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.     

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

饱和多孔介质动力响应移动单元法分析

移动单元法在处理移动荷载下结构动力行为分析方面具有求解高效的优势,但目前针对饱和多孔介质动力响应的移动单元法的研究成果甚少。根据饱和多孔介质u-p格式动力控制方程,利用移动坐标系建立了饱和多孔介质瞬态及稳态动力控制方程的移动单元列式,通过编制相应的计算程序将计算结果与已有文献结果对比验证了算法的正确和有效性。基于移动单元法建立了移动荷载下饱和沥青路面-弹性基层系统计算模型,分析了移动荷载下该模型的瞬态动力响应规律,并与其稳态动力响应进行了对比分析,分析表明,其水动力特性较稳态响应呈现出明显的瞬态效应。基于稳态动力响应结果分析了荷载速度、排水边界、渗透系数对饱和沥青路面动力响应的影响规律,算例研究结果可以为分析水动力作用下沥青路面水稳定性功能损伤机制提供参考。     

A finite element algorithm for parameter identification of material models for fluid saturated porous media

In this contribution an algorithm for parameter identification of geometrically linear Terzaghi–Biot‐type fluid‐saturated porous media is proposed, in which non‐uniform distributions of the state variables such as stresses, strains and fluid pore pressure are taken into account. To this end a least‐squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the finite element method. This strategy allows parameter identification based on in situ experiments. In order to improve the efficiency of the minimization process, a gradient‐based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled two‐phase problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a slope stability problem, in which a quadratic Drucker–Prager plasticity model for the solid and a linear Darcy law for the fluid are combined. Copyright © 2001 John Wiley & Sons, Ltd.     

Large deformation dynamic analysis of saturated porous media with applications to penetration problems

This paper outlines the development as well as implementation of a numerical procedure for coupled finite element analysis of dynamic problems in geomechanics, particularly those involving large deformations and soil-structure interaction. The procedure is based on Biot’s theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of the soil is represented by either the Mohr Coulomb or Modified Cam Clay material model. The interface between soil and structure is modelled by the so-called node-to-segment contact method. The contact algorithm uses a penalty approach to enforce constraints and to prevent rigid body interpenetration. Moreover, the contact algorithm utilises a smooth discretisation of the contact surfaces to decrease numerical oscillations. An Arbitrary Lagrangian–Eulerian (ALE) scheme preserves the quality and topology of the finite element mesh throughout the numerical simulation. The generalised-α method is used to integrate the governing equations of motion in the time domain. Some aspects of the numerical procedure are validated by solving two benchmark problems. Subsequently, dynamic soil behaviour including the development of excess pore-water pressure due to the fast installation of a single pile and the penetration of a free falling torpedo anchor are studied. The numerical results indicate the robustness and applicability of the proposed method. Typical distributions of the predicted excess pore-water pressures generated due to the dynamic penetration of an object into a saturated soil are presented, revealing higher magnitudes of pore pressure at the face of the penetrometer and lower values along the shaft. A smooth discretisation of the contact interface between soil and structure is found to be a crucial factor to avoid severe oscillations in the predicted dynamic response of the soil.     

饱和多孔介质动力应变局部化分析中的内尺度律

对饱和多孔介质动力应变局部化分析中的材料内尺度律问题进行研究，讨论了当软化发生时饱和多孔介质分析的动力学稳定性问题，研究工作表明，由于液体相的作用，饱和多孔材料的动力学特性与单相固体材料有着明显的不同，特别是当应变局部化发生时，在特定情况下将仍存在可通过材料软化区域的动力波，也就是波动问题仍具有弥散特性，在此基础上，给出多孔材料的内尺度律的判定公式，讨论了内尺度律存在的条件。     

可压缩流体饱和孔隙介质中孔隙压力波传播数值分析

首次将高精度时空守恒元/解元方法推广到可压缩流体饱和孔隙介质中孔隙压力波传播的数值计算中。将孔隙度梯度从源（汇）项中分离,直接引入流通量,改进了理论模型。通过对孔隙介质激波问题的数值模拟,验证了方法的精度和有效性。在此基础上,提出了孔隙介质中二维黎曼问题,并揭示了孔隙压力波存在接触间断、激波、膨胀波、压缩波等复杂的结构特征。该成果对二氧化碳地质封存、二氧化碳提高石油采收率、页岩气压裂开采以及地震破裂过程的研究具有重要的理论与应用意义。     

Modeling of dynamic cohesive fracture propagation in porous saturated media

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.     

含液各向异性多孔介质应变局部化分析

工程中的含液多孔介质如饱和或非饱和岩土材料往往具有各向异性特性。采用Rudnicki建立的针对岩土材料的各向异性本构模型,对轴对称压缩试验中的含液多孔介质骨架的各向异性力学行为进行了分析;基于不连续分叉理论,导出了静态非渗流条件下处于轴对称应力状态的含液多孔介质应变局部化发生的临界模量、剪切带方向以及不连续速度矢量的显式表达式,在此基础上计算并讨论了材料参数变化和孔隙液体存在对各向异性多孔介质应变局部化的影响。     

Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd.     

Explicit meshfree solution for large deformation dynamic problems in saturated porous media

In this paper a new methodology to simulate saturated soils subjected to dynamic loadings under large deformation regime (locally up to 40% in equivalent plastic strain) is presented. The coupling between solid and fluid phases is solved through the complete formulation of the Biot’s equations. The additional novelty lies in the employment of an explicit time integration scheme of the \(u-w\) (solid displacement–relative fluid displacement) formulation which enables us to take advantage of such explicit schemes. Shape functions based on the principle of maximum entropy implemented in the framework of Optimal Transportation Meshfree schemes are utilized to solve both elastic and plastic problems.     

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。     

频域内饱和多孔介质的参数反演分析

基于Biot理论,假定固体颗粒和孔隙内流体均不可压缩,建立了以固体骨架位移表示的的控制方程.考虑单层饱和多孔介质在竖向简谐荷载作用下一维动力响应,通过理论推导获得了骨架位移、应力以及孔隙流体压力等物理量的解析表达式.基于饱和土的简谐动力模型试验数据,与所得到的理论解答相结合,将饱和多孔介质材料参数反演问题归结为非线性多峰函数的最优化问题.全局最优解的求解采用了遗传算法和模拟退火算法,并通过试验和数值算例验证了所得材料参数的正确性.     

A stable meshfree method for fully coupled flow-deformation analysis of saturated porous media

A fully coupled meshfree algorithm is proposed for numerical analysis of Biot’s formulation. Spatial discretization of the governing equations is presented using the Radial Point Interpolation Method (RPIM). Temporal discretization is achieved based on a novel three-point approximation technique with a variable time step, which has second order accuracy and avoids spurious ripple effects observed in the conventional two-point Crank Nicolson technique. Application of the model is demonstrated using several numerical examples with analytical or semi-analytical solutions. It is shown that the model proposed is effective in simulating the coupled flow deformation behaviour in fluid saturated porous media with good accuracy and stability irrespective of the magnitude of the time step adopted.     

Micromechanics of saturated and unsaturated porous media

The homogenization method is used to determine the formulation of the behaviour of both saturated and unsaturated porous media. This approach makes it possible to assess the validity of the effective stress concept as a function of the properties of the porous media at the microscopic scale. Furthermore, the influence of the morphologies of the solid and fluid phases on the macroscopic behaviour is studied. The strain induced by drying is examined as a function of the morphological properties. Copyright © 2002 John Wiley & Sons, Ltd.     

Hybrid time integration and coupled solution methods for nonlinear finite element analysis of partially saturated deformable porous media at small strain

The goal of the paper is to determine the most efficient, yet accurate and stable, finite element nonlinear solution method for analysis of partially saturated deformable porous media at small strain. This involves a comparison between fully implicit, semi‐implicit, and explicit time integration schemes, with monolithically coupled and staggered‐coupled nonlinear solution methods and the hybrid combination thereof. The pore air pressure p_a is assumed atmospheric, that is, p_a=0 at reference pressure. The solid skeleton is assumed to be pressure‐sensitive nonlinear isotropic elastic. Coupled partially saturated ‘consolidation’ in the presence of surface infiltration and traction is simulated for a simple one‐dimensional uniaxial strain example and a more complicated plane strain slope example with gravity loading. Three mixed plane strain quadrilateral elements are considered: (i) Q4P4; (ii) stabilized Q4P4S; and (iii) Q9P4; “Q” refers to the number of solid skeleton displacement nodes, and “P” refers to the number of pore fluid pressure nodes. The verification of the implementation against an analytical solution for partially saturated pore water flow (no solid skeleton deformation) and comparison between the three time integration schemes (fully implicit, semi‐implicit, and explicit) are presented. It is observed that one of the staggered‐coupled semi‐implicit schemes (SIS(b)), combined with the fully implicit monolithically coupled scheme to resolve sharp transients, is the most efficient computationally. Copyright © 2015 John Wiley & Sons, Ltd.     

Embedded discontinuity finite element modeling of fluid flow in fractured porous media

In many geomaterials, particularly rocks and clays, permeability is greatly enhanced by the presence of fractures. Fracture sets create an overall permeability that is anisotropic, enhanced in the directions of the fractures. In modeling the fractures via a finite element method, for example, meshing around these fractures can become quite difficult and result in computationally intensive systems. In this article, we develop a relatively simple method for including the fractures within the elements. Flow through the bulk medium is assumed to be governed by Darcy’s law, and the flow on the fracture by a generalization of the law. This model is embedded in a finite element framework, with the fractures passing through the elements. In this formulation, elements with fractures are given an enhanced permeability in the direction of the fractures. With these enhancements, the material essentially becomes anisotropically more permeable in the direction of fracture sets.     

Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

Finite element procedures for numerical solution of various engineering problems are often based on variational formulations. In this paper, a parametric variational principle applicable to elastic-plastic coupled field problems in consolidation analysis of saturated porous media is presented. This principle can be used to solve problems where materials are inconsistent with Drucker's postulate of stability, such as in non-associated plasticity flow or softening problems. The finite element formulation was given, and it can be solved by either the conventional method or a parametric quadratic programming method.