Solution of quasi‐static large‐strain problems by the material point method

A procedure for solving quasi‐static large‐strain problems by the material point method is presented. Owing to the Lagrangian–Eulerian features of the method, problems associated with excessive mesh distortions that develop in the Lagrangian formulations of the finite element method are avoided. Three‐dimensional problems are solved utilizing 15‐noded prismatic and 10‐noded tetrahedral elements with quadratic interpolation functions as well as an implicit integration scheme. An algorithm for exploiting the numerical integration procedure on the computational mesh is proposed. Several numerical examples are shown. Copyright © 2010 John Wiley & Sons, Ltd.     

固结问题有限元法时步自适应研究

关于提高有限元法解的精度和稳定性问题已受到不少学者的重视。基于Biot固结理论,为提高有限元法计算的精度和稳定性,研究了固结过程中的时步自适应。采用基本原理推导出时步控制公式,从而全面控制应力和孔隙压力场。研究结果有助于准确模拟应力应变的发展,对粘土心墙土石坝等建筑物的设计及施工有重要意义。     

Analytical solutions of linear finite‐ and small‐strain one‐dimensional consolidation

Analytical solutions are presented for linear finite‐strain one‐dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one‐ and two‐way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small‐strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small‐strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non‐linear finite‐strain consolidation. They also clarify a formerly perplexing aspect of finite‐strain solution charts first noted in numerical solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

确定固结系数的固结速率半对数法

基于太沙基一维固结理论,推导了固结速率与固结时间的解析关系,为固结系数的求解开辟了新方法。该方法避免了图解法的缺陷,消除了初始沉降和次固结的影响。求解中采用最小二乘法原理,便于计算机数据处理。通过与现有方法比较,发现该方法准确、可靠和简便,可以在实际工程中推广应用。     

Finite volume approach for finite strain consolidation

The paper presents the finite volume formulation and numerical solution of finite strain one‐dimensional consolidation equation. The equation used in this study utilises a nonlinear continuum representation of consolidation with varying compressibility and hydraulic conductivity and thus inherits the material and geometric nonlinearity. Time‐marching explicit scheme has been used to achieve transient solutions. The nonlinear terms have been evaluated with the known previous time step value of the independent variable, that is, void ratio. Three‐point quadratic interpolation function of Lagrangian family has been used to evaluate the face values at discrete control volumes. It has been shown that the numerical solution is stable and convergent for the general practical cases of consolidation. Performance of the numerical scheme has been evaluated by comparing the results with an analytical solution and with the piecewise piecewise‐linear finite difference numerical model. The approach seems to work well and offers excellent potential for simulating finite strain consolidation. Further, the parametric study has been performed on soft organic clays, and the influence of various parameters on the time ate consolidation characteristics of the soil is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust partitioned block preconditioners for large‐scale geotechnical applications with soil–structure interactions

Soil–structure interaction problems are commonly encountered in geotechnical practice and remarkably characterized with significant material stiffness contrast. When solving the soil–structure interaction problems, the employed Krylov subspace iterative method may converge slowly or even fail, indicating that the adopted preconditioning method may not suit for such problems. The inexact block diagonal preconditioners proposed recently have been shown effective for the soil–structure interaction problems; however, they haven't been exploited to full capabilities. By using the same partition strategy according to the structure elements and soil elements, the partitioned block symmetric successive over‐relaxation preconditioners or partitioned block constraint preconditioners are proposed. Based on two pile‐group foundation problems and a tunnel problem, the proposed preconditioners are evaluated and compared with the available preconditioners for the consolidation analysis and the drained analysis, respectively. In spite of one additional solve associated with the structure block and multiplications with off‐diagonal blocks in the preconditioning step, numerical results reveal that the proposed preconditioners obviously possess better performance than the recently developed inexact block preconditioners. Copyright © 2013 John Wiley & Sons, Ltd.     

强夯法加固地基的多重耦合分析

强夯法加固地基的机理非常复杂,影响因素众多,且涉及到多重耦合现象。笔者综合考虑地基士的流、固、动力耦合和地基与夯锤接触表面的动力耦合情况,给出了基于三维有限单元法的计算方法和迭代格式,并对一具体算例进行了耦合数值分析,总结了地基位移、应力及接触反力等在强夯作用时间内的变化规律和在空间上的分布特征。经与实际工程资料对比,结果令人满意。说明所建立的耦合方法可用于强夯加固法求解,并提出了适宜动力分析的有效方法,可应用于其它同类问题的分析计算中。     

Reflection–transmission matrix method for the consolidation of a multilayered saturated soil

The consolidation of the layered saturated soil is an important issue in civil engineering and has been investigated extensively during the past decades. In this study, based on the Biot's theory, the reflection–transmission matrix (RTM) method for treating the layered saturated soil under axisymmetric consolidation is developed. To decouple the governing equations of the Biot's theory, the McNamee displacement functions are introduced, and the general solution for the saturated soil is obtained using the Laplace and Hankel transforms. In order to develop the RTM method for the layered saturated soil, based on the obtained general solution, the static wave vector corresponding to the state vector of the saturated soil and the transform matrix relating the aforementioned two vectors are defined. Also, the transfer matrices corresponding to the two vectors are introduced, and the representations of the RTMs for the static wave vector of the saturated soil are presented. As the state vector, static wave vector, and the transform matrix relating the two vectors are all defined in the global coordinate system, the RTMs obtained in this study thus have a reasonable physical meaning. By using the RTMs for the layered saturated soil, the solutions for the layered saturated soil subjected to external sources are derived. Comparison of results due to the proposed RTM method with some existing results and results due to the transfer matrix method validates the developed RTM method. Some numerical results are obtained based on the proposed RTM method for the layered saturated soil. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytical layer‐element method for non‐axisymmetric consolidation of multilayered soils

A numerically efficient and stable method is developed to analyze Biot's consolidation of multilayered soils subjected to non‐axisymmetric loading in arbitrary depth. By the application of a Laplace–Hankel transform and a Fourier expansion, the governing equations are solved analytically. Then, the analytical layer‐element (i.e. a symmetric stiffness matrix) describing the relationship between generalized displacements and stresses of a layer is exactly derived in the transformed domain. Considering the continuity conditions between adjacent layers, the global stiffness matrix of multilayered soils is obtained by assembling the inter‐related layer‐elements. Once the solution in the Laplace–Hankel transformed domain that satisfies the boundary conditions has been obtained, the actual solution can be derived by the inversion of the Laplace–Hankel transform. Finally, numerical examples are presented to verify the theory and to study the influence of the layered soil properties and time history on the consolidation behavior. Copyright © 2011 John Wiley & Sons, Ltd.     

考虑地下水浸没作用的固结沉降计算方法

研究了地下水浸没对附加应力减小的作用,同时分析了附加应力变化对最终沉降量的影响,给出了考虑地下水浸没作用的大、小应变条件下的固结沉降计算公式,并对几种工况下的计算结果进行了对比分析。结果表明,考虑地下水浸没作用对地基固结沉降的影响随荷载和土压缩性以及土层厚度的增加而增大,采用大变形固结理论计算固结沉降较符合实际情况。     

强夯法加固的主要设计参数研究

综合利用土体动力学理论,结合弹塑性有限元分析,研究了不同地基条件、不同的夯击方式下土体的应力-应变特征,从理论上确定了不同地基条件下,强夯法施工中的设计参数选定方法,包括锤重、落距、夯距等。在常用的地基或填方参数情况下,有效加固范围是夯锤直径的1.5～2.5倍。以此作为强夯设计依据,对工程实践具有一定的指导意义。     

A stepwise damping‐solvent extraction method for large‐scale dynamic soil–structure interaction analysis in time domain

Time‐domain analysis of dynamic soil–structure interaction based on the substructure method plays an increasing role in practical applications as compared with the frequency‐domain analysis. Efficient and accurate modelling of the unbounded soil or rock medium has been a key issue in such an analysis. This paper presents a subregional stepwise damping‐solvent extraction formulation for solving large‐scale dynamic soil–structure problems in the time domain. Accuracy and efficiency of the formulation are evaluated in detail for a classical problem involving a rigid strip foundation embedded in a half‐space. A practical large‐scale soil–structure interaction problem, which represents a high concrete gravity dam subjected to seismic load, is then analysed using the proposed method. Various responses of the dam, including time histories of the crest displacement and acceleration and contours of the peak principal stresses within the dam body, are presented. Comparisons are also made between these results with those obtained using other models for the unbounded medium. Copyright © 2007 John Wiley & Sons, Ltd.     

非饱和土拟二维平面应变固结问题的解析计算方法

基于Fredlund非饱和土一维固结理论,建立了二维平面应变条件下的固结方程组,并得到了单层非饱和土平面应变条件下的解析解。基于相关理论,假设体变系数和渗透系数都为常量,同时考虑到瞬时加载条件下,沿着土体深度方向上产生均匀或者线性分布的初始超孔隙压力,建立了二阶二元偏微分方程组。求解时,引入函数方法来降低方程的阶数,然后通过分离变量法获得方程的通解。在此基础上,结合一个针对单面排水条件下二维平面应变问题案例,通过与数值解对比,验证了所提方法的正确性。并采用所提方法计算获得了二维平面下超孔隙水压力、气压力沿垂直和水平方向消散的等时线,通过计算对比,分析了不同线性分布情况下,初始超孔隙压力对固结消散过程的影响。研究结果表明:初始超孔隙压力的不同分布对超孔隙气压力消散的影响几乎可以忽略,而对超孔隙水压力消散的影响更大。     

天然沉积结构性土的次固结变形预测方法

结构性土存在着其特有的变形和强度特性,次固结特性也表现出明显区别于与重塑土。通过对连云港天然沉积原状土和重塑土进行一维压缩次固结试验,研究了典型结构性土的次固结特性。试验结果表明,土体由于受结构性影响,结构破坏前后其次固结特性发生明显变化;结构屈服前（固结压力小于固结屈服压力）不发生次固结变形或次固结变形甚微;当土体处于屈服状态时,土体次固结变形突然增大,次固结系数Cα出现峰值;结构屈服后（固结压力大于固结屈服压力）,Cα随固结压力的增大而减小,表现为与当前的应力水平和时间密切相关的特性,应力水平对Cα的影响会随着次固结时间的增长而削弱。基于以上机制,建立了考虑结构性影响的次固结变形计算模型,该模型中Cα不仅与压缩指数Cc有关,且也与时间有关,基于该模型计算得到的Cα值和次固结变形均与试验值吻合较好。     

An efficient finite–discrete element method for quasi‐static nonlinear soil–structure interaction problems

An efficient finite–discrete element method applicable for the analysis of quasi‐static nonlinear soil–structure interaction problems involving large deformations in three‐dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil–structure interaction problems was also investigated by simulating a large‐scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd.     

基于数值建模方法的弹塑性固结问题解耦研究

研究了弹塑性固结问题的解耦方法。首先,在数值建模方法下得出土的弹塑性本构关系,推导了两类问题下的应力-应变关系统一矩阵式,并将数值建模方法与Biot固结理论相结合,建立了基于此本构关系的固结问题控制方程的增量形式。考虑应力路径的影响,讨论了此类液-固耦合问题的解耦条件,导出了在该条件下的扩散方程和非耦合控制方程,并编制有限元程序计算了两个典型算例,通过对比分析表明,该方法简单合理,能考虑剪胀性对固结规律的影响。     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical theory for one‐dimensional consolidation of clayey soils exhibiting rheological characteristics under time‐dependent loading

This paper presents analytical solutions to the one‐dimensional consolidation problem taking into consideration the rheological properties of clayey soil under variable loadings. A four‐element rheological model is introduced, and different loading types are involved, i.e. constant loading, one‐step loading, triangular loading, rectangular loading, and isosceles–trapezoidal cyclic loading. The differential equations governing consolidation are solved by the Laplace transform. Based on the solutions obtained, the influences of the rheological parameters and loading conditions on the consolidation process are investigated. It has been shown that the consolidation behavior is mainly governed by four dimensionless parameters, a₁, a₂, b, and T_v0. Load shape has a great influence on the rate of consolidation. A decrease either in the modulus of the spring in the Kelvin body or in the viscosity coefficient of independent dashpot will slow down the rate of consolidation. An increase in the viscosity coefficient of the dashpot in the Kelvin body will make the rate of consolidation increase at an early stage but decrease at a later stage. For isosceles–trapezoidal cyclic loading, the consolidation rate in each cycle reaches a maximum at the end of the constant loading phase and the minimum at the end of this cycle. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

This paper introduces an exact analytical solution for governing flow equations for one‐dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one‐way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two‐way drainage system where both soil ends allow free dissipation of pore‐air and pore‐water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first‐order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.