不排水不可压缩条件下两相介质的两重网格算法

对于不排水、不可压缩饱和软土地基的固结问题的有限元分析,可以用Biot固结方程来考虑土体颗粒与孔隙水间的相互作用。由于受Babuska-Brezzi稳定条件的限制,用常规的等插值u-p混合有限元法求解将导致孔隙压力出现紊乱的结果。提出了基于位移和压力线性等插值函数的两重网格,但位移独立变量总数大于独立压力变量总数的计算方法,可以满足Babuska-Brezzi稳定条件,使得位移场和压力场单元插值阶数保持一致。通过几个简单算例验证了提出方法的正确性。     

Transverse and longitudinal fluid flow modelling in fractured porous media with non‐matching meshes

A new discrete fracture model is introduced to simulate the steady‐state fluid flow in discontinuous porous media. The formulation uses a multi‐layered approach to capture the effect of both longitudinal and transverse permeability of the discontinuities in the pressure distribution. The formulation allows the independent discretisation of mesh and discontinuities, which do not need to conform. Given that the formulation is developed at the element level, no additional degrees of freedom or special integration procedures are required for coupling the non‐conforming meshes. The proposed model is shown to be reliable regardless of the permeability of the discontinuity being higher or lower than the surrounding domain. Four numerical examples of increasing complexity are solved to demonstrate the efficiency and accuracy of the new technique when compared with results available in the literature. Results show that the proposed method can simulate the fluid pressure distribution in fractured porous media. Furthermore, a sensitivity analysis demonstrated the stability regarding the condition number for wide range values of the coupling parameter.     

非共面复合加载条件下桶形基础稳定性研究

采用荷载-位移联合搜索方法,对于饱和软黏土地基上裙板式桶形基础在水平荷载H、力矩M与扭矩T的非共面复合加载条件下的稳定性进行了比较系统的三维有限元分析,主要探讨了在不同荷载空间内桶形基础的破坏包络轨迹。在分析中,地基土服从基于Tresca屈服准则的理想弹塑性本构关系。计算结果表明,与传统共面复合加载情况相比,非共面复合加载条件下桶形基础的破坏包络面形状有较大差异。非共面复合加载情况下,包络面形状不依赖于基础埋深比,可用简单的圆或椭圆方程进行描述。根据有限元计算结果,将已有的三自由度破坏包络面方程扩展到六自由度复合加载空间内,进而初步建议了一个六自由度破坏包络面方程,并对于实际工程中常用的桶形基础埋深比,给出了方程中偏心度参数取值的确定方法。该方程可用来合理评价复杂荷载条件下软黏土地基上桶形基础承载力。     

基于非饱和土固结理论的有限元强度折减法

库水位下降使库岸坡体内产生饱和－非饱和非稳定渗流,非稳定渗流作用是边坡失稳的重要原因之一。为了分析非稳定渗流对边坡稳定性的影响,首先推导了固、液两相孔隙介质的固结方程,考虑了土体渗流与变形的耦合作用。在此基础上结合有限元强度折减法求解边坡稳定安全系数,将渗流、变形及稳定分析采用一套统一的有限元方法。并通过算例分析了库水位骤降情况下,坡体的渗透系数、水位降落比对稳定安全系数的影响,计算结果表明,所提的理论和方法是有效可行的,为饱和-非饱和非稳定渗流作用下边坡稳定问题的分析提供了实用工具。     

水位波动下非饱和心墙土坝体的渗流和稳定性

基于Richards方程,对坝体的饱和-非饱和渗流场进行了模拟,再根据饱和-非饱和渗流场和非饱和土抗剪强度公式,对坝体的稳定性进行了分析。结果表明,水位骤降过程中坝体的安全系数通常呈现先缓慢增加后迅速减小的变化过程,分析坝体失稳时塑性区和位移场发现,水位下降的初期,坝体左侧坡体的安全系数要低于坝体右侧坡体,但水位下降到一定程度,右侧坡体的安全系数迅速减小,并先于左侧坡体失稳;采用有限元强度折减法用于多坡面边坡稳定分析时,只能获得最小安全系数的包络线;心墙具有隔水防渗的作用,对水位变化渗流具有阻尼作用。     

Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model

The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non-linear stress–strain behaviour of soil. The Cam Clay model is revised to model the stress–strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.     

Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming

In this paper, the formulation of the lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming is described. The finite element concept was used to discretize the soil mass into 3‐noded triangular elements. The stress field was modeled using a linear interpolation within the elements while stress discontinuities were permitted to occur at the shared edges of adjacent elements. An elliptical yield criterion was adopted to model the anisotropic undrained strength of the clay. A statically admissible stress field was defined by enforcing the equilibrium equations within all triangular elements and along all shared edges of adjacent elements, stress boundary conditions, and no stress violation of the anisotropic strength envelope cast in the form of a conic quadratic constraint. The lower bound solution of the proposed formulation was solved by second‐order cone programming. The proposed formulation of the anisotropic undrained strength criterion was validated through comparison of the model's predictions with the known exact solutions of strip footings, and was applied to solve undrained stability of a shallow unlined square tunnel. Computational performance between the proposed approach of second‐order cone programming and linear programming was examined and discussed.     

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation

This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.     

Coupled discrete element and finite volume solution of two classical soil mechanics problems

One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier–Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAM for the computational fluid dynamics. The particle–fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.     

Dynamics of unsaturated soils using various finite element formulations

Unsaturated soils are three‐phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress–strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Two‐phase dynamic analysis by material point method

This paper extends the material point method to analyze coupled dynamic, two‐phase boundary‐valued problems via a velocity formulation, in which solid and fluid phase velocities are the variables. Key components of the proposed approach are the adoption of Verruijt's sequence of update steps when integrating over time and the enhancement of volumetric strains. The connection between fractional step method and the time‐stepping algorithm presented in this paper is addressed. Enhancement of volumetric strains allows lower order variations in pressure and mitigates spurious pressure fields and locking that plague low‐order finite‐element implementations. A stress averaging technique to smoothen stress variations is proposed, and the local damping procedure adopted by FLAC is extended to handle two‐phase problems. Special Kelvin‐Voigt boundaries are developed to suppress reflections at artificial boundaries. Idealized examples are presented to demonstrate the capability of the proposed framework to accurately capture the physics of wave propagation, consolidation and wave attack on a sea dike. Copyright © 2012 John Wiley & Sons, Ltd.     

考虑前期降雨过程的边坡稳定性分析

基于三峡库区实测降雨资料,研究了不同初始条件对不同土体边坡稳定性影响,建议了能够反映边坡含水状态的初始条件选取方法。在此基础上,采用非饱和渗流分析方法研究了前期降雨对不同土体边坡稳定性影响,以典型的砂土和黏土边坡为例初步探索了前期降雨对边坡稳定性影响规律。结果表明：初始条件对不同土体边坡稳定性影响不同;建议将多年平均降雨量对应的稳态渗流场作为初始条件进行非饱和渗流分析。边坡土体渗透系数越低,边坡稳定性受前期降雨的影响越大、影响时间也越长。砂土和黏土边坡稳定性分析时建议至少考虑15 d以上的前期降雨,对于砂土边坡还应根据这15 d前面5 d的降雨情况确定是否需要增加计算天数。短历时高强度前期降雨对砂土边坡稳定性影响更大,而长历时低强度前期降雨对黏土边坡稳定性影响更大。累积前期降雨量可以作为判断边坡最小安全系数出现时刻的依据。砂土边坡出现最小安全系数时刻与10 d累积前期降雨量最大的时刻较为吻合,而黏土边坡则与15 d累积前期降雨量最大的时刻较为吻合。     

Limit analysis for saturated porous media without fluid flow calculation

Application of yield design to porous media usually requires a preliminary calculation of the fluid flow net. The stability analysis is then carried out with seepage forces associated with the flow. We assume here that the flow is steady and that the yield criterion is defined by a function of the effective stress tensor. The formulation that we propose here allows taking into account seepage force in the expression of the kinematic stability conditions by means of hydraulic boundary conditions without calculation of the fluid flow. One obtains a formulation of the kinematic condition similar to the case of classic, non-porous media. The method is illustrated by two examples: a cylinder subjected to fluid flow and a vertical cut. It can be adapted to various boundary conditions and to the case of a criterion defined by a function of a generalized effective stress tensor. We also give a method to derive rigorous lower bounds using approximate fluid pressure field. Copyright © 2004 John Wiley & Sons, Ltd.     

库水位下降过程中土坡稳定强度折减有限元分析

采用强度折减有限元法,考虑边坡土体的非饱和-非稳定渗流过程,从坡体内浸润线位置、土体的渗透系数、水位下降速率、下降比及基质吸力等5个方面研究了水位下降过程中岸坡的整体稳定性。结果表明,水位下降速率对高渗透性土坡内孔压的影响显著,对低渗透性土坡内孔压影响较小,对边坡安全系数的影响程度可达15%。     

Transient bifurcation condition of partially saturated porous media at finite strain

Bifurcation of unsaturated soils into a localized shear band is a ubiquitous failure mode of partially saturated soils. The density and degree of saturation have major impacts on the inception of localized deformations in unsaturated soils. Unsaturated fluid flow may dramatically change the density and degree of fluid saturation of unsaturated soils. Therefore, the unsaturated fluid flow is a potential trigger for shear banding in such materials. In this paper, we derive a simplified bifurcation condition of localized deformation in unsaturated soils under the local transient condition at finite strain. This transient bifurcation condition is implemented into a nonlinear finite element code to study the inception of localized deformation in unsaturated soil specimens. Numerical simulations are conducted to study the impact of soil fabrics of density, a ‘bonding’ variable, and intrinsic permeability on the inception of localized failures via the transient bifurcation criterion. Mesh sensitivity analysis is performed to demonstrate the viscosity effect of unsaturated fluid flow on the localized deformation. Numerical simulations demonstrate that the transient bifurcation condition can detect the localized deformation triggered by the internal unsaturated fluid flow process in unsaturated soils. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite element modelling of transport of organic chemicals through soils

Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed.     

相间相互作用原理与土壤水动力学基本方程

进一步阐明了多相介质力学分析的相间相互作用原理.应用相间相互作用原理重新推导了饱和土壤和非饱和土壤水分运动的控制方程,使两者具有统一的表达形式和理论基础.说明了达西定律的物理意义,在此基础上给出了非饱和土壤导水系数与饱和土壤渗透系数之间关系的表达式,该表达式在饱和条件下退化为饱和土的渗透系数.引用大连地区亚粘土和硅微粉在非饱和稳态渗流条件下的渗透试验结果验证了导水系数和饱和土的渗透系数之间的关系.     

Modelling of coupled fluid‐mechanical problems in fractured geological media using enriched finite elements

Geological environments, such as petroleum reservoirs, normally exhibit physical discontinuities, for example, fractures and faults. Because of the reduced thickness of these discontinuities, finite element formulations with strong discontinuity have been applied to the numerical modelling of geological environments. Until now, two relevant characteristics of petroleum reservoirs have not been addressed by these formulations. The first is the pore pressure jump in the direction normal to a discontinuity in a fluid‐mechanical coupling condition, which is present primarily in sealing faults owing to the contrast of permeability with the porous medium. The absence of this jump can affect the prediction of the deformability of a physical discontinuity. Furthermore, reservoir models frequently use coarse meshes. Thus, the method used to evaluate the pore pressure in the discontinuity may exhibit a strong dependence relative to the mesh refinement. Based on these characteristics, in this study, a formulation of an enriched finite element for application to coupled fluid‐mechanical problems with pre‐existing physical discontinuities saturated by a single fluid is presented. The formulation employs discontinuous interpolation functions and enables the reproduction of jumps of displacement and pore pressure associated with a discontinuity inside the element without the need to discretise it. An approximation to estimate the pore pressure in the discontinuity was developed, one which seeks to minimise the influence of refinement. The element's response is verified by comparison with a one‐dimensional analytical solution and simple examples that are simulated using commercial software. Copyright © 2015 John Wiley & Sons, Ltd.     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.