A superposition scheme to obtain fundamental boundary element solutions in multi‐layered elastic media

A superposition scheme is proposed to obtain a fundamental solution for boundary elements in multi‐layered elastic media. A three‐layered elastic region is obtained by superposing two sets of bonded half‐planes and subtracting one infinite plane. Therefore, the solution for an element in a layered media can be expressed in terms of bonded half‐plane solutions and an infinite‐plane solution. The major advantages of this superposition scheme are: (1) it is unnecessary to introduce elements at the interface, (2) it can be extended to higher‐order element, and (3) it may be applicable to three dimensions easily. The accuracy and performance of the developed model is illustrated by two examples. For the problem of a pressurized two‐dimensional crack within a three‐layered system, the comparison with other numerical results shows the model is quite accurate and efficient. The model is also used for a study of a practical two‐dimensional mining problem in South Africa, i.e. stoping through a dyke with material properties different from the host rock. Copyright © 2000 John Wiley & Sons, Ltd.     

层状土中多缺陷桩的导纳曲线计算及初步应用

本文应用第一作者曾提出的不均匀土中多缺陷桩动力学模型和单因素分析法,对导纳曲线进行分析,获取桩身完整性信息.     

Vertical impedance of an end‐bearing pile in viscoelastic soil

This paper presents a new method to derive the analytical solution for the vertical impedance of an end‐bearing pile in viscoelastic soil. The soil is assumed as a homogeneous and isotropic layer, and the pile is considered as a one‐dimensional Euler rod. Considering both the vertical and radial displacements of soil and soil–pile coupled vibration, the governing equations of the soil and pile are established. The volumetric strain of soil is obtained by transformation on the equations of soil and variable separation method. Then the vertical and radial displacements of soil are obtained accordingly. The displacement response and impedance function of pile are derived based on the continuity assumption of the displacement and stress between the pile and soil. The solution is verified by being compared with an existing solution obtained by introducing potential functions. Furthermore, a comparison with two other simplified solutions is conducted. Numerical examples are presented to analyze the vibration characteristics of the pile. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of pile‐raft foundations under complex loads in layered soils

Considering there is hardly any concerted effort to analyze the pile‐raft foundations under complex loads (combined with vertical loads, horizontal loads and moments), an analysis method is proposed in this paper to estimate the responses of pile‐raft foundations which are subjected to vertical loads, horizontal loads and moments in layered soils based on solutions for stresses and displacements in layered elastic half space. Pile to pile, pile to soil surface, soil surface to pile and soil surface to soil surface interactions are key ingredients for calculating the responses of pile‐raft foundations accurately. Those interactions are fully taken into account to estimate the responses of pile‐raft foundations subject to vertical loads, horizontal loads and moments in layered soils. The constraints of the raft on vertical movements, horizontal movements and rotations of the piles as well as the constraints of the raft on vertical movements and horizontal movements of the soils are considered to reflect the coupled effect on the raft. The method is verified through comparisons with the published methods and FEM. Then, the method is adopted to investigate the influence of soil stratigraphy on pile responses. The study shows that it is necessary to consider the soil non‐homogeneity when estimating the responses of pile‐raft foundations in layered soils, especially when estimating the horizontal responses of pile‐raft foundations. The horizontal loads and the moments have a significant impact on vertical responses of piles in pile‐raft foundations, while vertical loads have little influence on horizontal responses of piles in pile‐raft foundations in the cases of small deformations. The proposed method can provide a simple and useful tool for engineering design. Copyright © 2013 John Wiley & Sons, Ltd.     

Settlements and stresses of multi‐layered grounds and improved grounds by equivalent elastic method

The investigation of equivalent elastic method is made to predict settlements and stresses of multi‐layered grounds and improved grounds. Analytical models to represent the heterogeneous elastic properties of layers in vertical and horizontal directions for multi‐layered grounds and improved grounds are proposed in taking into account the equivalent elastic modulus and the equivalent thickness. By introducing the equivalent thickness derived from Terzaghi's formula of the vertical stress, the equivalent elastic method of using the equivalent elastic modulus and the equivalent thickness is applied to the formulations concerning immediate settlements and vertical stresses in multi‐layered grounds and improved grounds. Comparison is performed between rigorous solutions and simulations for immediate settlements and vertical stresses in multi‐layered grounds and improved grounds. It is found that the proposed method is able to describe properly the characteristics of distributions for settlements and vertical stresses in multi‐layered grounds and improved grounds. Copyright © 2007 John Wiley & Sons, Ltd.     

层状地基中轴向受荷单桩的边界元法分析

以层状地基内部作用一竖向集中力时的广义Mindlin解作为边界单元法的基本解,对层状地基中的轴向受荷单桩进行了分析,对基本解的奇异性处理方法进行了改进。考虑了桩的可压缩性和长径比对桩-土荷载传递规律和沉降特性的影响,编制了计算程序,并进行了数值分析和计算。结果表明,该方法具有较快的计算速度和良好的计算精度。     

Method of initial parameters for laterally loaded piles embedded in layered soils

The method of initial parameters (MIP) was originally developed to solve the problem of a beam on an elastic foundation with applied concentrated forces along the span, which introduce discontinuities in the mathematical formulation of the problem. MIP is modified in this paper so that it can be used for solving the problem of a laterally loaded pile with discontinuities due to soil layering along the length of the pile. In this paper, the basis of MIP is outlined, and its use to find the deflection, slope, bending moment and shear force of laterally loaded piles is illustrated. Example problems of laterally loaded piles embedded in multi-layered soil media are provided.     

横观各向同性地基中管桩扭转振动响应解析解

考虑地基沉积过程中产生的竖向和水平向力学性质的差异,对横观各向同性地基中管桩扭转振动频域响应进行了理论研究。基于横观各向同性材料的本构关系以及桩-土耦合扭转振动,建立了桩土系统定解问题,通过Laplace变换和分离变量法求得了桩周土和桩芯土扭转振动位移形式解。通过桩-土接触面的连续条件,求得了管桩扭转频域响应解析解,并得到了桩顶复动刚度和速度导纳的表达式。将所得解退化到横观各向同性地基中实心桩解以及均匀地基中管桩解,并与已有文献进行了对比,验证了解的合理性。通过数值算例,分析了桩周土和桩芯土的横观各向同性力学参数对桩顶扭转复刚度及速度导纳的影响。     

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.     

地下管线弹性波探测波场的建模与分析

在地下管线弹性波探测中,由位于地下圆孔边界上有限时长的力源激发形成瞬态场,应用波函数展开法对此波场进行建模。以波函数和待定系数组成的级数序列描述探测波场中的势函数,根据界面处应力和位移连续的边界条件求解待定系数,从而得到波场中弹性波的解析解。据此进行数值研究,分析探测波场中弹性波的传播特征,说明了散射波的类型以及能量对比关系,并总结了反射信号幅值与地下管线物理参数之间由声阻抗匹配程度支配的反射信号强度变化规律,而管线半径对反射信号强度的影响要大于物理参数的作用。最后以实验结果验证上述结论。     

Consolidation analysis of saturated multi‐layered soils with anisotropic permeability caused by a point sink

This paper presents the analytical layer‐element method to analyze the consolidation of saturated multi‐layered soils caused by a point sink by considering the anisotropy of permeability. Starting from the governing equations of the problem, the solutions of displacements and stresses for a single soil layer are obtained in the Laplace–Hankel transformed domain. Then, the analytical layer‐element method is utilized to further derive the solutions for the saturated multi‐layered soils in the transformed domain by combining with the boundary conditions of the soil system and continuity conditions between adjacent layers. The actual solutions in the physical domain can be acquired by the inversion of Laplace–Hankel transform. Numerical results are carried out to show the accuracy and stability of the proposed method and evaluate the influence of sink depth and anisotropic permeability on excess pore pressure and surface settlement. Copyright © 2011 John Wiley & Sons, Ltd.     

弹性矩形板下横观各向同性多层地基分析

利用弹性矩形板与多层地基表面的竖向位移协调条件与光滑接触条件,由横观各向同性多层地基应力与位移非耦合的传递矩阵解,推导出弹性矩形板下竖向应力和位移的解析解。在此基础上,编制了相应的程序,并进行了数值计算。计算结果表明：矩形板刚度对板底竖向位移及板中心下的竖向应力有着较为显著的影响;板底竖向位移及板中心下的竖向应力随着板刚度的增加而减小,相同荷载作用下横观各向同性地基与均匀各向同性地基模型的计算结果差异较大,实际工程中很有必要采用更符合土体性质的横观各向同性地基模型     

黏弹性地基中PCC桩扭转振动响应解析方法研究

考虑土体材料的黏性阻尼和桩-土扭转耦合振动,把桩看作一维杆,将土体视作三维轴对称黏弹性介质,对黏弹性地基中现浇混凝土大直径管桩（简称PCC桩）扭转振动频域特性进行了理论研究,采用Laplace变换和分离变量的方法求得了桩顶扭转频域响应解析解。将所得解完全退化到实心桩的解,并与经典平面应变解进行对比,验证了解析解的合理性。分析了桩长以及土体黏性阻尼系数对桩顶速度导纳和复动刚度的影响,得到了各参数对桩扭转振动特性影响的规律。分析表明：桩周土黏性阻尼系数增大可以显著提高桩顶扭转复动刚度和减小速度导纳振荡幅值,而桩芯土黏性阻尼系数的影响不明显;桩长越长,桩顶复动刚度越大,速度导纳振荡幅值越小,但当桩长增大到一定程度时,再继续增加桩长,桩顶复动刚度基本没有改变。     

顶管推进引起施工场地竖向附加荷载分析

基于层状体系解析刚度矩阵理论解,结合5节点Gauss-Legendre求积公式,提出了层状地基中顶管施工正面附加推力、掘进机与土体之间摩擦力以及共同作用力引起的附加荷载计算方法,分析了顶管推进引起的土体竖向附加荷载分布规律,也研究了地基等效均质性、土层力学参数、计算点间距以及顶管埋深等因素对顶管施工诱发附加荷载的影响效应。研究结果表明,掘进摩擦力引起的附加荷载在掘进面前方迅速达到压应力峰值,其量值大小和影响范围均要大于正面附加推力,是顶管施工引起临近地层附加荷载的主要影响因素。此外,层状地基土体参数的改变会对顶管施工扰动地层的附加荷载产生一定影响,地基等效均质性、计算点间距以及顶管埋深等因素对附加荷载大小及分布均存在显著影响。成果可为合理制定顶管开挖对周围土工环境的保护措施提供一定理论依据,也可为其他盾构隧道工程提供一定的理论参考。