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.     

Modeling coupled THM processes of geological porous media with multiphase flow: Theory and validation against laboratory and field scale experiments

A FEM model for analysis of fully coupled multiphase flow, thermal transport and stress/deformation in geological porous media was developed based on the momentum, mass and energy conservation laws of the continuum mechanics and the averaging approach of the mixture theory over a three phase (solid–liquid–gas) system. Six processes (i.e. stress–strain, water flow, gas flow, vapor flow, heat transport and porosity evolution processes) and their coupling effects are considered, which not only makes the problem well-defined, but renders the governing PDEs closed, complete, compact and compatible. Displacements, pore water pressure, pore gas pressure, pore vapor pressure, temperature and porosity are selected as basic unknowns. The physical phenomena such as phase transition, gas solubility in liquid, thermo-osmosis, moisture transfer and moisture swelling are modeled. As a result, the relative humidity and other related variables in porous media can be evaluated on a sounder physical basis. A three dimensional computer code, THYME3D, was developed, with eight degrees of freedom at each node. The laboratory CEA Mock-up test and the field scale FEBEX benchmark test on bentonite performance assessment for underground nuclear waste repositories were used to validate the numerical model and the software. The coupled THM behaviors of the bentonite barriers were satisfactorily simulated, and the effects and impacts of the governing equations, constitutive relations and property parameters on the coupled THM processes were understood in terms of more straightforward interpretation of physical processes at microscopic scale of the porous media. The work developed enables further in-depth research on fully coupled THM or THMC processes in porous media.     

煤层气产出过程中气—水两相流与煤岩变形耦合数学模型研究

气－水二相流和煤岩变形耦合作用是煤层气产出过程中一种复杂的物理现象，为准确描述这一现象，本文建立了气－水二相流和煤岩变形的微分方程，并用有限元分别将它们进行离散化，然后讨论了煤岩变形模型和气－水二相流模型进行耦合数值求解的方法。     

月表撞击坑形成过程数值模拟理论与方法

数值模拟是研究撞击坑形成过程的一种主要方法,尤其是认识撞击坑形成机制的重要手段。撞击坑形成过程数值模拟的基本原理是用离散方法描述物质在高速撞击作用下的运动及状态,在模拟中首先将物质与空间划分成离散的网格,在每一次迭代计算中逐步求解各个网格的形变、运动与状态改变的规律。牛顿运动定律、物质的连续体模型与热力学方程是撞击坑形成过程数值模拟的理论基础,牛顿运动定律以偏微分方程的形式贯穿在离散化的网格空间中,物质的连续体模型将物质的屈服强度与破裂、温度、孔隙、振动等联系起来,而热力学方程则通过其他热力学参数计算网格单元内物质的压强与物质所处的状态。     

Numerical convergence study of iterative coupling for coupled flow and geomechanics

In this paper, we consider algorithms for modeling complex processes in porous media that include fluid and structure interactions. Numerous field applications would benefit from a better understanding and integration of porous flow and solid deformation. Important applications in environmental and petroleum engineering include carbon sequestration, surface subsidence, pore collapse, cavity generation, hydraulic fracturing, thermal fracturing, wellbore collapse, sand production, fault activation, and waste disposal, while similar issues arise in biosciences and chemical sciences as well. Here, we consider solving iteratively the coupling of flow and mechanics. We employ mixed finite element method for flow and a continuous Galerkin method for elasticity. For single-phase flow, we demonstrate the convergence and convergence rates for two widely used schemes, the undrained split and the fixed stress split. We discuss the extension of the fixed stress iterative coupling scheme to an equation of state compositional flow model coupled with elasticity and a single-phase poroelasticity model on general hexahedral grids. Computational results are presented.     

非饱和土中热−湿−盐耦合作用的稳态分析

以多孔介质理论为基础,研究了稳态条件下非饱和土中温度?水分?盐分多场耦合问题。考虑非饱和土的孔隙被液态水、溶解的盐分、水蒸气和干燥气体等填充,在质量和能量守恒的基础上获得了非饱和土中水分、气体、盐分的质量守恒方程以及能量守恒方程。考虑一维稳态问题,选取温度、孔隙气压、孔隙水压和盐溶液浓度以及它们的导数作为状态变量,得到了问题的状态方程组。在给定的边界条件下,采用打靶法求解了该强耦合的非线性变系数微分方程组,通过与已有的试验结果相比较,验证了模型的有效性。基于数值算例,参数分析了含水率、温度边界、孔隙率等条件对非饱和土中温度场、水分场和盐分场分布的影响规律。     

构造成矿非线性动力学:1.递增应力流变学模型

本文提出了构造成矿作用动力学研究的递增应力流变学方法。利用该方法将构造变形、应力、流体流动、地球化学反应及成岩成矿作用等多过程耦合起来，可以从多种地质过程的耦合与反馈作用对构造成矿的动力学演化过程进行１～３维数值模拟。模拟的主要内容是在各种过程耦合作用下，以下描述构造成矿体系的主要变量的时空演化：（１）与成矿流体的形成和性质有关的变量，如地层中矿物（包括成矿物质）的溶解速率、流体中各组分的浓度与饱和度、流体温度、压力、离子强度等；（２）与构造变形和流体运移有关的各变量，如应力与变形速率、岩石孔隙度、构造（断裂）渗透率等；（３）与沉淀成矿有关的变量，如矿物（金瞩矿物和脉石矿物）的成核速率、各矿物的沉淀量等；（４）上述各有关变量间的时空耦合关系，如断裂渗透率时空演化与流体流动、汇聚和成矿的耦合关系等。     

构造-流体-成矿体系的反应-输运-力学耦合模型和动力学模拟

建立了一个综合的构造流体成矿体系的反应输运力学耦合动力学模型。利用有限元方法求解岩石变形、断裂作用和断裂网络统计动力学、流体流动、有机和无机地球化学反应及成岩成矿作用、压力溶液和其它压实力学、热迁移的方程组 ,可以对构造流体成矿体系的动力学演化过程进行 1～ 3维数值模拟。模拟的主要内容是在各种过程耦合作用下描述构造流体成矿体系的主要变量的时空演化 :( 1)与成矿流体的形成和性质有关的变量 ,如地层中矿物 (包括成矿物质 )的溶解速率、流体中各组分的浓度与饱和度、流体温度、压力、离子强度等 ;( 2 )与构造变形和流体运移有关的各变量 ,如应力与变形速率、岩石孔隙度、构造 (断裂 )渗透率等 ;( 3 )与沉淀成矿有关的变量 ,如矿物 (金属矿物和脉石矿物 )的成核速率、各矿物的沉淀量等 ;( 4 )上述各有关变量间的时空耦合关系 ,如断裂渗透率时空演化与流体流动、汇聚和成矿的耦合关系等。以湖南沃溪金锑钨矿床为例 ,应用该模型和方法对成矿动力学过程和动力学机制进行了初步的模拟与分析。     

混凝土混合硬化黏塑性损伤统本构模型

传统的黏塑性统一本构模型只能用于金属类材料的本构分析,而不适用于混凝土的本构分析.基于此,以不可逆热力学理论为基础,选定了涉及混合硬化参量的Helmholtz自由能函数,推导出混凝土的黏塑性损伤耦合本构模型.通过对混凝土硬化模型的分析,构造了含运动硬化和等向硬化内变量的非相关流动势函数,又推导出流动方程以及内变量演化方程.所建模型对混凝土试验曲线的数值模拟显示,其能够正确描述混凝土的率相关性、非弹性体积膨胀特性、加载过程的软硬化特性以及由断裂和损伤引起的应力软化现象.     

Hydromechanical coupling in geologic processes

Earth's porous crust and the fluids within it are intimately linked through their mechanical effects on each other. This paper presents an overview of such "hydromechanical" coupling and examines current understanding of its role in geologic processes. An outline of the theory of hydromechanics and rheological models for geologic deformation is included to place various analytical approaches in proper context and to provide an introduction to this broad topic for nonspecialists. Effects of hydromechanical coupling are ubiquitous in geology, and can be local and short-lived or regional and very long-lived. Phenomena such as deposition and erosion, tectonism, seismicity, earth tides, and barometric loading produce strains that tend to alter fluid pressure. Resulting pressure perturbations can be dramatic, and many so-called "anomalous" pressures appear to have been created in this manner. The effects of fluid pressure on crustal mechanics are also profound. Geologic media deform and fail largely in response to effective stress, or total stress minus fluid pressure. As a result, fluid pressures control compaction, decompaction, and other types of deformation, as well as jointing, shear failure, and shear slippage, including events that generate earthquakes. By controlling deformation and failure, fluid pressures also regulate states of stress in the upper crust. Advances in the last 80 years, including theories of consolidation, transient groundwater flow, and poroelasticity, have been synthesized into a reasonably complete conceptual framework for understanding and describing hydromechanical coupling. Full coupling in two or three dimensions is described using force balance equations for deformation coupled with a mass conservation equation for fluid flow. Fully coupled analyses allow hypothesis testing and conceptual model development. However, rigorous application of full coupling is often difficult because (1) the rheological behavior of geologic media is complex and poorly understood and (2) the architecture, mechanical properties and boundary conditions, and deformation history of most geologic systems are not well known. Much of what is known about hydromechanical processes in geologic systems is derived from simpler analyses that ignore certain aspects of solid-fluid coupling. The simplifications introduce error, but more complete analyses usually are not warranted. Hydromechanical analyses should thus be interpreted judiciously, with an appreciation for their limitations. Innovative approaches to hydromechanical modeling and obtaining critical data may circumvent some current limitations and provide answers to remaining questions about crustal processes and fluid behavior in the crust. Electronic Publication     

不连续面在双重介质热-水-力三维耦合分析中的有限元数值实现

在建立双重介质热-水-力耦合微分控制方程的基础上,提出了裂隙岩体热-水-力耦合的三维力学模型,对不同介质分别建立以节点位移、水压力和温度为求解量的三维有限元格式,开发了双重介质热-水-力耦合分析的的三维有限元计算程序,在有限元数值分析中不连续面应力计算采用等厚度空间8节点节理单元进行离散,而不连续面渗流和热能计算时采用平面4节点等参单元进行离散,这样保证了不同介质之间的水量、热量交换和两类模型接触处节点水头、温度和位移相等。通过高温岩体地热开发算例,揭示了在热-水-力耦合作用下不连续面处于低应力区,其张开度随运行时间的延长呈非线性增加,非稳定渗流阶段不连续面显著地控制着渗流场的整体分布,它的水头远高于拟连续岩体介质的水头,而进入稳定渗流阶段不连续面的控渗作用不明显,由于高温岩体地热开发系统中存在大规模的热量补给,不连续面对岩体温度场分布的影响并不显著。     

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.     

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameterB, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data.     

Numerical modeling of seismic triggering,evolution, and deposition of rapid landslides: Application to Higashi–Takezawa (2004)

A mathematical model is developed for the dynamic analysis of earthquake‐triggered rapid landslides, considering two mechanically coupled systems: (a) the accelerating deformable body of the slide and (b) the rapidly deforming shear band at the base of the slide. The main body of the slide is considered as a one‐phase mixture of Newtonian incompressible fluids and Coulomb solids sliding on a plane of variable inclination. The evolution of the landslide is modeled via a depth‐integrated model of the Savage–Hutter type coupled with: (a) a cyclic hysteretic constitutive model of the Bouc–Wen type and (b) Voellmy's rheology for the deformation of the material within the shear band. The original shallow‐water equations that govern the landslide motion are appropriately reformulated to account for inertial forces due to seismic loading, and to allow for a smooth transition between the active and the passive state. The capability of the developed model is tested against the Higashi–Takezawa landslide. Triggered by the 2004 Niigata‐ken Chuetsu earthquake, the slide produced about 100m displacement of a large wedge from an originally rather mild slope. The mechanism of material softening inside the shear band responsible for the surprisingly large run‐out of the landslide is described by a set of equations for grain crushing‐induced pore‐water pressures. The back‐analysis reveals interesting patterns on the flow dynamics, and the numerical results compare well with field observations. It is shown that the mechanism of material softening is a crucial factor for the initiation and evolution of the landslide, while viscoplastic frictional resistance is a key requirement for successfully reproducing the field data. Copyright © 2009 John Wiley & Sons, Ltd.     

A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow

We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical and numerical aspects of surface–subsurface flow modeling are presented. This work was supported by National Science Foundation grant DMS-0411413.     

Unsaturated hydro-mechanical-chemo coupled constitutive model with consideration of osmotic flow

Since low permeability rock has the potential to behave as an actual semi-permeable osmotic membrane, chemical osmosis may have an effect on water flow and needs to be accounted for in analysis. Hence, an advanced fully coupled formulation for modelling unsaturated hydro, chemical and mechanical effects is here presented based on modified mixture theory. Firstly, the classical Darcy’s law has been modified to include the chemical potential. Secondly, the mechanical deformation, which affects the permeability, has been coupled with the water and chemical flows by using Helmholtz free energy and the Gibbs–Duhem equation. Finally, an illustrative numerical example with relevance to radioactive waste disposal has been analysed to investigate the performance of the coupled formulation and the relative influence of parameters.     

高温下混凝土水力、热及变形耦合数学模型

针对受高温载荷的混凝土提出了一个水力-热-变形耦合的数学模型,模型中采用了3种不同的连续介质：水蒸汽与干燥空气的混合气体相,液态水以及固态混凝土骨架。在连续介质的Navier-Stokes方程基础上,推导了各相介质的质量守恒方程、动量守恒方程以及混合物整体的能量守恒方程。为了简化问题,引入了若干假设,给出了基于文献资料数据拟合的某些变量的用基本未知量表达的经验公式,建立了基于物理定律的各类运动学变量与其热力学共轭力的本构关系,并给出了系统偏微分方程。     

A supercoarsening multigrid method for poroelasticity in 3D coupled flow and geomechanics modeling

The Galerkin finite-element discretization of the force balance equation typically leads to large linear systems for geomechanical problems with realistic dimensions. In iteratively coupled flow and geomechanics modeling, a large linear system is solved at every timestep often multiple times during coupling iterations. The iterative solution of the linear system stemming from the poroelasticity equations constitutes the most time-consuming and memory-intensive component of coupled modeling. Block Jacobi, LSOR, and Incomplete LU factorization are popular preconditioning techniques used for accelerating the iterative solution of the poroelasticity linear systems. However, the need for more effective, efficient, and robust iterative solution techniques still remains especially for large coupled modeling problems requiring the solution of the poroelasticity system for a large number of timesteps. We developed a supercoarsening multigrid method (SCMG) which can be multiplicatively combined with commonly used preconditioning techniques. SCMG has been tested on a variety of coupled flow and geomechanics problems involving single-phase depletion and multiphase displacement of in-situ hydrocarbons, CO₂ injection, and extreme material property contrasts. Our analysis indicates that the SCMG consistently improves the convergence properties of the linear systems arising from the poroelasticity equations, and thus, accelerates the coupled simulations for all cases subject to investigation. The joint utilization of the two-level SCMG with the ILU1 preconditioner emerges as the most optimal preconditioning/iterative solution strategy in a great majority of the problems evaluated in this work. The BiCGSTAB iterative solver converges more rapidly compared to PCG in a number of test cases, in which various SCMG-accelerated preconditioning strategies are applied to both iterators.     

Simulation of air storage aquifer by finite element model

A finite element model is developed to simulate the behaviour of an aquifer used as storage space for a compressed air energy storage (CAES) system. The governing equations describing a two-phase flow of air and water are coupled non-linear partial differential equations and are solved by the Galerkin approach. The resulting computer model is applied to a gas percolation problem. Upon verification of the numerical results, the model is employed to simulate the air-water displacement in a storage reservoir during daily air cycling. The corresponding saturation variations and the effects of reservoir permeability on the system are presented. The results obtained are essential in establishing storage design and stability criteria for long-term operation of compressed air energy storage systems.