Consolidation analysis of a cross-anisotropic homogeneous elastic soil using a finite layer numerical method

This paper presents a finite layer procedure for Biot's consolidation analysis of layered soils using a cross-anisotropic elastic constitutive model. The program is first verified using published results. Then, using this program, the influences of cross-anisotropy on the immediate settlement, the final settlement, and the consolidation behaviour are investigated by changing one model parameter at one time. The results obtained using the cross-anisotropic elastic model are compared with results using an isotropic elastic model. It is found that the cross-anisotropy has very large influences on the immediate settlement, the final settlement, and the consolidation behaviour. Curves or tables of the immediate settlement coefficients, the final settlement coefficients, and the average degree of consolidation are obtained and presented in the paper. These curves or tables can be easily used to estimate the immediate settlement, the final settlement, and the consolidation settlement of a cross-anisotropic soil. Copyright © 2004 John Wiley & Sons, Ltd.     

横观各向同性土的简明破坏机制解释

由于沉积等作用使得天然土材料内部颗粒排列表现为各向异性。土材料的各向异性使得材料内各平面滑动的内摩擦角不同。因此,在分析各向异性土的破坏问题中,除了考虑来自外部的应力分布以外,还需考虑土材料内部的强度分布。以横观各向同性土为例,阐述了同时考虑材料外部应力分布与材料内部强度分布下各向异性土的破坏机制。为说明,文中假定横观各向同性土内部各平面的内摩擦角正切值随空间方向而线性分布。外部加载进行时,横观各向同性土材料内部各处的应力不断变化,当其内部某处首次出现的应力达到该处的强度时,土材料发生破坏。进一步通过类比得出：区别于金属,各向同性土不是在最大剪应力面而是在最大剪压比面发生破坏;区别于各向同性土,各向异性土不是在最大剪压比面而是在最大剪压强比面发生破坏。     

有限元和有限层元研究横向同性土对建筑物沉降的影响

从常规三轴压缩试验得到横观各向同性土层的力学参数,综合9种来自于不同国家和地区的横观各向同性土层的土样参数,研究分析了横观各向同性土层参数对建筑物沉降的影响。作为典型例子,对上海一幢剪力墙结构的箱形基础与横观各向同性土进行共同作用分析,并与各向同性土层上的分析结果进行比较,结果表明：横观各向同性土层参数对沉降的影响有些不同,尤其是不排水加载条件确定的土层参数影响的结果大不相同。     

Three-dimensional finite element modelling for consolidation due to groundwater withdrawal in a desaturating anisotropic aquifer system

A poroelastic numerical model is presented to evaluate three-dimensional consolidation due to groundwater withdrawal from desaturating anisotropic porous media. This numerical model is developed based on the fully coupled governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. Two different cases of unsaturated aquifers are simulated for the purpose of comparison: a cross-anisotropic soil aquifer, and a corresponding isotropic soil aquifer composed of a geometrically averaged equivalent material. The numerical simulation results show that the anisotropy has a significant effect on the shapes of three-dimensional hydraulic head distribution and displacement vector fields. Such an effect of anisotropy is caused by the uneven partitioning of the hydraulic pumping stress between the vertical and horizontal directions in both groundwater flow field and solid skeleton deformation field. Copyright © 1999 John Wiley & Sons, Ltd.     

Kinematic hardening predictions of large stress-reversals in 3-D test on loose sand

A rotational kinematic hardening constitutive model with the capability of predicting the behavior of soil during 3-D stress-reversals has been developed. An existing elasto-plastic constitutive model, the Single Hardening Model, utilizing isotropic hardening serves as the basic framework in these formulations. To this framework is added the capability of handling cross-anisotropic behavior as well as the kinematic hardening mechanism to capture inherent anisotropy of the sand in addition to the large stress-reversals. The model involves thirteen parameters, which can be determined from simple laboratory experiments, such as isotropic compression, drained triaxial compression and triaxial extension tests. The results from a series of true triaxial tests with large stress-reversals performed on loose cross-anisotropic Santa Monica Beach sand are employed for comparison with predictions.     

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.     

倾斜土层地震液化诱发大变形数值分析方法

基于有限元理论,进行了缓坡土层地震液化引起大变形的数值方法研究,即采用二维有效应力动力有限元方法进行分析,在液化分析过程的每一时段考虑地震液化和振动软化得到土单元的模量,通过非线性静力方法计算每时段地震液化引起的大变形,得到土层各深度处的水平和竖向位移。由算例分析了地震动和土层坡度等因素的影响,通过对比分析表明了该方法的有效性,可为工程场地地震地质灾害评价提供参考数据。     

Numerical analysis of axially loaded vertical piles and pile groups

A numerical method, based on a simplified elastic continuum boundary element method, is presented for the settlement analysis of axially loaded vertical piles and pile groups. The soil flexibility coefficients are evaluated using the analytical solutions for a layered elastic half space. Results are presented and compared with existing published solutions for the following cases: (i) piles in homogeneous soil, (ii) piles in finite soil layer, (iii) piles end-bearing on stiffer layer, (iv) piles socketted into stiffer bearing layer, and (v) piles in Gibson soil. Reasonably good agreement is obtained between the present solutions and existing published solutions.     

横观各向同性软土地基上大圆筒防波堤稳定性研究

对于横观各向同性软土地基上沉入式大圆筒防波堤结构提出了一种准三维上限极限分析方法,所假设的破坏机制为大圆筒结构绕筒体内中轴线上某点发生转动失稳,泥面处形成楔体破坏,而筒底部形成圆弧滑裂面。本方法可以考虑土的三轴压缩、拉伸强度与直剪强度的差异。利用ABAQUS分别进行平面应变以及三维有限元分析,软土采用Hill本构模型,所得到的破坏模式以及大圆筒结构水平承载力与上限极限分析方法吻合较好,同时可以得出考虑地基土各向异性的大圆筒结构承载力比不考虑时有较大降低。     

Time‐dependent behaviour of a rigid foundation on a transversely isotropic soil layer

An analytical solution is presented in this paper to study the time‐dependent settlement behaviour of a rigid foundation resting on a transversely isotropic saturated soil layer. The governing equations for a transversely isotropic saturated soil, within Biot's poroelasticity framework, are solved by means of Laplace and Hankel transforms. The problem is subsequently formulated in the Laplace transform domain in terms of a set of dual integral equations that are further reduced to a Fredholm integral equation of the second kind and solved numerically. The developed analytical solution is validated via comparison with the existing analytical solution for an isotropic saturated soil case, and adopted as a benchmark to examine the sensitivities of the mesh refinement and the locations of truncation boundaries in the finite element simulations using ABAQUS. Particular attention is paid to the influences of the degree of soil anisotropy, boundary drainage condition, and the soil layer thickness on the consolidation settlement and contact stress of the rigid foundation. Copyright © 2009 John Wiley & Sons, Ltd.     

层状地基上弹性地基梁的有限元-边界元耦合分析

将地基视为多层各向同性弹性体,对Euler-Bernoulli梁进行有限单元离散分析,对地基-梁接触面采用边界积分法求解,根据地基-梁接触面的竖向位移协调和光滑接触条件,应用有限元与边界元耦合的方法推导出各向同性成层弹性地基上的Euler-Bernoulli梁的半数值半解析解。基于文中理论,编制了相应的程序,通过与现有文献对比,验证了文中理论的正确性,对比分析了分层地基与等效均匀地基两种模型上的弹性地基梁。研究结果表明,分层地基与等效均匀地基两种模型上弹性地基梁性状差异较大,实际弹性地基梁计算中应采用分层地基模型。     

Dynamic response of a soft soil layer to flow and periodical disturbance

The dynamic response of a soft soil layer of finite thickness under the mutual effects of flow and periodical disturbance at the free surface is discussed in this work. The homogeneous water is governed by potential theory and the soil layer obeys Biot's theory of poroelasticity. The boundary‐value problem is solved by an analytical algorithm, in which the wave number is found first. Secondly, the closed form solutions are found by a two‐parameter perturbation method with the boundary‐layer correction. The results are also compared with those of the poroelastic soil layer of infinite thickness to show the impermeable rigid boundary effect. Copyright © 2003 John Wiley & Sons, Ltd.     

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。     

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。     

横向扩展液化土中单桩-土系统的非线性分析

将地震液化场地分为地表的上覆未液化土层、底部的未液化基层以及夹在两者之间的液化土层,基于桩-土相互作用的非线性Winkler模型,考虑桩弯曲的非线性弯矩-曲率本构关系和桩的几何非线性变形,建立了液化土层横向扩展下桩非线性大挠度变形的基本控制方程,并利用打靶法进行了数值求解。同时,给出了桩线弹性小变形情形下的解析解。通过与非线性有限元解和线弹性小变形解析解的比较,验证了文中打靶法的有效性和可靠性。用数值方法分析了液化土层横向扩展对桩力学性能的影响,结果表明：非线性桩-土相互作用和桩材料非线性效应强于桩的几何非线性效应,随着液化土层横向扩展位移的增加,几何非线性效应逐渐增大,此时,应采用完全非线性模型进行桩力学行为的分析。     

多层横观各向同性地基轴对称固结的传递矩阵解

从横观各向同性地基轴对称Biot固结的基本方程出发,通过关于t的Laplace变换和关于r的Hankel变换,得到关于z的一阶常微分方程组。然后,对变换域内的基本未知量进行线性化处理,建立了变换域内的基本状态变量在z = 0处和任意深度处z的显式关系。利用传递矩阵法,结合层间连续性条件和边界条件,得到了多层横观各向同性地基的Biot固结轴对称问题的解答。该解答能避免随着层数增加而需要求解大型方程组的困难,明显地提高了计算效率。     

Solution of the unsaturated soil moisture equation using repeated transforms

An alternative method of solution for the linearized ‘theta‐based’ form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ξ. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis‐equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi‐analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

Steady‐state analytical solutions of flow and deformation coupling due to a point sink within a finite fluid‐saturated poroelastic layer

An exact steady‐state closed‐form solution is presented for coupled flow and deformation of an axisymmetric isotropic homogeneous fluid‐saturated poroelastic layer with a finite radius due to a point sink. The hydromechanical behavior of the poroelastic layer is governed by Biot's consolidation theory. Boundary conditions on the lateral surface are specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of the governing equations. Ordinary differential equations in the transformed domain are solved, and then the analytical solutions in the physical space for the pore pressure and the displacements are finally obtained by using finite Hankel inversions. The analytical solutions at some special locations such as the top and bottom surfaces, lateral surface, and the symmetrical axis are given and analyzed. And a case study for the consolidation of a water‐saturated soft clay layer due to pumping is conducted. The analytical solution is verified against the finite element solution. Meanwhile, an analysis of coupled hydromechanical behavior is carried out herein. The presented analytical solution is an exact solution to the practical poroelastic problem within an axisymmetric finite layer. It can provide us a better understanding of the poroelastic behavior of the finite layer due to fluid extraction. Besides, it can be applied to calibrate numerical schemes of axisymmetric poroelasticity within finite domains. Copyright © 2017 John Wiley & Sons, Ltd.     

Static analysis of vertically loaded pile group in multilayered transversely isotropic soils

In this paper, a coupling approach is presented to study the static responses of vertically loaded pile group embedded in multilayered transversely isotropic soils. The individual pile in pile group is modeled by the finite element method, while the analytical layer-element method is applied to represent the soil's behavior. Then, the interaction equation of piles and soils is obtained by considering the force equilibrium and displacement compatibility conditions and solved by a FORTRAN program. The results computed by the proposed approach compare favorably with those from some existing solutions and field test. Some typical parametric analysis cases are investigated to study the effect of soil anisotropy, pile stiffness ratio, and pile spacing on the behavior of vertically loaded pile group.