A multidirectional semi‐analytical method for analysis of laterally loaded pile groups in multi‐layered elastic strata

A semi‐analytical method for calculating the response of single piles and pile groups subjected to lateral loading is developed in this paper. Displacements anywhere in the soil domain are tied to the displacements of the piles through decay functions. The principle of virtual work and the calculus of variations are used to derive the governing differential equations that describe the response of the piles and soil. The eigenvalue method and the finite difference technique are used to solve the system of coupled differential equations for the piles and soil, respectively. The proposed method takes into account the soil surface displacement along and perpendicular to the loading direction and produces displacement fields that are very close to those produced by the finite element method but at lower computational effort. Compared with the previous method that considered only the soil displacement along the loading direction, accounting for the multi‐directional soil displacement field produces responses for the piles and soil that are closer to those approximated by the finite element method. Copyright © 2016 John Wiley & Sons, Ltd.     

路基荷载下PCC刚性桩复合地基沉降简化计算

将路堤荷载作用下的刚性桩复合地基变形,简化为只有竖向变形,水平变形可以忽略,然后,应用土体的平衡、几何、物理方程,建立沉降计算的控制方程。桩土界面的接触条件按位移协调或产生滑移变形两种情况分别建立,采用有限差分法离散求解,可得桩、桩周土各自的沉降变形、桩土界面的摩擦力分布。与有限元分析和现场实测结果的对比表明,该简化方法具有较高的准确性,可以方便地应用到工程实际。     

Axial and lateral response of pile groups embedded in nonhomogeneous soils

A numerical method of analysis based on elasticity theory is presented for the analysis of axially and laterally loaded pile groups embedded in nonhomogeneous soils. The problem is decomposed into two systems, namely the group piles acted upon by external applied loads and pile–soil interaction forces, and a layered soil continuum acted upon by a system of pile–soil interaction forces at the imaginary positions of the piles. The group piles are discretized into discrete elements while the nonhomogeneous soil behaviour is determined from an economically viable finite element procedure. The load–deformation relationship of the pile group system is then determined by considering the equilibrium of the pile–soil interaction forces, and the compatibility of the pile and soil displacements. The influence of soil nonlinearity can be studied by limiting the soil forces at the pile–soil interface, and redistributing the ‘excess forces’ by an ‘initial stress’ process popular in elasto-plastic finite element analysis. The solutions from this approach are compared with some available published solutions for single piles and pile groups in homogeneous and nonhomogeneous soils. A limited number of field tests on pile groups are studied, and show that, in general, the computed response compares favourably with the field measurements.     

Variational elastic solution for axially loaded piles in multilayered soil

Most analytical or semi‐analytical solutions of the problem of load‐settlement response of axially loaded piles are based on the assumption of zero radial displacement. These solutions also are only applicable to piles embedded in either a homogeneous or a Gibson soil deposit. In reality, soil deposits consist of multiple soil layers with different properties, and displacements in the radial direction within the soil deposit are not zero when the pile is loaded axially. In this paper, we present a load‐settlement analysis applicable to a pile with circular cross section installed in multilayered elastic soil that accounts for both vertical and radial soil displacements. The analysis follows from the solution of the differential equations governing the displacements of the pile–soil system obtained using variational principles. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. We compare the results from the present analysis with those of an analytical solution that considers only vertical soil displacements. The analysis presented in this paper also provides useful insights into the displacement and strain fields around axially loaded piles. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of laterally loaded piles with rectangular cross sections embedded in layered soil

An analysis is developed to determine the response of laterally loaded rectangular piles in layered elastic media. The differential equations governing the displacements of the pile–soil system are derived using variational principles. Closed‐form solutions of pile deflection, the slope of the deflected curve, the bending moment and the shear force profiles can be obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. The new analysis allows insights into the lateral load response of square, rectangular and circular piles and how they compare. Copyright © 2007 John Wiley & Sons, Ltd.     

Soil resistances for laterally loaded rigid piles in multi-layered elastic soil

ABSTRACT

Short stubby piles like monopiles and large diameter drilled shafts undergo rigid body translation and rotation when subjected to a lateral force and/or a moment at the head. A method of analysis for these piles embedded in multi-layered elastic soil is developed using the variational principles of mechanics. Using this analysis, the soil resistance against pile movement can be rigorously related to the soil elastic constants, and the pile head displacement and rotation can be quickly calculated. The equilibrium equations for pile and soil displacements are obtained using the principle of virtual work and solved using an iterative algorithm. Pile responses obtained from the analysis match well with those obtained from three-dimensional finite element analyses in which the same inputs of loads, geometry, and material properties are given. Based on the new analysis, fitted equations for soil resistance parameters are developed, which can be used to directly calculate the pile head displacement and rotation without the use of the iterative algorithm. Numerical examples are provided that demonstrate how the method can be used to analyse practical problems.     

水平循环荷载下桩基变形特性的离心模型试验研究

波浪、船舶等长期水平循环荷载作用下,桩基将不可避免地产生附加应力和变形。针对饱和黏土地层,开展离心模型试验研究了船舶系泊水平荷载作用下单桩和群桩的变形特性。发现水平循环加-卸载诱发了桩周土体的塑性变形,进而导致桩身产生了不可恢复的水平位移和弯曲变形。随着循环荷载的增加,单桩和群桩的桩顶最大水平位移和残余水平位移均同时增加,但残余水平位移明显小于最大水平位移。单桩的桩顶残余水平位移与最大位移比值介于0.17～0.22;群桩的桩顶残余水平位移与最大水平位移比值介于0.30～0.84。水平循环加-卸载作用下,桩身残余弯曲应变明显小于最大弯曲应变。单桩的残余弯曲应变与最大弯曲应变比值介于0.13～0.50;群桩的桩身残余弯曲应变与最大弯曲应变比值介于0.23～0.82。群桩前桩的残余和最大弯曲应变明显大于后桩,前桩与后桩的最大弯曲应变、残余应变比值分别高达3.2和3.1。因此,前桩要采取合理的加固和保护措施,以确保桩基长期服役的安全性。     

Variation of limiting lateral soil pressure with depth for pile rows in clay

Pile group interaction effects on the lateral pile resistance are investigated for the case of a laterally loaded row of piles in clay. Both uniform undrained shear strength and linearly increasing with depth shear strength profiles are considered. Three-dimensional finite element analyses are presented, which are used to identify the predominant failure modes and to calculate the reduction in lateral resistance due to group effects. A limited number of two-dimensional analyses are also presented in order to examine the behaviour of very closely spaced piles. It is shown that, contrary to current practice, group effects vary with depth; they are insignificant close to the ground surface, increase to a maximum value at intermediate depths and finally reduce to a constant value at great depth. The effect of pile spacing and pile–soil adhesion are investigated and equations are developed for the calculation of a depth dependent reduction factor, which when multiplied by the limiting lateral pressure along a single pile, provides the corresponding variation of soil pressure along a pile in a pile row. This reduction factor is used to perform p–y analyses, which show that, due to this variation of group effects on the lateral soil pressures with depth, the overall group interaction effects depend on the pile length. Comparisons are also made with approaches used in practice that assume constant with depth reduction factors.     

Nonlinear analysis of laterally loaded rigid piles in cohesive soil

This article presents a method for the nonlinear analysis of laterally loaded rigid piles in cohesive soil. The method considers the force and the moment equilibrium to derive the system equations for a rigid pile under a lateral eccentric load. The system equations are then solved using an iteration scheme to obtain the response of the pile. The method considers the nonlinear variation of the ultimate lateral soil resistance with depth and uses a new closed‐form expression proposed in this article to determine the lateral bearing factor. The method also considers the horizontal shear resistance at the pile base, and a bilinear relationship between the shear resistance and the displacement is used. For simplicity, the modulus of horizontal subgrade reaction is assumed to be constant with depth, which is applicable to piles in overconsolidated clay. The nonlinearity of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The validity of the developed method is demonstrated by comparing its results with those of 3D finite element analysis. The applications of the developed method to analyze five field test piles also show good agreement between the predictions and the experimental results. The developed method offers an alternative approach for simple and effective analysis of laterally loaded rigid piles in cohesive soil. Copyright © 2011 John Wiley & Sons, Ltd.     

Elastic analysis of laterally loaded pile in multi-layered soil

An analysis is developed to determine the response of laterally loaded piles in layered elastic media. The differential equations governing pile deflections in different layers due to a concentrated static force and/or moment acting at the pile head are obtained using the principle of minimum potential energy and calculus of variations. The differential equations are solved analytically using the method of initial parameters. Pile deflection, slope of the deformed axis of the pile, bending moment and shear force can be reliably obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. It is observed that soil layering has a definite impact on pile response and must be taken into account for proper analysis and design. The analysis forms the basis for future formulations that can consider stress–strain nonlinearity.     

Study on laterally loaded piles with rectangular and circular cross sections

The conventional approach in the design of laterally loaded piles with rectangular cross section involves the simplification of converting the rectangular cross section of the pile to an equivalent circular cross section. An analysis to determine the response of laterally loaded rectangular or circular piles in elastic soil is presented in which this simplification is not required. The analysis is based on the solution of differential equations governing the displacements of the pile–soil system derived using energy principles. The pile geometry and the elastic constants of the soil and pile are the input parameters to the analysis. Using this analysis, comparisons are made between the response of rectangular and circular piles in elastic soil. Based on the proposed solution scheme, a user-friendly spreadsheet program (LATPAXL) was developed that can be used to perform the analysis. In addition, simple equations obtained by regression analysis of the pile head deflection and bending moment profiles are proposed. Examples illustrate the use of the analysis.     

On the influence of vertical loads on the lateral response of pile foundation

The influence of vertical loads on the lateral response of group piles installed in sandy soil and connected together by a concrete cap is studied through finite elements analyses. The analyses focus on the five piles in the middle row of 3 × 5 pile groups. The vertical load is applied by enforcing a vertical displacement equivalent to 2% of the pile diameter through the pile cap prior to the application of the lateral loads. The results have shown that the lateral resistance of the leading pile (pile 1) does not appear to vary considerably with the vertical load. However, the vertical load leads to 23%, 36%, 64%, and 82% increase in the lateral resistance of piles 2–5, respectively. The increase in the lateral pressures in the sand deposit is the major driving factor to contribute the change in the lateral resistance of piles, depending on the position of the pile in the group. The distribution of lateral loads among piles in the group tends to be more uniform when vertical loads were considered leading to a more economical pile foundation design.     

Nonlinear analysis of laterally loaded rigid piles in cohesionless soil

In this paper, a method is developed for nonlinear analysis of laterally loaded rigid piles in cohesionless soil. The method assumes that both the ultimate soil resistance and the modulus of horizontal subgrade reaction increase linearly with depth. By considering the force and moment equilibrium, the system equations are derived for a rigid pile under a lateral eccentric load. An iteration scheme containing three main steps is then proposed to solve the system equations to obtain the response of the pile. To determine the ultimate soil resistance and the modulus of horizontal subgrade reaction required in the analysis, related expressions are selected by reviewing and assessing the existing methods. The degradation of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The developed method is validated by comparing its results with those of centrifugal tests and three-dimensional finite element analysis. Applications of the developed method to laboratory model and field test piles also show good agreement between the predictions and the experimental results.     

边坡土体侧移模式对抗滑桩影响分析

在开挖、降雨或地震等外部因素作用下,边坡土体很容易进入局部或瞬态大变形乃至失稳滑动,使抗滑桩产生附加位移及弯矩。基于两阶段分析方法,采用Winkler模型模拟抗滑单桩与土之间的相互作用,建立单桩水平位移控制方程组,根据内力与位移的连续条件得到考虑不同土体侧移模式下求解桩身响应的矩阵解析表达式,并采用现场监测数据及Poulos弹性理论进行验证,证明该方法是合理可行的,并通过参数分析土体侧移对抗滑桩水平承载性状的影响程度。分析结果表明,土体侧移模式包括最大侧移值、分布形状及重心、侧移势等,对抗滑桩的挠度和弯矩均有显著影响,在工程设计中应予以充分重视。     

Numerical simulations of landslide-stabilizing piles: a remediation project in Söke,Turkey

A catastrophic landslide following a rainy season occurred in the backyard of a school building in Söke, Turkey. The landslide caused property damage and adversely affected the present forest cover. Immediately after the landslide, double-row stabilizing piles were designed and constructed based on the findings of two-dimensional (2D) finite element (FE) analyses to take an urgent precaution. To remedy the problem, pile displacements were monitored using inclinometers, and it was observed that the measured displacements were greater than the values calculated in the design stage. Accordingly, two different three-dimensional (3D) numerical FE models were used in tandem with the inclinometer data to determine the load transfer mechanism. In the first model, numerical analyses were made to predict the pile displacements, and while the model predicted successfully the displacement of the piles constructed in the middle with reasonable accuracy, it failed for the corner piles. In the second model, the soil load transfer between piles was determined considering the sliding mass geometry, the soil arching mechanism and the group interaction between adjacent piles. The results of the second model revealed that the middle piles with large displacements transferred their loads to the corner piles with smaller displacements. The generated soil loads, perpendicular to the sliding direction, restricted pile deformations and piles with less displacement were subjected to greater loads due to the bowl-shaped landslide. A good agreement between the computed pile displacements and inclinometer data indicates that the existing soil pressure theories should be improved considering the position of the pile in the sliding mass, the depth and deformation modulus of stationary soil, the relative movement between the soil and piles and the relative movement of adjacent piles.     

Permeable piles: An alternative to improve the performance of driven piles

This paper investigates the soil displacements and excess pore pressures induced by driven piles using a combined 3D finite and infinite element approach. The analyses are compared with analytical evaluations and field measurements. Consolidation analysis is conducted to illustrate the variation in pore pressure with time. A technique of drilling drainage holes on the pipe pile is proposed in this paper to accelerate the dissipation of pore pressure to improve the performance of displacement piles. It has been noticed that optimal performance of piles can be obtained by assigning openings in piles within the bottom 50% of the pile length.     

BEM analysis of the interaction factor for vertically loaded dissimilar piles in saturated poroelastic soil

This paper focuses on an analysis by the boundary element method (BEM) of the pile-to-pile interaction for pile groups with dissimilar piles of different pile lengths embedded in saturated poroelastic soil. The behaviour of the poroelastic homogeneous soil is governed by Biot’s consolidation equations. The pile–soil system is decomposed into extended soil and fictitious piles. Considering the compatibility of vertical strain between fictitious piles and soil, the second kind of Fredholm integral equations were obtained to predict the axial force and settlement along pile shafts numerically. For the analysis of the interaction factor, two loading conditions for a two-dissimilar-pile system were proposed: (a) only one pile is loaded and (b) each pile is subjected to a load proportional to the pile length. Furthermore, the two-pile system was extended to pile groups with a rigid cap to capture the optimum design where each pile shares the same loading at the pile heads. The optimum results require shortening the peripheral piles and elongating internal piles, and the consolidation effect needs to be considered due to the adjustment of loading distribution among piles.     

Prediction of load displacement response of single piles under uplift load

Load displacement response and ultimate resistance of piles in sand under uplift load are predicted by load transfer approach. The pile is divided into number of segments and assigned geometrical and material properties according to actual soil pile situation. The shaft resistance is obtained analytically in accordance with existing studies. The proposed method takes into account the length, diameter and relevant surface characteristics of pile and soil properties. The load displacement characteristics and the value of uplift capacity of vertical piles from field test have been predicted. Reasonable agreement has been found out between predicted and observed values of uplift capacity. Load transfer mechanism is capable of predicting the nonlinear variation of load-displacement response of piles.     

Numerical investigation of pile installation effects in sand using material point method

The installation of displacement piles in sand leads to severe changes in the stress state, density and soil properties around the pile tip and shaft, and therefore has a significant influence on the pile bearing capacity. Most current numerical methods predicting pile capacity do not take installation effects into account, as large deformations can lead to mesh distortion and non-converging solutions. In this study, the material point method (MPM) is applied to simulate the pile installation process and subsequent static pile loading tests. MPM is an extension of the finite element method (FEM), which is capable of modelling large deformations and soil-structure interactions. This study utilizes the moving mesh algorithm where a redefined computational mesh is applied in the convective phase. This allows a fine mesh to be maintained around the pile tip during the installation process and improves the accuracy of the numerical scheme, especially for contact formulation. For the analyses a hypoplastic constitutive model for sand is used, which takes into account density and stress dependent behaviour. The model performs well in situations with significant stress level changes because it accounts for very high stresses at the pile tip. Numerical results agree with centrifuge experiments at a gravitational level of 40 g. This analysis confirms the importance of pile installation effects in numerical simulations, as well as the proposed numerical approach’s ability to simulate installation and static load tests of jacked displacement piles.     

Vertical amplitude reduction of Rayleigh waves by a row of piles in a poroelastic half‐space

A row of rigid piles is addressed as the countermeasures for isolating Rayleigh waves in a poroelastic half‐space. The complex characteristic equations for Rayleigh waves are derived via Biot's theory and their existence conditions are given. The piles are modeled as Euler–Bernoulli beams with longitudinal displacements and the diffracted field by each pile is constructed only with Rayleigh waves. Six infinite linear systems of algebraic equations are obtained in terms of the equilibrium of forces and continuity of displacements at the pile–soil interfaces. The systems are subsequently solved in the complex least‐squares sense. The influence of certain pile and soil characteristics such as the permeability of poroelastic soil, spacing between the piles and length of the piles on the isolating performance of a pile barrier is investigated. Computed results show that the permeability of poroelastic soil displays a significant effect on the vertical amplitude reduction of Rayleigh waves. Copyright © 2009 John Wiley & Sons, Ltd.