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.     

Uplift Mechanisms of Pipes Buried in Sand

Reliable design against upheaval buckling of offshore pipelines requires the uplift response to be predicted. This paper describes a model-scale investigation into the mechanisms by which uplift resistance is mobilized in silica sand, and illustrates how the observed mechanisms are captured in prediction models. A novel image-based deformation measurement technique has been used. The results show that peak uplift resistance is mobilized through the formation of an inverted trapezoidal block, bounded by a pair of distributed shear zones. The inclination of the shear zone is dependent on the soil density, and therefore dilatancy. After peak resistance, shear bands form and softening behavior is observed. At large pipe displacements, either a combination of a vertical sliding block mechanism and a flow-around mechanism near the pipe or a localized flow-around mechanism without surface heave is observed, depending on the soil density and particle size.     

Effect of Compressive Load on Uplift Capacity of Model Piles

Thirty six tests on model tubular steel piles embedded in sand were carried out in the laboratory to assess the effects of compressive load on uplift capacity of piles considering various parameters. The model piles were of 25 mm outside diameter and 2 mm wall thickness. The soil–pile friction angles were 21 and 29° in loose and dense conditions of sand. The piles were embedded in sand for embedment length/diameter ratios of 8,16, and 24 inside a model tank. They were subjected to a static compressive load of 0, 25, 50, 75, and 100% of their ultimate capacity in compression and subjected to pull out loading tests. The experimental results indicated that the presence of the compressive load on the pile decreases the net uplift capacity of a pile and the decrease depends on the magnitude of the compressive load. A logical approach, based on the experimental results, has been suggested to predict the net uplift capacity of a pile considering the presence of compressive load.     

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.     

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.     

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.     

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.     

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.     

Experimental Investigation of Clear-Water Local Scour at Pile Groups

Experiments of local scour around pile groups are carried out under steady clear-water scour conditions. A variety of conditions including different pile group arrangements, spacing, flow rates, and sediment grain sizes are considered. In total, 112 experiments are carried out. It is observed that the scour-hole depth for some cases of pile groups increases as much as two times more than its magnitude for the case of single piles. The data from this study and some laboratory experiment data from previous works are used to derive a correction factor to predict the maximum local scour depth for the pile groups. Two well-known equations, i.e., Federal Highway Administration, Hydraulic Engineering Circular No. 18, HEC-18 (reported by Richardson and Davis in 2001) and the New Zealand pier scour equation (reported by Melville and Coleman in 2000) are considered. The prediction of scour hole based on the present correction agrees well with the observations.     

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.     

Uplift Behavior of Blade-Underreamed Anchors in Silty Sand

To evaluate the uplift behavior of anchors installed by the blade underreaming system, a numerical model for anchors in silty sand has been developed in this study and the calculated results are compared to the results of full scale anchor pullout tests. Although the blade-underreamed anchor tends to be irregular in shape due to possible collapse of the borehole, the excavated anchor showed an underreamed body of approximately multiple-stepped shape. Despite the difference in shape, the numerical results indicate that the difference between the load–displacement curve of the multiple-stepped anchor and that of the conical shaped anchor is small. In addition, the anchorage behavior of conical shaped anchors calculated from this numerical model was in good agreement with those of full scale anchor tests. No sign of progressive soil yielding along the underreamed body was found from the numerical analysis. So, the pull-out capacity of this underreamed anchor increases more than linearly with the length of the underream. Since only a small underream angle is needed to generate a substantial increase in anchor pull-out resistance, the ultimate pull-out capacity of the blade-underreamed anchor is found to be higher than that of straight shaft anchor in silty sand.     

Use of State-Dependent Strength in Estimating End Bearing Capacity of Piles in Sand

The pressure and density dependence of the shear strength of sand poses a tricky problem in pile foundation design. In this study, a correlation is suggested to link the effective friction angle of sand with its initial confining pressure and relative density, and a simple approach incorporating this correlation is presented for predicting pile end bearing capacity. Assessment of the approach against pile load tests shows reasonably good agreement between predictions and measurements. It is also shown that the effect of the state-dependent strength is particularly important in cases where long piles are installed in dense sand deposits and the use of critical state friction angle will produce a conservative prediction in such cases.     

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).     

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.     

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.     

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.     

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.     

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.     

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.