceous shale in the high-strength, thickbedded limestone. Two important boundaries of the Jiweishan rockslide are the headscarp and western crack, which are defined by subvertical and conjugate joint sets. The western crack subparallel to the escarpment face has formed under stress release adjacent to Blacksmith Valley. The back scarp, dipping opposite to bedding dip, has been generated because of gravitational creep. It is well known that a subsidence basin can form above a mined-out area, and displacement vectors of the ground surface point to the subsidence center. Therefore, underground mining definitely contributed to widening and extending of two persistent cracks, as well as karstic dissolution. Although a presheared weak interlayer and persistent cracks existed prior to the slide, the geological structure would usually be considered unfavorable for translational rockslide because the strata dip into the cliff face. In addition, the strata do not dip in a direction conducive to topple failures. An important factor of the Jiweishan rockslide is the karstic belt striking in the apparent dip direction towards the free face. Because of long-term karstic dissolution, a belt of rock with generally low strength existed prior to failure of the rupture surface. This karstic belt was revealed after the slide, and intensive karst, including conduits, clay
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Figure 5. Creep test results of saturated specimens under normal stress of 1.5 MPa. (A) Displacement curves under different shear stress values. (B) Displacement and velocity curves under critical shear stress.
filling, stalactites, dissolution pores, and solution cavities, could be observed. CENTRIFUGE MODELLING Series of centrifuge modelling tests were performed to reveal the initial failure mechanism and reproduce the failure process. High-resolution aerial photographs showed that the sliding mass consisted of hexahedronshaped blocks and a prism-shaped block (Figure 2). The rear hexahedron-shaped block acted on the prismshaped block until shear failure and consequently a slide in the apparent dip occurred. The prism-shaped block in the front played a key role in resisting the slide. The centrifuge models of the sliding mass were made by casting the driving blocks and the key block using a mixture of cement, barite, and gypsum in specific quantities (Feng et al., 2013). The joints were simulated by inserting sheets of geotextile between blocks. The geotextile sheets, replicating a sliding surface, were coated with
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The Jiweishan Landslide Table 1. Rheological strength of weak intercalated layer determined by creep tests.
Water Content Natural
Saturated
Figure 6. Isochronal curves of creep tests under 1.5 MPa normal stress. (A) Natural water content. (B) Saturated.
grease to produce a low friction angle and weak cohesion. The karstic belt in the apparent dip direction was produced by coating epoxy resin in vertically spaced strips between bare rocks. The models did not contain an excavation simulation beneath the sliding mass because the panels are much thinner than the escarpment, and this would have been difficult to install in the centrifuge model. The tests primarily focused on the movement of the blocks. Laser sensors, which were denoted by block number, were set up to monitor the lateral displacement of several blocks. Using highresolution cameras from different perspectives, the initial failure process of the apparent dip slide of the centrifuge model was recorded. The monitoring system is shown in Figure 7. Two models are presented in this study. The sliding mass of slope-LF (large block; Feng et al., 2013) consisted of five large driving blocks and one key block, whereas in slope-SF (small block; Feng et al., 2014), the driving blocks were reconstructed with 32 small
Normal Stress (MPa)
Shear Strength (MPa)
Internal Friction Angle (u)
Cohesion (kPa)
0.5 1 1.5 0.5 1 1.5
0.423 0.651 0.964 0.402 0.587 0.877
29.6
96
27.2
88
blocks to restore the jointed rock mass. After the models were transferred to the centrifuge box and the acquisition system was connected, centrifugal acceleration was increased step by step until slope failure occurred. Movement of the sliding mass as recorded by laser sensors during flight is shown in Figure 8. The displacement history plots remained steady prior to critical acceleration, indicating that the blocks remained stable. This is because the driving forces are smaller than the resisting forces. Abrupt changes in displacement occurred when acceleration reached 80g in slope-LF and 73g in slope-SF, corresponding to instant slope failures. At critical acceleration, the key block was squeezed out, and the driving blocks slid downhill before turning towards the apparent dip direction. Notably, the critical accelerations for model slopeLF and model slope-SF were 80g and 73g, respectively, while the only difference between them was the constitution of the sliding mass. It appears that a model with more discrete structure is more likely to fail. Based on the similitude law of centrifuge modelling, the scaling factor for a friction angle is 1:1 and for cohesion is inversely proportional to the centrifugal acceleration. Assuming the models at different accelerations correspond to a prototype of the same size, increasing acceleration can be considered as cohesiondeducing for the prototype (Cargill and Ko, 1983; Zhang and Hu, 1990; and Zhang et al., 2008). In the field, limestone resting on a weak layer creeps under gravity for extended time periods, inducing pre-collapse dislocations such as the back scarp (Xu et al., 2009; Yin et al., 2010). A decrease in the cohesion of the weak layer (caused by water percolation) could accelerate the rate of rock creep, giving rise to tension cracks that originate from joints. At Jiweishan, stress and strain accumulated near the toe of the key block until the slope abruptly broke through the weak karstic belt in the apparent dip direction. This was followed by a rapid rockslide of the driving blocks. Figure 9 shows the initiation of the apparent dip slide in the centrifuge models.
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Figure 8. Monitoring results of centrifuge tests. (A) Displacement of blocks 1 and 3 during test LF. (B) Displacement of blocks 1, 3, and 4 during test SF.
Figure 7. Design of models and monitoring systems in the centrifuge tests. The models slope-LF and slope-SF are of the same size. Their difference is in the constitution of the driving blocks; there are five large active driving blocks in model slope-LF and 32 small blocks in model slope-SF. LS1–LS4 represent laser sensors. (A) Schematic plan view of model slope-LF in a centrifuge box (units: mm). (B) Schematic cross section of model slope-LF in a centrifuge box (units: mm). (C) Oblique view photograph of model slope-SF in a centrifuge box.
NUMERICAL SIMULATION For numerical simulations, we established a schematic geological model shaped like the centrifuge model (Figure 10). The simulation was performed using 3DEC and was based on a discrete element method. The model was 800 m long, 400 m wide, and 700 m high. Subvertical cracks forming the boundaries of the sliding mass were pre-installed.
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Two processes, creep and larger-scale deformation after instantaneous failure, were included. After stress initialization, parameters deduced from the centrifuge tests based on the similitude scale law were assigned to corresponding joints. Figure 11 shows the displacement vectors of the sliding mass during the simulation, and Figure 12 shows displacement histories in relation to time steps. Because the friction angle is much smaller than the dip angle, the slide mass creeps under gravity (Figure 11A). The slide mass moves to the north at the crest and gradually turns slightly NNE at the front. The rear blocks exhibit significant displacement to the north and act on the key block at the front, which stays relatively stable (Figure 12a). Stress concentration would occur in the key block. When the weak layer softens, the key block is driven to failure. Displacement vectors illustrate the apparent dip slide of the sliding mass (Figure 11B), and mobilization towards the cliff increases sharply (Figure 12B). Underground mining activity would cause changes in the stress state, underground water field, and the strength of the weak interlayers, leading to slope deformation and/or rockslide (Tang, 2009; Marschalko et al., 2012). When underground mining was terminated, slow slope deformation could last for years, even for decades. Strength reduction of weak interlayers
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Figure 10. Model for numerical simulation. The black dots and numbers represent historical points on the sliding mass. The mined area is located in the coal-bearing layer and beneath the key block (the prism-shaped block). The direction of x is to the east, while z is to the north.
intersecting the shear scar of the karstic belt and the weak interlayer. LIMIT EQUILIBRIUM ANALYSIS
Figure 9. Images of the rockslide initiation captured by camera for slope-LF (A) and slope-SF (B). (A) Gravitational dislocations of the slide blocks were apparent before rapid slide. The driving blocks slid downslope, and the key block (red block at the front) was squeezed out. The red arrows indicate the slide directions of the blocks. (B) Most of the blocks dropped off the slip surface, and some accumulated at the corner of the vertical boundary (at the toe).
due to heavy precipitation and rock movement could accelerate slope deformation process. As soon as lower parameters were assigned to the weak interlayer, the resisting force decreased, becoming less than the driving force and causing instant failure of the slope. As can be seen in Figure 12, an abrupt increase in displacement occurs, particularly in the key block. This indicates instantaneous failure of the slope. The displacement to the east over time illustrates that the displacement of the key block into the open air is much greater than that of the driving blocks, indicating the apparent dip slide of the key block (Figure 12B). The key block slides to N21uE, parallel to the line
The fundamental purpose of limit equilibrium analysis is to obtain a safety factor for the qualitative assessment of landslide stability. The geometry of the Jiweishan rockslide has been calculated. However, a dynamic model with physical and mechanical parameters of the rock mass and joints is still required for the limit equilibrium analysis. Centrifuge tests and numerical simulations indicated that the Jiweishan rockslide was initiated when the rear rock mass slid downhill and drove the front key block through the karstic belt in the apparent dip direction. Therefore, a limit equilibrium model can be built by combining the driving and key blocks. Along the line intersecting the two planes, both blocks slide due to translation slip of wedge failure; however, this does not occur in the same direction or geometry. As evidence, clear striae on the weak layer and subvertical boundaries were observed in the field (Feng, 2012). A schematic model for limit equilibrium analysis is proposed in Figure 13. The factor of safety (FOS) is the ratio of the resisting force to the driving force. For an apparent dip rockslide, the FOS is dependent upon the key
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Figure 11. Displacement vectors of the sliding mass. (A) Creep phase. (B) Weakening of slip surface strength.
block. By resolving all forces acting on the driving block and key block into components that are parallel to the intersection line and normal to the sliding planes, the FOS of the key block can be calculated. The solution is based on the following assumptions: (a) the blocks maintain contact, thus ensuring force transmission from the driving block to the key block; (b) the forces act through the centroid of a block, thus ensuring there is no moment causing rotational displacement; (c) the interface between the two blocks is frictionfree; and (d) the shear strength τ of the sliding surface is defined by cohesion c, friction angle φ, and normal stress σ, which are related by the equation τ 5 c + σtanφ. 348
Figure 12. Displacement histories in relation to time steps. The history numbers refer to historical points, and their locations are marked in Figure 10. The units for displacement are meters. (A) In the direction of the y-axis. (B) In the direction of the x-axis.
The FOS for an apparent dip landslide is given as follows (Feng et al., 2012): S1R ¼ ðmw:S 1 qtanua xtanub ÞW1 ðca Aa þ cb Ab Þ; (1) F ¼ ½ca Aa2 þ cc Ac þ tanua ðrW2 þ sS1R Þ þ tanuc ðyW2 þ zS1R Þ =ðmw:S 2 W2 þ mS 1:S2 S1R Þ; (2) where ca, cb, and cc are cohesion values; Aa, Ab, and Ac are areas; φc, φc, and φc are internal friction angles of the
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Figure 13. Schematic limit equilibrium model for the apparent dip slides. The terms Na1 and Na2 are the total normal forces of the driving block and the key block on plane a (slip surface), Nb is the total normal force on plane b (western boundary), Nc is the total normal force on plane c (karstic belt), S1 is the driving force of the driving block, S1R is the residual force of the driving block, S2 is the driving force of the key block, and W1 and W2 are the weights of the driving block and the key block, respectively.
slip surface, western boundary, and karstic belt, respectively. In general, Na1 and Na2 are the total normal forces of the driving block and the key block on plane a (slip surface), Nb is the total normal force on plane b (western boundary), Nc is the total normal force on plane c (karstic belt); S1 is the driving force of the driving block, S1R is the residual force of the driving block, S2 is the driving force of the key block; and W1 and W2 are the weights of the driving block and the key block, respectively. Here, mna.nb represents the unit vector component of Na1 and Nb in each other’s direction. So, q ¼ ðmna:nb mw:nb mw:na Þ= 1 m2 na:nb ; x ¼ ðmna:nb mw:na mw:nb Þ= 1 m2 na:nb ; r ¼ ðmna:nc mw:nc mw:na Þ= 1 m2 na:nc ; s ¼ ðmna:nc mS 1:nc mS 1:na Þ= 1 m2 na:nc ; and y ¼ ðmna:nc mw:na mw:nc Þ= 1 m2 na:nc ; z ¼ ðmna:nc mS 1:na mS 1:nc Þ= 1 m2 na:nc : To calculate the FOS, the geometry and physical– mechanical parameters are required. The geometry, such as the attitude of structures forming the rockslide boundaries and the length of the intersection lines of the structures, is known for both the prototype and the model of the Jiweishan rockslide. Using the space vector method, the volume, slide direction, and force acting orientation can be found. For the centrifuge model, the weight of slide mass W should be replaced by W9: W 0 ¼ n W ;
(3)
where n is the centrifuge acceleration. The FOS under different centrifugal accelerations during flight can be calculated. As centrifuge acceleration increases, the FOS values of the key block and the driving block decrease. This is because the friction and driving force are proportional to centrifuge acceleration, but cohesion remains unchanged during the test. Therefore, the ratio of cohesion and friction (or driving force) continues to decrease. As a result, the FOS declines rapidly at low acceleration and gradually at high acceleration. The FOS of the driving blocks is 1.02 and approaches a critical state when the acceleration reaches 10g. The FOS of the key block is 4.34, after which the driving blocks begin to creep and thrust onto the key block. When acceleration reaches 80g, the FOS of the key block is 1.01, at which point it breaks through along the karstic belt in the apparent dip direction. INITIATION MECHANISM The catastrophe of the Jiweishan rockslide demonstrates how important an accurate recognition of slope failure mode is for behavior prediction and risk assessment. Hungr and Evans (2004) proposed a classification for failure mechanisms of large rockslides involving a type of toe-constrained slide, such as the Madison Canyon slide (Hadley 1978; Glastonbury and Fell, 2000), the Frank slide (Cruden and Hungr, 1986; Benko and Stead, 1998), and the Sanxicun landslide (Yin et al., 2016), that had no explicit discontinuities evident at the surface of the toe but instead had to break out through the rock mass. In such cases, steep tensional joints in the crest area are required and “the sliding body must deform internally in order for sliding to occur” (Hungr and Evans, 2004, p. 4). The Jiweishan rockslide exhibited a similar toebreak mechanism. It is an east-facing cuesta landform, and bedding dips steeply to the northwest. The limestone rested on a carbonaceous shale interlayer and was actively driving on the stable rock mass at the toe. The stable key blocks played a role in resistance. Geological research has shown that underground mining in escarpment areas induces deep and subvertical cracks parallel to the cliff (Liu, 2010). The western crack is most likely caused by mining, because its distance (125–152 m) from the cliff is beyond the local valley relief influence area. The joints and cracks strike approximately parallel or orthogonal to the cliff, and there were no observed release discontinuities at the toe. Moreover, the weak interlayer dips slightly opposite to the slope; therefore, massive rock slope failure was not expected. However, a sudden, large rockslide eventually occurred on June 5, 2009. The key blocks broke along the karstic belt orientation and moved in
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the apparent dip direction. Oriented striae and vertical karst tunnels with filler and calcite crust were also observed on the rupture surface (Figure 2). Inspection of the terrain before the landslide confirmed that the rupture surface coincided with and probably originated from a gully (Feng, 2012). As a catchment, the gully is an active karstic area, and the rock mass is relatively weak. Assuming that the rock mass at the toe is in a state of uniaxial compression, the weak karstic belt is similar to a weak plane, which is prone to shear failure. Brittle failure of the karstic belt in the apparent dip direction led to a catastrophic rockslide. The Jiweishan rockslide was a compound slide with strain weakening on slip surface and lateral restraints (Fell et al., 2007). The passive wedge was constrained by the weak bedding interlayer and a conjugate joint set moving to N7uE. The slide broke through the lateral karstic belt and failed in the manner of a wedge with two planes, moving to N21uE.
The Jiweishan rockslide illustrates a unique mechanism of massive rock slope failure where the slope breaks out through a key block at the toe, leading to an apparent dip slide confined by four planes. This rockslide provides insight for better understanding the mechanism of obliquely inclined rock slope failure. Accurate recognition depends on knowledge of not only the structures but also the characteristics of the rock mass. Rockfalls may be the only pre-collapse warning signs prior to a large slide, and vertical scarps always indicate tension failure and the potential direction of movement. ACKNOWLEDGMENTS This study was conducted with financial support from the China Geology Survey (no. 12120114079101), the Ministry of Science and Technology of the People’s Republic of China (no. 2012BAK10B01-3), and the National Natural Science Foundation of China (no. 41302246).
CONCLUSIONS The cause of the apparent dip slide from obliquely inclined rock slope failure can be explained in terms of topography, lithology, karst, mining activity, and geological structure. An east-facing cuesta landform provided an open face for apparent dip slide displacement. Carbonaceous shale sandwiched by thicklayered limestone served as the pre-sheared surface. The conjugate tectonic joints, one set of which developed into a headscarp under hundreds of thousands of years of gravitational creep, cut the failure mass into a massive structure. Caused by local valley relief and mining, the other set of joints grew into the western plane. Intense karst developed in the thick limestone, particularly at the toe. Isolated by the tectonic joints, the sliding body thrust on the key block, causing it to shear through the toe in the apparent dip direction. The rupture surface developed in the intense karst belt, which extended into the toe area. Centrifuge modelling tests showed that the driving blocks lost stability prior to the massive slide, and the instantaneous apparent dip slide occurred at a specific model acceleration. The results suggest that the initial failure was a progressive process from the crest to the toe. Numerical modelling illustrated a similar deformation tendency in which the displacement decreased downhill during creep. As the strength of the weak layer decreased, the slope exhibited a sudden rise in displacement. The modelling tests were validated by the limit equilibrium method. We conclude that the strength reduction of the sliding plane due to longterm creep and groundwater infiltration was partly responsible for the slope failure.
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Study of the Damage Mechanics and Dewatering Recovery Programs for the Shield Tunnel under the Yangtze River BAOTIAN XU1 School of Earth Science and Engineering, Nanjing University, Nanjing, 210093, China xubt@nju.edu.cn
JIANFEI QIU Jiangsu Changshu Electric Power Company Limited, Suzhou, 215500, China 99421289@qq.com
QIAN SUN CHANGHONG YAN School of Earth Science and Engineering, Nanjing University, Nanjing, 210093, China Sun, 105720747@qq.com; Yan, 88185397@qq.com
BU XU Jiangsu Changshu Electric Power Company Limited, Suzhou, 215500, China 568828179@qq.com
SHI LIU CANHUI CHE The First Institute of Hydrology and Engineering Geological Prospecting, Anhui Prospecting Bureau, 233000, China Liu, zhangqingxubt@sohu.com; Che, 80915419@qq.com
Key Terms: Shield Tunnel, Damage Mechanism, Recovery Program, Yangtze River
ABSTRACT A case is presented about damages due to leakage and inrushing water that developed in the segmented pre-casted concrete liner of a shield tunnel under the Yangtze River. Various possible causes were considered to explain the damage mechanism. The opening and distribution due to differential settlement caused by the leakage of biogas or water in the shield tunnel were analyzed. The damage mechanism of the aquifuge, which occurred under the tunnel through exertion of a high piezometric head in the lower confined aquifer, was analyzed. The tensile-shear damage mechanism of the aquifuge was studied, and the judgment formulas, which were used to determine whether surface water bursting occurred, were derived. Two dewatering recovery
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Corresponding author email: xubt@nju.edu.cn
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programs were simulated by the finite difference method in conjunction with MODFLOW software. From the simulation results, the hydraulic gradient and settlements caused by decreased pore pressure were calculated. The optimal dewatering scheme and protection mea� surements are suggested.
INTRODUCTION With a rapid increase in construction of underground structures in China, shield tunneling has been widely used in construction activities (Shang et al., 2004; Wang et al., 2007; Li et al., 2009; and Lin et al., 2013). The shield tunneling method has been used for metro tunnel construction in China due to its advantages, such as rapid construction, easy control of soil deformation, and less disturbance to ground traffic (Maidl et al., 1996; Li and Chen, 2012). In recent years, the shield tunneling method has been used in China for tunnels under rivers with a great water
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surface width, such as the Weisan Road tunnel and metro line 3 in Nanjing. These two tunnels are located under the Yangtze River. Shield tunneling often encounters technical issues, such as ground subsidence, lining damage (crack, chipped scale, and leakage), and malfunction of the shield machine (Kavvadas, 2005; Li et al., 2007; Jung et al., 2011; Zhang et al., 2011; TĂłth et al., 2013; and Min et al., 2015). These adverse conditions are quite evident in the geological environment, which has a high piezometric head and increased soil and water pressures and poses a great difficulty to shield tunneling. The damage from accidents can lead to great losses. With the advance of a shield machine, a gap at the shield tail develops between the ground and the outer face of the liner segments; as a result, a properly grouted tail gap becomes the key issue for ground settlement control (Leca and New, 2007). In practice, grouting of shield tunneling includes grouting of the tail void (first-phase injection) and grouting directly through segments (second-phase injection) (Vittorio et al., 2007). However, due to the more uncertain factors of geological conditions, such as high piezometric head, biogas, strata distribution, etc., grouting will not solve all problems. Previous research results indicate that water leakage into the tunnel is a critical factor that affects the postconstruction ground and shield tunnel settlement. In a low-permeability environment, the tunnel leakage introduces a long-term drainage boundary for the ground around the tunnel, which tends to decrease pore-water pressure and increase the effective stress of the soil around the shield tunnel, causing ground and tunnel settlement. The leakage results in the lateral displacement of the shield tunnel, which may further aggravate the tunnel leakage (Zhang et al., 2015). A leakage accident in a shield tunnel under the Yangtze River occurred when the shield was being pushed into the receiving shaft. The accident resulted in quicksand and water bursting; water was injected into the tunnel to balance the internal and external soil-water pressure. This study focuses on the damage mechanism and the dewatering recovery program of the tunnel leakage. First, the engineering background, such as the geological conditions and construction processes, is described. Then, the leakage mechanism between rings is analyzed. Furthermore, the dewatering well layout and environmental effects are discussed. Last, the recovery program is evaluated. In engineering practice, a water-bursting accident due to leakage is seldom observed in a shield tunnel. The tunnel presented in this paper is buried under the Yangtze River, which exerts a great piezometric head. The shield driving method has been used for tunnels through the strata under rivers with great width and depth. Therefore, the work presented in this paper
provides a new contribution to similar engineering construction projects. BACKGROUND Leakage under the Shield Tunnel Jiangsu Changshu Power Plant Co., Ltd., is located in the northeast of Changshu City, Jiangsu Province, China. It is 24 km away from the city center and situated on the south bank of the Yangtze River (Figure 1). The shield-driven programs were designed for the double-conveyance water tunnels (east line and west line) for the power plant. The river width where the tunnel is located is about 5.4 km, and the maximum depth of the river is more than 10 m. The distance between the east line and the west line is approximately 21 m (Figure 2). The outside and inside diameters of the tunnel are 4.8 m and 4.2 m, respectively. The originating well (portal) of the shield tunnel is 25 m away from the embankment of the Yangtze River. The total length of the tunnel is approximately 943 m. The length of the section under dry land is approximately 30 m, while the remaining section crosses under the riverbed. The west line tunnel was successfully completed on March 31, 2011. However, when the lining of the last segment (the 1,048th ring) in the east line tunnel was installed, a dangerous accident involving quicksand and bursting water emerged at the bottom of the joint position between the 1,030th and 1,031st rings (Figure 3). The time following the 1,031st segment installation until the accident was approximately 3 days. During the 3 days, leakage of water occurred around the tunnel segments, but the leakage flux was very small and was not given much attention. After the accident, water was injected into the tunnel to balance the internal and external soilwater pressure, and the whole tunnel was submerged by the water. The position of the accident was 900 m away from the tunnel portal. The leakage resulted in a great differential settlement between the bottom of the tunnel and the riverbed (Figure 4A and B). The maximum settlements at the bottom of the tunnel and the riverbed were 1,922 mm and 2,332 mm, respectively. The maximum settlement point was located at the 1,030th ring. The maximum horizontal displacement occurred at the 1,041st ring; the maximum eastward deviation from the tunnel axis was 1.1 m. The differential displacements resulted in cracking and opening between the rings. The portion of the tunnel that had obvious cracks between rings, as surveyed by the divers, was from the 1,000th to 1,048th rings. The dominant sediments, largely sand and silt, settled inside the tunnel. A maximum thickness of sand and silt exceeding 2 m
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Figure 1. Location of the tunnel in China.
was found in the tunnel after the leakage (Figure 3). To ensure the smooth completion of the project, some measurements were required on the 1,000th to 1,048th rings (identified as the “special section”). The considered measurements included the following: (1) For the needs of tunnel recovery, dewatering schemes were adopted to decompress the piezometric head.
(2) In order to finish the construction of the tunnel, a deep excavation recovery program was designed for the section of the damaged shield tunnel. (3) In view of the fact that a long section of the shield tunnel was damaged due to the cracks between the segments, the damaged section could not be used as part of the conveyance tunnel. From a geotechnical safety point
Figure 2. Plan view of the shield tunnel.
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Figure 3. Location of damage to the tunnel during construction.
of view, a recovery program of permanent occlusion was determined to be installed at the 950th ring, and the special section will be abandoned. Using detailed site investigation and analysis, the occurrence of the described dangerous situation was attributed to the presence of rich biogas in layers 2 and 3 and the water-bearing stratum in layer 3. Therefore, the recovery construction phase required dewatering of the piezometric head and release of the biogas in the confined aquifer. Hydraulic Conditions The basic geological conditions of the site and the layout of the tunnels are diagrammed in Figure 3. The site stratigraphy is listed in Table 1. The
foundation soils in the study site are all Quaternary sediments, which are continuously distributed in the construction site. According to the geotechnical investigation report, there are seven soil layers in the foundation. The dominant layers through the tunnel are layers 1 and 2. Confined water is largely restricted in the sandy soil layers and tends to occur in layers 3, 5, 6, and 7. In layers 2 and 3, decaying plant debris and biogas were found. Based on the geotechnical investigation, after the drilling was completed, a slurry erupted from some boreholes, but this phenomenon did not occur in all of 58 of the boreholes. It is concluded that the biogas was partially distributed like gas pocket. Numerical and monitoring methods were carried out for the shield tunnels in Shanghai, and ground and tunnel responses induced by partial
Figure 4. Displacements along the longitudinal direction of the east line tunnel: (a) Settlements of the tunnel and the riverbed and (b) horizontal displacements of the tunnel.
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Xu, Qiu, Sun, Yan, Xu, Liu, and Che Table 1. The distribution of soil layers and permeability coefficients. Strata Layer 1 2 3 4 5 6 7
Layer Thickness (m)
Elevation of Layer Bottom (m)
Kv
Kh
Adopted Method
Muddy silty clay Silty clay Sandy silt Silty clay Silty sand Fine sand Coarse sand
10.2–15.8 6.5–10.8 8.6–14.2 4.4–5.2 7.6–10.2 10.8–18.4 —
−21.6 to −13.8 −30.2 to −24.8 −41.4 to −38.2 −44.8 to −41.1 −55.5 to −50.4 −70.4 to −52.4 Not exposed
5.616610−3 0.02 3 0.02 12 18 30
6.48610−4 0.013 1 0.013 7 9 15
Laboratory test Laboratory test Field experiments Laboratory test Field experiments Empirical value Empirical value
leakage in saturated clay with anisotropic permeability were analyzed (Zhang et al., 2015). The research results indicate that partial tunnel leakage at one side causes the largest ground surface settlement of 57 mm, but the ground surface settlements caused by leakage at two sides, i.e., uniform tunnel leakage, are 50.7 mm and 49.1 mm, respectively. In this study, if the pore pressure due to the gas pocket were released by the shield tunneling, it would induce an additional load on the soil layer and the following differential settlement under the tunnel. The buried depth of the elevation of the piezometric head of layer 3 is from −0.503 to −0.158 m, but the elevation of the piezometric head of layer 5 is from −1.083 to −0.27 m. This observation shows the difference in water head between the two aquifers. During the survey, the average water level of the river was approximately 1.0 m. The river depth at the special section is approximately 10.0 m. The permeability parameters of the strata are listed in Table 1. The parameters of layers 1, 2, and 4 were obtained by laboratory falling head permeability tests. The parameters of layers 3 and 5 were determined by in situ pumping tests, and the rest of the data were based on experience and determined in previous studies (Wang et al., 2012). The bottom level of the tunnel at the 1,030th ring was −25.0 m, but the bottom elevation of layer 2 was about −27.2 m. During the investigation, pumping tests were conducted. Two wells were installed near the special section. The well screens of the two wells were located in layer 3 and layer 5. The pumping results indicate that when pumping was carried out in layer 3, the piezometric head in layer 5 underwent almost no changes. Similarly, when pumping was carried out in layer 5, the piezometric head in layer 3 underwent almost no changes. The pumping tests indicated that hydraulic connection between layers 3 and 5 was not obvious. When pumping in layer 3, the water level in the other pumping wells decreased rapidly, but the water level of layer 5 changed very little. Though the river water and layer 5 have a great
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Coefficient of Permeability (m/d)
Type of Soil Layer
piezometric head, their recharge contribution to layer 3 was very slow. The clay layers 1, 2, and 4, with poor permeability (Table 1), could be considered as aquitards or relative aquifuges.
Geology and Soil Properties After the damage accident, 58 boreholes were drilled to obtain high-quality soil samples. The subsurface soils around the shield tunnel consisted of silty clay, and fine to coarse sand. The soils are all the Quaternary deposits around the tunnel, and they are distributed widely across the riverbed. The samples for laboratory analysis were obtained from borehole cores from the site. Average values of these properties were used in the present analysis. The strength parameters of the various soils were measured using triaxial (consolidated undrained [CU]) tests. Before each soil specimen was subjected to shearing, it was consolidated isotropically to the cor‐ responding in-site effective mean normal stress. A summary of the soil properties obtained through laboratory and in situ testing is given in Table 2, along with additional geotechnical properties. The results of analyses of the grain-size distributions of more than 40 samples are summarized in Table 3. LEAKAGE DAMAGE MECHANISM OF THE SHIELD TUNNEL In recent years, ground and tunnel responses induced by partial leakage in saturated clay with anisotropic permeability have been studied. The existing results indicate that tunneling operations in lowpermeability saturated soils often result in significant long-term ground movement and tunnel settlement (Cooper et al., 2002; Wongsaroj et al., 2007; Mair, 2008; and Zhang et al., 2015). It is very clear that water leakage into the tunnel introduces a long-term drainage boundary for the ground around the tunnel, and the pore-water pressure tends to decrease. The
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Sandy silt
Silty clay
Silty sand
Fine sand
Coarse sand
3
4
5
6
7
Penetration Test.
Silty clay
2
*Standard
Muddy silty clay
Material
1
Strata Layer Min Max Number of samples Average Min Max Number of samples Average Min Max Number of samples Average Min Max Number of samples Average Min Max Number of samples Average Min Max Number of samples Average Min Max Number of samples Average
Value 16.8 19.0 50 17.8 15.4 21.2 50 18.4 18.2 19.4 50 18.9 16.4 20.2 50 18.3 18.7 19.6 50 19.1 18.6 20.4 50 19.2 17.9 19.4 50 18.7
Unit Weight (kN/m3)
2.64
2.72
2.69
2.72
2.70
2.71
2.73
Specific Gravity, Gs 31.2 41.2 50 35.8 30.4 41.3 50 36.7 26.0 32.8 50 30.0 30.1 38.4 50 36.6 30.2 36.8 50 34.6 20.0 31.2 50 28.1 — — — —
Water Content (%) 0.89 1.32 50 1.23 0.86 1.16 50 1.04 0.84 1.02 50 0.93 0.89 1.20 50 1.09 0.80 0.92 50 0.87 0.76 0.94 50 0.87 — — — —
Void Ratio 11.4 14.8 50 12.6 18.4 12.6 50 16.4 8.4 10.2 50 9.1 11.8 15.4 50 14.2 — — — — — — — — — — — —
Plasticity Index
Table 2. Geotechnical properties of the soil materials.
2 8 40 4 4 11 40 7 5 16 40 8 3 11 40 6 5 18 40 9 10 21 40 16 — — — —
SPT* N 5.4 7.5 50 6.8 6.8 8.9 50 7.2 14.8 18.6 50 16.3 6.8 10.4 50 8.7 14.2 19.6 50 18.6 21.4 27.5 50 25.8 30.2 51.4 50 44.6
Compression Modulus, Es (MPa)
0.66 0.83 10 0.78 0.54 0.71 10 0.60 0.46 0.68 10 0.52 0.64 0.73 10 0.68 0.49 0.62 10 0.52 0.51 0.68 10 0.65 0.38 0.47 10 0.43
Coefficient of Lateral Pressure, K0
6.2 15.6 30 11.8 6.8 12.5 30 9.5 0 6.0 30 2.8 5.6 10.7 30 7.9 0 0 30 0 0 0 30 0 0 0 30 0
c9 (kPa)
8.8 16.8 30 13.0 21.2 28.7 30 24.4 24.0 31.4 30 29.0 15.6 21.4 30 18.8 24.0 34.2 30 28.8 16.8 24.6 30 20.4 30.0 37.5 30 35.0
Ф9 (u)
Shear Strength Parameters
Yangtze River Damage Mechanics and Dewatering Programs
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Xu, Qiu, Sun, Yan, Xu, Liu, and Che Table 3. Grain-size distribution of the sandy soils. Strata Layer
Type of Soil Layer
3
Sandy silt
5
Silty sand
6
Fine sand
Grain-Size Distribution (%) Value
2.0–0.50 mm
0.50–0.25 mm
0.25–0.075 mm
0.075–0.005 mm
,0.005 mm
Coefficient of Uniformity, Cu
Min Max Average Min Max Average Min Max Average
— — — — — — 0.8 17.6 6.2
— — — 0 6.8 4.2 4.2 22.4 12.3
12.3 30.2 24.1 32.4 60.4 50.4 34 75.2 68.4
50.2 74.3 68.9 26.5 48.7 37.8 4.9 18.2 13.3
0 9.6 7.0 0 8.7 5.8 — — —
4.2 9.4 7.3 1.6 7.6 6.6 1.609 1.820 1.680
effective stress of the soil tends to increase, causing ground and tunnel settlement (Zhang et al., 2015). For a shield tunnel built in saturated clay, the surcharge due to engineering activities or decreases of pore pressure may induce the opening and stagger of segmental joints and generate segmental cracks. Therefore, leakage occurs at the locations of the circumferential and longitudinal segmental joints, cracks, and grouting holes (Wongsaroj et al., 2007). Because the large leakage of water did not occur before water started rushing into the tunnel, why did the segment crack? The biogas found by the geological survey after the accident could provide a good explanation for this phenomenon (Figure 3). The biogas in the soils around the tunnel was partially distributed, wherein the scope of the distribution was like a gas pocket with much higher pressure. From monitoring, before this accident, little biogas was detected, but after the accident, the biogas concentration in the tunnel increased quickly. These observations indicate that the damage location of the tunnel was near the gas pocket. The leakage of biogas might be an explosive type. It could also decrease pore pressure and loads in the soil layer. As such, the settlement or crack started in the soils under the bottom plate of the tunnel, resulting in confined water bursting and inrushing. It is difficult to monitor the pressure of the biogas, but it seems reasonable that the maximum biogas pressure could be assumed to be same as the pressure caused by the overlying soil and water mass. According to the above discussion, the accident that occurred in this tunnel showed at least the following problems: (1) the leakage of biogas or water started before quicksand and water bursting; (2) after the leakage accident, settlement induced propagation of the segmental cracks; (3) the accumulated sediments in the tunnel after the accident included residual accumulation of numerous zones or layers of sands and silts, which were from soil layer 3, which indicates that the aquitard soil layer 2 below the tunnel was cracked by high piezometric head in the confined water layer 3;
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and (4) the quicksand induced substantial settlement of the shield rings.
Settlement of the Tunnel The settlement due to the additional load of the soils can be calculated by the layer-wise summation method (Wang et al., 2009): s¼
n X DPi u Hi ; Esi i¼1
(1)
where s is the total additional settlement caused by dewatering (m); φ is the empirical coefficient, defined as 1.0 in this calculation; n denotes the number of soil layers in the calculation range; ΔPi represents the additional load of the calculated soil layer caused by dewatering (kPa); Esi is the compression modulus of the calculated soil layer (kPa); and Hi is the thickness of the calculated soil layer (m). The additional load of the soil layer caused by decreasing pore pressure can be calculated as follows: DP ¼ cw ðh1 h2 Þ;
(2)
where h1 and h2 are the piezometric heads in the calculated soil layer before and after dewatering (m); and γw is the specific weight of the water (kN/m3). Partial tunnel leakage rather than uniform tunnel leakage caused a greater decrease of pore pressure at the spring line with a greater degree of tunnel deflection and larger ground surface settlement. Furthermore, the partial leakage at one side of the shield tunnel caused notable tunnel lateral movement (Zhang et al., 2015). This example indicates that biogas leakage in the soils can cause a greater decrease of pore pressure and larger settlement of the tunnel. The
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Soil Flow When soil flow emerges, the critical hydraulic gradient of the soils can be given by the following equation (Lu, 2002): icr ¼ ðGs 1Þ=ð1 þ eÞ;
(3)
where icr is the critical hydraulic gradient; Gs is the specific gravity of the soils; and e is the void ratio. So, to prevent the soils from the adverse impact due to seepage deformation, the hydraulic gradient should be expressed by the following equation: i icr =Fs ;
(4)
where i is the actual hydraulic gradient in the soils, and Fs is the factor of safety, which has a recommended value of between 2.0 and 2.5. Thus, the critical hydraulic gradient of layer 3 is 0.88 as calculated by the related parameters. If Fs is considered, i would be less than 0.35 (when Fs 5 2.5) or 0.44 (when Fs 5 2.0). The actual hydraulic gradient in the soils after leakage reached more than 10.0 as calculated from the piezometric head. So, according to Eq. 3 and Eq. 4, soil flow must have occurred under the tunnel. However, before soil flow occurred, the clay layer 2 overlying the sandy layer 3 must have been damaged and cracked.
Uplift and Cracking of the Aquifuge The uplift and cracking of the clay layer was obvious in the studied tunnel. For proper excavation, the piezometric head should be more than 1 m below the bottom plate to facilitate construction. The stabil‐ ity of the bottom plate can be calculated as follows (Wang et al., 2009): X
H cs Fs cw Hw ;
(5)
where H is the distance from the bottom plate of the foundation pit to the top plate of a confined aquifer (m); γs is the unit weight of soils in the calculation domain (kN/m3); Hw is the distance from the piezometric head of the confined water to the top plate of the confined aquifer (m); and Fs is the factor of safety, defined as 1.10 in this calculation. According to Eq. 5, the distance from the bottom plate of the tunnel to the top plate of the confined aquifer was only 2.2 m, and the distance from the piezometric head of the confined water to the top plate of the confined aquifer was nearly 24 m. The values are not consistent with Eq. 5. However, Eq. 5 is suit‐ able for the foundation condition, which has a large free surface. The bottom plate was uplifted or heaved by the piezometric head of the confined water, and, subsequently, at a weak surface position, the soils became cracked, and the tensile failure occurred. The tensile-shear zone is under the tensile failure zone, as diagrammed in Figure 5A. The damage mechanism has been explained in detail by Sun and Zhou (2011) and Sun et al. (2012). However, the leakage and cracking in the tunnel under study have a great difference with the bottom plate of the foundation pit. The key problem is that the size of the exposed top surface under the tunnel of the clay layer (layer 2) due to opening and distribution of the segments is very small; the crack width varied from a few millimeters to a few centimeters. The surface of clay layer 2 was unable to accommodate the upward deformation bulge (Figure 5B). So, after cracking, the height of the tensile failure zone would be very small or almost close to zero. Thus, the tensile-shear zone was formed at a weak position of the soils. Based on the bursting mechanisms, such as overall heaving, water and sand inrushing in contact between the soil and underground structures, and surface boiling, judgment methods that determine whether inrushing happens were studied using numerical and theoretical analyses (Sun et al., 2012). The judgment formulas that determine whether surface boiling happens were derived by Sun et al. (2012). The bearing capacity along the tensile-shear zone can be given by the following equation: T ¼ cH þ
H
Z
maximum decreasing value of the piezometric head in the studied soils is 24 m, so the settlement calculated by Eq. 1 is 148.2 mm. The actual maximum settle‐ ment under the tunnel is 1,922 mm. It is obvious that the soils were not only compressed by the additional load due to decreasing pore pressure, but they were also eroded by the high hydraulic gradient. The seep‐ age deformation of soil flow in the large volume of sandy soil also became quite pronounced. The large amounts of sand and silt in the sediment after the accident could be envisioned as good proof of seepage deformation in layer 3.
K0 cs htg/dh:
(6)
0
After integration: T ¼ cH þ
K0 c H 2 tg/; 2 s
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(7)
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Xu, Qiu, Sun, Yan, Xu, Liu, and Che
Figure 5. Sketch of the surface boiling mode: (a) uplift and cracking of the bottom plate of the foundation pit, and (b) tension and shear of the aquifuge.
where T is the tensile-shear bearing capacity (kN); K0 is the lateral earth pressure coefficient; H is the distance from the bottom plate of the tunnel to the top plate of the confined aquifer (m); c is the cohesion of the clay (kPa); ϕ is the friction angle of the clay (u); and γs is the unit weight of the soils (kN/m3). So, to prevent the soils under the tunnel from uplift damage by the confined water pressure, the relation between T and Hw should be considered using the following equation: ðcs H þ T Þ=cw Hw Fs ;
(8)
where Fs is the factor of safety, given as 1.10 in this calculation too, referring to Eq. 5. By the given conditions and parameters, the calculated factor of safety from Eq. 8 is 0.76, which is far less than 1.1. So, once the cracks emerge between segments of the tunnel, the aquifuge (layer 2) will be damaged inevitably with the following inrush of water and sand. The quicksand resulted in noticeable erosion in the sandy soil (layer 3) and created greater settlement.
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DISCUSSION OF DEWATERING RECOVERY PROGRAMS In view of the fact that a long section of the shield tunnel was damaged due to the cracks between the segments, the damaged section could not be used as part of the conveyance tunnel. The portion of the tunnel with obvious cracks between rings, as surveyed by the divers, is from the 1,000th to 1,048th rings. From a geotechnical safety point of view, a recovery program of permanent occlusion was determined to be installed at the 950th ring (Figure 3). This position means that the special section from the 951st to 1,048th rings of the tunnel would have to be abandoned. The piezometric water level had to be decreased under the bottom plate of the tunnel before any proposed recovery plan could be contemplated. Therefore, it was necessary to dewater the piezometric head and release the biogas in the soils for tunnel recovery. Dewatering Program Design Because the dewatering operation would have to be accomplished before recovery, the dewatering program
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Figure 6. Layout of dewatering wells for the different schemes: (a) scheme I and (b) scheme II.
needed to consider some problems to protect the remnant section and the west line tunnel. The detrimental consequences of dewatering include the following: (1) Dewatering will induce additional load in the soil layer and increase settlement, and all the differential settlement will result in cracking of the segments; (2) dewatering will induce a greater hydraulic gradient in the soils, which may induce seepage deformation in the sandy soils near the tunnel. According to Eq. 4, the critical hydraulic gradient should not be more than 0.44. These factors needed to be considered in the dewatering program design. During the investigation stage, pumping tests were carried out. Based on the test results, it was observed that the hydraulic connection between layer 3 and 4 could almost be neglected, and clay layer 4 could be considered as a tight aquifuge. So, the aquifer dewatering was confined to water layer 3. The leakage was mainly located at the special section of the east line tunnel. It was concluded that the dewatering wells would only be arranged around the special section (Figure 6A). The filter tubes or the depressurizing well would be installed in layer 3 (Figure 7). Effects of the Dewatering Program To evaluate the effects of dewatering, a three-dimensional numerical simulation based on the results of field pumping tests was performed to simulate the dewatering (Wang et al., 2012, 2014; Xu et al., 2014). The governing equation for the unsteady flow of the confined aquifer is given in Eq. 9.
and sink (1/d); ss is the specific storage at the point (x, y, z) (l/m); t is time (hr); Ω is the computational domain; h0 is the initial water table at the point (x, y, z) (m); Γ1 is the first type of boundary condition; Γ2 is the second type of boundary condition; nx, ny, nz are the unit-normal vectors on the boundary along the x, y, and z directions; and q is the lateral recharge per unit area on boundary Γ2 (m3/d). For simplification, the soils are assumed to be isotropic in the horizontal direction, so Kxx 5 Kyy (Kh). The above mathematical model is usually solved with the finite difference method (Wang et al., 2014) by the software MODFLOW. The calculation range is 1250 m 6 1250 m, and the depth is 87 m. The three-dimensional model includes seven layers, 172 rows, and 172 columns (Figure 8). The mesh is dense at the special section, and it gradually becomes sparse from the center outwards. The boundary conditions of the model were defined as the constant water head boundaries. The bottom plane of the sand layer was regarded as the zero-flux boundary. The drawdown results of scheme I are shown in Figure 9. The hydraulic gradient and settlements (calculated by Eq. 1) are listed in Table 4. From the simulation results, after dewatering, the water level throughout the special section will decrease to a level below the bottom plate of the tunnel. The dewatering procedure meets the requirement. For construction requirements, the piezometric head of layer 3 should be depressurized down to 1 m below the bottom plate of the tunnel, so drawdown in the special section must be more than 25 m. The hydraulic gradient of
8 @ @ @ @h @h @h @h > > @x Kxx @x þ @y Kyy @y þ @z Kzz @z W ¼ Ss @t ðx; y; zÞ 2 X > < hðx; y; z; tÞ ¼ h ðx; y; z; tÞ ðx; y; zÞ 2 C 0 1 ; @h @h @h K þ K þ K C ¼ qðx; y; z; tÞ ðx; y; zÞ 2 C j > xx yy zz 2 2 @nx @ny @nz > > : hðx; y; z; tÞj t¼t0 ¼ h0 ðx; y; zÞ ðx; y; zÞ 2 X where kxx, kyy, kzz (Kv) are the coefficients of permeability along the x, y, and z directions (cm/s); h is the water table at the point of (x, y, z) (m); W is the source
(9)
the soils due to pumping will be less than the critical values, which are given by the Eq. 3 and Eq. 4. To facilitate the analysis, the monitoring points are
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Xu, Qiu, Sun, Yan, Xu, Liu, and Che
Figure 7. Diagram of the depressurizing well structure.
set along the tunnel extension direction both on the east line and on the west line tunnels. The monitoring points are indicated in Figure 9. The monitoring points are arranged at equal spacing; the distance between adjacent points is approximately 21.8 m. The maximum settlement calculated by Eq. 1 on the east line tunnel is 61.7 mm, which is located at
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monitoring point Eo4 (Eo1, 2, and 3 are located in the tunnel section that will be abandoned). The maximum settlement on the west line tunnel is 148.2 mm, where the maximum settlement points are located at Wo1 and Wo2. The maximum hydraulic gradient in the longitudinal direction is 0.34, which is less than the critical
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Figure 8. Three-dimensional ďŹ nite difference model for dewatering numerical simulation.
0.44 and meets the requirement of Eq. 4. As this scheme causes significant settlement on the west line tunnel, it might induce new cracks between tunnel segments. Dewatering should decrease the water level and reduce the effect around the west line tunnel.
The second dewatering scheme considered has a layout of wells as indicated in Figure 6B. The drawdown results from the numerical simulation are shown in Figure 10. The hydraulic gradient and settlements (calculated by Eq. 1) are listed in Table 5.
Figure 9. Drawdown contours of the dewatering scheme I.
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Xu, Qiu, Sun, Yan, Xu, Liu, and Che Table 4. Calculation results of scheme I.
Calculation Point Eo1 Eo2 Eo3 Eo4 Eo5 Eo6 Wo1 Wo2 Wo3 Wo4 Wo5 Wo6 Wo7
Piezometric Head before Dewatering (m)
Piezometric Head after Dewatering (m)
Drawdown (m)
−1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1
−25 −21 −15 −11 −7 −5 −25 −25 −25 −19 −13 −9 −7
24 20 14 10 6 4 24 24 24 18 12 8 6
From the simulation results, after dewatering, the water level throughout the special section will decrease to a level below the bottom plate of the tunnel. The dewatering accomplishes the requirement. The maximum settlement calculated by Eq. 1 on the east line tunnel is 49.4 mm, which is located at monitoring point Eo4. The maximum settlement on the west line tunnel is 123.5 mm, where the maximum settlement points are located at Wo1 and Wo2. However, this procedure will produce a greater hydraulic gradient in the longitudinal direction, with a maximum value of 0.46, i.e., more than the critical 0.44 level. Although this value exceeds the allowable
Hydraulic Gradient
Settlement (mm)
Settlement Difference (mm/m)
Longitudinal Direction
Cross Direction
— — — 61.7 37.0 24.7 148.2 148.2 148.2 111.1 74.1 49.4 37.0
— — — 1.2 1.2 0.6 0 0 0 1.7 1.7 1.2 0.6
0.34 0.36 0.28 0.20 0.13 0.11 — — — — — — —
0.00 0.16 0.09 0.06 0.03 — — — — — — — —
amount of Eq. 3, it is very close to the allowable amount. To decrease the hydraulic gradient in the longitudinal direction at the special section, the new pumping wells should be arranged on the south side of the exiting well location. However, if the number of pumping wells increases, it will produce even greater decreases in the water level and cause greater settlement on the intact tunnel section, which should be protected. Based on sound geotechnical judgments, scheme II should be a more reasonable dewatering choice for tunnel recovery. However, decreasing the piezometric head in the special section, causing great settlement,
Figure 10. Drawdown contours of dewatering scheme II.
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Yangtze River Damage Mechanics and Dewatering Programs Table 5. Calculation results of scheme II.
Calculation Point Eo1 Eo2 Eo3 Eo4 Eo5 Eo6 Wo1 Wo2 Wo3 Wo4 Wo5 Wo6 Wo7
Piezometric Head before Dewatering (m)
Piezometric Head after Dewatering (m)
Drawdown (m)
−1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1
−25 −19 −13 −9 −7 −5 −21 −21 −19 −15 −11 −9 −7
24 18 12 8 6 4 20 20 18 14 10 8 6
will inevitably be harmful to the tunnel, especially for the west line tunnel. So, proper protection procedures, such as grouting or installation of recharge wells, should be used for the west line tunnel. Based on this detailed analysis, a wall of jet-grouting piles (Figure 11) was installed. The length of the wall was 109 m, and the width was 1.8 m. The bottom of the wall was located in layer 4. The distance between the wall and the east line tunnel was 9.35 m. The grouting method around the tunnel was prepared for the potential emergencies of leakage and water bursting. After grouting reinforcement and installation of a protecting wall for the positions near the special section, the dewatering and recovery operation was
Figure 11. Diagrams of wall of jet-grouting piles: (a) cross section and (b) longitudinal section.
Hydraulic Gradient
Settlement (mm)
Settlement Difference (mm/m)
Longitudinal Direction
Cross Direction
— — — 49.4 37.0 24.7 123.5 123.5 111.1 86.4 61.7 49.4 37.0
— — — 1.2 0.6 0.6 0 0 0.6 1.2 1.2 0.6 0.6
0.46 0.42 0.32 0.21 0.12 0.06 — — — — — — —
0.35 0.34 0.22 0.16 0.08 0.02 — — — — — — —
carried out. The occlusion steel plates (Figure 12) were installed on December 7, 2013. The recovery of the shield tunnel was successful. From the monitoring results, it was found that the settlements on the protection section were very small, which marks the successful completion of dewatering.
CONCLUSIONS In this paper, the settlement and cracking mechanisms of a shield tunnel under the condition of high piezometric head pressure were analyzed. Then, tunnel recovery schemes were discussed. The findings from this research can be summarized as follows:
Figure 12. Installation of occlusion steel plates.
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(1) The partial biogas leakage of the shield tunnel in the clay layer can cause greater decreases of pore pressure similar to water leakage and may induce larger settlement and cracking of the tunnel segments. (2) The aquifuge soil layer below the bottom of the tunnel can be cracked due to differential settlement and high piezometric head in the underlying confined water layers. The crack would induce inrushing of water and sand. Because the soils are eroded, this results in greater settlement, opening, and stagger. (3) The failure zone of the aquifuge, under the tunnel where greater pore pressure was exerted, can be considered as a tensile-shear mechanics type. The judgment formulas of the tensile-shear mechanism can easily explain the inrushing of water and sand in the studied tunnel. (4) Based on the damage mechanism, the effects of settlement and seepage deformation were considered in the dewatering recovery scheme. By numerical simulation, dewatering would inevitably cause great settlement on the west line tunnel, and therefore the proper protection measures needed to be carried out. ACKNOWLEDGMENTS This study was financially supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangsu Province, China (grant nos. 41202174 and BE2015675). REFERENCES COOPER, M. L.; CHAPMAN, D. N.; ROGERS, C. D.; AND CHAN, A. H., 2002, Movements in the Piccadilly Line tunnels due to the Heathrow Express construction: Geotechnique, Vol. 52, No. 4, pp. 243–257. JUNG, H. S.; CHOI, J. M.; CHUN, B. S.; PARK, J. S.; AND LEE, Y. J., 2011, Causes of reduction in shield TBM performance—A case study in Seoul: Tunnelling and Underground Space Technology, Vol. 26, No. 3, pp. 453–461. KAVVADAS, M. J., 2005, Monitoring ground deformation in tunnelling: Current practice in transportation tunnels: Engineering Geology, Vol. 79, No. 1–2, pp. 93–113. LECA, E. AND NEW, B., 2007, ITA/AITES report 2006 on settlements induced by tunneling in soft ground: Tunnelling and Underground Space Technology, Vol. 22, No. 2, pp. 119–149. LI, G. C.; DING, L. Y.; WU, X. G.; LUO, H. B.; AND LI, X. Q., 2007, Ground settlement prediction during construction of Wuhan Yangtze River Tunnel: Chinese Journal of Rock Mechanics and Engineering, Vol. 26, No. S2, pp. 3631–3638 (in Chinese). LI, X. G. AND CHEN, X. S., 2012, Using grouting of shield tunneling to reduce settlements of overlying tunnels: Journal of Construction Engineering and Management, Vol. 138, pp. 574–584. LI, Y.; EMERIAULT, F.; KASTNER, R.; AND ZHANG, Z. X., 2009, Stability analysis of large slurry shield-driven tunnel in
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