层状地基中基于Laplace变换的桩基横向振动阻抗计算

基于Laplace变换,对层状地基中桩土横向振动阻抗计算问题进行了研究。考虑土层天然分层的特性及桩顶轴向力的参与作用,结合频域内桩-土动力文克尔理论,采用传递矩阵法并通过拉普拉斯变换,将振动微分方程变成代数方程以求解桩的横向振动响应参数,并导出了单桩横向振动阻抗。基于所得解,进一步计算出桩-土-桩水平动力相互作用因子。通过实例分析对比,验证其有效性和可行性。该方法计算工作量小,易于理解,计算结果与已有结果具有良好的一致性,并能保证解的连续性,对桩-土动力相互作用的研究具有一定的实用意义。     

隧道开挖引起邻近单桩水平反应分析

隧道开挖会降低邻近桩基承载力,如何更为合理评价桩基水平附加响应是需要解决的问题。基于Pasternak双参数地基模型和三折线弹塑性荷载传递模型,采用两阶段分析法,并考虑侧向土体作用及地基土层的非均质特性,提出了更符合实际的单桩水平反应简化分析方法。通过与Winkler地基梁法及边界元法的对比分析,验证了方法的合理性。结合对单桩水平反应的多种影响因素进行参数分析,通过各因素相应的修正系数来对基准工况中单桩最大水平反应进行修正,得到计算工况中单桩的最大水平位移和最大弯矩。分析结果表明,桩基水平位移计算时可忽略侧向土体作用,而弯矩计算时应予以考虑;桩基计算工况的最大水平位移 最大弯矩 与平均地层损失比 呈现线性关系,而与隧道半径R、隧道轴线深度H、桩距隧道中心线距离x及桩身柔度系数 均呈现非线性关系。     

文克尔地基模型下液化土桩基水平振动响应分析

在桩基顶部承受竖向荷载作用的条件下,将完全液化后的上层土体视为流体,将桩基等效为欧拉-伯努利梁模型,探讨了桩底嵌固时桩基顶部的水平振动阻抗。运用流体动力方程模拟顶部液化土层的运动,运用文克尔地基模拟下部非液化分层土的运动。结合传递矩阵法,利用液化土与非液化分层土交界面处的位移、转角和内力连续条件,得到桩基顶部和底部的相关位移?内力表达关系式。根据桩基底部的嵌固条件,求得桩顶阻抗的表达式。与已有文献解进行对比,验证了分析过程的正确性。对阻抗影响条件进行参数分析,表明液化深度、轴力和流体密度大小对桩顶阻抗有不同的影响。     

Axial kinematic response of end‐bearing piles to P waves

Kinematic pile–soil interaction under vertically impinging seismic P waves is revisited through a novel continuum elastodynamic solution of the Tajimi type. The proposed model simulates the steady‐state kinematic response of a cylindrical end‐bearing pile embedded in a homogeneous viscoelastic soil stratum over a rigid base, subjected to vertically propagating harmonic compressional waves. Closed‐form solutions are obtained for the following: (i) the displacement field in the soil and along the pile; (ii) the kinematic Winkler moduli (i.e., distributed springs and dashpots) along the pile; (iii) equivalent, depth‐independent, Winkler moduli to match the motion at the pile head. The solution for displacements is expressed in terms of dimensionless transfer functions relating the motion of the pile head to the free‐field surface motion and the rock motion. It is shown that (i) a pile foundation may significantly alter (possibly amplify) the vertical seismic excitation transmitted to the base of a structure and (ii) Winkler moduli pertaining to kinematic loading differ from those for inertial loading. Simple approximate expressions for kinematic Winkler moduli are derived for use in applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Three-dimensional analysis of a pile-group foundation

A non-linear three-dimensional finite element procedur is developed and applied for the analysis of pile group foundations. The numerical procedure allows for elastic, non-linear elastic and elastic-plastic hardening behaviour of sand. In order to include the interaction effects involving relative slip and debonding, the thin-layer interface element is used. The predictions for displacements and loads obtained from the numerical procedure are compared with laboratory model test results of a pile group. Displacements, stresses and forces distribution in various components of the pile group are also examined. Furthermore, the effects of the non-linear soil response and relative motions at the interface are indentified and discussed.     

Uncoupled analysis of stabilizing piles in weathered slopes

This paper describes a simplified numerical approach for analyzing the slope/pile system subjected to lateral soil movements. The lateral one-row pile response above and below the critical surface is computed by using load transfer approach. The response of groups was analyzed by developing interaction factors obtained from a three-dimensional nonlinear finite element study. An uncoupled analysis was performed for stabilizing piles in slope in which the pile response and slope stability are considered separately. The non-linear characteristics of the soil–pile interaction in the stabilizing piles are modeled by hyperbolic load transfer curves. The Bishop's simplified method of slope stability analysis is extended to incorporate the soil-pile interaction and evaluate the safety factor of the reinforced slope. Numerical study is performed to illustrate the major influencing parameters on the pile-slope stability problem. Through comparative studies, it has been found that the factor of safety in slope is much more conservative for an uncoupled analysis than for a coupled analysis based on three-dimensional finite element analysis.     

刚性桩复合地基地震响应的简化分析方法

面对越来越大量的工程应用,刚性桩复合地基的抗震性能成为亟待研究的课题。基于动力文克尔地基理论,提出了单桩复合地基的地震响应分析模型,推导了其地震响应的动力微分方程组,并构造了有限差分的求解方法,研究并探讨了不同影响因素变化下的地震响应性状,得到了一些有益于工程设计的规律性结论。     

Load transfer approach for laterally loaded piles

A two‐parameter model has been proposed previously for predicting the response of laterally loaded single piles in homogenous soil. A disadvantage of the model is that at high Poisson's ratio, unreliable results may be obtained. In this paper, a new load transfer approach is developed to simulate the response of laterally loaded single piles embedded in a homogeneous medium, by introducing a rational stress field. The approach can overcome the inherent disadvantage of the two‐parameter model, although developed in a similar way. Generalized solutions for a single pile and the surrounding soil under various pile‐head and base conditions were established and presented in compact forms. With the solutions, a load transfer factor, correlating the displacements of the pile and the soil, was estimated and expressed as a simple equation. Expressions were developed for the modulus of subgrade reaction for a Winkler model as a unique function of the load transfer factor. Simple expressions were developed for estimating critical pile length, maximum bending moment, and the depth at which the maximum moment occurs. All the newly established solutions and/or expressions, using the load transfer factor, offer satisfactory predictions in comparison with the available, more rigorous numerical approaches. The current solutions are applicable to various boundary conditions, and any pile–soil relative stiffness. Copyright © 2001 John Wiley & Sons, Ltd.     

浅埋隧道施工对建筑物桩基的影响分析

浅埋隧道穿越上部桩基础的问题值得关注。在概述目前研究成果的基础上,采取两阶段分析方案,利用分层土体的剪切位移法,着重分析了浅埋隧道开挖引起的土体移动对隧道顶桩位移及轴力的影响,并与整体有限元计算结果进行了比较,结果表明该计算方法是合理的,且计算量小,无需建立复杂的计算模型,在工程领域有较好的实用性。     

A Winkler model approach for vertically and laterally loaded piles in nonhomogeneous soil

An investigation is made to present analytical solutions provided by a Winkler model approach for the analysis of single piles and pile groups subjected to vertical and lateral loads in nonhomogeneous soils. The load transfer parameter of a single pile in nonhomogeneous soils is derived from the displacement influence factor obtained from Mindlin's solution for an elastic continuum analysis, without using the conventional form of the load transfer parameter adopting the maximum radius of the influence of the pile proposed by Randolph and Wroth. The modulus of the subgrade reaction along the pile in nonhomogeneous soils is expressed by using the displacement influence factor related to Mindlin's equation for an elastic continuum analysis to combine the elastic continuum approach with the subgrade reaction approach. The relationship between settlement and vertical load for a single pile in nonhomogeneous soils is obtained by using the recurrence equation for each layer. Using the modulus of the subgrade reaction represented by the displacement influence factor related to Mindlin's solution for the lateral load, the relationship between horizontal displacement, rotation, moment, and shear force for a single pile subjected to lateral loads in nonhomogeneous soils is available in the form of the recurrence equation. The comparison of the results calculated by the present method for single piles and pile groups in nonhomogeneous soils has shown good agreement with those obtained from the more rigorous finite element and boundary element methods. It is found that the present procedure gives a good prediction on the behavior of piles in nonhomogeneous soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Selection of p–y curves for the design of single laterally loaded piles

Two-dimensional finite element analysis has been used to find load–transfer relationships for translation of an infinitely long pile through undrained soil for a variety of soil-constitutive models. It has been shown that these load–transfer curves can be used as p–y curves in the analysis of single piles undergoing lateral pile head loading in undrained soils with non-linear stress–strain laws. Lateral pile response deduced from 2-D analysis input to the subgrade reaction method has been compared to the behaviour of a single pile analysed using three-dimensional finite element analysis. Good agreement between the two methods for non-linear soils suggests that the 2-D analysis may form a useful design method for calculation of p–y curves. Copyright © 1999 John Wiley & Sons, Ltd.     

隧道开挖对邻近单桩竖向受力特性影响

在分析隧道开挖对邻近单桩竖向受力特性影响时,基于荷载传递法和Winkler地基模型,利用两阶段分析法通过迭代求解给出隧道开挖与邻近单桩相互作用的弹塑性解答。通过与离心机试验的短期和长期试验结果的对比,分析了隧道开挖对邻近单桩的竖向影响,从而验证该方法的合理性和适用性。讨论了隧道开挖情况下隧道中心线距地表的距离、隧道中心线与桩轴线的距离、平均地层损失比、桩长、桩径、桩身强度6种因素对邻近单桩竖向受力特性的影响,提出隧道开挖对邻近单桩的竖向受力特性的影响规律。结果表明：随着隧道中心线距地表距离的增加,桩身沉降和桩身轴力先增大然后逐渐减小;随着隧道轴线与桩轴线距离的增加,桩身沉降逐渐减小,桩身轴力增大到一定值后逐渐减小;随着平均地层损失比的增加桩身沉降不断增大,桩身轴力逐渐增大到稳定值。     

两阶段法分析基坑开挖对邻近桩基的影响

采用两阶段分析方法,基于Winkler地基模型以及桩土变形协调条件,建立单桩水平位移控制方程。应用简化Mindlin方程,分析桩-桩相互作用及桩-土相互影响。结合以上几点,建立群桩控制微分方程组求解。最后的算例分析将该方法的计算结果与离心机试验结果进行对比。     

基于影像源法的基坑开挖对邻近单桩影响简化分析

邻近建筑物进行基坑开挖会使桩基产生附加变形和内力,降低其承载能力,如果桩基变形过大会威胁到上部结构的安全。针对该领域目前存在的三维有限元数值模拟法建模复杂且计算耗时的现状,同时为了充分利用基坑围护位移较易通过现场监测技术获取的优势,提出了基于影像源法的基坑开挖引起邻近单桩变形影响的两阶段简化分析方法。同时,引入了Kerr地基模型,并针对Winkler地基模型进行改进,弥补了Winkler地基不能考虑土体连续性的缺陷。在第1阶段基于影像源法,由基坑围护变形计算基坑开挖引起的土体水平自由场位移;第2阶段分别基于Winkler和Kerr地基模型,将土体自由场位移施加于桩基,建立桩基在被动位移扰动下的微分控制方程,得到基坑开挖对邻近桩基影响的简化解析解,包括基坑开挖引起桩基的水平位移、弯矩和剪力等。将计算结果与既有理论结果、监测数据以及三维有限元数值模拟结果进行对比,取得了较好的一致性,其中基于Kerr地基模型的简化解比基于Winkler地基模型的简化解更为精确。该简化方法可为有效分析基坑开挖对邻近桩基的变形影响提供一定理论依据。     

基于Winkler模型的有效桩长研究

有效桩长的定义有基于承载力角度和沉降角度两种方法,由于影响因素的多样性,有效桩长的研究比较复杂。运用桩顶刚度控制法确定有效桩长。基于Winkler地基模型,以荷载传递法为工具,推导出双层土的桩顶刚度计算公式,并对有效桩长影响因素进行了分析。结果表明,桩径的增大有效桩长增加;土层刚度比(第二层土刚度与第一层土刚度之比)增大有效桩长减小;桩端刚度的增大对有效桩长的影响都不明显,第一土层厚度的增加在一定范围内对提高有效桩长是有用的     

Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model is investigated to provide analytical solutions of settlement of a rectangular pile subjected to vertical loads in nonhomogeneous soils. For a vertically loaded pile with a rectangular cross section, the settlement influence factor of a normal pile in nonhomogeneous soils is derived from Mindlin's solution for elastic continuum analysis. For short piles with rectangular and circular cross sections, the modified forms of settlement influence factors of normal piles are produced taking into account the load transfer parameter proposed by Randolph for short circular piles. The modulus of subgrade reaction along a rectangular pile in nonhomogeneous soils is expressed by using the settlement influence factor related to Mindlin's solution to combine the elastic continuum approach with the subgrade‐reaction approach. The relationship between settlement and vertical load for a rectangular pile in nonhomogeneous soils is available in the form of the recurrence equation. The formulation of settlement of soils surrounding a rectangular pile subjected to vertical loads in nonhomogeneous soils is proposed by taking into account Mindlin's solution and both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. The difference of settlement between square and circular piles is insignificant, and the settlement of a rectangular pile decreases as the aspect ratio of the rectangular pile cross section increases. The comparison of results calculated by the present method for a rectangular pile in nonhomogeneous soils has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of vertically loaded pile groups

An approach is presented for the analysis of linear and non-linear responses of vertically loaded pile groups. The soil behaviour of individual piles in modelled using load-transfer curves and the pile-soil-pile interaction is determined based on Mindlin's solution. Good agreement between the present method of analysis and the rigorous boundary integral method is observed for the computation of the response of pile groups embedded in a homogeneous, isotropic elastic half-space. The computed non-linear response of pile groups compares favourably with measured results from field load tests.     

基于荷载传递法的单桩非线性受力性状分析软件开发及其应用

基于荷载传递法的单桩非线性受力性状分析软件,可灵活选用不同的荷载传递函数如双曲线模型和软化模型等分析单位侧阻与桩土相对位移间的关系及桩端位移和桩端阻力间的关系,并将桩分成若干桩段以考虑地基土的成层性,且在分析单桩的非线性受力性状的过程中可考虑地下水的影响。该软件得出的单桩受力性状与实际情况吻合较好,提出的基于荷载传递法的单桩非线性受力性状的分析软件是合理可行的,在单桩非线性受力性状的分析上具有一定的实用价值。     

Analysis of piled raft with nodular pile subjected to vertical load using a Winkler model approach

An investigation is made to present analytical solutions provided by a Winkler model approach for analysis of piled rafts with nodular pile subjected to vertical loads in nonhomogeneous soils. The vertical stiffness coefficient along a piled raft with the nodular pile in nonhomogeneous soils is derived from the displacement given by the Mindlin solution for elastic continuum analysis. The vertical stiffness coefficients for the bases of the raft and the nodular part in the nodular pile in a soil are expressed by the Muki solution for the 3‐D elastic analysis. The relationship between settlement and vertical load on the pile base is presented considering the Mindlin solution and the equivalent thickness in the equivalent elastic method. The interaction factor between the shaft of the nodular pile and the soil is expressed taking into account the Mindlin solution and the equivalent elastic modulus. The relationship between settlement and vertical load for a piled raft with the nodular pile in nonhomogeneous soils is obtained by using the recurrence equation of influence factors of the pile for each layer. The percentage of each load carried by both nodular pile and raft subjected to vertical load is represented through the vertical influence factors proposed here. Comparison of the results calculated by the present method for piled rafts with nodular piles in nonhomogeneous soils has shown good agreement with those obtained from the finite element method and a field test. Copyright © 2016 John Wiley & Sons, Ltd.     

双排抗滑桩上滑坡推力近似解析方法

双排抗滑桩是加固大型滑坡的常用工程措施之一,在实际工程设计计算中的关键环节在于简单且合理地确定作用于前后排桩上的滑坡推力。将抗滑桩受荷段前侧坡体视为水平向的温克勒（Winkler）地基,基于弹性地基梁模型,并充分考虑桩体受荷段与锚固段的变形连续性,通过迭代算法确定出后排抗滑桩受荷段前侧坡体抗力,进而可对排间坡体采用传递系数法计算出前排桩桩后滑坡推力,给出了相关的理论计算公式。通过室内模型试验验证了所提方法的合理性,并针对一大型基覆式滑坡实例,具体计算出了前后排桩上的设计滑坡推力荷载。所提计算方法可为实际工程的简化设计提供参考。