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.     

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.     

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.     

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.     

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: 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.     

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.     

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.     

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.     

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.     

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.     

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.     

Behavior of Pile Groups Subject to Excavation-Induced Soil Movement

Centrifuge model tests have been conducted on free-head and capped-head pile groups consisting of two, four, and six piles located adjacent to an unstrutted deep excavation in sand. It is found that when two free- or capped-head piles are arranged in a row parallel to the retaining wall, the interaction effect between piles is insignificant. When two piles are arranged in a line perpendicular to the wall, the existence of a front pile would reduce the detrimental effect of excavation-induced soiled movement on the rear pile. In addition, the provision of a pile cap for two piles arranged in a line would exert a significant influence on the behavior of the pile group. For free-head four- or six-pile groups, the induced bending moment decreases as the number of piles increases. Moreover, the interior piles of the pile group always experience lower bending moments than those of peripheral piles as the latter have more exposure to the excavation-induced soil movement and are thus more adversely affected. For the capped-head four- or six-pile groups, it can be established that the provision of a pile cap would help to moderate the pile-group deflection against soil movement as the rear piles, that are located farther away from the wall and thus less affected by the soil movement, would drag the front piles back.     

Centrifuge Modeling of Ship Impact Loads on Bridge Pile Foundations

Bridges that cross navigable waterways may be affected by accidental ship impacts. To better characterize ship impact loads on bridge pier structures, a comprehensive centrifuge model test program involving 48 ship impact tests was performed on a 2×3 pile group and a 3×3 pile group founded in saturated silty sand. These model tests simulated groups of 2-m-diameter by 31.5-m-long pipe piles. The effects of three factors related to the ship (tonnage, speed, and bow structure) and two factors related to the bridge pier structure (superstructure mass and pile-group size) were investigated through these impact tests. The characteristics of the ship impact load were identified and the mechanism of the ship-bridge collision was analyzed. The test results show that the ship impact load was highly dependent on the ship bow structure and the ship impact speed. The test results were compared with other published data and the AASHTO loads. An empirical equation was suggested to relate the ship impact load to the five influencing factors.     

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.     

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.     

Three-Dimensional Analysis of Lateral Pile Response using Two-Dimensional Explicit Numerical Scheme

A procedure for exploiting a two-dimensional (2D) explicit, numerical computer code for the 3D formulation of dynamic lateral soil-pile interactions is considered. The procedure is applied to two models using simultaneous computation of a series of plane strain boundary value problems, each of which represents a horizontal layer of soil. The first model disregards the shear forces developed between the horizontal layers, and may be considered as a generalized Winkler model. The second model takes account of these forces by coupling the behavior of the horizontal layers. Several verification problems for a single pile and pile groups in a homogeneous soil layer modeled as a viscoelastic material were solved and compared to known solutions in order to assess the reliability of the models. Excellent agreement was observed between results of the present analyses and existing solutions.     

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.     

Employment of the P-Multiplier in Pile-Group Analysis

This paper discusses the variation of the P-multiplier (Pm) used with the p-y curve to assess the response of a pile group under lateral loads, which is a crucial topic for the design of bridge pile foundations. Pm is influenced by the site geotechnical conditions (i.e., soil profile, type and properties), pile front and side spacings, and pile-group deflection. The presented study shows the needs to incorporate these factors with the recommended sets of Pm to avoid any compromise or uncertainty when Pm is treated as a single (unique) value based only on pile spacings. The current study addresses these influential elements using the strain wedge (SW) model technique, suggested Pm values, and data collected from full-scale pile-group load tests. The experimental results show that Pm is not unique and must be assessed based on the site geotechnical conditions along with the pile-row front and side spacings. Because the employed Pm values must be a function of these influential factors, additional full- and model-scale load tests with different pile spacings and soil types might be required. The paper also emphasizes that using other techniques, such as the SW model, in addition to the P-multiplier could increase the confidence in the predicted pile-group lateral response.