多孔介质中含均相/非均相反应传质过程数值模拟

结合化学反应方程式,并应用多孔多相介质溶混污染物输运过程的数值模型,对多孔多相介质中含均相/非均相化学反应传质过程进行了数值模拟。化学反应主要包含均相快速/慢速和非均相快速/慢速等5种化学反应过程,溶质输运行为的控制机制主要考虑对流、扩散及降解、吸附等。基于原有的隐式特征线Galerkin离散化的有限元方法,求解模型控制方程的边值初值问题,求解过程中把均相化学反应物质中按照反应物和生成物分开,非均相反应物质按照固相和液相分开,对均相反应物及非均相液相物质浓度耦合求解,而均相生成物和非均相固相物质独立求解。使方程组按照其不同类型进行分类,同时可减少未知数的个数。对于含有非线性内状态变量的右端项进行迭代求解。数值例题结果验证了所提出的数值方法的有效性、计算精度和稳定性。     

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.     

Numerical modelling of competitive components transport with non‐linear adsorption

A characteristic finite element (CFE) algorithm for modelling contaminant transport problems coupled with non‐linear competitive adsorption is presented. An alternative algorithm, termed as the transport‐equilibrium Petrov–Galerkin (TEPG) methods in this paper, is also presented for comparison. Through analyses of a number of examples with Peclet number ranging from zero to infinity, it is shown that the CFE algorithm is very competitive with the middle–point TEPG method in terms of accuracy, stability and efficiency. The fully explicit and fully implicit TEPG methods are found to be less appropriate for transport problems coupled with non‐linear equilibrium equations. Copyright © 2000 John Wiley & Sons, Ltd.     

Estimation of base settlement from the surface subsidence profile: Plane‐field of displacements

According to Litwiniszyn's theory, subsidence over a yielding underground geo‐structure is seen as a stochastic (Markov) process. This theory leads to a single, linear parabolic differential equation of diffusion–convection type (D–C equation) in the plane‐field of displacements. If the boundary conditions for the governing D–C equation are prescribed along the shear bands, i.e. at ‘moving’ boundaries—it has been observed from small‐scale model experiments that the subsiding process is always confined between a set of inclined shear bands—then the resulting equation is nonlinear. The inverse problem for this nonlinear equation, i.e. the problem of determining the base displacement using the surface subsidence as ‘initial’ condition, is ill‐posed and estimation of the base displacement from a given surface subsidence profile is not possible. In the present paper the domain of integration of the governing D–C equation is fixed (and bounded)—the boundaries are not evolving. Hence, the governing equation remains linear parabolic. The advantage is that this linear differential equation admits an analytical solution, under the trap‐door mechanism assumption, that enables a direct solution to the inverse problem. Copyright © 2008 John Wiley & Sons, Ltd.     

Efficient reliability method for implicit limit state surface with correlated non‐Gaussian variables

In contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u‐space), the reliability analysis that is simply realized in the original space (x‐space, non‐Gaussian type) would be more efficient for practical use, for example, with the Low and Tang's constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for first‐order reliability method is derived in this paper. Also, the new algorithm is simply formulated in x‐space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non‐Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed‐form solution. With the aid of numerical differentiation analysis in x‐space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces. Copyright © 2015 John Wiley & Sons, Ltd.     

Implicit numerical integration for a kinematic hardening soil plasticity model

Soil models based on kinematic hardening together with elements of bounding surface plasticity, provide a means of introducing some memory of recent history and stiffness variation in the predicted response of soils. Such models provide an improvement on simple elasto‐plastic models in describing soil behaviour under non‐monotonic loading. Routine use of such models requires robust numerical integration schemes. Explicit integration of highly non‐linear models requires extremely small steps in order to guarantee convergence. Here, a fully implicit scheme is presented for a simple kinematic hardening extension of the Cam clay soil model. The algorithm is based on the operator split methodology and the implicit Euler backward integration scheme is proposed to integrate the rate form of the constitutive relations. This algorithm maintains a quadratic rate of asymptotic convergence when used with a Newton–Raphson iterative procedure. Various strain‐driven axisymmetric triaxial paths are simulated in order to demonstrate the efficiency and good performance of the proposed algorithm. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite-element method in modeling geologic transport processes

Deterministic mathematical modeling of complex geologic transport processes may require the use of odd boundary shapes, time dependency, and two or three dimensions. Under these circumstances the governing transport equations must be solved by numerical methods. For a number of transport phenomena a general form of the convective-dispersion equation can be employed. The solution of this equation for complicated problems can be solved readily by the finite-element method. Using quadrilateral isoparametric elements or triangular elements and a computational algorithm based on Galerkin's procedure, solutions to unsteady heat flux from a dike and seawater intrusion in an aquifer have been obtained. These examples illustrate that the finite-element numerical procedure is well suited for solving boundary-value problems resulting from modeling of complex physical phenomena.     

Numerical solution for consolidation and desiccation of soft soils

The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

Displacement‐controlled method and its applications to material non‐linearity

For the analysis of non‐linear problems, the displacement‐controlled method (DCM) has a more extensive application scope and more powerful abilities than the load‐controlled method (LCM). However, difficulties of the DCM's procedure not amenable to most finite element implementations of the conventional LCM have restricted its applications in geomechanics. By means of Sherman–Morrison's theorem, the solution of DCM is improved. The improved procedure is characterized by high efficiency, good numerical stability and a programme structure similar to LCM. Two aspects of applications of DCM are illustrated. The first application is to compute the response of a structure under a given load level like the conventional finite element analysis. The second application is to trace the equilibrium path of a structure under a given load distribution type. A simple but effective algorithm is presented for automatically adjusting the step length in tracing the equilibrium path. Examples illustrate that the proposed procedures are suited for modelling complicated non‐linear problems in geomechanics. Copyright © 2005 John Wiley & Sons, Ltd.     

Implicit integration of a mixed isotropic–kinematic hardening plasticity model for structured clays

In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Three‐dimensional finite elements for the analysis of soil contamination using a multiple‐porosity approach

A three‐dimensional finite‐element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non‐equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro‐pores of aggregated topsoils, as well as non‐equilibrium sorption. A Galerkin weighted‐residual statement for the three‐dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer. Copyright © 2005 John Wiley & Sons, Ltd.     

Boundary Element based Discontinuous Deformation Analysis

A Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Study of the free surface flow of water–kaolinite mixture by moving particle semi‐implicit (MPS) method

The flow of water–kaolinite mixtures exhibits a non‐Newtonian nature that differs from the flow of Newtonian fluid. The varying viscosities and shear history of non‐Newtonian fluid flows necessitate the use of a rheology model in moving particle semi‐implicit (MPS) for the numerical studies. On the other hand, the Lagrangian method has the advantage of handling free surface flows with large deformation and fragmentation. This study proposes a mesh‐free Lagrangian method, namely, the MPS method, together with a simple rheology model to investigate the non‐Newtonian free surface flows. The rheological parameters required in the rheology model are determined based upon experiments. The proposed method is applied to a water–kaolinite mixture collapse problem and is proved to be capable of reproducing the significant flow features observed in laboratory experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

不流动水与非平衡吸附作用对溶质运移影响的数值模型-MIENESOR

不流动水与非平衡吸附作用对溶质在孔隙介质中的运移有很大影响,“两点-两区”模型是目前研究不流动水与非平衡吸附作用的较为完善和实用的模型。在溶质运移的“两点-两区”模型的基础上,同时考虑了土壤对溶质的平衡和非平衡吸附作用,开发了MIENESOR数值模型,并给出了基于有限差和有限元法联合的数值解,编制了相应的计算机程序。对MIENESOR数值模型的案例验算表明：该模型能很好地揭示溶质在包气带和含水层中运移的规律,所开发的计算机程序稳定性较强,可用于实际。     

A fully convex reformulation of the original Matsuoka–Nakai failure criterion and its implicit numerically efficient integration algorithm

This paper presents a reformulation of the original Matsuoka–Nakai criterion for overcoming the limitations which make its use in a stress point algorithm problematic. In fact, its graphical representation in the principal stress space is not convex as it comprises more branches, plotting also in negative octants, and it does not increase monotonically as the distance of the stress point from the failure surface rises. The proposed mathematical reformulation plots as a single, convex surface, which entirely lies in the positive octant of the stress space and evaluates to a quantity which monotonically increases as the stress point moves away from the failure surface. It is an exact reproduction, and not an approximated one, of the only significant branch of the original criterion. It is also suitable for shaping in the deviatoric plane the yield and plastic potential surfaces of complex constitutive models. A very efficient numerical algorithm for the implicit integration of the proposed formulation is presented, which enables the evaluation of the stress at the end of each increment by solving a single scalar equation, both for associated and non‐associated plasticity. The algorithm can be easily adapted for other smooth surfaces with linear meridian section. Finally, a close expression of the consistent Jacobian matrix is given for achieving quadratic convergence in the external structural newton loop. It is shown that all this results in extremely fast solutions of boundary value problems. Copyright © 2013 John Wiley & Sons, Ltd.     

饱和多孔介质中水力-力学-传质耦合过程的混合有限元法

对饱和多孔介质提出了一个含溶混污染物输运（传质）过程的混合元方法,其中污染物输运过程数学模型包含了对流、机械逸散、分子弥散和吸附等机制。固相位移、应变和有效应力,孔隙水压力、压力空间梯度和Darcy速度,污染物浓度、浓度空间梯度和浓度流量在单元内均为独立变量分别插值。基于胡海昌-Washizu三变量广义变分原理,结合可以滤掉虚假振荡的特征线方法,推导出饱和土中水力-力学-传质耦合问题控制方程的单元弱形式,并导出了混合元计算公式。数值模拟证明了所提出的方法可以提供与传统4点积分方案同样精度,同时能够提高计算效率。     

A coupled two‐phase fluid flow and elastoplastic deformation model for unsaturated soils: theory,implementation, and application

Although numerous numerical models have been proposed for simulating the coupled hydromechanical behaviors in unsaturated soils, few studies satisfactorily reproduced the soil–water–air three‐phase coupling processes. Particularly, the impacts of deformation dependence of water retention curve, bonding stress, and gas flow on the coupled processes were less examined within a coupled soil–water–air model. Based on our newly developed constitutive models (Hu et al., 2013, 2014, 2015) in which the soil–water–air couplings have been appropriately captured, this study develops a computer code named F²Mus3D to investigate the coupled processes with a focus on the above impacts. In the numerical implementation, the generalized‐α time integration scheme was adopted to solve the equations, and a return‐mapping implicit stress integration scheme was used to update the state variables. The numerical model was verified by two well‐designed laboratory tests and was applied for modeling the coupled elastoplastic deformation and two‐phase fluid flow processes in a homogenous soil slope induced by rainfall infiltration. The simulation results demonstrated that the numerical model well reproduces the initiation of a sheared zone at the toe of the slope and its propagation toward the crest as the rain infiltration proceeds, which manifests a typical mechanism for rainfall‐induced shallow landslides. The simulated plastic strain and deformation would be remarkably underestimated when the bonding stress and/or the deformation‐dependent nature of hydraulic properties are ignored in the coupled model. But on the contrary, the negligence of gas flow in the slope soil results in an overestimation of the rainfall‐induced deformation. Copyright © 2015 John Wiley & Sons, Ltd.