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).     

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.     

Lateral Spreading Forces on Bridge Piers and Pile Caps in Laterally Spreading Soil: Effect of Angle of Incidence

In this paper, the kinematic forces which may be applied to bridge piers or pile caps from laterally spreading surficial cohesive soil layers (nonliquefied crusts) through which they pass are considered. Such forces often represent the largest load component acting on a structure and/or foundation during liquefaction-induced lateral spreading. Both circular and square structural inclusions are considered, and particular attention is paid to the orientation of the inclusion to the direction of spreading, here defined as the angle of incidence (θ). Experimental modeling was conducted using a modified direct shearbox to simulate the spreading of kaolin past structural inclusions at various θ. Load-displacement data and particle image velocimetry analysis revealed that the ultimate load for both square and circular cases may be determined using a wedge-based upper-bound plasticity analysis. For circular sections, this ultimate load is independent of θ due to radial symmetry. The ultimate load on square sections was found to depend more significantly on θ and a simple analytical method is presented to account for this. The method suggests that the ultimate loads acting on square bridge piers or pile caps will be a maximum when the spreading soil impinges on the corners of the inclusion, at which time the ultimate load will be 19–26% larger (depending on the soil-structure interface roughness) than for spreading impinging on the edge of the inclusion. Experimental tests suggested a value of 22%. Finally, the tests support previous results suggesting that when the underlying soil is unable to carry redistributed shear stress (i.e., when it is liquefied) load-displacement curves in the crustal layers are less stiff than for typical retaining structures under static conditions. The displacement at soil yield was found to be between 20–30% of the height of the inclusion in the layer, and also depends on θ in the case of square inclusions.     

Liquefaction-Induced Lateral Spreading in Near-Fault Regions during the 1999 Chi-Chi, Taiwan Earthquake

We document and analyze incidents of liquefaction-induced lateral ground deformation at five sites located in the near-fault region of the 1999 Chi-Chi Taiwan earthquake. Each of the lateral spreads involved cyclic mobility of young alluvial soils towards a free face at creek channels. In each case, the lateral spreading produced relatively modest lateral displacements (approximately 10–200?cm) in parts of the spreads not immediately adjacent to channel slopes. For each site, we present displacement vectors across the spread features, which are based on mapping performed within three weeks of the earthquake. We review the results of detailed subsurface exploration conducted at each site, including cone penetration test soundings, borings with standard penetration testing, and laboratory index tests. We back-analyze the field displacements using recent empirical and semiempirical models and find that the models generally overestimate the observed ground displacements. Possible causes of the models’ overprediction bias include partial drainage of the liquefied soils during shaking, low but measurable plasticity of some of the soils’ fines fraction, and the absence of nonspread sites in the empirical databases used to develop existing empirical and semi-empirical lateral spread displacement prediction models.     

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.     

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 Model Study of Laterally Loaded Pile Groups in Clay

A series of centrifuge model tests has been conducted to examine the behavior of laterally loaded pile groups in normally consolidated and overconsolidated kaolin clay. The pile groups have a symmetrical plan layout consisting of 2, 2×2, 2×3, 3×3, and 4×4 piles with a center-to-center spacing of three or five times the pile width. The piles are connected by a solid aluminum pile cap placed just above the ground level. The pile load test results are expressed in terms of lateral load–pile head displacement response of the pile group, load experienced by individual piles in the group, and bending moment profile along individual pile shafts. It is established that the pile group efficiency reduces significantly with increasing number of piles in a group. The tests also reveal the shadowing effect phenomenon in which the front piles experience larger load and bending moment than that of the trailing piles. The shadowing effect is most significant for the lead row piles and considerably less significant for subsequent rows of trailing piles. The approach adopted by many researchers of taking the average performance of piles in the same row is found to be inappropriate for the middle rows, of piles for large pile groups as the outer piles in the row carry significantly more load and experience considerably higher bending moment than those of the inner piles.     

Strain Wedge Model Capability of Analyzing Behavior of Laterally Loaded Isolated Piles, Drilled Shafts, and Pile Groups

This paper demonstrates the application of the strain wedge (SW) model to assess the response of laterally loaded isolated long piles, drilled shafts, and pile groups in layered soil (sand and/or clay) and rock deposits. The basic goal of this paper is to illustrate the capabilities of the SW model versus other procedures and approaches. The SW model has been validated and verified through several comparison studies with model- and full-scale lateral load tests. Several factors and features related to the problem of a laterally loaded isolated pile and pile group are covered by the SW model. For example, the nonlinear behavior of both soil and pile material, the soil-pile interaction (i.e., the assessment of the p-y curves rather than the adoption of empirical ones), the potential of soil to liquefy, the interference among neighboring piles in a pile group, and the pile cap contribution are considered in SW model analysis. The SW model analyzes the response of laterally loaded piles based on pile properties (pile stiffness, cross-sectional shape, pile-head conditions, etc.) as well as soil properties. The SW model has the capability of assessing the response of a laterally loaded pile group in layered soil based on more realistic assumptions of pile interference as compared to techniques and procedures currently employed or proposed.     

Settlement Ratio of Pile Groups in Sandy Soils from Field Load Tests

This note studies settlement ratio, Rs, of pile groups in sandy soils, defined as the ratio of the settlement of a pile group to that of a single pile at the same average load per pile. 31 cases of field pile-group load tests and the corresponding field single-pile load tests were collected for this study. More than one-half of the cases consist of 3-diameter spaced, 9-pile groups. Based on the field test data, statistical analyses of Rs at different load levels were conducted for pile groups with cap-ground contact (PGCs) and pile groups with freestanding caps (PGFs), respectively. The mean of Rs decreases with the load level for both PGCs and PGFs, whereas the coefficient of variation of Rs increases with the load level. The influence of cap-ground contact on Rs does not appear to be significant based on a comparison of the mean Rs values of these PGCs and PGFs. In addition, a comparative study on Rs and group resistance ratio Rr, which is defined as the ratio of the average resistance of a pile in a group to that of a single pile at the same settlement, was conducted to clarify possible misunderstanding between Rs and pile group efficiency factor η for driven pile groups in sandy soils. The value of Rs compares settlement at the working load and is often larger than unity. The value of η compares failure loads, which occur at different settlements for pile groups and their respective single piles. η is usually larger than unity due to soil densification and additional contributions from the cap-ground contact for PGCs.     

Pile Response to Lateral Spreads: Centrifuge Modeling

The paper presents results of eight centrifuge models of vertical single piles and pile groups subjected to earthquake-induced liquefaction and lateral spreading. The centrifuge experiments, conducted in a slightly inclined laminar box subjected to strong in-flight base shaking, simulate a mild, submerged, infinite ground slope containing a 6-m-thick prototype layer of liquefiable Nevada sand having a relative density of 40%. Two- and three-layer soil profiles were used in the models, with a 2-m-thick nonliquefiable stratum placed below, and in some cases also above the liquefiable Nevada sand. The model piles had an effective prototype diameter, d, of 0.6 m. The eight pile models simulated single end-bearing and floating reinforced concrete piles with and without a reinforced concrete pile cap, and two 2×2 end-bearing pile groups. Bending moments were measured by strain gauges placed along the pile models. The base shaking liquefied the sand layer and induced free field permanent lateral ground surface displacements between 0.7 and 0.9 m. In all experiments, the maximum permanent bending moments, Mmax occurred at the boundaries between liquefied and nonliquefied layers; the prototype measured values of Mmax ranged between about 10 and 300 kN?m. In most cases the bending moments first increased and then decreased during the shaking, despite the continued increase in free field displacement, indicating strain softening of the soil around the deep foundation. The largest values of Mmax were associated with single end-bearing piles in the three-layer profile, and the smallest values of Mmax were measured in the end-bearing pile groups in the two-layer profile. The companion paper further analyzes the Mmax measured in the single pile models, and uses them to calibrate two limit equilibrium methods for engineering evaluation of bending moments in the field. These two methods correspond to cases controlled, respectively, by the pressure of liquefied soil, and by the passive pressure of nonliquefied layers on the pile foundation.     

Effect of Soil Permeability on Centrifuge Modeling of Pile Response to Lateral Spreading

This paper presents experimental results and analysis of six model centrifuge experiments conducted on the 150?g-ton Rensselaer Polytechnic Institute centrifuge to investigate the effect of soil permeability on the response of end-bearing single piles and pile groups subjected to lateral spreading. The models were tested in a laminar box and simulate a mild infinite slope with a liquefiable sand layer on top of a nonliquefiable layer. Three fine sand models consisting of a single pile, a 3×1 pile group, and a 2×2 pile group were tested, first using water as pore fluid, and then repeated using a viscous pore fluid, hence simulating two sands of different permeability in the field. The results were dramatically different, with the three tests simulating a low permeability soil developing 3–6 times larger pile head displacements and bending moments at the end of shaking. Deformation observations of colored sand strips, as well as measurements of sustained negative excess pore pressures near the foundations in the “viscous fluid” experiments, indicated that an approximately inverted conical zone of nonliquefied soil had formed in these tests at shallow depths around the foundation, which forced the liquefied soil in the free field to apply its lateral pressure against a much larger effective foundation area. Additional p-y and limit equilibrium back-analyses support the hypothesis that the greatly increased foundation bending response observed when the soil is less pervious is due to the formation of such inverted conical volume of nonliquefied sand. This study provides evidence of the importance of soil permeability on pile foundations response during lateral spreading for cases when the liquefied deposit reaches the ground surface, and suggests that bending response may be greater in silty sands than in clean sands in the field. Moreover, the observations in this study may serve as basis for realistic practical engineering methods to evaluate pile foundations subjected to lateral spreading and pressure of liquefied soil.     

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.     

Probabilistic Performance-Based Procedure to Evaluate Pile Foundations at Sites with Liquefaction-Induced Lateral Displacement

Liquefaction-induced ground deformation has caused major damage to bridge and wharf structures in past earthquakes. Large lateral ground displacements may induce significant forces in the foundation and superstructure, which may lead to severe damage or even collapse. A performance-based earthquake engineering (PBEE) approach can provide an objective assessment of the likely seismic performance, so that agencies can evaluate bridge or wharf structures, compare retrofit strategies, and rank them within their overall system. In this paper, a probabilistic PBEE design procedure that incorporates findings from recent research on this problem is presented. The proposed approach can provide answers in terms that are meaningful to owners, such as expected repair costs and downtimes. The methodology is validated through its application to a well-documented case history. Results show that the proposed approach provides a good estimate of the seismic performance of pile-supported structures at sites with liquefaction-induced lateral displacement.     

Theoretical p-y Curves for Laterally Loaded Single Piles in Undrained Clay Using Bezier Curves

An alternative method was introduced for predicting the nonlinear p-y curves for monotonic unidirectional laterally loaded single piles in uniform undrained clay. On the basis of numerical studies, closed-form solutions were developed for locating the start of yield (ye); the ultimate yield point (yu); and the initial stiffness, Ki of the p-y curve. The nonlinear section of the curve between the start of the yield and the ultimate yield point was represented by Bezier polynomials (also known as de Casteljau’s algorithm). Using these relationships, a direct method of constructing the p-y curves was presented considering either tension failure or no tension failure of soils. For a typical pile configuration, the resulting load-deflection response was observed to compare favorably with the predictions from FLAC analysis and Matlock.     

Liquefaction-Induced Lateral Spreading at Izmit Bay During the Kocaeli (Izmit)-Turkey Earthquake

This paper presents a study of liquefaction-induced lateral ground displacements along the coast of Izmit Bay during the 1999 Kocaeli (Izmit)-Turkey earthquake. The paper discusses: (1) observed ground displacements after the earthquake, (2) the results of field investigations by means of borings and in situ index tests, including standard penetration tests, static cone penetration tests, and piezocone tests, (3) analyses of expected lateral displacements using two empirical models and one semiempirical model, and (4) comparisons between observed and calculated lateral ground movements. The three models provide inconsistent predictions of observed lateral ground displacements, with one method overpredicting and two methods both overpredicting and underpredicting observed lateral ground displacements by large amounts. Thus, it appears that there is a need for improved engineering tools for prediction of small to moderately significant lateral ground displacements (lateral displacements of approximately 0.1–2.5?m) at soil sites with similar ground characteristics to the case history sites presented herein.     

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.     

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.     

Rotational Restraint of Pile Caps during Lateral Loading

A pure fixed-head (zero-rotation) condition at the top of a group of laterally loaded piles is seldom achievable in the field, even when piles are installed in a group that is “rigidly” constrained by a stiff concrete pile cap. Assuming complete fixity during design (zero rotation at the pile head) can result in underestimated values of pile-head deflection, and incorrect estimates of the magnitude and the location of maximum bending moments. A simple and practical approach is presented for estimating the moment restraint that is provided by the pile cap at the top of a pile group. The moment restraint, represented by the rotational restraint coefficient (KMθ), serves as a boundary condition for analyzing groups of laterally loaded piles. Full-scale field tests performed on two pile groups with concrete pile caps show that the proposed method for estimating rotational restraint provides results that are in good agreement with measured field performance.     

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.     

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.