Displacement interaction among energy piles bearing on stiff soil strata

This study presents an analysis of the displacement interaction among general configurations of energy piles bearing on stiff soil strata that are subjected to thermal loads. This work integrates recent analyses investigating the displacement interaction among predominantly floating energy piles subjected to thermal loads in deep uniform soil deposits. To address this challenge, design charts for energy piles resting on either infinitely or finitely rigid soil strata are presented, applied and validated for the analysis of the vertical displacement of predominantly end-bearing energy pile groups subjected to thermal loads using the interaction factor method.     

能量桩群桩工作特性简化分析方法研究

采用双曲线模型模拟桩土界面上的力学行为,利用剪切位移法反映剪应力在土层中的传递,考虑群桩之间的相互作用,建立了热?力耦合作用下能量桩群桩基础工作特性的简化分析方法。该方法能反映桩土界面上的非线性、桩顶的约束条件和能量桩位置的影响,可直接计算所有桩的位移和轴力。与现有方法相比,计算得到的双桩相互作用因子更加合理。通过与文献中试验数据的对比表明,若只有局部桩经历温度变化,能量桩运行过程中各桩之间存在差异变形,基础出现倾斜,桩顶荷载发生重分布。所建立方法计算方便,能合理模拟能量桩群桩基础的主要工作特性,可用于大规模能量桩群桩基础的设计计算。     

基于能量法的轴横向荷载作用下单桩受力变形分析

轴向和横向荷载作用下单桩的受力变形分析是桩基研究的重点内容之一。单桩在水平荷载作用下会产生一定的水平位移与弯矩,而此时作用轴向荷载会使得桩体出现一定的压曲与附加弯矩,以致轴横向荷载作用下的单桩受力变形与单独作用水平荷载或轴向荷载的单桩存在较大的区别。故本文基于能量法,首先分别建立轴横向荷载作用下单桩的受力变形能量方程以及桩周土体能量方程,然后考虑桩土变形协调与一定的桩土相互作用,基于最小势能原理得到单桩变形控制微分方程,并采用幂级数法进行求解,最终得到轴横向荷载作用下单桩受力变形分析的幂级数解答。通过编程计算,将本文方法计算结果与试验结果、数值分析结果、规范法计算结果进行对比分析,验证了本文方法的合理性和可行性。在此基础上,基于本文解答进行了影响参数分析,结果表明:桩体长径比、桩土弹性模量比、桩周土模量深度变化系数均对轴横向受荷单桩的桩身水平位移与最大弯矩值有一定的影响,其中桩周土模量深度变化系数以不小于0.6为宜。     

The interaction factor method for energy pile groups

Prior to this study, no simplified yet rational methods were available for estimating the vertical displacements of energy pile groups subjected to thermal loads. Observing such a challenge, the goal of this study has been threefold: (i) to extend the interaction factor concept from the framework of conventional pile groups to that of energy pile groups, (ii) to present charts for the analysis of the displacement interaction between two identical energy piles over a broad range of design conditions, and (iii) to propose, apply and validate the interaction factor method for the displacement analysis of energy pile groups.     

多向荷载作用下层状地基刚性桩筏基础分析

提出一种多向荷载作用下层状地基中刚性桩筏基础的计算方法。基于剪切位移法,采用传递矩阵形式分析了竖向荷载下桩顶面-桩顶面相互作用;引入修正桩侧地基模量,采用有限差分法分析了水平荷载下桩顶面-桩顶面相互作用;基于层状弹性半空间理论,分析了多向荷载下桩顶面-土表面、土表面-桩顶面、土表面-土表面的相互作用关系。建立了桩土体系柔度矩阵,得到了多向荷载下层状地基中刚性桩筏基础的受力和变形的关系以及桩的内力和变形沿桩身分布规律。通过与有限元对比,验证了该方法的合理性和修正地基模量的优越性,并对多向荷载作用下的桩筏基础进行了计算分析,计算结果表明,水平力将会引起桩筏基础的倾斜。     

Response of Pile Groups Driven in Sand Subjected to Combined Loads

Although the loads applied on piles are usually a combination of both vertical and lateral loads, very limited experimental research has been done on the response of pile groups subjected to combined loads. Due to pile–soil–pile interaction in pile groups, the response of a pile group may differ substantially from that of a single pile. This difference depends on soil state and pile spacing. This paper presents results of experiments designed to investigate pile interaction effects on the response of pile groups subjected to both axial and lateral loads. The experiments were load tests performed on model pile groups (2 × 2 pile groups) in calibration chamber sand samples. The model piles were driven into the sand samples prepared with different relative densities using a sand pluviator. The combined load tests were performed on the model pile groups subjected to different axial load levels, i.e., 0 (pure lateral loading), 25, 50, and 75% of the ultimate axial load capacity of the pile groups, defined as the load corresponding to a settlement of 10% of the model pile diameter. The combined load test results showed that the bending moment and lateral deflection at the head of the piles increased substantially for tests performed in the presence of axial loads, suggesting that the presence of axial loads on groups of piles driven in sand is detrimental to their lateral capacity.     

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.     

Thermo-mechanical behavior of energy piles in high plasticity clays

Energy piles make use of constant and moderate ground temperature for efficient thermal control of buildings. However, this use introduces new engineering challenges because the changes of temperature in the foundation pile and ground induce additional deformations and forces in the foundation element and coupled thermo-hydro-mechanical phenomena in the soil. Several published full-scale tests investigated this aspect of energy piles and showed thermally induced deformation and forces in the foundation element. In parallel, significant progress has been made in the understanding of thermal properties of soils and on the effect of cyclic thermal load on ground and foundation behavior. However, the effect of temperature on the creep rate of energy piles has received practically no attention in the past. This paper reports the experimental results of an in situ tension thermo-mechanical test on an energy pile performed in a very stiff high plasticity clay. During the in situ test, the pile was subjected to thermal loading by circulating hot water in fitted pipes, simulating a thermal load in a cooling-dominated climate, at different levels of mechanical loading. The axial strain and temperature in the pile, and the load–displacement of the pile were monitored during the tension test at different locations along the center of the pile and at the pile head, respectively. The data showed that as the temperature increases, the observed creep rate of the energy pile in this high plasticity clay also increases, which will lead to additional time-dependent displacement of the foundation over the life time of the structure. It was also found that the use of geothermal piles causes practically insignificant thermally induced deformation and loads in the pile itself.     

Analysis of rectangular piles subjected to lateral loads in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model based on two lateral soil displacement components in a three‐dimensional soil is investigated to provide analytical solutions of horizontal response of a rectangular pile subjected to lateral loads in nonhomogeneous soil. The two lateral displacement components of a soil surrounding the rectangular pile are represented by the Fourier series of displacement potential functions in the elastic three‐dimensional analysis. The lateral stiffness coefficient of the rectangular pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient taking into account rocking rotation of a rigid pile shaft. The relationship between horizontal displacement, rotation, moment, and shear force for the rectangular pile subjected to horizontal loads in nonhomogeneous soil is obtainable in the form of the recurrence equation. The formulation of lateral displacement and rotation for a rectangular pile subjected to lateral loads on the pile base in nonhomogeneous soil is proposed by taking into account Mindlin's equation and the equivalent thickness for soil layers in the equivalent elastic method. The difference of lateral behavior between square and circular piles subjected to lateral loads is insignificant. The effect of aspect ratio of the rectangular pile on the lateral behavior is great for the lower stiffness ratio between pile and soil and the larger length–equivalent diameter ratio. The effect of the value of Poisson's ratio of soil on lateral stiffness coefficient is relatively small except Poisson's ratio close to 0.5. The comparison of the results calculated by the current method for a rectangular pile subjected to lateral loads in nonhomogeneous soil has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2015 John Wiley & Sons, Ltd.     

基于两阶段法的堆载对公路桥梁桩基础影响分析

首先基于布西奈斯克解,将表面作用有集中荷载时半无限弹性体的应力变形解在荷载作用区域利用复合辛普森公式进行数值积分,得到了表面处于不同形式的分布荷载作用下土体自由场水平及竖直方向应力和变形的计算公式。结合有限差分法及Mindlin位移解分别推导出弹性地基中桩顶作用有集中荷载时单桩桩、土单元的位移,两者结合便得到主动桩的分析方法。通过将堆载作用下的土体自由场位移施加于桩上把上述自由场分析及主动桩分析结合起来,推导出堆载作用下被动单桩的竖向和水平向承载特性的分析方法。选取地表附近作用有矩形均布荷载的计算工况,通过与有限元计算结果的对比验证了所提出的分析方法的正确性;将所提出的方法计算结果与某处工程案例中实测数据结果进行对比,分析表明利用该方法分析堆载对邻近桩基的水平及竖向影响是合理可靠的。     

A simplified analysis method for piled raft and pile group foundations with batter piles

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to vertical, lateral, and moment loads, using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. Both the vertical and lateral resistances of the piles as well as the raft base are incorporated into the model. Pile–soil–pile, pile–soil–raft and raft–soil–raft interactions are taken into account based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with several existing methods for single piles, pile groups and piled rafts. Workable design charts are given for the estimation of the lateral displacement and the load distribution of piled rafts from the stiffnesses of the raft alone and the pile group alone. Additionally, parametric studies were carried out concerning batter pile foundations. It was found that the use of batter piles can efficiently improve the deformation characteristics of pile foundations subjected to lateral loads. Copyright © 2002 John Wiley & Sons, Ltd.     

Development of a three-dimensional soil model for the dynamic analysis of end-bearing pile groups subjected to vertical loads

This paper presents a new analytical model for calculating the steady-state impedance of pile groups subjected to vertical dynamic loads. The derived solution allows considering effects of radially but also vertically propagating soil waves on the soil attenuation function, pile interaction factor, and pile group impedance. The proposed model provides accurate estimates of the soil stress field and of the response of the pile group in the low as well as in the high-frequency range, unlike earlier solutions based on the plane-strain model to describe the soil surrounding the piles, which ignores the vertical soil stress gradient. The latter assumption results in underestimating pile group impedance and overestimating radiation damping for frequencies lower than the cutoff frequencies of the system, which are explicitly captured with the proposed solution.     

导管架平台桩-土相互作用试验系统研制及应用

海洋环境中的导管架平台承受着风浪、地震等水平荷载,而平台的稳定对桩基础有严格要求,故研究水平荷载下导管架平台桩-土系统变形规律和相互作用机制具有重要意义。研制了1套导管架平台桩-土相互作用试验系统,主要由导管架平台试验模型子系统、电动伺服加载子系统、传感器与数据采集子系统、振动测试子系统组成,可用于研究冲击荷载、静载、循环荷载下导管架平台的桩身变形规律、桩基周围土体响应及平台的振动特性。通过初步试验结果表明,该系统能够如实反映水平荷载下桩-土间的相互作用和导管架平台的振动特性,验证了该系统的有效性。     

Three-dimensional finite element study of a single pile response to multidirectional lateral loadings incorporating the simplified state-dependent dilatancy model

Waves and winds can induce lateral loads on piles, which are often multidirectional. The objective of this study is to investigate the response of a single pile subjected to unidirectional and multidirectional lateral loadings using the finite element analysis program ABAQUS. A simplified version of the state-dependent dilatancy model was implemented and embedded into the program to simulate the behavior of the soil around the pile. The results of the analyses indicate that the lateral resistance of the pile along one horizontal direction under multidirectional loading is lower than that under unidirectional loading. The degree of reduction of the resistance increases with the aspect ratio of the displacement path at the pile head. The directions of the force increment vector and the displacement increment vector are generally non-coaxial under multidirectional loading. The soil-pile interaction and soil responses under multidirectional loading are also significantly different than those under unidirectional loading.     

Analysis of piles subjected to lateral soil movements using a three‐dimensional displacement approach

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral soil movements in nonhomogeneous soil. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient that is obtained from the analytical solution, taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to lateral soil movements in nonhomogeneous soil is obtainable in the form of the recurrence equation. For the relationship between the lateral pressure and the horizontal displacement, it is assumed that the behavior is linear elastic up to lateral soil yield, and the lateral pressure is constant under the lateral soil yield. The interaction factors between piles subjected to both lateral load and moment are calculated, taking into account the lateral soil movement. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account the Mindlin equation and the equivalent thickness for soil layers in the equivalent elastic method. For lateral movement, lateral pressure, bending moment, and interaction factors, there are small differences between results obtained from the 1‐D and the 3‐D displacement methods except a very flexible pile. Copyright © 2015 John Wiley & Sons, Ltd.     

水平荷载作用下风电机桩基础的离心模型试验研究

桩基础是近海风机经常采用的基础形式。由于风电机组对基础的承载力和变形有着严格的要求,而水平荷载常常是控制荷载,因此,研究水平荷载作用下风机桩基础的应力、变形特性具有重要意义。针对风机单桩基础,选取典型的黏土地基,进行了水平加载条件下的离心模型试验,重点分析了桩身的响应及桩周围土体的变形特点。试验结果表明,在水平荷载作用下,桩顶的水平位移随着水平力的增加而增加,位移的增加速率在临界荷载之后增长较快;桩身弯矩分别在埋深1/5和3/5处附近分别出现极大值和极小值,且桩底具有一定弯矩值;桩周围土体的变形随着离桩距离的增加而减小,可分为主动区和被动区。桩对土体变形的影响区域随着水平力的增加而不断扩展,最后基本稳定在2倍桩径范围内。     

A new dynamic interaction factor for the analysis of pile groups subjected to vertical dynamic loads

Τhis paper presents an analytical method for calculating the steady-state impedance factors of pile groups of arbitrary configuration subjected to harmonic vertical loads. The derived solution allows considering the effect of the actual pile geometry on the contribution of pile-soil-pile interaction to the response of the group, via the introduction of a new dynamic interaction factor, defined on the basis of soil resistance instead of pile displacements. The solution is first validated against a published solution for single piles that accounts for the effect of pile geometry on the generated ground vibrations. Accordingly, we show that the derived soil attenuation factor agrees well with existing solutions for pile groups in the high frequency range, but considerable differences are observed in both the stiffness and damping components of the computed impedance when the relative spacing between piles decreases. Numerical results obtained for typical problem parameters suggest that ignoring pile geometry effects while estimating the contribution of pile-soil-pile interaction in the response may lead to inaccurate results, even for relative large pile group spacings.

     

A three‐dimensional displacement approach for analysis of laterally loaded piles in nonhomogeneous soil

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral loads in nonhomogeneous soil. The rocking stiffness coefficient of the pile shaft in homogeneous soil is derived from the analytical solution taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient taking into account the rocking rotation of a rigid pile shaft. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to horizontal loads in nonhomogeneous soil is obtainable in the form of the recurrence equation. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account Mindlin's equation and the equivalent thickness for soil layers in the equivalent elastic method. There is little difference between lateral, rocking, and couple stiffness coefficients each obtained from both the two‐dimensional and three‐dimensional methods except for the case of Poisson's ratio near 0.5. The comparison of results calculated by the current method for a pile subjected to lateral loads in homogeneous and nonhomogeneous soils has shown good agreement with those obtained from analytical and numerical methods. Copyright © 2017 John Wiley & Sons, Ltd.     

考虑桩桩相互作用的双排支护桩受力变形分析

双排桩支护结构的变形与内力计算是其设计计算的重要内容之一。双排支护桩结构是由前排桩、后排桩及桩顶连系梁组成的空间门架式结构。在承受水平荷载时,后排桩向坑内发生挠曲变形,挤压桩间土体,同时桩间土体又对前排桩产生推力,使得前排桩向坑内发生挠曲变形,挤压前排桩桩前土体,以致该支护结构在传递水平荷载时,前后排桩及桩间土体之间存在非常复杂的相互作用。本文基于上述双排桩支护结构受力变形特性,将前、后排桩均视为竖向放置的弹性地基梁,以欧拉伯努利双层梁理论考虑前后排桩的相互作用,以水平向弹簧模拟桩间土相互作用,以朗肯土压力计算作用于后排桩的主动土压力,以弹性抗力法计算作用于前排桩基坑底面以下的被动土压力,以基坑底面为界人为将前、后排桩分为上下部分,并通过桩身各段的受力平衡建立前后排桩的挠曲变形控制微分方程,然后通过桩端约束及基坑坑底平面处的连续条件得到方程的解析解,给出了一种考虑桩桩相互作用以及桩土相互作用的双排桩支护结构计算方法。最后结合两个实例,将本文方法计算结果与实例结果进行对比分析,验证本文方法的可行性,以期为双排桩支护结构在工程中的设计计算提供借鉴。     

Seismic response of pile foundations in liquefiable soil: parametric study

The performance of pile foundations in liquefiable soil subjected to earthquake loading is a very complex process. The strength and stiffness of the soil decrease due to the increase in pore pressure. The pile can be seriously destroyed by the soil liquefaction during strong earthquakes. This paper presents the response of vertical piles in liquefiable soil under seismic loads. A finite difference model, known as fast Lagrangian analysis of continua, is used to study the pile behavior considering a nonlinear constitutive model for soil liquefaction and pile?Csoil interaction. The maximum lateral displacement and maximum pile bending moment are obtained for different pile diameters, earthquake predominant frequencies, Arias intensities, and peak accelerations. It is found that the maximum lateral displacement and the maximum pile bending moment increase when the predominant earthquake frequency value decreases for a given peak acceleration value.