Footing Settlement on a Consolidating Soil Layer with Stochastic Properties

Geotechnical engineering applications are characterized by various sources of uncertainties, most of them attributed to the stochastic nature of soil parameters and their properties. In particular, soil’s inherent random heterogeneity, inexact measurements and insufficient data necessitate numerical methods that incorporate the stochastic soil properties for a realistic representation of the soil behavior. In this paper, the process of consolidation of saturated soils is examined on the basis of the coupled u–p finite element formulation. A generalized Newmark implicit time integration scheme is implemented to treat the time integration of the coupled consolidation equations. A benchmark geotechnical engineering problem of a strip footing resting on a saturated soil layer is analyzed. The soil permeability coefficient k, as well as the elastic modulus E, are treated as lognormal random fields in two dimensions. The investigation of the effect of the spatial variability of the soil properties on the response of a footing–soil system is examined by means of the direct Monte Carlo simulation. The influence of the coefficient of variation and correlation length of the stochastic fields is quantified in terms of footing settlements, as well as excess soil water pore pressure. The effects of spatial variability of the permeability coefficient k and the elastic modulus E on the system response are demonstrated. It is shown that the footing differential settlement, along with generated excess pore pressures, is highly affected by the variation of the soil properties considered, as well as the correlation length of the underlying random fields.     

辽西风积土动力特性实验研究

通过一系列动态三轴实验,研究了原状饱和辽西风积土在不同固结压力条件下的动态强度、动态弹性模量和阻尼比。结果表明,辽西风积土的破坏动态强度随着固结围压和固结应力比的增大而增大,而动态剪切强度明显区别于静态剪强度;其动态弹模量随着固结应力比和固结围压的增加而增加,而阻尼比随着固结应力比和固结围压的增大而减小。同时,分别拟合得到最大动态弹模量和最大阻尼比与有效固结应力的关系式,并且对动态弹模量和阻尼比进行了归一化处理。     

A CONSOLIDATION MODEL OF GROUP WELLS ON COMPOSITE FOUNDATION1)

针对复合地基固结问题,考虑井阻和土体径竖向渗流的影响,建立 以"桩-土-桩"为单元的复合地基群井计算模型,采用解析解法,推导出瞬时载荷作用下复合地基群井固结解析解,讨论了复合地基固结特点和孔压等的变化规律。研究表明,复合地基群井固结模型为复合地基固结理论的研究提供了一种新思路,在井径比大于5 时,基于中心桩、边桩流量相等假设,复合地基群井固结理论所求固结度和传统固结理论所求固结度相差很小,可忽略不计;桩体渗透系数、内外扰动区土体径向渗透系数、土体竖向渗透系数越大,复合地基固结速率越快;堆载越大,最终达到稳定时的沉降量和竖向应变越大;地基表层土体的孔压消散速率和竖向应变速率大于地基深部土体。     

考虑热渗效应的有限长圆柱热固结解

在作者已建立的饱和多孔介质耦合非线性热弹性理论基础上,考虑热渗效应,建立了饱和多孔介质耦合热弹性固结方程,并推导了有限长圆柱热固结问题的解析解,进而以温控三轴试验的试样为例进行了算例分析,同时利用COMSOL软件进行了数值模拟,并将解析结果和数值结果进行对比．结果表明：在不排水条件下,影响试样最终孔压大小的参数是：土的泊松比>弹性模量>水的体膨胀系数,渗透系数对孔压变化影响不大,考虑与不考虑水土压缩性不影响孔压的计算;相对线弹性情况,考虑非线弹性膨胀系数随温度变化时的孔压有所下降,轴向应变变化很小．     

垂直受荷群桩在半空间饱和土中的稳态反应

研究了均质半空间饱和土中群桩在垂直稳态荷载作用下的动力反应问题。半空间饱和土采用Biot提出的三维波动原理。将桩看作是一维的弹性杆单元。利用圆形简谐载荷作用下的Biot固结方程的基本解和桩土之间的变形协调条件得到饱和土中群桩的第二类Fredholm积分方程,群桩的动力阻抗采用动力相互作用因子的方法。分析桩距等参数对群桩阻抗、轴力和孔压等的影响。本文的方法可以用于计算层状饱和土中群桩的动力反应问题。     

用DQM求解成层地基一维非线性固结问题

由于多层地基的一维非线性固结问题求解的复杂性,其解析解很难求得。本文基于Davis和Raymond一维非线性固结理论,利用DQM(Differential Quadrature Method)导了初始有效应力沿深度变化、任意边界条件、任意荷载作用下成层地基一维非线性固结的统一表达式,求得了孔压、有效应力和平均固结度的解答。通过解的收敛性分析讨论了DQM解的有效性。由于DQM解对于固结间题各种复杂条件具有统一的矩阵表达式,更便于编程计算和工程应用。最后,用本文解答对三层地基一维非线性固结问题进行了讨论。     

Plane strain consolidation of soil layer with anisotropic permeability

This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface （z=0） and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot＇s consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot＇s consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils.     

One-Dimensional Consolidation of Layered and Visco-Elastic Soils under Arbitrary Loading

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VERTICAL VIBRATION ANALYSIS OF AXISYMMETRIC SATURATED SOIL

Based on Biot’s dynamic consolidation equations,by means of Laplace-Hankel transform technology,the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived.In- fluence of the reflected wave generated by the boundary was revealed.Numerical results indicate that the vibration frequency has some effect on the vertical displacement of satu- rated soil.The vertical displacement at the surface of saturated soil lags in phase with the load.Furthermore,the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied,but when the load becomes stable,the effect is inapparent.     

Plane strain consolidation of a multi-layered soil with anisotrpic permeability and compressible constituents

对多层地基的平面应变固结问题进行了研究,并同时考虑了土体的渗透各向异性和孔隙 流体的可压缩性. 从平面应变Biot固结的控制方程出发,对时间t, 坐标z和x进行 Laplace和Fourier变换,建立了地基表面(z=0)和任意深度z处的基本量 在Laplace-Fourier变换域内的传递矩阵关系. 利用传递矩阵 法,结合土层连续条件和边界条件,并应用Laplace-Fourier逆变换技术,推导出渗透各向 异性可压缩多层地基平面应变固结的理论解. 基于该解,编制了计算程序,并进行了 数值计算. 讨论了土体的渗透各向异性、孔隙流体的可压缩性以及地基的分层特性对地基固 结的影响,分析结果表明：土体的渗透各向异性、孔隙流体的可压缩性,以及地基的分层特 性对地基的固结行为有着重要的影响.     

辽西风积土动剪切模量与阻尼比特性试验研究

研究辽西风积土的动力特性离不开其动剪切模量与阻尼比这两个最基本的参数. 通过一系列动三轴试验, 分析了围压、固结比、振动频率对原状风积土的动剪切模量与阻尼比的影响情况, 并探讨了其产生的机理. 通过试验数据分析表明, 风积土的动剪切模量随围压的增大而增大, 但阻尼比随围压的增大而减小; 动剪切模量随固结比的增大而增大, 阻尼比随固结比的增大而减小; 动剪切模量和阻尼比均随振动频率的增大而增大, 但影响较小, 不如前两个因素明显.     

Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization

We compute Pareto fronts that estimate the upper bounds of the bulk modulus and fluid permeability cross-property space for periodic porous materials over a range of porosities. The fronts are generated numerically using topology optimization, which is a systematic, free-form design algorithm for optimizing material layouts. The presented microstructures demonstrate the trade-off between the bulk modulus and fluid permeability achievable with a multifunctional porous material and will be useful for designers of materials for which both stiffness and permeability are important. Our results suggest that the range of achievable stiffness and permeability properties is significantly restricted when considering elastic isotropy, as compared to cubic elastic symmetry. The estimated bounds are of practical importance given the lack of microstructure-independent theoretical cross-property bounds.     

土-基础相互作用隔震体系地震随机响应分析

视地基土为各向同性的弹性半空间,用弹簧-粘性阻尼器模拟土对结构的影响,将地震激励模拟为平稳随机过程,对基础隔震体系的随机响应进行了分析。分析结果表明,地基土的性质对隔震结构有直接影响,但其影响比非隔震结构小得多。     

考虑热渗效应的有限热源固结近似解1）

通过建立考虑热渗效应和热流固耦合效应的饱和土体固结方程,研究了无限长圆柱热固结问题. 利用Fourier 和Laplace 变换及其逆变换,给出了热固结问题的解析解;然后对空间内无限长圆柱形热源问题进行研究,得到非等温条件下柱体周围饱和土体温度、孔隙水压力的近似解,并总结其规律,分析了热渗系数、固结系数对温度作用下土体固结的影响.     

Efficient stochastic finite element methods for flow in heterogeneous porous media. Part 2: Random lognormal permeability

Efficient and robust iterative methods are developed for solving the linear systems of equations arising from stochastic finite element methods for single phase fluid flow in porous media. Permeability is assumed to vary randomly in space according to some given correlation function. In the companion paper, herein referred to as Part 1, permeability was approximated using a truncated Karhunen-Loève expansion (KLE). The stochastic variability of permeability is modeled using lognormal random fields and the truncated KLE is projected onto a polynomial chaos basis. This results in a stochastic nonlinear problem since the random fields are represented using polynomial chaos containing terms that are generally nonlinear in the random variables. Symmetric block Gauss-Seidel used as a preconditioner for CG is shown to be efficient and robust for stochastic finite element method.     

考虑桩体内径向渗流的复合地基固结解

考虑了桩体内径竖向组合渗流和涂抹区土体水平渗透系数的两种变化模式,得到了此类固结问题的控制方程.采用新的初始条件,得到了控制方程的解答,给出了桩周土体和桩体内的平均孔压.在此基础上,把桩体的固结压缩引人对复合地基总平均固结度的定义中,分别给出了复合地基按应力和按应变定义的总平均固结度.结果表明:按应力和按应变定义的复合地基的总平均固结度相等;考虑桩体内径向渗流比不考虑桩体内径向渗流的复合地基固结度要小,而且随着桩间距的增大,两者之间的差值逐渐减小;考虑涂抹区水平渗透系数逐渐变化比假定涂抹区水平渗透系数保持不变的复合地基的总平均固结度大.     

Dynamic response of a pile embedded in elastic half space subjected to harmonic vertical loading

An analytical method is developed to investigate the dynamic response of a pile subjected to harmonic vertical loading.The pile is modeled as a one-dimensional(1D)elastic rod.The elastic soil is divided into a homogeneous half space underlying the base of pile and a series of infinitesimally thin layers along the vertical shaft of pile.The analytical solution for the soil-pile dynamic interaction problem is obtained by the method of Hankel transformation.The proposed solution is compared with the classical plane strain solution.Arithmetical examples are presented to demonstrate the sensitivity of the vertical impedance of the pile to relevant parameters.     

饱和土中端承桩纵向振动特性研究

基于饱和多孔介质理论研究了三维轴对称条件下端承桩在饱和土中的纵向耦合振动. 首先通 过引入势函数对Biot动力固结方程解耦，采用算子分解方法及分离变量法求得饱和土层振动 解，进而利用桩土完全耦合条件得到桩土系统定解. 然后对桩顶的频率和时域响应进行参数 研究，结果表明，桩的长径比和桩土模量比对桩顶动力响应有较大影响，而渗透力对其影响 较小. 最后将幅频及时域反射波理论拟合结果与桩基实测结果加以对比，结果表明理论曲线 与实测曲线规律一致.     

渗透固结试验装置的改进

针对传统固结仪不能进行渗透试验的不足,对固结仪进行了改装。改装后的固结仪不仅可以交叉进行固结、渗透试验,以研究不同荷载作用下土样的渗透特性,而且可以通过三通阀控制排水条件,进行双面排水固结试验,或在单面排水条件下量测固结过程中试样不排水面处的孔隙水压力,也可通过串联固结仪分别研究试样不同截面处孔隙水压力的消散规律。新仪器具有构造简单,密封性能好的特点。通过与常规固结、渗透试验的结果对比,验证了采用改装固结仪测定固结模型参数的可靠性。另外,通过单面排水固结试验发现了孔压滞后现象。