Wave-induced soil response in an unsaturated anisotropic seabed of finite thickness

An analytical solution for the wave-induced soil response is developed for a seabed of finite thickness subject to a three-dimensional (3-D) wave system produced by two intersecting waves of equal properties. These 3-D exact solutions for the pore pressure and effective stresses, proposed for a non-cohesive soil matrix of finite depth in a homogeneously unsaturated and anisotropic condition, are readily reducible to the limiting two-dimensional cases of progressive and standing waves, for which no explicit solutions are available for finite thickness. The effects of soil isotropy, degree of saturation, seabed thickness and grain size on the wave-induced pore pressure are discussed in detail. The explicit solutions presented in this study for the wave-induced pore pressure and effective stresses should benefit the laboratory experiments and field monitoring programs carried out in soil of finite depth.     

A semi-analytical method for the wave-induced seabed response

A general semi-analytical method is presented for the analysis of seabed response under wave action during a storm. The seabed is idealized as a poro-elastic medium filled with a single compressible fluid with anisotropic flow. The coupled process of fluid flow and deformation of soil skeleton is formulated in the framework of Biot's theory. The analysis for the response of homogeneous seabed of finite thickness under a plane progressive wave is developed first, followed by an extension for the case of a layered seabed. A generalization for three-dimensional response of seabed is also developed for a general wave field which provides the analyses for seabed response under short-crested or standing waves in the vicinity of a structure. Some numerical examples illustrating the proposed analyses are also presented.     

Bearing capacity of square footings on reinforced layered soil

In the present study, an approximate method has been suggested to calculate the ultimate bearing capacity of a square footing resting on reinforced layered soil. The soil is reinforced with horizontal layers of reinforcement in the top layer of soil only. The pre requisite to the method is the ultimate bearing capacity of unreinforced layered soil, which can be determined from the methods already available in literature. The results have been validated with the model tests conducted on two layered soil compacted at different densities and the top layer reinforced with horizontal layers of geogrid reinforcement.     

列车荷载下轨道系统-层状横观各向同性饱和地基动力响应

基于Biot波动理论,构建列车荷载-轨道系统-双层状横观各向同性饱和地基模型,将模型分为上覆路轨系统和地层系统。对上覆路轨系统和地层系统处理,并利用双重Fourier变换技术,在变换域中将横观各向同性饱和地基动力响应的求解简化为求解一个6阶控制方程的特征值问题,进而得到了列车荷载作用下双层横观各向同性饱和地基力响应的解析结果。利用离散Fourier逆变换得到数值计算结果,重点分析了上下土层的刚度和泊松比对位移和孔隙水压力和剪切应力响应的影响,结果表明,上、下土层刚度差异对地基动力响应有较大影响,土层各向异性参数中模量的影响较泊松比大。计算结果可为软土路基加固深度的确定提供理论依据。     

砂柱排水真空阻滞效应的试验和动力学解释

含低渗透盖层的强透水层在排水过程中可能产生包气带真空并阻滞排水。这种真空阻滞效应具有什么动力学特征,是岩土渗流领域有待解决的新课题。以细砂作为粗砂的盖层,进行了双层结构砂柱的排水试验,观测到了包气带真空度先快速增大,然后缓慢减小的过程,排水速率显著低于无细砂覆盖的情况。细砂盖层厚度越大,真空阻滞效应越强烈。基于水-气渗流理论提出了解释试验现象的水流方程和气流方程,并得到了排水早期和后期真空度变化的近似解析公式,说明真空度峰值随盖层厚度呈非线性增加趋势。对试验结果进行参数分析,发现盖层透气性在排水后期明显大于早期,反映了盖层含水率对透气性的影响。     

三维横观各向同性成层地基的传递矩阵解

通过解耦变换推导出三维直角坐标系下横观各向同性地基的非耦合状态方程;利用双重Fourier变换以及Cayley-Hamilton定理得到了单层地基的传递矩阵;结合边界条件和层间连续条件进而得其传递矩阵解。编制了相应程序并进行了数值计算与分析,结果表明：数值结果与已有文献结果十分吻合,地基的横观各向同性性质与成层性质对受荷地基中竖向位移和应力的影响较为显著。     

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.     

基于层间位移协调的承压水降压引起土层变形分析

承压水降压引起的地面沉降由含水层、弱透水层和潜水层的变形组成。当承压层降压时间短、弱透水层固结变形较小时,可以假设弱透水层为严格的隔水层。采用层状弹性体系理论,基于位移协调条件分别建立了单井抽水以及第三类基坑工程降水（隔水帷幕插入降水含水层）引起的土层变形分析模型,与数值模拟和现场抽水试验结果的对比,验证了文中方法的正确性。研究结果表明,上覆土层弹性参数变化对地表变形的影响可以忽略;抽水井附近的土层变形呈现“上小下大”特点,一定距离以外含水层与地面沉降大致相等,根据承压含水层降深要求,可估算出基坑外的水位降深。     

Folder: A numerical tool to simulate the development of structures in layered media

We present Folder, a numerical toolbox for modelling deformation in layered media subject to layer parallel shortening or extension in two dimensions. The toolbox includes a range of features that ensure maximum flexibility to configure model geometry, define material parameters, specify numerical parameters, and choose the plotting options. Folder builds on an efficient finite element method model and implements state of the art iterative and time integration schemes. We describe the basic Folder features and present several case studies of single and multilayer stacks subject to layer parallel shortening and extension. Folder additionally comprises an application that illustrates various analytical solutions of growth rates calculated for the cases of layer parallel shortening and extension of a single layer with interfaces perturbed with a single sinusoidal waveform. We further derive two novel analytical expressions for the growth rate in the cases of layer parallel shortening and extension of a linear viscous layer embedded in a linear viscous medium of a finite thickness. These solutions help understand mechanical instabilities in layered rocks and provide a unique opportunity for benchmarking of numerical codes. We demonstrate how Folder can be used for benchmarking of numerical codes. We test the accuracy of single-layer folding simulations using various 1) spatial and temporal resolutions, 2) iterative algorithms for non-linear materials, and 3) time integration schemes. The accuracy of the numerical results is quantified by: 1) comparing them to analytical solutions, if available, or 2) running convergence tests. As a result, we provide a map of the most optimal choice of grid size, time step, and number of iterations to keep the results of the numerical simulations below a given error for a given time integration scheme. Folder is an open source MATLAB application and comes with a user-friendly graphical interface. Folder is suitable for both educational and research purposes.     

Vertical deformation of rigid foundations of arbitrary shape on layered soil media

A numerical procedure is described for the analysis of vertical deformation of smooth, rigid foundations of arbitrary shape on homogeneous and layered soil media. The contact area at the interface of the foundation and soil medium is approximated by square subdivisions. The response of the system is then obtained from the superposition of the influence of the individual subdivisions. The flexibility influence coefficients are based on equivalent smooth, rigid circular areas with the same contact area as the square subdivisions. For foundations on a homogeneous, isotropic elastic half-space, the flexibility coefficients are given analytically by the integrated forms of the Boussinesq's solution. For a layered soil medium, the flexibility coefficients are determined from an axisymmetric finite element analysis which is essentially two dimensional. Thus, there is no necessity for a full three-dimensional finite element analysis. Comparison with solutions obtained using the integral transform technique for smooth, rigid rectangular foundations on a homogeneous, isotropic elastic half-space shows good agreement. Parametric solutions are presented for the response of rectangular foundations on some ‘typical’ soil profiles. The use of a simplified method to estimate the settlement of rectangular foundations on a layered soil medium by superposing solutions for homogeneous, elastic strata is discussed.     

Finite layer analysis of laterally loaded piles in cross-anisotropic soils

This paper presents a finite layer method for the analysis of laterally loaded piles in isotropic and cross-anisotropic layered soils. Excellent agreement is found between the isotropic solutions computed by the finite layer method and the more rigorous finite element method. Some theoretical solutions are presented to demonstrate the effect of soil anisotropy. Two full scale field case histories have been analysed by the method using isotropic and cross-anisotropic soil models.     

Effect of compressible parameters on vertical vibration of an elastic pile in multilayered poroelastic media

This paper mainly investigates the influences of compressible parameters on the vertical vibration of a pile embedded in layered poroelastic soil media. The pile is treated as a 1D elastic bar by the finite element method, and fundamental solutions for the layered poroelastic soils due to a vertical dynamic load are obtained by the analytical layer element method. Based on the compatibility conditions, the pile-soil dynamic interaction problem is solved. The numerical scheme has been compiled into a Fortran program for numerical calculation. Influences of the pile-soil stiffness ratio, compressible parameters, vibration frequency and the soil stratification are discussed.     

Bearing Capacity of Shallow Foundation on Two Clay Layers by Numerical Approach

Natural soils are often deposited in layers. The estimation of the bearing capacity of the soil, using conventional bearing capacity theory based on the properties of the top layer, introduces significant inaccuracies if the thickness of the top layer is comparable to the width of the rigid footing placed on the soil surface. Saturated normally consolidated and lightly overconsolidated clays indicate that under undrained condition the cohesion of soil mass increases almost linearly with depth. A few theoretical studies have been proposed in the literature to incorporate the variation of cohesion with depth in the computation of the ultimate bearing capacity of strip and circular footings. In this paper, after reviewing previous works, numerical computations using the FLAC code (Fast Lagrangian Analyses of Continua) are reported to evaluate the two layered clays effect on the bearing capacity beneath rigid strip footing subject to axial static load. The results of the bearing capacity relating to the relative thickness of the top layer, the strength ratio of the soil two-layered clays and the rates of the increase of soil cohesion with depth are presented in Tables and graphs. The obtained results are compared with previous published results available in the literature.     

Interference effect of two nearby strip footings on layered soil: theory of elasticity approach

In recent times, rapid urbanisation coupled with scarcity of land forces several structures to come up ever closer to each other, which may sometime cause severe damage to the structures from both strength and serviceability point of view, and therefore, a need is felt to devise simplified methods to capture the effect of footing interference. In the present study, an attempt has been made to model the settlement behaviour of two strip footings placed in close spacing on layered soil deposit consisting of a strong top layer underlying a weak bottom layer. Theory of elasticity is employed to derive the governing differential equations and subsequently solved by the finite difference method. The perfectly rough strip footings are considered to be resting on the surface of two-layer soil system, and the soil is assumed to behave as linear elastic material under a range of static foundation load. The effect of various parameters such as the elastic moduli and thickness of two layers, clear spacing between the footings and footing load on the settlement behaviour of closely spaced footings has been determined. The variation of vertical normal stress at the interface of two different soil layers as well as at the base of the failure domain also forms an important part of this study. The results are presented in terms of settlement ratio (ξ_δ), and their variation is obtained with the change in clear spacing between two footings. The present theoretical investigation indicates that the settlement of closely spaced footings is found to be higher than that of single isolated footing, which further reduces with increase in the spacing between the footings.     

Permeability of Layered Soils: An Extended Study

The coefficient of permeability of stratified soil deposits, when the flow is normal to the orientation of the bedding planes, has been observed to deviate from the value calculated theoretically. This deviation has been successfully explained in the past for a two-layer soil system by considering the coefficient of permeability of the exit layer as the controlling factor. The present technical note deals with the results from the study of permeability behavior of three-layer soil system. This study reinforces the point that the coefficient of permeability of a layered soil system, when the flow is normal to the orientation of the bedding planes, depends upon the relative positioning of the layers with different values of coefficient of permeability in the system.     

瑞利波特性刚度矩阵分析方法

沿水平方向从半无限体分层系统截取出有限厚度分层固体系统,截取边界设置为刚性边界。将固体系统分层细化,由刚度矩阵方法可得到表面波在该系统频散特性,利用瑞利波位移在底层衰减特性从表面振型波可筛选出瑞利振型波,这些瑞利振型波与某一频率范围半无限体分层系统瑞利振型波对应,其频率下限与截取厚度有关,截取厚度越大,频率下限越小。同时还分析了分层细化厚度、截取厚度与分析频率关系。     

考虑波致孔压累积与应力耦合效应的埋置管线周围海床响应特征与机制分析

波浪导致的海床液化是埋置管线失稳的一个重要因素。超静孔隙水压力累积引起的液化深度较深,对海底管线稳定性的影响较大,因此波浪作用下管线-海床系统的累积响应特征一直受到研究者的重点关注。本文基于考虑孔压累积与海床应力耦合发展的数值计算模型,对非线性行进波作用下含埋置管线的海床累积响应特征进行了模拟计算,并与非耦合模型的计算结果进行了对比分析,结果表明,当考虑孔压累积与海床应力的耦合效应时,管线附近累积孔压在水平方向上的不均匀分布会导致海床循环剪应力的增大,从而会极大地促进管线周围海床累积孔压的发展,增大管线的影响范围; 忽略孔压累积与海床应力的耦合效应,会在一定程度上低估管线周围海床的液化深度,不利于管线的安全。     

三维层状饱和地基动力Green函数的薄层法求解

建立了三维层状饱和地基模型并在模型底部施加无反射边界条件,引入Fourier变换和正交变换将饱和地基Biot动力方程化为Love和Rayleigh模态方程,将地基沿深度方向划分为数个薄层单元并对单元位移场引入线性插值函数,从而将模态方程离散化,通过求解本征值问题最终给出了三维层状饱和地基的频域动力Green函数。分析了均质饱和地基的Love和Rayleigh模态的弥散特性,求解了均质和成层饱和半空间的Lamb问题,并与Philippacopoulos的数值积分解对比,说明了所求Green函数的正确性。所得Green函数无需关于Hankel函数进行数值逆变换且能直接考虑地基的成层性,提高了计算效率。     

基于传递矩阵法的层状土中管桩水平动力阻抗分析

在考虑土体分层特性的基础上,分别建立了管桩桩周土体和桩芯土体的水平振动控制方程。通过引入势函数并考虑桩周土和桩芯土径向位移和环向位移的边界条件及其奇偶性,求得了管桩-土动力相互作用的刚度系数和阻尼系数。将土体模拟为连续分布的弹簧-阻尼器,并考虑桩芯土和桩周土的作用,建立了层状土中管桩的水平振动方程。借助初参数法和传递矩阵法求解了管桩的水平振动,得到了管桩桩顶的水平动力阻抗。通过数值分析,得到了土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比、土层厚度等对管桩桩顶动力阻抗的影响规律。土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比对层状土中管桩水平振动的影响主要在低频处,土层厚度在较宽的频率范围内对管桩水平振动有影响;管桩壁越厚,桩周土的剪切模量越大时,管桩水平动力阻抗的绝对值越大。     

多阶多层复杂边坡稳定性的通用上限方法

极限分析上限方法在边坡稳定性评价中受到了广泛关注,但当前所取得的解析成果尚不能直接应用于解决任意多土层分布、多台阶的广义复杂层状边坡。基于组合对数螺线的旋转破坏机制,推导了具有任意坡面几何特征、任意多土层（含非水平土/岩层）边坡的外功率统一积分表达式及相应的虚功率方程,提出了多阶多层复杂边坡稳定性的通用极限分析上限方法;为克服积分式的复杂解析计算,引入了数值积分技术。在此基础上,结合最优化方法和强度折减技术,优化求解了复杂边坡的全局稳定性安全系数及相应的临界滑动面。通过多个典型算例的验证与对比分析,表明该方法具有较高的精度和广泛适用性。最后,针对典型多阶多层边坡实例,开展了上限法的深度拓展与应用研究,其结果为广义复杂层状边坡的稳定性评价提供了新思路。