Experimental modeling of shear behavior of reinforced concrete pile caps 01 aug

IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013

ISSN 2320 – 6020

Experimental Modeling of Shear Behavior of Reinforced Concrete Pile Caps Ambareesh Kumar

ABSTRACT: The application of bending theory based methods and strut-and-tie models for the design of pile caps to resist shear is still a subject of debate, with the latest is code permitting both methods but not giving much guidance as to their use. The former UK design standards for concrete buildings and bridges, recently withdrawn, gave more guidance, and it is likely that these methods will continue to be used by designers. However, there is considerable discrepancy between these standards, particularly with regard to the width of cap over which shear enhancement at short spans may be applied, and how much longitudinal reinforcement to take as a tie in the strut-and-tie method. Both standards are also seen as conservative. To gain a better understanding of the problem and assess the available design methods, nonlinear finite-element analysis has been performed to investigate the shear behavior of four-pile reinforced concrete pile caps, under full-width vertical loading. The models were validated against an experimental program that included an optical photogrammetric method for measuring full field displacements. An extensive parametric study was carried out, varying shear span, cap width, and reinforcement ratio over a practical range. The conservatism of the Indian design standards and the real shear capacity of the pile caps were found to be a function of shear enhancement factor and the width of the cap over which shear enhancement is applied. Strut-and-tie behavior was observed in the models, and a commonly used strut-and-tie method was found to give fairly good predictions. A modified strut-and-tie method is suggested for this particular configuration of a four-pile cap under full-width loading, which gives more accurate predictions. This is especially so for samples with large transverse pile spacing, where a significant proportion of the longitudinal reinforcement over the width of the cap can be assumed to participate in the yielding ties.

KEY WORDS: Shear Behavior, Load Deflection Analysis, Cap Failure.

Introduction A reinforced concrete (RC) pile cap is an example of a shortspan, relatively deep beam, which can also be wide relative to its depth if the transverse pile spacing is large, such that twodimensional spanning behavior can become significant. The design standards contain two main methods for their design to resist shear.[1] The first is deep beam theory, developed by Regan (1971) for one-way spanning beams, in which the assumption is made of a critical opening inclined shear crack, above which is a compression zone of concrete. Shear failure occurs when the concrete fails in compression. The depth of the concrete compression zone is related to the relative rotation of the two surfaces of the crack.

The second is the strut-and-tie method (STM), which is based on the concept of longitudinal and transverse bottom reinforcement acting as ties with inclined compressive struts joining the pile heads and the center of application of the load.[2]

There is discrepancy between the deep beam theory based design formulae in the Indian design standards IS2911-1979 (Indian Standards Institution 1979) and IS2911 (Indian Standards Institution 1984) because of different definitions of the width of the cap for which shear enhancement may be applied, which leads to differences of a factor of two or three between predicted capacities.[1] Fundamentally, overall, only a limited experimental data set is available to verify the current design approaches. Tests of the shear capacity of a series of reduced-scale pile caps under full-width vertical loading with uniform bottom reinforcement in both directions have been carried out. It was found that both IS code deep beam theory-based design formulae gave conservative predictions. The STM in the standards gave better predictions, suggesting the shear behavior of a pile cap can be described physically in this way, but becomes conservative when transverse pile spacing is large [2].

This paper describes the development of nonlinear finiteelement analysis (FEA) models of the experimental samples and their verification against the experimental results. The FEA has then been extended to cover a wider range of pile cap dimensions by means of a parametric study of further analyses.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013

ISSN 2320 – 6020 boards were placed between the top platen, spreader beam, and cap to avoid stress concentrations causing local crushing.

The pile cap was set on the lower platen temporarily supported on wedges and self-leveling screed poured underneath the steel piles to ensure an even contact testing frame area.

Horizontal restraint at the pile bases was minimized by means of plastic sheets under the piles between which oil was placed.

The pile bases experienced a vertical reactions, but because the pile bending stiffness was much lower than the cap, analysis showed that the behavior of applied vertical load of the cap.

Fig.1: Reinforced concrete four-pile cap under a vertical loading Two-way behavior of the caps under load was observed in the FEA and it became apparent that the STM indeed provides a reasonable physical description of the shear behavior.[2] The results from the parametric study are used to suggest a modified STM, which gives improved predictions of capacity, especially for wide transverse pile spacing.

Pile Cap Experiments A total of 9 pile cap samples in three batches were tested. The experimental setup used to achieve the configuration of loading and supports shown in Fig. 1.

The caps were instrumented to measure load and displacements recorded by linear potentiometers distributed over the soffit. Crack distribution and propagation were highlighted by hand on the surfaces and photographed. In addition, a full-field distribution of strain on the front surface of the cap was obtained using digital photogrammetry. Results from the experiments, including the development of cracking with the load, at final crack patterns, and the typical loaddisplacement show the cap. The shear enhancement application factor, A, is defined as A = benh ∕b Where benh is the width over which shear enhancement is considered effective according to IS 2911 (i.e., the sum of the width of all relevant strips centered on pile heads), and b is the overall cap width. The experimental samples consisted of two series. In Series A, av∕d was varied with A constant, by varying longitudinal pile spacing with constant transverse pile spacing. Series B was designed vice versa to vary A under constant av∕d, by varying the transverse pile spacing with constant longitudinal pile spacing. It had a lower reinforcement ratio than Series A so the effect of this quantity could also be investigated.

Results from the most successful final batch of nine samples are the verification of the FEA described herein. The depth d in Fig. 1 was kept constant at 130 mm, the steel pile diameter hp at 100 mm, the width hc of the loading spreader beam at 100 mm, and the pile depth dp at 90 mm. The remainder of the dimensions that were varied is given in Table 1 for the nine samples, along with the reinforcement details and concrete strengths for each cap. The parameter μ is the ratio between transverse pile spacing and the pile diameter (μ ¼ ly∕hp).

Reinforcement was uniformly distributed with equal percentages in both directions. Mean reinforcement yield strength f y of 500 N∕mm2 and mean ultimate strength of 646 N∕mm2 were obtained by testing. Concrete cube strength fcu was the mean of three results for each pile cap, on 150 mm cubes.

Table 1: Experiment sample detail

The Nine sample testing 5, 7.5, 10-ton Universal-testing machine at the M.M.M. Engineering Collage Gorakhpur was used. The hydraulic actuator lifts the lower steel plates. Soft

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013 Cap deflection The early bending and shear cracks appearing in the cap in the elastic stage did not change the initial stiffness of the cap. The deflection of the center of the cap soffit increased linearly and remained in a small range, not more than 5-15mm. The deflection suddenly increased after the onset of the yield stage, the point that was normally marked by the beginning of the maturing of the critical shear crack or the central bending crack on the front or back surfaces.

ISSN 2320 – 6020 which is not ideal. The cap under vertical loading may have a maximum or up limit shear capacity. The shear capacity reduces with reducing depth of vertical loading ending up with brittle punching shear failure at lowest shear failure load when the cap is under concentered loading.

The deflection could be very large in the yield stage before the structure finally failed, implying the failure was rather ductile.

This could either be because of the yield behavior of the longitudinal reinforcement in bending failure or a gradual softening of the compressive concrete strut in the shear failure.

This proved that in structures of short shear span, even in the absence of shear reinforcement, shear cracking does not necessarily result in immediate failure. The ductile behavior in pile caps with large transverse pile spacing may also be because of the cap’s transverse behavior i.e. the ductile behavior of the transverse reinforcement which caused the cap to remain ductile even when the shear crack on the cap front and back surfaces appeared.

The load pattern on a cap’s shear mechanism So far, all results have been for pile caps subject to the vertical loading. It is expected that the shear capacity and mechanism may vary with the load pattern, and so in order to study its deflection, the shear behaviors of experimental samples under a concentrated load, and a model in the parametric study under a vertical loading with reduced depth of pile cap were investigated.

In experimental work, three different types of sample were used in 9 specimens divided into Series A, B and C with same size dimensions. All these square samples were subject to a concentrated vertical load applying the cap of 250mm× 250mm steel plate. The reinforcement layout in cap A to C

was closest to the experimental samples in this research.

Therefore, 1(A to C) was chosen for comparison. The dimensions and material properties of 1(A to C) are shown in Table. The depth of the pile was 130mm.

This section has shown that the shear mechanism and the shear capacity of pile caps and the accuracy of each design method are influenced by the load pattern. The load pattern may cause the shear mechanism to change from a normal shear failure explained by the bending theory based shear formulae to a punching shear failure. Current bending theory based shear formulae, STM and the punching shear prediction for pile caps (e.g. at a constant perimeter surrounding the loading lying on 20% the pile diameter inside the inner edge of the piles) do not consider the influence of the load pattern

Fig.2: pile cap bending failure The ratio of the FEA to the experimental failure load is close to 1.0.Some of the remaining caps did not fail completely across their whole width in the experiments because of asymmetric loading, so their true failure load should have been higher, hence explaining their ratio being above 1.0. It was concluded from the validation that the FEA gave an adequate representation of the experimental results (particularly failure load) with the parameters chosen, making them suitable for use in the extended parametric study described later.

Model Output In the experiments, a full-field strain distribution on the cap front surface was obtained by digital photogrammetry.

Concrete strain at the level of the main longitudinal reinforcement was observed in all cases to be greater than the reinforcement yield strain of 0.0026 over the whole longitudinal span. Thus it is likely that the reinforcement was acting as a yielding tie at the ultimate load. This observation is supported by the FEA of most samples.

For example, for 1B2A σsx reaches yield (500 MPa) over almost the whole longitudinal span, for the width of the pile head and between the pile and the front surface. Between the piles, σsx reaches yield at mid longitudinal span but reduces significantly toward the line of pile support, suggesting twoway spanning behavior.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013

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Comparison of the Failure Loads between Experiments by given table:

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013

ISSN 2320 – 6020 the onset of yield and mature at the failure step. The observations of a yielding main longitudinal reinforcement tie, a transverse tie at elastic stress, which depends on transverse pile spacing and diagonal compressive splitting cracks, point toward strut-and-tie behavior. The failure criterion stress that σv and crack strain εcr can be observed in the FEA output. The compression between the pile head and the loaded area, idealized as an equivalent strut linking the pile head with a point under the wall loading between the center of the cap top and the top front edge.

Parametric Study The FEA was extended with nine further models under vertical loading, with the range of key dimensions. Other dimensions were consistent with the experimental samples.

The range of av∕d and μ for the experimental samples is indicated by the dashed lines.

The geometry idealization, boundary conditions, element type, and constitutive models for concrete and reinforcement were as previously described. The reinforcement in the cap was 8,10mm bars at 198,160-mm spacing in both directions, and the steel piles were again unreinforced but with an artificially high strength. Concrete Young’s modulus was taken as 28 GPa, Poisson’s ratio as 0.2, fcu as 25 MPa, and ft as 2.5 MPa. Ultimate crack strain εcrult was taken as 0.001 to improve convergence.

This two-way behavior is confirmed by the stress in the transverse reinforcement σsy. Transverse ties under significant elastic stress are observed concentrated over the pile head, with stress greater for larger transverse pile spacing. This implies potential for bending or shear cracking in the transverse direction.

In all the FEAs of the experimental samples, diagonal splitting cracks linking the wall loading to the pile head are present at

Fig. 3 Pile Cap Failure of Bending Zone Predicted Pile cap Failure Loads The failure load of the pile cap as a function of various depth of cap at applying the pressure in cap to check the cracking load and failure load at design load. Longitudinal and transverse reinforcement of pile cap at equally provided of both direction. The cap becomes more two-way spanning and v becomes less dependent on av∕d, especially for av∕d< 0:81; the proportion of cap width over which shear enhancement is effective is decreasing. For smaller av∕d, e.g., < 0:31, this trend

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continues with v reducing noticeably once μ increases beyond 3.0.

Predicted Failure Mechanisms Most parametric study models had ductile failures that were either in bending or shear judged by the crack distribution on the front surface, and in the latter case by the occurrence of a yielding reinforcement tie over the whole longitudinal span.

Pile Caps with large lx failed by bending with wide mid span cracks and stress in the longitudinal reinforcement σ sx increasing toward mid span. Diagonal splitting cracks on the front surface become more apparent at smaller a v∕d, as for pile cap.

Fig. 5 Punching Shear Failure of Pile Cap

Fig. 6 Shear Failure of Pile Cap

Fig. 4 Pile Cap Failure at Corner of Pile For the majority of caps, the longitudinal reinforcement yielded across the whole width of the cap at mid span, either in shear or bending failure. The range with large l y (μ > 4) and relatively small lx for which this was not the case and in which yielding occurs on a strip over each pile head. With larger l x, the yielding strip can be wider than three times the pile diameter when μ > 3, even extending across the whole cap width.

The objective of this project was to evaluate the strength properties of concrete paving mixtures in the laboratory to develop the relationships among compressive strength, tensile strength, flexural strength, and stress wave propagation. The ultimate goal of this research was to collect a database to develop a performance-related specification and thereby improve the specifications and quality assurance procedures for hydraulic cement concrete pavements of pile cap.

Fig. 7 Specimen on Testing Frame

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013

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Fig. 8 Failure of Pile Cap Concrete batches were mixed in the laboratory using the materials proposed for a specific paving project. The mixture proportions were based on the mix designs accepted for use on the project. To develop the relationship between load and deflection of pile cap strength, the mixtures tested should have a range of property values.

Experimental result of pile cap In the following discussion, the ratio of failure load predicted

by FEA to those from the deep beam theory based shear formula and the STM in IS2911.[1] In each case, the partial factor on material strength γm = 1.0.

A global multiplying factor of 2.0 could be applied to the IS2911 formula, although this would lack clear physical meaning. A strut-and-tie model is permitted as an alternative design method in the Indian Standards, with the model comprising concrete struts transferring the load from the center of the loaded area to the centers of each pile cap head, reacted by reinforcement ties in both directions.

The standards differ in the amount of longitudinal reinforcement assumed or permitted to participate in the longitudinal tie. IS2911 envisages the longitudinal reinforcement as uniformly distributed across the cap width, with the longitudinal ties to be the reinforcement within strips no wider than three times the pile diameter centered on the piles. In IS2911, all longitudinal reinforcement can be included in the ties, provided 80% of it is placed in strips anchored directly over the pile heads. The IS2911 approach is seen as more practical because concentrating the reinforcement over the pile heads in line with can cause problems with punching shear, especially under concentrated loads. Neither standard considers the strength of the concrete strut, although this is addressed in the Eurocodes (British Standards Institution 2004) and in US and Canadian standards.

Eurocode detailing provisions state that the longitudinal reinforcement should be concentrated in the “stress zones between the tops of the piles” (British Standards Institution 2004, 2005).

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013 This may be taken by designers to mean entirely confined to over the pile heads, in which case the implication is that all such reinforcement may be taken to participate in the longitudinal tie. US standards have a similar provision that longitudinal reinforcement should be anchored in the nodal zones in the strut-and-tie model. At small pile transverse spacing (A = 1), the STM matches well with FEA, while for large transverse pile spacing (A < 1 or μ > 3) the FEA failure load is higher than from the STM.[3] This can be explained by the longitudinal yielding tie being wider than the limit of three times the pile diameter in IS 2911 and even extending over the whole cap width when μ > 3. A yielding tie can also form in the transverse direction.

Conclusions Nonlinear FEA has been carried out to investigate shear capacity and behavior of pile caps under full-width vertical loading with deferent depth, verified against the results of a series of reduced-scale experiments. The most important observation from the FEA, backed by the experimental observations of load and deflection curve represents the behavior of pile cap.

Current deep beam theory based design formulae are conservative for pile caps, and although the STM in UK standards IS 2911 gives a better prediction; it fails to do so for caps with large transverse pile spacing. The FEA has shown that transverse reinforcement plays an important role, and the width of longitudinal reinforcement participating in the yielding tie can be larger than three times the pile diameter centered on each pile. A new STM is proposed in which longitudinal reinforcement across 90% of the cap width is included in the ties, and the span of the longitudinal ties is slightly reduced to account for the pile diameter and width of the wall loading. This method improves the prediction of capacity especially for caps with large transverse pile spacing, provided that the longitudinal pile spacing is not excessively short and the cap fails in a ductile manner with yielding of the main longitudinal reinforcement.

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References 1. CODE OF PRACTICE FOR design AND CONSTRUCTION OF pile foundation of IS 2911 1979 And IS 2911 1984.

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“Building code requirements for structural concrete.”

ACI 318R-05, Farmington Hills, MI. 5. Bazant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Mater. Constr., 16(3), 155–177.

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