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.     

Seismic Behavior of Soil-Pile-Structure Interaction in Liquefiable Soils: Parametric Study

Nonlinearity of the soil medium plays a very important role on the seismic behavior of soil-pile-structure interaction. The problem of soil-pile-structure interaction is further complicated when the piles are embedded in liquefiable soil medium. A finite-element code was developed in MATLAB to model three-dimensional soil-pile-structure systems. Frequency dependent Kelvin elements (spring and dashpots) were used to model the radiation boundary conditions. A work-hardening plastic cap model was used for constitutive modeling of the soil medium. The pore pressure generation for liquefaction was incorporated by a two-parameter volume change model reported in the literature. In this paper, a 2×2 pile group in liquefiable soil is considered and a parametric study is conducted to investigate its seismic behavior. The effects of loading intensity and stiffness of the soil on the seismic behaviour of the soil-pile system are investigated, considering nonlinearity and liquefaction of the soil medium for a wide range of frequencies of harmonic excitations. The inertial interaction attributable to a structure is analyzed for a system consisting of a four-storied portal frame on the pile group-soil subsystem. The responses of the structure are investigated for harmonic excitation and transient excitations. The importance of consideration of nonlinearity and liquefaction of the soil medium for analysis and design of a pile-supported structure is highlighted. Results from an analysis considering a practical soil-pile problem are presented to demonstrate the applicability of the developed algorithm for a practical problem.     

Seismic Displacement of Slopes Reinforced with Piles

The seismic stability of slopes reinforced with a row of piles is analyzed using the kinematic theorem of limit analysis within the framework of the pseudostatic approach. An existing method which is based on the theory of plasticity is used to determine the lateral forces provided by the piles. Expressions for calculating the yield acceleration coefficient are derived. Then, based on Newmark’s sliding block concept, the permanent displacement induced by an earthquake shocking can be calculated by the integrals of seismic records. An example is investigated to illustrate the validity of this method and the effects of piles on a restraining slope’s dynamic deformation.     

Numerical Solution for Laterally Loaded Piles in a Two-Layer Soil Profile

Piles are often embedded in a layered soil profile, such as sand or clay layer underlain by rock. Several existing solutions are available for laterally loaded piles in a layered soil system. However, these solutions are only applicable to constant soil stiffness for each layer. In this paper, a variational approach is employed to numerically solve the problem of laterally loaded piles in layered soils using beam on an elastic foundation model. The soil stiffness can be either constant with depth or linearly varying with depth. The numerical solution is validated against an existing solution for linearly varying soil stiffness in a single soil layer system and an existing solution for a two-layer soil system with constant soil stiffness. Case studies using the proposed solution for field lateral load tests on full size drilled shafts embedded in weak rock with an overlying sand layer are presented. The simplicity and the relative ease of using the solution make it a good alternative approach for estimating the deflection and moment responses of a laterally loaded pile in a two-layer soil profile.     

Experimental Response of Piles in Sand under Compound Motion

This paper describes a fundamental experimental study on the vertical, horizontal, and rocking dynamic behavior of single pile foundations in granular soils. Aimed at generating an extensive experimental database with sufficient parametric variations to clarify a number of issues, multiple series of canonical small-strain forced-vibration centrifuge tests were performed on two model piles using the technique of random vibration and impact loading. Correlated well with vertical- and horizontal-centric dynamic tests within the experimental program, a novel hybrid-mode test method by means of eccentric excitation is validated and employed for the characterization of the foundation responses in general planar motion. A large set of experimental data for different length scales were generated and synthesized in the frequency domain in the form of directional force-response transfer functions. By virtue of the physical measurements, the validity and limitations of two fundamental elastodynamic pile solutions pertaining to the physical dynamic soil-foundation problem are also evaluated.     

Undrained Lateral Pile Response in Sloping Ground

Three-dimensional finite element analyses were performed to study the behavior of piles in sloping ground under undrained lateral loading conditions. Piles of different diameter and length in sloping cohesive soils of different undrained shear strength and several ground slopes were considered. Based on the results of the finite element analyses, analytical formulations are derived for the ultimate load per unit length and the initial stiffness of hyperbolic p-y curves. New p-y criteria for static loading of piles in clay are proposed, which take into account the inclination of the slope and the adhesion of the pile-slope interface. These curves are used through a commercial subgrade reaction computer code to parametrically analyze the effect of slope inclination and pile adhesion on lateral displacements and bending moments. To validate the proposed p-y curves, a number of well documented lateral load tests are analyzed. Remarkable agreement is obtained between predicted and measured responses for a wide range of soil undrained shear strength and pile diameter, length, and stiffness.     

Investigation on the Impact of Seasonally Frozen Soil on Seismic Response of Bridge Columns

This paper presents the development of numerical models that investigated the seismic response of a simple two span prototype bridge system during warm and frozen temperatures. Models from both temperature conditions were subjected to a range of seismic intensities to examine the effect of seasonal freezing on the response of the system. Stiffness characteristics were defined using cyclic models of a bridge pier that were previously developed and validated using results from an experimental program on identical full-scale column-foundation units, which were tested during the summer and winter months. Dynamic characteristics of the seismic models were defined using approaches found in the literature. Frozen conditions increased the maximum bending moment and shear force demands for all seismic intensities, with nonlinearity in the column/foundation reducing the difference between the peak responses at higher intensities. At the depth of maximum foundation shear for the frozen model, demand was three times higher than the unfrozen for the 500-year return period and twice during the 2,500-year event. This is significant as one will assume shear is not critical at this location if the effects of frozen conditions are ignored. Apart from the smallest intensity event, increased peak lateral displacements were developed by the warm model down the length of the column and foundation. However, the displacement demand to capacity ratio was higher at the column top for the frozen model, exceeding the capacity during the 2,500-year return period event.     

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.     

Seismic Performance of a River Dike Improved by Sand Compaction Piles

Sand compaction piling is one of the commonly used countermeasures for earthquake liquefaction hazard of river dikes. This paper presents a case study of the performance of an instrumented dike in northeast Japan that was improved by sand compaction piles and subjected to the 2003 Northern Miyagi Earthquake, with the aim to better understand the effectiveness of this ground improvement method. Simulation has been carried out by means of a fully coupled numerical procedure which employs a sophisticated cyclic elastoplastic constitutive model and the updated Lagrangian algorithm. Comparisons between the field measurements and the computed responses, including the time histories of accelerations and pore-water pressures at different locations, show reasonably good agreement. Numerical simulation has also been made of the same dike but without ground improvement to identify the effects of sand compaction piles in altering the performance of the dike. The study demonstrates that the comprehensive numerical procedure is a promising tool for development of seismic performance-based design of earth structures.     

Numerical Modeling of Seismic Response of Rigid Foundation on Soft Soil

A numerical model was developed to simulate the response of two instrumented, centrifuge model tests on soft clay and to investigate the factors that affect the seismic ground response. The centrifuge tests simulated the behavior of a rectangular building on 30?m uniform and layered soft soils. Each test model was subjected to several earthquakelike shaking events at a centrifugal acceleration level of 80g. The applied loading involved scaled versions of an artificial western Canada earthquake and the Port Island ground motion recorded during the 1995 Kobe Earthquake. The centrifuge model was simulated with the three-dimensional finite-difference-based fast Lagrangian analysis of continua program. The results predicted with the use of nonlinear elastic–plastic model for the soil are shown to be in good agreement with measured acceleration, soil response, and structural behavior. The validated model was used to study the effect of soil layering, depth, soil–structure interaction, and embedment effects on foundation motion.     

Drag Force on Single Piles in Clay Subjected to Surcharge Loading

Piles driven into clay are often subjected to indirect loading as a result of the surcharge applied on the surrounding area. During the drained period, both the piles and the soil undergo downward movements caused by the axial and the surcharge loading, respectively. Depending on the relative movement of the pile–soil system, positive and negative skin friction develop on the pile’s shaft. Negative skin friction is the drag force that may be large enough to reduce the pile capacity and/or to overstress the pile’s material causing fractures or perhaps structural failure of the pile, and/or possibly pulling out the pile from the cap. A numerical model that uses the finite element technique combined with the soil responses according to Mohr–Coulomb criteria was developed for case simulation. The computer program CRISP (developed by Cambridge University) was used in this study. The numerical model was first tested against the results predicted by the bearing capacity theories for pile foundations in clay subjected to axial loading. Upon achieving satisfactory results, the numerical model was then used to generate data for piles subjected to surcharge loading. The predicted values were compared well with the field data and the empirical formulae available in the literature. Based on the results of the present investigation, design charts and procedures are presented to predict the location of the neutral plane and to estimate the drag force acting on the pile’s shaft for a given pile–soil–loading conditions. In the case of excessive drag force, coating the pile’s shaft with a thin layer of bitumen is advisable to eliminate or minimize the drag force. The design procedure presented herein would provide the means to establish the need and the extent of the pile coating. Furthermore, it demonstrates the role of the factor of safety on both pile capacity and the depth of the neutral plane.     

Small-Strain Behavior of Granular Soils. II: Seismic Response Analyses and Model Evaluation

Using the recorded response at two vertical array sites, the SimSoil model presented in the companion paper is evaluated. The SimSoil model, which describes the small strain nonlinear behavior of granular materials, is implemented as a material model in AMPLE2000, a nonlinear, one-dimensional site response analysis code. Shear wave velocity profiles and laboratory test data available for both the La Cienega site, which was instrumented over 250?m, and the Lotung site, which was instrumented over 47?m, were used to determine SimSoil model parameters. Predictions from AMPLE2000 are compared with the measured response at several elevations for earthquakes that resulted in both nonlinear and nearly linear soil behavior. Using the available laboratory data and known input motions, the predictions of the response at these sites matched the recorded response well for varied magnitudes of shaking with a single set of parameters for each site.     

Analysis of Laterally Loaded Piles in Soil with Stiffness Increasing with Depth

This article reports a variational solution and its spreadsheet calculation procedure for the analysis of laterally loaded piles in a soil with stiffness increasing with depth. The aim of the paper is to provide solutions that can be used simply with recourse only to spreadsheet calculation to solve the displacement and bending moment of laterally loaded piles, so that they can be easily applied in practice as an alternative approach to analyze the response of laterally loaded 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.     

Behavior of Step Tapered Bored Piles in Sand under Static Lateral Loading

The behavior of step tapered bored piles in sand, under static lateral loading, was examined by field tests at one site in Kuwait. A total of 14 bored piles including two instrumented piles were installed for lateral loading. The soil profile consists of medium dense sand with weak cementations and no groundwater was encountered in the boreholes. Laboratory tests were carried out to determine the basic soil characteristics and the strength parameters. Both the ultimate lateral capacity and the deflections at applied loads were examined. The results indicate increased lateral load carrying capacity and decreased deflections at different applied loads for the step tapered piles due to the enlargement or strengthening of the upper section of the piles. The advantages of using this type of pile is emphasized including the cost saving resulting from an economical design.     

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.     

Wedge Failure Analysis of Soil Resistance on Laterally Loaded Piles in Clay

A fundamental study of pile-soil systems subjected to lateral loads in clay soil was conducted by using experimental tests and a lateral load-transfer approach. The emphasis was on an improved wedge failure model developed by considering three-dimensional combination forces and a new hyperbolic p-y criterion. A framework for determining the p-y curve on the basis of both theoretical analysis and experimental load test results is proposed. The proposed p-y method is shown to be capable of predicting the behavior of a large-diameter pile under lateral loading. The proposed p-y curves with an improved wedge model are more appropriate and realistic for representing a pile-soil interaction for laterally loaded piles in clay than the existing p-y method.     

Effect of Nonlinear Soil Behavior on Inelastic Seismic Response of a Structure

The characteristics of the earthquake motions at the base of a structure are affected by the properties of the underlying soil through the soil amplification and soil–structure interaction phenomena. In this paper the effect of nonlinear soil behavior on the elastic and inelastic response spectra of the motions that would be recorded at the free surface of a soft soil deposit or at the base of each structure is investigated. The analyses are conducted for a soil layer by itself and for a complete soil structure system using a finite element discretization of the soil in cylindrical coordinates and an approximate linear iterative procedure to simulate nonlinear behavior. Studies are conducted for structures, with a constant base and variable height modeled as equivalent linear or nonlinear single degree of freedom systems and an input motion at the base of the soil deposit representative of rock outcrop motions. Both mat and pile foundations are considered. The results illustrate clearly the importance of the nonlinear soil behavior.     

Role of Shear Keys in Seismic Behavior of Bridges Crossing Fault-Rupture Zones

This paper examines the role of shear keys at bridge abutments in the seismic behavior of “ordinary” bridges. The seismic responses of bridges subjected to spatially uniform and spatially varying ground motions for three shear-key conditions—nonlinear shear keys that break off and cease to provide transverse restraint if deformed beyond a certain limit; elastic shear keys that do not break off and continue to provide transverse restraint throughout the ground shaking; and no shear keys—are examined. Results show that seismic demands for a bridge with nonlinear shear keys can generally be bounded by the demands of a bridge with elastic shear keys and a bridge with no shear keys for both types of ground motions. While ignoring shear keys provides conservative estimates of seismic demands in bridges subjected to spatially uniform ground motion, such a practice may lead to underestimation of some seismic demands in bridges in fault-rupture zones that are subjected to spatially varying ground motion. Therefore, estimating the upper bounds of seismic demands in bridges crossing fault-rupture zones requires analysis for two shear-key conditions: no shear keys and elastic shear keys.     

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.