Centrifuge Modeling of Torsionally Loaded Pile Groups

This paper reports a series of centrifuge model tests on torsionally loaded 1×2, 2×2, and 3×3 pile groups in sand. The objectives of the paper are to investigate: (1) the response of the pile groups subjected to torsion; (2) the way in which the applied torque is transferred in the pile groups; (3) the internal forces mobilized in these torsionally loaded pile groups and their contributions to resist the applied torque; and (4) the influence factors that affect the load transfer, such as soil density and pile-cap connection. In these model tests, the group torsional resistances of the pile groups increased monotonically in the test range of twist angles up to 8°. Both torsional and lateral resistances of the individual piles were simultaneously mobilized to resist the applied torque. The torsional resistances were substantially mobilized at small twist angles, while the lateral resistances kept increasing in the whole range of twist angles. Thus, the contribution of the torsional resistances to the applied torque decreased at large twist angles. The piles at different locations in a pile group could develop not only different horizontal displacements, but also different pile–soil–pile interactions and load–deformation coupling effect, hence, the torsional and lateral resistances of the piles are a function of pile location. The soil density had a more significant effect on the torsional resistances than on the lateral resistances of the group piles.     

Liquefaction-Induced Settlement of Pile Groups in Liquefiable and Laterally Spreading Soils

The results of a series of dynamic centrifuge tests on model pile groups in (level) liquefied and laterally spreading soil profiles are presented. The piles are axially loaded at typical working loads, which has enabled liquefaction-induced settlements of the foundations to be studied. The development of excess pore pressures within the bearing layer (dense sand) was found to lead to a reduction in pile capacity and potentially damagingly large coseismic settlements. As the excess pore pressure increased, these settlements were observed to exceed postshaking downdrag-induced settlements, which occur due to the reconsolidation of liquefied sand around the pile shaft. In resisting settlement, the pile cap was found to play an important role by compensating for the capacity lost by the piles. This was shown to be achieved by the development of dilative excess pore pressures beneath the pile cap within the underlying loose liquefied sand which provide increasing bearing capacity with settlement. The centrifuge test data show good qualitative and quantitative agreement with the limited amount of model and full-scale data currently available in the literature. The implications of settlement for the design of piled foundations to serviceability conditions in both level and sloping ground are discussed, with settlement becoming an increasingly important consideration for laterally stiffer piles. Finally, empirical relationships have been derived from the test data to relate suitable static safety factors to given increases in excess pore pressure in the bearing layer within a performance-based design framework (i.e., based on limiting displacements).     

Role of Linear Elasticity in Pile Group Analysis and Load Test Interpretation

This paper compares linear-elastic and nonlinear pile group analysis methods through settlement analyses of hypothetical scenarios and real case studies, and elaborates on the implications for interpretation of pile load test data. Comparisons between linear-elastic and nonlinear methods justify the proposition that pile-to-pile interaction is dominated by linear elasticity, characterized by the small-strain soil stiffness. As the size of a pile group increases, nonlinearity in individual pile behavior becomes overwhelmed by the interaction effects. In such cases, similar estimates will be achieved by both linear and nonlinear methods if the soil modulus is derived from the initial tangent, rather than some secant stiffness, assessed from the load test data. The study clarifies the capabilities and limitations of linear elasticity in pile group analysis and provides guidance on pile test interpretation for analysis of pile group response.     

Theoretical Study on Pile Length Optimization of Pile Groups and Piled Rafts

Pile groups are frequently designed with equal or similar pile lengths. However, the significant interaction effects among equal-length piles imply that this may not be the optimized configuration. This paper presents the optimization analyses of piled rafts and freestanding pile groups, where pile lengths are varied across the group to optimize the overall foundation performance. The results of the analyses are applicable in cases where the piles derive a majority of the capacity from the frictional resistance. It is demonstrated that, with the same amount of total pile material, an optimized pile length configuration can both increase the overall stiffness of the foundation and reduce the differential settlements that may cause distortion and cracking of the superstructure. The benefits of the optimization can be translated to economic and environmental savings as less material is required to attain the required level of foundation performances. The reliability of the optimization benefits in relation to construction-induced variability is also discussed.     

Bearing Capacity of Piled Rafts on Soft Clay Soils

The conventional design of a piled foundation is based on a bearing capacity approach, and neglects the contribution of the raft. As a consequence, piled foundations are usually designed by overconservative criteria. With respect to the conventional approach, a more rational and economical solution could be obtained by accounting for the contribution of the raft toward the overall bearing capacity, but this potential is not exploited due to the lack of theoretical and experimental research on the behavior of piled rafts at failure. Based on both experimental evidence and three-dimensional finite element analyses, a simple criterion is proposed to evaluate the ultimate vertical load of a piled raft as a function of its component capacities, which can be simply evaluated by the conventional bearing capacity theories. The results presented in the paper thus provide a guide to assess the safety factor of a vertically loaded piled raft.     

Liquefaction-Induced Softening of Load Transfer between Pile Groups and Laterally Spreading Crusts

Laterally spreading nonliquefied crusts can exert large loads on pile foundations causing major damage to structures. While monotonic load tests of pile caps indicate that full passive resistance may be mobilized by displacements on the order of 1–7% of the pile cap height, dynamic centrifuge model tests show that much larger relative displacements may be required to mobilize the full passive load from a laterally spreading crust onto a pile group. The centrifuge models contained six-pile groups embedded in a gently sloping soil profile with a nonliquefied crust over liquefiable loose sand over dense sand. The nonliquefied crust layer spread downslope on top of the liquefied sand layer, and failed in the passive mode against the pile foundations. The dynamic trace of lateral load versus relative displacement between the “free-field” crust and pile cap is nonlinear and hysteretic, and depends on the cyclic mobility of the underlying liquefiable sand, ground motion characteristics, and cyclic degradation and cracking of the nonliquefied crust. Analytical models are derived to explain a mechanism by which liquefaction of the underlying sand layer causes the soil-to-pile-cap interaction stresses to be distributed through a larger zone of influence in the crust, thereby contributing to the softer load transfer behavior. The analytical models distinguish between structural loading and lateral spreading conditions. Load transfer relations obtained from the two analytical models reasonably envelope the responses observed in the centrifuge tests.     

Pile Spacing Effects on Lateral Pile Group Behavior: Load Tests

To investigate group interaction effects as a function of pile spacing, full-scale cyclic lateral load tests were performed on pile groups in stiff clay spaced at 3.3, 4.4, and 5.65 pile diameters in the direction of loading with as many as five rows of piles. Group interaction effects decreased considerably as pile spacing increased from 3.3 to 5.65D. Lateral resistance was a function of row location in the group, rather than location within a row. For a given deflection, the leading (first) row piles carried the greatest load, while the second and third row piles carried successively smaller loads. Fourth and fifth row piles carried about the same load as the third row piles. For a given load, the maximum bending moments in the trailing row piles were greater than those in the lead row, but these effects decreased as spacing increased. Cyclic loading reduced the peak load by about 15% after 15 cycles; however, distribution of load within the pile group was essentially the same as at the peak load. Gaps significantly reduced resistance for small deflections.     

Optimization of Pile Groups Using Hybrid Genetic Algorithms

This paper presents an automated optimal design method using a hybrid genetic algorithm for pile group foundation design. The design process is a sizing and topology optimization for pile foundations. The objective is to minimize the material volume of the foundation taking the configuration, number, and cross-sectional dimensions of the piles as well as the thickness of the pile cap as design variables. A local search operator by the fully stressed design (FSD) approach is incorporated into a genetic algorithm (GA) to tackle two major shortcomings of a GA, namely, large computation effort in searching the optimum design and poor local search capability. The effectiveness and capability of the proposed algorithm are first illustrated by a five by five pile group subjected to different loading conditions. The proposed optimization algorithm is then applied to a large-scale foundation project to demonstrate the practicality of the algorithm. The proposed hybrid genetic algorithm successfully minimizes the volume of material consumption and the result matches the engineering expectation. The FSD operator has great improvement on both design quality and convergence rate. Challenges encountered in the application of optimization techniques to design of pile groups consisting of hundreds of piles are discussed.     

Simple Energy-Based Method for Nonlinear Analysis of Incompressible Pile Groups in Clays

This note presents a method for predicting nonlinear response of pile groups in clays, subjected to vertical loads. The method is based on mobilizable strength design (MSD) concepts, in which the mobilized strength is associated with the shear strains developed in the soil. The suggested procedure is incremental, and requires evaluation of a displacement field. A simple procedure of superposition of pattern functions is suggested for the construction of a complete displacement field. The incremental procedure allows for the variation of the displacement field throughout the loading process, according to principles of minimum energy and compatibility requirements among the piles. Essentially, the procedure allows consideration of a nonlinear continuum between the piles. The pattern functions are an adaptive form of the logarithmic function suggested by Randolph and Wroth in 1979. Under small load levels, when the soil is essentially elastic, the procedure yields values comparable to those from the elastic solution of Randolph and Wroth. At larger strain levels, nonlinear pile group response is simulated based on the soil constitutive models specified by the practitioner. The method is applicable to cases where shaft loading does not induce volume changes in the soil. The method is compared with three dimensional finite difference simulation of undrained loading of pile groups with a nonlinear soil constitutive model. Fair agreement is observed.     

Static Pushover Analyses of Pile Groups in Liquefied and Laterally Spreading Ground in Centrifuge Tests

Monotonic, static beam on nonlinear Winkler foundation (BNWF) methods are used to analyze a suite of dynamic centrifuge model tests involving pile group foundations embedded in a mildly sloping soil profile that develops liquefaction-induced lateral spreading during earthquake shaking. A single set of recommended design guidelines was used for a baseline set of analyses. When lateral spreading demands were modeled by imposing free-field soil displacements to the free ends of the soil springs (BNWF_SD), bending moments were predicted within ?8% to +69 (16th to 84th percentile values) and pile cap displacements were predicted within ?6 to +38%, with the accuracy being similar for small, medium, and large motions. When lateral spreading demands were modeled by imposing limit pressures directly to the pile nodes (BNWF_LP), bending moments and cap displacements were greatly overpredicted for small and medium motions where the lateral spreading displacements were not large enough to mobilize limit pressures, and pile cap displacements were greatly underpredicted for large motions. The effects of various parameter relations and alternative design guidelines on the accuracy of the BNWF analyses were evaluated. Sources of bias and dispersion in the BNWF predictions and the issues of greatest importance to foundation performance are discussed. The results of these comparisons indicate that certain guidelines and assumptions that are common in engineering design can produce significantly conservative or unconservative BNWF predictions, whereas the guidelines recommended herein can produce reasonably accurate predictions.     

Data Reduction of Horizontal Load Full-Scale Tests on Bored Concrete Piles and Pile Groups

This paper proposes a new approach for data reduction of horizontal load full-scale tests on piles and pile groups. This approach has been developed on results from tests run on bored concrete piles embedded in homogeneous and nonhomogeneous ground. Due to nonlinear response of pile material and also to nonhomogeneous embedding ground, the problem of fitting reliable curves for representing strains along shafts is increased. It is suggested that B-splines fixed by a weighted least-squares algorithm should be used to overcome that problem. Taking advantage of the mathematical properties of B-splines, an algorithm for computing the internal force distribution amongst pile heads direct from test results is also proposed for pile groups. It is shown that the integration of the curvatures to compute pile movements should be done using natural boundary conditions instead of pile head measurements whenever possible. Despite the concrete crack, the distribution of bending moments can be computed from curvatures provided a reliable reinforced concrete model is used. Finally, it is proposed to compute the soil reactions by the integration of bending moments, solving an integral equation by again using B-spline functions.     

Centrifuge Modeling of Large-Diameter Bored Pile Groups with Defects

In this research, centrifuge model pile-load tests were carried out to failure to investigate the behavior of large-diameter bored pile groups with defects. The model piles represented cast-in-place concrete piles 2.0?m in diameter and 15?m in length. Two series of static loading tests were performed. The first series of tests simulated the performance of a pile founded on rock and a pile with a soft toe. The second series of tests simulated the performance of three 2×2 pile groups: One reference group without defects, one group containing soft toes, and one group with two shorter piles not founded on rock. The presence of soft toes and shorter piles in the defective pile groups considerably reduced the pile group stiffness and capacity. As the defective piles were less stiff than the piles without defects, the settlements of the individual piles in the two defective pile groups were different. As a result, the applied load was largely shared by the piles without defects, and the defective pile groups tilted significantly. The rotation of the defective pile groups caused large bending moments to develop in the group piles and the pile caps. When the applied load was large, bending failure mechanisms were induced even though the applied load was vertical and concentric. The test results confirm findings from numerical analyses in the literature.     

Lateral Behavior of Pile Groups in Layered Soils

Assessment of the response of a laterally loaded pile group based on soil–pile interaction is presented in this paper. The behavior of a pile group in uniform and layered soil (sand and/or clay) is evaluated based on the strain wedge model approach that was developed to analyze the response of a long flexible pile under lateral loading. Accordingly, the pile’s response is characterized in terms of three-dimensional soil–pile interaction which is then transformed into its one-dimensional beam on elastic foundation equivalent and the associated parameter (modulus of subgrade reaction Es) variation along pile length. The interaction among the piles in a group is determined based on the geometry and interaction of the mobilized passive wedges of soil in front of the piles in association with the pile spacing. The overlap of shear zones among the piles in the group varies along the length of the pile and changes from one soil layer to another in the soil profile. Also, the interaction among the piles grows with the increase in lateral loading, and the increasing depth and fan angles of the developing wedges. The value of Es so determined accounts for the additional strains (i.e., stresses) in the adjacent soil due to pile interaction within the group. Based on the approach presented, the p–y curve for different piles in the pile group can be determined. The reduction in the resistance of the individual piles in the group compared to the isolated pile is governed by soil and pile properties, level of loading, and pile spacing.     

Reliability Verification Using Proof Pile Load Tests

Proof pile load tests are an important means to cope with uncertainties in the design and construction of pile foundations. In this paper, a systematic method to incorporate the results of proof load tests not conducted to failure into the design of pile foundations is developed. In addition, illustrative acceptance criteria for driven piles based on proof load tests are proposed for use in a reliability-based design. Finally, modifications to conventional proof test procedures are studied so that the value derived from proof tests can be maximized. Whether or not a proof test is conducted to failure, its results can be used to update the probability distribution of the pile capacity using the method proposed in this paper. Hence, contributions of the proof test can be included in foundation design in a logical manner by considering several load test parameters such as the number of tests, the test load, the factor of safety, and test results. This adds value to proof load tests and warrants improvements in the procedures for acceptance of pile foundations using proof load tests. A larger test load for proof tests, say 1.5 times the predicted pile capacity, is recommended since it will yield more information about the capacity statistics and thus allow for more economical designs.     

Load Testing of a Closed-Ended Pipe Pile Driven in Multilayered Soil

Piles are often driven in multilayered soil profiles. The accurate prediction of the ultimate bearing capacity of piles driven in mixed soil is more challenging than that of piles driven in either clay or sand because the mechanical behavior of these soils is better known. In order to study the behavior of closed-ended pipe piles driven into multilayered soil profiles, fully instrumented static and dynamic axial load tests were performed on three piles. One of these piles was tested dynamically and statically. A second pile served as reaction pile in the static load test and was tested dynamically. A third pile was tested dynamically. The base of each pile was embedded slightly in a very dense nonplastic silt layer overlying a clay layer. In this paper, results of these pile load tests are presented, and the lessons learned from the interpretation of the test data are discussed. A comparison is made of the ultimate base and limit shaft resistances measured in the pile load tests with corresponding values predicted from in situ test-based and soil property-based design methods.     

Termination Criteria for Jacked Pile Construction and Load Transfer in Weathered Soils

Pile jacking is a piling technique that provides a noise- and vibration-free environment in the construction site. To improve termination criteria for pile jacking and to better understand the behavior of jacked piles, two steel H piles were instrumented, installed at a weathered soil site, and load tested. A set of termination criteria was applied to the test piles, which includes a minimum blow count from the standard penetration test, a specified final jacking force, a minimum of four loading cycles at the final jack force, and a specified maximum rate of pile settlement at the final jacking force. The two test piles passed all required acceptance criteria. Punching shear failure occurred at the failure load for both piles and the shaft resistance consisted of approximately 80% of the pile capacity. Based on the results of field tests in Hong Kong and Guangdong and several centrifuge tests, a relation between the ratio of the pile capacity Pult to the final jacking force PJ and the pile slenderness ratio is established. The Pult/PJ ratio is larger than 1.0 for long piles but may be smaller than 1.0 for short piles. A regression equation is established to determine the final jacking force, which is suggested as a termination criterion for jacked piles. The final jacking force can be smaller than 2.5 times the design load for very long piles, but should be larger than 2.5 times the design load for piles shorter than 37 times the pile diameter.     

Simplified Approach for the Seismic Response of a Pile Foundation

Pseudostatic approaches for the seismic analysis of pile foundations are attractive for practicing engineers because they are simple when compared to difficult and more complex dynamic analyses. To evaluate the internal response of piles subjected to earthquake loading, a simplified approach based on the “p-y” subgrade reaction method has been developed. The method involves two main steps: first, a site response analysis is carried out to obtain the free-field ground displacements along the pile. Next, a static load analysis is carried out for the pile, subjected to the computed free-field ground displacements and the static loading at the pile head. A pseudostatic push over analysis is adopted to simulate the behavior of piles subjected to both lateral soil movements and static loadings at the pile head. The single pile or the pile group interact with the surrounding soil by means of hyperbolic p-y curves. The solution derived first for the single pile, was extended to the case of a pile group by empirical multipliers, which account for reduced resistance and stiffness due to pile-soil-pile interaction. Numerical results obtained by the proposed simplified approach were compared with experimental and numerical results reported in literature. It has been shown that this procedure can be used successfully for determining the response of a pile foundation to “inertial” loading caused by the lateral forces imposed on the superstructure and “kinematic” loading caused by the ground movements developed during an earthquake.     

Simplified Lateral Load Analyses of Fixed-Head Piles and Pile Groups

The characteristic load method (CLM) can be used to estimate lateral deflections and maximum bending moments in single fixed-head piles under lateral load. However, this approach is limited to cases where the lateral load on the pile top is applied at the ground surface. When the pile top is embedded, as in most piles that are capped, the additional embedment results in an increased lateral resistance. A simple approach to account for embedment effects in the CLM is presented for single fixed-head piles. In practice, fixed-head piles are more typically used in groups where the response of an individual pile can be influenced through the adjacent soil by the response of other nearby piles. This pile–soil–pile interaction results in larger deflections and moments in pile groups for the same load per pile compared to single piles. A simplified procedure to estimate group deflections and moments was also developed based on the p-multiplier approach. Group amplification factors are introduced to amplify the single pile deflection and bending moment to reflect pile–soil–pile interaction. The resulting approach lends itself well to simple spreadsheet computations and provides good agreement with other generally accepted analytical tools and with values measured in published lateral load tests on groups of fixed-head piles.