Accurate and stablised time integration strategy for saturated porous media dynamics

Acta Geotechnica - When applying equal-order monolithic schemes for the solution of incompressible fluid saturated porous media dynamics, the resulting pressure field often exhibit spurious...     

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.     

含裂隙饱和多孔介质流-固耦合的扩展有限元分析

基于应力平衡方程、渗流连续性方程以及改进的Biot有效应力原理,建立了含裂隙可变形饱和多孔介质流-固全耦合问题的控制方程。流体在介质和裂隙中的流动均满足达西定律,得到的非线性全耦合方程不仅反映多孔介质内部物理量的耦合效应,还考虑介质与裂隙之间的耦合作用。扩展有限元法在处理含裂隙问题时具有独特的优势,采用普通有限元和扩展有限元法构建了数值计算体系。在进行空间离散时,介质内部的位移和孔隙压力均采用普通的有限元进行离散;裂隙处的位移模式引入扩展有限元中的两类附加位移函数,以反映裂隙面的位移强不连续性和裂隙端部的应力奇异性;引入孔隙压力加强函数,以体现裂隙法向孔隙压力的弱不连续特征。使用向后差分格式进行时间离散。算例验证了该模型和算法的正确性和有效性,分析了裂隙的存在对流体流动的延迟作用、裂隙中张开位移及孔隙压力等物理量的分布情况,讨论了渗透率、外部流量的改变对计算结果的影响。     

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.     

空心圆柱饱和多孔介质热固结问题的解析解

基于考虑热渗效应和等温热流效应的热-水-力耦合的线性热弹性固结控制方程,建立无限长空心圆柱饱和多孔介质热固结问题的一种理论求解方法。该方法先给出Laplace变换域上的解,然后,利用Stehfest法求其数值逆变换。该理论解考虑了空心圆柱体内、外透水界面随时间变化的外力和温度荷载耦合作用过程。最后,通过一算例分析了饱和多孔介质的热固结特征,给出其温度、孔压、位移和应力的演化规律     

A model for moisture and heat flow in fractured unsaturated porous media

The present study investigates propagation of a cohesive crack in non‐isothermal unsaturated porous medium under mode I conditions. Basic points of skeleton deformation, moisture, and heat transfer for unsaturated porous medium are presented. Boundary conditions on the crack surface that consist of mechanical interaction of the crack and the porous medium, water, and heat flows through the crack are taken into consideration. For spatial discretization, the extended finite element method is used. This method uses enriched shape functions in addition to ordinary shape functions for approximation of displacement, pressure, and temperature fields. The Heaviside step function and the distance function are exploited as enrichment functions for representing the crack surfaces displacement and the discontinuous vertical gradients of the pressure and temperature fields along the crack, respectively. For temporal discretization, backward finite difference scheme is applied. Problems solved from the literature show the validity of the model as well as the dependency of structural response on the material properties and loading. Copyright © 2016 John Wiley & Sons, Ltd.     

A boundary integral method for steady flow in unsaturated porous media

The governing equation for steady flow in a homogeneous, partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function which varies exponentially with capillary-pressure head. The resulting linear field equation is a steady Fokker–Planck equation and is well-suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is often used in soil physics and is known to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM for obtaining numerical solutions is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code and a finite element code that solves the fully non-linear problem is excellent, and is achieved at a substantial advantage in computer processing time. As an illustrative example, the code is applied to determine the distribution of moisture in the vicinity of a tunnel.     

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 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.     

饱和多孔介质热-水-力控制方程耦合项的意义及耦合影响分析

基于饱和多孔介质完全耦合条件下热-水-力控制方程的一般形式,对各耦合项的物理意义进行了分析。以等温条件下水-力耦合的Biot渗透固结理论和等压条件下热-力耦合的热弹性理论两种退化形式为基础,给出耦合系数的物理意义及其函数表达式。研究表明,其中一些耦合系数实际上有相同的物理意义和数学形式,因而可使控制方程得到简化。针对不同的介质特性以及热、水、力条件,给出几种特定情形下控制方程的简化形式。以无限大多孔介质中球域热源的热力学响应分析为例,对一些耦合项的影响程度进行了比较研究。     

A low-dimensional subsurface model for saturated and unsaturated flow processes: ability to address heterogeneity

A low-dimensional model that describes both saturated and unsaturated flow processes in a single equation is presented. Subsurface flow processes in the groundwater, the vadose zone, and the capillary fringe are accounted for through the computation of aggregated hydrodynamic parameters that result from the integration of the governing flow equations from the bedrock to the land surface. The three-dimensional subsurface flow dynamics are thus described by a two-dimensional equation, allowing for a drastic reduction of model unknowns and simplification of the model parameterizations. This approach is compared with a full resolution of the Richards equation in different synthetic test cases. Because the model reduction stems from the vertical integration of the flow equations, the test cases all use different configurations of heterogeneity for vertical cross-sections of a soil-aquifer system. The low-dimensional flow model shows strong consistency with results from a complete resolution of the Richards equation for both the water table and fluxes. The proposed approach is therefore well suited to the accurate reproduction of complex subsurface flow processes.     

A flow mechanism for layering in a heterogeneous porous medium

The flow of a particle fluid mixture through a heterogeneous permeable material is studied with a view to obtaining characteristic fingerprints for the structures that such flows may exhibit. This flow has a variable density and behaves as a compressible fluid, with the compressibility derived from the variations of the local field variables. Both pressure-sensitive or speed-fluctuation-dependent rheologies are studied in the steady state and a speed-fluctuation-dependent material is studied in a time-dependent analysis. The salient findings are that for a pressure-sensitive material structures normal to the mean flow direction are obtained. For the speed-fluctuation-dependent rheology, the pressure structures are normal to the mean flow, whereas the density structures are aligned with the flow (fingering).Electronic Supplementary Material Electronic Supplementary Material is available in the online version of this article at .     

Modeling coupled unsaturated and saturated nitrate distribution of the aquifer Westliches Leibnitzer Feld, Austria

The aquifer Westliches Leibnitzer Feld, Austria, is a significant resource for regional and supraregional drinking water supply for more than 100,000 inhabitants, but the region also provides excellent agricultural conditions. This dual use implicates conflicts (e.g., non-point source groundwater pollution by nitrogen leaching), which have to be harmonized for a sustainable coexistence. At the aquifer scale, numerical models are state-of-the-art tools to simulate the behavior of groundwater quantity and quality and serve as decision support system for implementing groundwater protecting measures. While fully and iteratively coupled simulation models consider feedback between the saturated and unsaturated zone, sandy soil conditions and groundwater depths beneath the root zone allow the use of a unidirectional sequential coupling of the unsaturated water flow and nitrate transport model SIMWASER/STOTRASIM with FEFLOW for the investigation area. Considering separated inputs of water and nitrogen into groundwater out of surface water bodies, agricultural, residential and forested areas, first simulation results match observed groundwater tables, but underestimate nitrate concentrations in general. Thus, multiple scenarios assuming higher nitrogen inputs at the surface are simulated to converge with measured nitrate concentrations. Preliminary results indicate that N-input into the groundwater is strongly dominated by contributions of agricultural land.     

An adaptive time integration scheme for blast loading on a saturated soil mass

This paper presents a time integration scheme capable of simulating blast loading of relatively high frequency on porous media, using coarse meshes. The scheme is based on the partition of unity finite element method. The discontinuity is imposed on the velocity field, while the displacement field is kept continuous. The velocity discontinuity is postulated to occur in the time domain. The developed time integration scheme is unconditionally stable and has controllable numerical dissipation in the high frequency range. An important feature of the time scheme is that it allows for controlling the numerical damping in a consistent way. The time scheme has been implemented in combination with Biot’s theory of wave propagation in saturated porous media. Numerical examples have demonstrated that the proposed time scheme is, in addition to being accurate and stable, highly effective for coarse meshes. This makes the developed scheme suitable for large scale finite element analysis.     

An edge-based smoothed point interpolation method for elasto-plastic coupled hydro-mechanical analysis of saturated porous media

An edge-based smoothed point interpolation method is adopted for coupled hydro-mechanical analysis of saturated porous media with elasto-plastic behaviour. A novel approach for the evaluation of the coupling matrix of the porous media is adopted. Stress integration is performed using the substepping method, and the modified Newton-Raphson approach is utilised to address the nonlinearities arising from the elasto-plastic constitutive model used in the formulation. Numerical examples are studied and the results are compared with analytical solutions and those obtained from the conventional finite element method (FEM) to evaluate the performance of the proposed model.     

Transport in a 2-D saturated porous medium: A new method for particle tracking

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.