Numerical Investigation of the Effect of Vertical Load on the Lateral Response of Piles

The laboratory and field test data on the response of piles under the combined action of vertical and lateral loads is rather limited. The current practice for design of piles is to consider the vertical and lateral loads independent of each other. This paper presents some results from three-dimensional finite-element analyses that show the significant influence of vertical loads on a pile’s lateral response. The analyses were performed in both homogeneous clayey soils and homogeneous sandy soils. The results have shown that the influence of vertical loads on the lateral response of piles is to significantly increase the capacity in sandy soils and marginally decrease the capacity in clayey soils. In general, it was found that the effect of vertical loads in sandy soils is significant even for long piles, which are as long as 30 times the pile width, while in the case of clayey soils, the effect is not significant for piles beyond a length of 15 times the width of the pile. The design bending moments in the laterally loaded piles were also found to be dependent on the level of vertical load on the piles.     

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.     

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.     

Lateral Loaded Pile Response in Liquefiable Soil

This paper provides a new analysis procedure for assessing the lateral response of an isolated pile in saturated sands as liquefaction develops in response to dynamic loading such as that generated during earthquake shaking. This new procedure predicts the degradation in pile response and soil resistance due to the free-field excess porewater pressure generated by the earthquake, along with the near-field excess porewater pressure generated by lateral loading from the superstructure. The new procedure involves the integration of the developing (free- and near-field) porewater pressure in the strain wedge (SW) model analysis. The current SW model, developed to evaluate drained response (a nonlinear three-dimensional model) of a flexible pile in soil, has been extended in this paper to incorporate the undrained response of a laterally loaded pile in liquefied sand. This new procedure has the capability of predicting the response of a laterally loaded isolated pile and the associated modulus of subgrade reaction (i.e., the p–y curve) in a mobilized fashion as a result of developing liquefaction in the sand. Current design procedures assume slight or no resistance for the lateral movement of the pile in the liquefied soil which is a conservative practice. Alternatively, if liquefaction is assessed not to occur, some practitioners take no account of the increased free-field porewater pressure, and none consider the additional near-field porewater pressure due to inertial interaction loading from the superstructure; a practice that is unsafe in loose sands.     

Lateral Resistance of Single Pile Located Near Geosynthetic Reinforced Slope

An extensive program of laboratory tests was carried out to study the effect of reinforcing an earth slope on the lateral behavior of a single vertical pile located near the slope. Layers of geogrid were used to reinforce a sandy slope of 1 (V):1.5 (H) made with sands of three different unit weights representing dense, medium dense, and loose relative densities. Several configurations of geogrid reinforcement with different numbers of layers, vertical spacing, and length were investigated. The experimental program also included studies of the location of pile relative to the slope crest, relative density of sand, and embedment length of pile. The results indicate that stabilizing a soil slope has a significant benefit of improving the lateral load resistance of a vertical pile. The improvement in pile lateral load was found to be strongly dependent on the number of geogrid layers, layer size, and relative density of the sand. It was also found that soil reinforcement is more effective for piles located closer to the slope crest. Based on test results, critical values are discussed and recommended.     

Cyclic Lateral Load Behavior of a Pile Cap and Backfill

A series of static cyclic lateral load tests were performed on a full-scale 4×3 pile group driven into a cohesive soil profile. Twelve 324-mm steel pipe piles were attached to a concrete pile cap 5.18×3.05?m in plan and 1.12?m in height. Pile–soil–pile interaction and passive earth pressure provided lateral resistance. Seven lateral load tests were conducted in total; four tests with backfill compacted in front of the pile cap; two tests without backfill; and one test with a narrow trench between the pile cap and backfill soil. The formation of gaps around the piles at larger deflections reduced the pile–soil–pile interaction resulting in a degraded linear load versus deflection response that was very similar for the two tests without backfill and the trenched test. A typical nonlinear backbone curve was observed for the backfill tests. However, for deflections greater than 5 mm, the load-deflection behavior significantly changed from a concave down shape for the first cycle to a concave up shape for the second and subsequent cycles. The concave up shape continued to degrade with additional cycles past the second and typically became relatively constant after five to seven cycles. A gap formed between the backfill soil and the pile cap, which contributed to the load-deflection degradation. Crack patterns and sliding surfaces were consistent with that predicted by the log spiral theory. The results from this study indicate that passive resistance contributes considerably to the lateral resistance. However, with cyclic loading the passive force degrades significantly for deflections greater than 0.5% of the pile cap height.     

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.     

Pile Response Adjacent to Braced Excavation

The excavation of soil for the construction of basements or cut-and-cover tunnels results in ground movements. One particular concern is that the excavation-induced lateral soil movements may adversely affect any nearby pile foundation. The lateral loads imposed by the soil movements induce bending moments and deflections in the pile, which may lead to structural distress and failure. This paper presents the results of an actual full-scale instrumented study that was carried to examine the behavior of an existing pile due to nearby excavation activities resulting from the construction of a 16 m deep cut-and-cover tunnel. The pile was located 3 m behind a 0.8 m thick diaphragm wall. Excavation to the formation level that was 16 m below the ground surface resulted in a maximum lateral pile movement of 28 mm. A simplified numerical procedure based on the finite-element method was used to analyze the pile response. Generally, the theoretical predictions were in reasonable agreement with the measured results.     

Applicability of Conventional p-y Relations to the Analysis of Piles in Laterally Spreading Soil

This paper presents a kinematic analysis of a single pile embedded in a laterally spreading layered soil profile and discusses the relevancy of conventional analysis models to this load case. The research encompasses the creation of three-dimensional (3D) finite-element (FE) models using the OpenSees FE analysis platform. These models consider a single pile embedded in a layered soil continuum. Three reinforced concrete pile designs are considered. The piles are modeled using beam-column elements and fiber-section models. The soil continuum is modeled using brick elements and a Drucker-Prager constitutive model. The soil-pile interface is modeled using beam-solid contact elements. The FE models are used to evaluate the response of the soil-pile system to lateral spreading and two alternative lateral load cases. Through the computation of force density-displacement (p-y) curves representative of the soil response, the FE analysis (FEA) results are used to evaluate the adequacy of conventional p-y curve relationships in modeling lateral spreading. It is determined that traditional p-y curves are unsuitable for use in analyses where large pile deformations occur at depth.     

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.     

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.     

Lateral Resistance of Short Single Piles and Pile Groups Located Near Slopes

Many transmission towers, high-rise buildings, and bridges are constructed near steep slopes and are supported by large-diameter piles. These structures may be subjected to large lateral loads, such as violent winds and earthquakes. Widely used types of foundations for these structures are pier foundations, which have large diameter with high stiffness. The behavior of a pier foundation subjected to lateral loads is similar to that of a short rigid pile, because both elements seem to fail by rotation developing passive resistance on opposite faces above and below the rotation point, unlike the behavior of a long flexible pile. This paper describes the results of several numerical studies performed with a three-dimensional finite-element method (FEM) of model tests and a prototype test of a laterally loaded short pile and pier foundation located near slopes, respectively. Initially, in this paper, the results of model tests of single piles and pile groups subjected to lateral loading, in homogeneous sand with 30° slopes and horizontal ground were analyzed by the three- dimensional (3D) finite-element (FE) analyses. Furthermore, field tests of a prototype pier foundation subjected to lateral loading on a 30° slope was reported. The FE analyses were conducted to simulate these results. The main purpose of this paper is the validation of the 3D elasto–plastic FEM by comparisons with the experimental data.     

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.     

Undrained Stability of Braced Excavations in Clay

Short-term undrained stability often controls the design of braced excavations in soft clays. This paper summarizes the formulation of numerical limit analyses that compute rigorous upper and lower bounds on the exact stability number and include anisotropic yielding, typical of K0-consolidated clays and bending failure of the wall. Calculations for braced cuts bound the actual failure conditions within ±5%, and highlight limitations of existing basal stability equations. The analyses clarify how wall embedment and bending capacity improve the stability of well braced excavations. Careful selection of mobilized strengths at shear strains in the range 0.6–1.0% are necessary to match the predictions of anisotropic limit analyses with nonlinear finite-element predictions of failure for the embedded walls. Two example applications from recent projects in Boston highlight the practicality of the numerical limit analyses for modeling realistic soil profiles and lateral earth support systems, but also focus attention on the need for careful selection of undrained strength parameters. Credible estimates of stability have also been obtained in reanalyzing a series of case studies reported in literature using isotropic strength parameters derived from field vane or laboratory simple shear tests.     

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.     

Free-Field Measurements to Disclose Lateral Reaction Mechanism of Piles Subjected to Soil Movements

Soil-pile interaction remains to be the most ambiguous yet one of the most crucial aspects in the design of laterally loaded soil-pile systems subjected to embankment-induced movements. This paper proposes a new method that is capable of producing soil stiffness degradation curves, which are the outcome of real field behavior through free-field measurements. Soil-pile interaction mechanism can be solved with the proposed method for any possible case either the piles are constructed before the embankment construction or during and after. For any time considered, the method enables the computation of resultant stress effects on the pile cross section and the accompanying deflections. To provide a basis of comparison, an example problem has been solved with the proposed method and with two well-known commercial finite-element softwares. Obtained results indicated the capability of the proposed method to disclose real field behavior, which can be attributed to its inherent property of being also an observational method.     

Seismic Behavior of Batter Piles: Elastic Response

Several aspects of the seismic response of groups containing nonvertical piles are studied, including the lateral pile-head stiffnesses, the “kinematic” pile deformation, and the “inertial” soil-pile-structure response. A key goal is to explore the conditions under which the presence of batter piles is beneficial, indifferent, or detrimental. Parametric analyses are carried out using three-dimensional finite-element modeling, assuming elastic behavior of soil, piles, and superstructure. The model is first used to obtain the lateral stiffnesses of single batter piles and to show that its results converge to the available solutions from the literature. Then, real accelerograms covering a broad range of frequency characteristics are employed as base excitation of simple fixed-head two-pile group configurations, embedded in homogeneous, inhomogeneous, and layered soil profiles, while supporting very tall or very short structures. Five pile inclinations are considered while the corresponding vertical-pile group results serve as reference. It is found that in purely kinematic seismic loading, batter piles tend to confirm their negative reputation, as had also been found recently for a group subjected to static horizontal ground deformation. However, the total (kinematic plus inertial) response of structural systems founded on groups of batter piles offers many reasons for optimism. Batter piles may indeed be beneficial (or detrimental) depending on, among other parameters, the relative size of the overturning moment versus the shear force transmitted onto them from the superstructure.     

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.     

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.     

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.