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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Raked Piles—Virtues and Drawbacks

This technical note examines some of the characteristics of behavior of pile groups containing raked piles, via a simplified and hypothetical example. Three cases are examined: (1) a group subjected to vertical and lateral loadings, with no ground movements; (2) a group subjected to vertical and lateral loadings, but with vertical ground movements also acting on the group; and (3) a group subjected to vertical and lateral loadings, but with horizontal ground movements acting on the group. In each case, the effect of pile rake on typical behavioral characteristics (group settlement, lateral deflection and rotation, and pile loads and moments) are examined. It is found that, while the presence of raked piles can provide some advantages when the group is subjected to applied vertical and lateral loadings, especially in relation to a reduction in lateral deflection, some aspects of group behavior may be adversely affected when either vertical or horizontal ground movements act on the group. Thus, caution must be exercised in employing raked piles when such ground movements are expected to occur.     

Blast-Induced Liquefaction for Full-Scale Foundation Testing

This paper describes a pilot test program that was carried out to determine the appropriate charge weight, delay, and pattern required to induce liquefaction for full-scale testing of deep foundations. The results of this investigation confirmed that controlled blasting techniques could successfully be used to induce liquefaction in a well-defined, limited area for field-testing purposes. The tests also confirmed that liquefaction could be induced at least two times at the same site with nearly identical results. Excess pore pressure ratios greater than 0.8 were typically maintained for at least 4 min after blasting. The test results indicate that excess pore pressure ratios produced by blasting could be predicted with reasonable accuracy when single blast charges were used. However, for multiple blast charges, measured excess pressures were significantly higher than would have been predicted for a single blast with the same charge weight. The measured particle velocity attenuated more rapidly with scaled distance than would be expected based on the upper bound relationship developed from previous case histories. Settlement was typically about 2.5% of the liquefied thickness, and about 85% of the settlement occurred within 30 min after the blast. Cone penetrometer test results show that blasting initially reduced the soil strength, but after several weeks the strength had substantially increased.     

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.     

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.     

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.     

Large-Deflection Mathematical Analysis of Rectangular Plates

A large-deflection mathematical analysis of rectangular plates under uniform lateral loading is presented in this paper. The analysis is based on solving two fourth-order, second-degree, partial differential Von Kármán equations relating the lateral deflections to the applied load. This paper provides a mathematical procedure which benefits from the software and hardware computing capabilities that were unavailable when mathematical modeling was last attempted. The solution is presented in a simple form suitable for direct practical use and can be easily implemented in common spreadsheet packages. Plates with two boundary conditions, namely, simply supported edges and held edges, are considered. Comparisons are held against earlier exact and approximate solutions, including results of finite element analyses. The results show close agreement with other exact analysis methods. The solution is able to produce the same results as other exact solutions, but with a much simpler and a more practical approach.     

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.     

Analytical Solution for Piles Supporting Combined Lateral Loads

Analytical solutions of normalized maximum deflection and normalized maximum moment for laterally loaded long piles in homogeneous elastoplastic soil under combined loads are presented in this paper. Both the normalized deflection surface and normalized moment surface are continuous and increasing constantly with normalized applied force and moment with various slopes. It shows that the normalized applied force and moment have different contributions to the deflection and moment. In general, the variation of normalized moment surface is relatively moderate compared to normalized maximum deflection. Due to the nonlinear effect, the deflections and moments using superposition approach will be on the unsafe side. The analytical solutions can be used for any elastic materials, any type of soil, and any shapes of pile cross section. Above all, the analytical solutions may be easily applied to calculate the maximum deflection or moment of lateral long piles subject to combined loads accurately using a calculator.     

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.     

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.     

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.     

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.