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.     

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.     

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.     

Ultimate Lateral Resistance of Pile Groups in Sand

Experimental investigations on model pile groups of configuration 1 × 1, 2 × 1, 3 × 1, 2 × 2, and 3 × 2 for embedment length-to-diameter ratios L∕d = 12 and 38, spacing from 3 to 6 pile diameter, and pile friction angles δ = 20° and 31°, subjected to lateral loads, were conducted in dry Ennore sand obtained from Chennai, India. The load-displacement response, ultimate resistance, and group efficiency with spacing and number of piles in a group have been qualitatively and quantitatively investigated. Analytical methods have been proposed to predict the ultimate lateral capacity of single pile and pile groups. The proposed methods account for pile friction angle, embedment length-to-diameter ratio, the spacing of piles in a group, pile group configuration, and soil properties. These methods are capable of predicting the lateral capacity of piles and pile groups reasonably well as noted and substantiated by the comparison with the experimental results of the writers and other researchers.     

Numerical Analysis of Laterally Loaded 3 × 3 to 7 × 3 Pile Groups in Sands

The coupled bridge foundation-superstructure finite-element code FLPIER was employed to predict the lateral response of the single piles and 3 × 3 to 7 × 3 pile groups founded in both loose and medium dense sands. The p-multiplier factors suggested by McVay et al. for laterally loaded pile groups with multiple pile rows were implemented for the predictions. The soil parameters were obtained through a back-analysis procedure based on single pile test results. The latter, as well as the numerical predictions of both the single and group tests, are presented. It was found that the numerical code FLPIER did an excellent job of predicting the response of both the single piles and the 3 × 3 to 7 × 3 pile groups. The latter involved the predictions of lateral load versus lateral deflection of the group, the shears and bending moments developed in the individual piles, and the distributions of the lateral loads in each pile row, which were all in good agreement with the measured results.     

Nonlinear Efficiency of Bored Pile Group under Lateral Loading

A 3×3 bored pile group consisting of nine cast-in-drilled-hole reinforced concrete shafts and a comparable single-shaft were subjected to reversed cyclic, lateral head loading to investigate group interaction effects across a wide range of lateral displacements. The piles had the same diameter of d = 0.61?m and similar soil conditions; however, various equipment constraints led to two differences: (1) a fixed head (zero rotation) boundary condition for the single pile versus minor pile cap rotation in the vertical plane for the group and (2) shaft longitudinal reinforcement ratios of 1.8% for the single pile and 1% for the group piles. To enable comparisons between the test results, a calibrated model of the single pile (1.8% reinforcement) was developed and used to simulate the response of a single shaft with 1% reinforcement. Additional simulations of the pile group were performed to evaluate the effects of cap rotation on group response. By comparing the simulated responses for common conditions, i.e., 1% reinforcing ratio and zero head rotation, group efficiencies were found to range from unity at lateral displacements <0.004×d to 0.8 at small displacements ～ 0.01–0.02×d and up to 0.9 at failure (displacements >0.04×d). Hence, we find that group efficiency depends on the level of nonlinearity in the foundation system. The general group efficiency, although not its displacement-dependence, is captured by p-multipliers in the literature for reinforced concrete, fixed-head piles.     

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.     

Soil–Pile Response to Blast-Induced Lateral Spreading. I: Field Test

Two full-scale experiments using controlled blasting were conducted in the Port of Tokachi on Hokkaido Island, Japan, to assess the behavior of a single pile, a four-pile group, and a nine-pile group subjected to lateral spreading. The test piles were extensively instrumented with strain gauges to measure the distribution of bending moment during lateral spreading which allowed the backcalculation of the loading conditions, as well as the assessment of damage and performance of the piles. Based on the test results, it was concluded that using controlled blasting successfully liquefied the soil, and subsequently induced lateral spreading in the 4–6% surface slope test beds. The free-field soil displacements in the vicinity of the test piles were over 40 cm for both tests. When compared with the results from the single pile case, the effect of pile head restraint from the pile cap improved overall pile performance by decreasing the displacement of the pile groups and lowering the maximum moments in individual piles within each group. Finally, backcalculated soil reactions indicated that the liquefied soil layer imparted insignificant force to the piles. In the companion to this paper (Part II), an assessment of the potential of using the p–y analysis method for single piles and pile groups subjected to lateral spreading is presented.     

Soil-Pile Response to Blast-Induced Lateral Spreading. II: Analysis and Assessment of the p–y Method

This paper presents an assessment of the potential of using the p–y analysis method for single piles and pile groups subjected to lateral spreading. The computed responses were compared with the results from the full-scale lateral spreading tests in Japan as presented in the Part I companion paper. The responses of the single piles subjected to lateral spreading were determined by imposing the known free-field soil movement profile to the Winkler spring model. The soil springs of nonliquefied soils used in this study were based upon standard p–y springs whereas zero spring stiffness was used for liquefied soils. For the case of pile groups, they were modeled as an equivalent single pile with a rotational spring at the pile head to simulate effect of pile head restraint. A decrease of soil spring stiffnesses using the p-multiplier approach was used to account for pile group effects. Based on the results of analyses, the computed responses of all sets of the test piles using a single set of baseline soil properties were in good agreement with the measured responses. These results suggest that the p–y analysis method may be used to estimate the behavior of piles subjected to lateral spreading.     

Development of Downdrag on Piles and Pile Groups in Consolidating Soil

Development of pile settlement (downdrag) of piles constructed in consolidating soil may lead to serious pile foundation design problems. The investigation of downdrag has attracted far less attention than the study of dragload over the years. In this paper, several series of two-dimensional axisymmetric and three-dimensional numerical parametric analyses were conducted to study the behavior of single piles and piles in 3×3 and 5×5 pile groups in consolidating soil. Both elastic no-slip and elasto-plastic slip at the pile–soil interface were considered. For a single pile, the downdrag computed from the no-slip elastic analysis and from the analytical elastic solution was about 8–14 times larger than that computed from the elasto-plastic slip analysis. The softer the consolidating clay, the greater the difference between the no-slip elastic and the elasto-plastic slip analyses. For the 5×5 pile group at 2.5 diameter spacing, the maximum downdrag of the center, inner, and corner piles was, respectively, 63, 68, and 79% of the maximum downdrag of the single pile. The reduction of downdrag inside the pile group is attributed to the shielding effects on the inner piles by the outer piles. The relative reduction in downdrag (Wr) in the 5×5 pile group increases with an increase in the relative bearing stiffness ratio (Eb/Ec), depending on the pile location in the group. Compared with the relative reduction in dragload (Pr), Wr at the corner pile is less affected by the group interaction for a given surcharge load. This suggests that the use of sacrificing piles outside the pile group will be more effective on Pr than on Wr. Based on the three cases studied, the larger the number of piles in a group, the greater the shielding effects on Wr. Relatively speaking, Wr is more sensitive to the total number of piles than to the pile spacing within a pile group.     

Group Interaction Effects on Laterally Loaded Piles in Clay

This paper presents the results of static lateral load tests carried out on 1×2, 2×2, 1×4, and 3×3 model pile groups embedded in soft clay. Tests were carried out on piles with length to diameter ratios of 15, 30, and 40 and three to nine pile diameter spacing. The effects of pile spacing, number of piles, embedment length, and configuration on pile-group interaction were investigated. Group efficiency, critical spacing, and p multipliers were evaluated from the experimental study. The experimental results have been compared with those obtained from the program GROUP. It has been found that the lateral capacity of piles in 3×3 group at three diameter spacing is about 40% less than that of the single pile. Group interaction causes 20% increase in the maximum bending moment in piles of the groups with three diameter spacing in comparison to the single pile. Results indicate substantial difference in p multipliers of the corresponding rows of the linear and square pile groups. The predicted field group behavior is in good agreement with the actual field test results reported in the literature.     

Behavior of Slender Piles Subject to Free-Field Lateral Soil Movement

Soil movements associated with slope instability induce shear forces and bending moments in stabilizing piles that vary with the buildup of passive pile resistance. For such free-field lateral soil movements, stress development along the pile element is a function of the relative displacement between the soil and the pile. To investigate the effects of relative soil-pile displacement on pile response, large-scale load tests were performed on relatively slender, drilled, composite pile elements (cementitious grout with centered steel reinforcing bar). The piles were installed through a shear box into stable soil and then loaded by lateral translation of the shear box. The load tests included two pile diameters (nominal 115 and 178?mm) and three cohesive soil types (loess, glacial till, and weathered shale). Instrumentation indicated the relative soil-pile displacements and the pile response to the loads that developed along the piles. Using the experimental results, an analysis approach was evaluated using soil p-y curves derived from laboratory undrained shear strength tests. The test piles and analyses helped characterize behavioral stages of the composite pile elements at loads up to pile section failure and also provided a unique dataset to evaluate the lateral response analysis method for its applicability to slender piles.     

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.     

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.     

Lateral Resistance of Full-Scale Pile Cap with Gravel Backfill

A static lateral load test was performed on a full-scale 3×3 pile group driven in saturated low-plasticity silts and clays. The steel pipe piles were attached to a concrete pile cap which created a “fixed-head” end constraint. A gravel backfill was compacted in place on the backside of the cap. Lateral resistance was therefore provided by pile–soil–pile interaction, as well as base friction and passive pressure on the cap. In this case, passive resistance contributed about 40% of the total resistance. The log–spiral method provided the best agreement with measured resistance. Estimates of passive pressure computed using the Rankine method significantly underestimated the resistance while the Coulomb method overestimated resistance. The cap movement required to fully mobilize passive resistance in the gravel backfill was about 6% of the cap height. This is somewhat larger than reported in other studies likely due to the underlying clay layer. The p-multipliers developed for the free-head pile group provided reasonable estimates of the pile–soil–pile resistance for the fixed-head pile group once gaps adjacent to the pile were considered.     

Pile Spacing Effects on Lateral Pile Group Behavior: Analysis

Using the results from three full-scale lateral pile group load tests in stiff clay with spacing ranging from 3.3 to 5.65, computer analyses were performed to back-calculate p multipliers. The p multipliers, which account for reduced resistance due to pile–soil–pile interaction, increased as pile spacing increased from 3.3 to 5.65 diameters. Extrapolation of the test results suggests that group reduction effects can be neglected for spacings greater than about 6.5 for leading row piles and 7–8 diameters for trailing row piles. Based on analysis of the full-scale test results, pile behavior can be grouped into three general categories, namely: (1) first or front row piles; (2) second row piles; and (3) third and higher row piles. p multiplier versus normalized pile spacing curves were developed for each category. The proposed curves yield p multipliers which are higher than those previously recommended by AASHTO in 2000, the US Army in 1993, and the US Navy in 1982 based on limited test data, but lower values than those proposed by Reese et al. in 1996 and Reese and Van Impe in 2001. The response (load versus deflection, maximum moment versus load, and bending moment versus depth) for each row of the pile groups computed using GROUP and Florida Pier generally correlated very well with measurements from the full-scale tests when the p multipliers developed from this test program were employed.     

Effect of Cracking on the Response of Pile Test under Horizontal Loading

Capacity-based design of structures limits the soil-structure interaction mechanism to the determination of the bearing capacity of a pile group. However, in many cases the criterion for the design of piles to resist lateral loads is not the ultimate lateral capacity but the deflection of the piles. Many procedures exist for estimating the response of single piles and pile groups under lateral loading, ranging from application of empirical relationships and simple closed-form solutions to sophisticated nonlinear numerical procedures. With the aim of investigating the effect of cracking, disregarded by most of the above-mentioned methods, a three-dimensional (3D) nonlinear analysis that accounts for cracking is presented. Response prediction correlates well with the experimental data from a full-scale pile load test. Interesting conclusions have also been drawn regarding the discretization of the computational domain and the combination of 3D numerical nonlinear analysis and the structural beam theory.     

Lateral Behavior of Vertical Pile Group Embedded in Stabilized Earth Slope

An experimental study of the lateral behavior of vertical pile groups embedded in reinforced and nonreinforced sandy earth slopes was carried out. The model tests include studies of group configurations, pile spacing, embedment length of pile, relative densities of sand, and location of pile groups relative to the slope crest. Several configurations of geogrid reinforcement with different lengths, widths, and number of layers were used to reinforce a sandy slope of 1 (V): 1.5 (H). Pile groups of 2×2 and 3×3 along with center-to-center pile spacing of 2D, 3D, and 4.5D and piles with embedment length to diameter ratios of L/D = 12 and 22 were considered. Based on test results, geogrid parameters that give the maximum lateral capacity improvement are presented and discussed.     

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.