循环荷载下成层饱水地基的一维固结

针对成层饱水地基模型，根据Ｔｅｒｚａｇｈｉ固结方程，运用Ｌａｐｌａｃｅ变换及矩阵传递法求解了循环荷载下成层饱水地基一维变形问题，得到了变换域内的通解。通过Ｌａｐｌａｃｅ逆变换计算了成层饱水地基在循环荷载下的一维变形及有效应力。经典的Ｔｅｒｚａｇｈｉ一维固结理论解是本文的一个特例，对于随时间任意变化荷载下成层的固结，只需利用Ｆｏｕｉｅｒ级数将荷载展开，就可用本文的方法求解。此外，本文对常见的循环荷载进行了变换，结合双层的地基算例，对各种循环荷载下地基中有效应力及变形进行了计算分析。结果表明：循环荷载下成层饱水地基固结，其有效应力和变形呈振荡增长，其变化步调与荷载并不一致，且振荡幅度不随时间减小。     

水泥搅拌桩加固坝基动力响应分析

以Biot固结方程为基础,采用有效应力法对水泥搅拌桩复合地基及细砂土层进行动力响应及液化分析。该法考虑了阻尼等因素的影响,将应力、位移及孔压等量耦合于Biot固结方程之中,从而可以计算地震期间的孔隙水压力、速度、正应力及剪应力的发展全过程,并探讨了上覆荷载、水泥搅拌桩桩长、置换率等因素对场地动力响应及液化的影响,对地基抗震设计及研究具有一定的指导意义。     

考虑非达西渗流的成层地基一维固结半解析解

在土中渗流遵从Hansbo非达西渗流的前提下,考虑实际工程中的变荷载,利用解析与数值相结合的半解析方法,对成层地基一维固结问题进行数值求解。将基于Hansbo非达西渗流的双层地基一维固结半解析解与相应的差分数值解进行对比,验证了半解析方法计算基于Hansbo非达西渗流下成层地基一维固结问题的可靠性。最后,对某三层地基考虑Hansbo非达西渗流的一维固结实例进行计算分析,结果表明：基于Hansbo非达西渗流下成层地基的沉降发展速率与超孔隙水压力的消散速率是不一致的。     

用传递矩阵法求解多层地基的轴对称问题

本文应用Hankel积分变换,求解单层弹性地基表面在轴对称荷载作用下位移和应力的初始函数解答,然后,利用矩阵传递方法求出多层地基位移和应力的一般表达式,不论弹性层数目多少,都不必求解任何联立方程。根据本文导出的公式编制了微型计算机程序。给出的算例说明了提供方法的正确性。     

埋置移动荷载作用下成层饱和地基的动力响应

利用Fourier变换和传递反射矩阵法（TRM法）研究了成层饱和地基在埋置移动荷载作用下的动力响应。土体被假设为完全饱和的多孔弹性介质并且服从Biot多孔弹性波动方程,用修正粘滞阻尼模型来描述土体的粘弹性行为,采用TRM法来考虑饱和地基的成层性,利用Fourier变换和Fourier逆变换得到了埋置移动荷载作用下饱和地基动力响应积分形式解答。当饱和成层地基退化单层饱和地基时,该文解与已有解能很好的吻合。最后,通过数值计算分析了埋置荷载深度﹑荷载速度、荷载频率及软硬夹层对动力响应的影响。     

任意荷载作用下层状横观各向同性弹性地基的直角坐标解

首次建立了在直角坐标系下层状地基力学问题的通用解法,改变了过去仅能在柱坐标系下进行求解此类的状况。首先将坐标系的原点选在荷载影响范围以外足够远处,从直角坐标系下的横观各向同性弹性问题的基本方程出发,利用Laplace变换及其微分性质,建立了单层横观各向同性弹性地基的状态控制方程,并利用状态空间理论给出了单层地基的解答。然后再利用传递矩阵技术,给出了任意荷载作用下的层状横观各向同性弹性地基的解析解。用提供的方法求解层状横观各向同性地基的非轴对称问题比在极坐标下求解简单、快捷。     

粘弹性层状地基轴对称问题的求解

由粘弹性体经 Laplace 和 Hankel 变换的基本方程式,得到了轴对称问题情形下无限粘弹性层不同深度应力位移向量间的传递矩阵,利用传递矩阵以及边界、层间完全接触条件求解了多种粘弹性模型的成层地基空间轴对称问题。     

层状地基一维固结电阻网法解答

考虑层状地基一维固结问题的复杂性,现有解答较为繁杂同时不便应用。该文基于Liebmann 电阻网原理,推导了初始孔压沿深度任意分布、荷载随时间任意变化作用下的孔压、平均固结度的解答。该解对于各种复杂条件均具有统一的矩阵表达式,便于编程计算和工程应用。通过与精确解的比较论证了该文方法的有效性。最后,对三层地基一维固结问题进行了分析和讨论。     

低标号混凝土芯砂石桩复合地基固结计算方法

针对低标号混凝土芯砂石桩复合地基这种软土地基处理新工法,建立了相应的考虑双面半透水边界条件固结计算模型;同时为考虑下卧层与加固区的孔压连续问题,基于双层散体材料桩复合地基固结理论和低标号混凝土芯砂石桩复合地基的特点,将低标号混凝土芯砂石桩复合地基固结问题转化为等效双层地基固结问题,采用解析法推导计算公式并得到相应的解析解。两种模型得到的超静孔压消散规律、固结度随时间增长规律与由现场实测数据推导出的规律相似,验证了本文提出的加固区模型和双层地基法在低标号混凝土芯砂石桩复合地基固结计算中的可行性和适用性。     

饱和土中桩竖向振动响应分析

基于Biot动力固结方程,研究了三维轴对称条件下饱和土中端承桩竖向耦合振动问题。首先对固结方程进行变形,通过算子分解法和分离变量法得到土体体积应变和空隙水压力的解,进而求得饱和土层竖向振动的解析表达式,然后联系桩土耦合条件,得到桩土系统的定解。通过与李强解对比,发现两解基本一致。对桩顶阻抗进行参数分析,得到一些有益的结论。     

论对称与非对称的Biot固结有限元方程组的一致性

论述了对称与非对称的Biot固结有限元方程组间的一致性,发现Biot固结有限元方程组系数矩阵是否对称是与平衡方程中与孔隙水压力有关的项是否进行分部积分有关。如果不对其进行分部积分,则得到非对称的系数矩阵;如果对其进行了分部积分,则得到对称的系数矩阵,此时两种情况下与之对应的结点力的意义也不相同。如果把结点力的意义处理成一种情况,则会发现这两种情况下的Biot固结有限元方程组是一致的。     

Boundary integral equation method for linear porous-elasticity with applications to soil consolidation

For physical phenomena governed by the Biot model of porous-elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two-dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous-elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever possible.     

Transfer matrix solutions to axisymmetric and non-axisymmetric consolidation of multilayered soils

Transfer matrix solutions are presented in this paper to study the axisymmetric and non-axisymmetric consolidation of a multilayered soil system under an arbitrary loading. Starting with the governing equations for consolidation problems of saturated soils, the relationship of displacements, stresses, excess pore water pressure, and flux between the points at the depth z, and on the ground surface (z = 0) is established in a transformed domain by introducing the displacement functions and using the integral transform technique. Then the transfer matrix method is used with the boundary conditions to obtain the analytical solutions in the transformed domain for the multilayered soil system. Numerical inversion of the integral transform of these analytical solutions results in the solutions for the actual problems. The numerical results for axisymmetric and non-axisymmetric Biot’s consolidation problems of a single layer and a multi-layered soil system are obtained and compared with existing results by others.     

海洋环境下桩-土相互作用问题的数值解

考虑波压力对海床土体应力状态的影响,基于Biot固结理论及虚拟桩技术对海洋桩-土相互作用体系进行了数学建模,并应用FlexPDE对所建立的数学模型进行了数值求解,得到了作用在桩体上的侧向土压力、桩体周围土体有效正应力以及自由场土体相对水平位移和相对垂直位移的分布,这些结果可为海洋桩基的设计与监测提供依据。     

A discontinuous Galerkin method with plane waves for sound‐absorbing materials

Poro‐elastic materials are commonly used for passive control of noise and vibration and are key to reducing noise emissions in many engineering applications, including the aerospace, automotive and energy industries. More efficient computational models are required to further optimise the use of such materials. In this paper, we present a discontinuous Galerkin method (DGM) with plane waves for poro‐elastic materials using the Biot theory solved in the frequency domain. This approach offers significant gains in computational efficiency and is simple to implement (costly numerical quadratures of highly oscillatory integrals are not needed). It is shown that the Biot equations can be easily cast as a set of conservation equations suitable for the formulation of the wave‐based DGM. A key contribution is a general formulation of boundary conditions as well as coupling conditions between different propagation media. This is particularly important when modelling porous materials as they are generally coupled with other media, such as the surround fluid or an elastic structure. The validation of the method is described first for a simple wave propagating through a porous material, and then for the scattering of an acoustic wave by a porous cylinder. The accuracy, conditioning and computational cost of the method are assessed, and comparison with the standard finite element method is included. It is found that the benefits of the wave‐based DGM are fully realised for the Biot equations and that the numerical model is able to accurately capture both the oscillations and the rapid attenuation of the waves in the porous material. Copyright © 2015 John Wiley & Sons, Ltd.     

A soil damage model expressed by a double scalar and its applications

Poroelasticity refers to the study of the mechanics of porous elastic materials that are saturated with compressible or incompressible fluids. When considering saturated poroelastic geomaterials, their consolidation response can be influenced by the evolution of damage in the porous skeleton. The objective of this paper is to examine the problem of consolidation response of damage-susceptible poroelastic geomaterials. Firstly, a new constitutive model of soft soils expressed by isotropic double scalar damage variables is developed and incorporated into Biot’s consolidation finite element equations via EDAPD program. Then, the EDAPD program is applied to analyze a soft subgrade reinforced by surcharge preloading technology. The comparison between the numerical predictions and the experimental data shows that the isotropic double scalar damage model presented in this paper is effective and feasible in analyzing the consolidation problem of damaged porous media.     

Biot理论与修正的Biot理论比较及讨论

对Biot理论和修正的Biot理论中的波动方程进行了详细推导,注明了每个参数的量纲和准确含义,并基于修正的Biot理论导出了三种不同形式的波动方程;对两种理论进行比较,得到了Biot弹性系数表达式,并分析了两者的应力及其对应关系;最后,着重对易被混淆的孔隙流体压力符号的正方向和含义,以及基本方程中部分参数的定义式进行了讨论,有助于更好地理解、应用Biot理论和修正的Biot理论。     

State space solution of non-axisymmetric Biot consolidation problem for multilayered porous media

In this paper, the non-axisymmetric Biot consolidation problem for multilayered porous media is studied. Taking stresses, pore pressure and displacements at layer interfaces as basic unknown functions, two sets of partial differential equations, which are independent each other, are formulated. Using Fourier expansion, Laplace transforms and Hankel transforms with respect to the circumferential, time and radial coordinates, respectively, the partial differential equations presented are reduced to the ordinary differential equations. Transfer matrices describing the transfer relation between the state vectors for a finite layer are derived explicitly in the transform space. Using the transfer matrices presented, three cases are studied for the lower surface: (1) permeable rough rigid base, (2) impermeable rough rigid base, and (3) poroelastic half space. The explicit solution in the transform space is presented. Considering the continuity condition at layer interfaces, the solutions of the non-axisymmetric Biot consolidation problems for multilayered semi-infinite porous media are presented in the integral form. The time histories of displacements, stresses and pore pressure are obtained by solving a linear equation system for discrete values of Laplace-Hankel transform inversions.     

The numerical solution of non-linear consolidation problems

It has long been recognized that permeability, compressibility and viscosity vary during the consolidation of soil. However, the introduction of these variations into consolidation theory leads to formidable difficulties due to their rendering the equations highly non-linear. Numerical methods are given herein which enable the governing equation to be solved for a variety of different non-linear laws.