A fully coupled hydro‐thermo‐poro‐mechanical model for black oil reservoir simulation

A fully coupled formulation of a hydro‐thermo‐poro‐mechanical model for a three‐phase black oil reservoir model is presented. The model is based upon the approach proposed by one of the authors which fully couples geomechanical effects to multiphase flow. Their work is extended here to include non‐isothermal effects. The gas phase contribution to the energy equation has been neglected based on a set of assumptions. The coupled formulation given herein differs in several ways when compared to the earlier work and an attempt is made to link the flow based formulation and mixture theory. The Finite Element Method is employed for the numerical treatment and essential algorithmic implementation is discussed. Numerical examples are presented to provide further understanding of the current methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

一种高温下混凝土化学塑性-损伤耦合本构模型

提出了一个用于模拟高温下混凝土化学塑性-损伤耦合本构行为的数值模型。发展了一个化学塑性-损伤耦合分析的一致性应力返回映射算法。为了保证对于全局守恒方程Newton迭代过程的2阶收敛率,推导并形成了一致性切线模量矩阵。数值算例显示了文中发展的化学塑性-损伤耦合本构模型在模拟高温下混凝土中复杂破坏过程的能力和有效性。     

A constitutive model for mechanical and chemo‐mechanical compaction in sedimentary basins and finite element analysis

Compaction and associated fluid flow are fundamental processes in sedimentary basin deformation. Purely mechanical compaction originates mainly from pore fluid expulsion and rearrangement of solid particles during burial, while chemo‐mechanical compaction results from Intergranular Pressure‐Solution (IPS) and represents a major mechanism of deformation in sedimentary basins during diagenesis. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modeling of purely mechanical and chemo‐mechanical compaction in sedimentary basins. Extending the concepts that have been previously proposed for the modeling of purely mechanical compaction in finite poroplasticity, deformation by IPS is addressed herein by means of additional viscoplastic terms in the state equations of the porous material. The finite element model integrates the poroplastic and poroviscoplastic components of deformation at large strains. The corresponding implementation allows for numerical simulation of sediments accretion/erosion periods by progressive activation/deactivation of the gravity forces within a fictitious closed material system. Validation of the numerical approach is assessed by means of comparison with closed‐form solutions derived in the context of a simplified compaction model. The last part of the paper presents the results of numerical basin simulation performed in one dimensional setting, demonstrating the ability of the modeling to capture the main features in elastoplastic and viscoplastic compaction. Copyright © 2016 John Wiley & Sons, Ltd.     

A thermo‐mechanical model for the catastrophic collapse of large landslides

In this work, a new thermo‐mechanical model is developed, applicable to large‐scale, deep‐seated landslides consisting of a coherent mass sliding on a thin clayey layer. The considered time window is that of catastrophic acceleration, starting at incipient failure and ending when the acquired displacement and velocity are such that the sliding material begins to break up into pieces. The model accounts for temperature rise in the slip zone due to the heat produced by friction, leading to water expansion, thermoplastic collapse of the soil skeleton, and subsequent increase of pore water pressure. The model incorporates the processes of heat production and diffusion, pore pressure generation and diffusion, and an advanced constitutive law for the thermo‐mechanical behavior of soil. An analysis of the Vajont landslide is presented as an example. A sensitivity analysis shows that friction softening is the mechanism most affecting the timescale of the final collapse of a slide, but also that the mechanism of thermal pressurization alone can cause a comparably catastrophic dynamic evolution. It is also shown that, all other factors being equal, thermo‐mechanical collapse will cause thicker slides to accelerate faster than shallow ones. Copyright © 2010 John Wiley & Sons, Ltd.     

A three‐phase thermo‐hydro‐mechanical finite element model for freezing soils

Artificial ground freezing (AGF) is a commonly used technique in geotechnical engineering for ground improvement such as ground water control and temporary excavation support during tunnel construction in soft soils. The main potential problem connected with this technique is that it may produce heave and settlement at the ground surface, which may cause damage to the surface infrastructure. Additionally, the freezing process and the energy needed to obtain a stable frozen ground may be significantly influenced by seepage flow. Evidently, safe design and execution of AGF require a reliable prediction of the coupled thermo‐hydro‐mechanical behavior of freezing soils. With the theory of poromechanics, a three‐phase finite element soil model is proposed, considering solid particles, liquid water, and crystal ice as separate phases and mixture temperature, liquid pressure, and solid displacement as the primary field variables. In addition to the volume expansion of water transforming into ice, the contribution of the micro‐cryo‐suction mechanism to the frost heave phenomenon is described in the model using the theory of premelting dynamics. Through fundamental physical laws and corresponding state relations, the model captures various couplings among the phase transition, the liquid transport within the pore space, and the accompanying mechanical deformation. The verification and validation of the model are accomplished by means of selected analyses. An application example is related to AGF during tunnel excavation, investigating the influence of seepage flow on the freezing process and the time required to establish a closed supporting frozen arch. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling of deformation response and chemo‐mechanical coupling in chalk

A constitutive relation is derived for describing the mechanical response of chalk. The approach is based on a phenomenological framework which employs chemo‐plasticity. The properties of the material are assumed to be affected by the physico‐chemical processes that occur through the interaction between the skeleton and the pore fluid. The underlying mechanism is discussed by invoking a micromechanical analysis. The performance of the framework is illustrated by examining the evolution of mechanical characteristics in the presence of different pore fluids. Copyright © 2006 John Wiley & Sons, Ltd.     

A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media

Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi‐analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element‐free Galerkin (EFG) mesh‐less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity equations, considers the hydro‐mechanical coupling between the crack and its surrounding porous medium. Therefore, the developed EFG model is capable of simulating fluid leak‐off and fluid lag phenomena. To create the discrete equation system, the Galerkin technique is applied, and the essential boundary conditions are imposed via penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions. For temporal discretization, a fully implicit scheme is employed. The final set of algebraic equations that forms a non‐linear equation system is solved using the direct iterative procedure. Modeling of cracks is performed on the basis of linear elastic fracture mechanics, and for this purpose, the so‐called diffraction method is employed. For verification of the model, a number of problems are solved. According to the obtained results, the developed EFG computer program can successfully be applied for simulating the complex process of hydraulic fracture propagation in porous media. Copyright © 2016 John Wiley & Sons, Ltd.     

Three‐dimensional transient thermo‐hydro‐mechanical fundamental solutions of unsaturated soils

The governing differential equations of unsaturated soils considering the thermo‐poro‐mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three‐dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed‐form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed‐form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution. Copyright © 2009 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.     

高温状态下加载速率对石灰岩力学效应研究

采用美国MTS810电液伺服材料试验机,对200 ℃高温状态下的石灰岩试件进行了5级不同加载速率下的单轴压缩试验,考察了石灰岩的全应力-应变曲线,给出了其峰值强度、峰值应变、弹性模量E随加载速率的变化特征。研究结果表明,(1) 石灰岩的峰值强度、弹性模量在加载速率v = 0.000 5～0.005 mm/s内,随加载速率增大呈急剧上升现象;当v = 0.005 0～0.5 mm/s内,随加载速率增大呈下降趋势;当v >0.5 mm/s后,呈现上升趋势。(2) 石灰岩的峰值应变在v = 0.000 5～0.005 mm/s内,随加载速率增大呈下降趋势;在v = 0.005～5.0 mm/s加载速率区段,峰值应变呈现缓慢上升现象。研究结果可为相关岩体的爆破效应及评价岩石工程的稳定性提供参考。     

A three‐dimensional staggered finite element approach for random parametric modeling of thermo‐hygral coupled phenomena in porous media

The aim of this paper is to present a three‐dimensional (3D) finite element modeling of heat and mass transfer phenomena in partially saturated open porous media with random fields of material properties. Randomness leads to transfer processes within the porous medium that naturally need a full 3D modeling for any quantitative assessment of these processes. Nevertheless, the counterpart of 3D modeling is a significant increase in computations cost. Therefore, a staggered solution strategy is adopted which permits to solve the equations sequentially. This appropriate partitioning reduces the size of the discretized problem to be solved at each time step. It is based on a specific iterative algorithm to account for the interaction between all the transfer processes. Accordingly, a suitable linearization of mass convective boundary conditions, consistent with the staggered algorithm, is also derived. After some validation tests, the 3D numerical model is used for studying the drying process of a cementitious material with regard to its intrinsic permeability randomness. Copyright © 2011 John Wiley & Sons, Ltd.     

A thermo‐mechanical model for variably saturated soils based on hypoplasticity

The paper presents a mechanical model for non‐isothermal behaviour of unsaturated soils. The model is based on an incrementally non‐linear hypoplastic model for saturated clays and can therefore tackle the non‐linear behaviour of overconsolidated soils. A hypoplastic model for non‐isothermal behaviour of saturated soils was developed and combined with the existing hypoplastic model for unsaturated soils based on the effective stress principle. Features of the soil behaviour that are included into the model, and those that are not, are clearly distinguished. The number of model parameters is kept to a minimum, and they all have a clear physical interpretation, to facilitate the model usefulness for practical applications. The step‐by‐step procedure used for the parameter calibration is described. The model is finally evaluated using a comprehensive set of experimental data for the thermo‐mechanical behaviour of an unsaturated compacted silt. Copyright © 2011 John Wiley & Sons, Ltd.     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Meso‐scale particle modeling of concrete deterioration caused by alkali‐aggregate reaction

A meso‐scale particle model is presented to simulate the expansion of concrete subjected to alkali‐aggregate reaction (AAR) and to analyze the AAR‐induced degradation of the mechanical properties. It is the first attempt to evaluate the deterioration mechanism due to AAR using the discrete‐element method. A three‐phase meso‐scale model for concrete composed of aggregates, mortar and the interface is established with the combination of a pre‐processing approach and the particle flow code, PFC2D. A homogeneous aggregate expansion approach is applied to model the AAR expansion. Uniaxial compression tests are conducted for the AAR‐affected concrete to examine the effects on the mechanical properties. Two specimens with different aggregate sizes are analyzed to consider the effects of aggregate size on AAR. The results show that the meso‐scale particle model is valid to predict the expansion and the internal micro‐cracking patterns caused by AAR. The two different specimens exhibit similar behavior. The Young's modulus and compressive strength are significantly reduced with the increase of AAR expansion. The shape of the stress–strain curves obtained from the compression tests clearly reflects the influence of internal micro‐cracks: an increased nonlinearity before the peak loading and a more gradual softening for more severely affected specimens. Similar macroscopic failure patterns of the specimens under compression are observed in terms of diagonal macroscopic cracks splitting the specimen into several triangular pieces, whereas localized micro‐cracks forming in slightly affected specimens are different from branching and diffusing cracks in severely affected ones, demonstrating different failure mechanisms. Copyright © 2012 John Wiley & Sons, Ltd.     

花岗岩力学特性的温度效应试验研究

通过实时高温（常温～850 ℃）加载和高温（常温～1 200 ℃）后冷却再加载两种情况下的单轴压缩试验,对不同高温下花岗岩的力学性质进行了研究,分析了两种情况下单轴抗压强度、弹性模量、纵波波速、剪切滑移应变等随温度的变化规律,并研究了热-力耦合效应。研究结果表明：（1）在实时高温加载作用下单轴抗压强度和弹性模量随着温度升高而发生连续劣化;（2）高温作用冷却后再加载,花岗岩在常温～600 ℃区间峰值强度变化不大,800 ℃左右岩样强度突然降低;（3）纵波波速随加热温度的升高而逐渐降低;（4）剪切滑移应变在800 ℃之前相对较小,且变化不大,之后便迅速增大,表现出明显的塑性;（5）提出了热-力耦合因子的概念,并借助其提出了一维非线性热-力耦合本构模型,模型曲线和试验曲线较吻合。     

基于热-水-力-损伤耦合数值模型的高地温水工高压隧洞围岩承载特性

针对高地温水工高压隧洞围岩的力学行为特点,在考虑岩体的渗透系数、热传导系数随岩体损伤发生变化的基础上,基于多物理场耦合理论,提出一种考虑硬岩强度力学参数劣化的含损伤演化的热-水-力-损伤耦合模型,并给出了该模型的FLAC3D数值实现方法。通过与物理模型试验结果对比,验证了模型的可靠性,进而利用该模型推演了高地温水工高压隧洞的多物理场耦合演化过程,分析了不同影响因素下的承载特性。研究结果表明：隧洞充水运行后,高地温水工高压隧洞的多场耦合效应显著,尤其高地温梯度和高内水压力联合作用下产生的迭加拉应力对围岩的承载安全具有不利影响;温度梯度、内水压力以及岩体线膨胀系数越大,隧洞围岩的损伤程度与开裂深度越大;当隧洞横断面的侧压力系数趋向于1时,洞周出现的宏观裂缝较多,且出现方位不确定;当隧洞横断面侧压力系数小于1/3时,洞周出现的宏观裂缝相对较少,且主要出现在与初始地应力的最大主应力方向相平行的方向上。常规锚喷支护对高地温水工高压隧洞的加固效果不佳。     

A coupled damage–plasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identification

The development of a coupled damage‐plasticity constitutive model for concrete is presented. Emphasis is put on thermodynamic admissibility, rigour and consistency both in the formulation of the model, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the model can be derived from two specified energy potentials, following procedures established beforehand. Based on this framework, a constitutive model featuring full coupling between damage and plasticity in both tension and compression is developed. Tensile and compressive responses of the material are captured using two separate damage criteria, and a yield criterion with a multiple hardening rule. A crucial part of this study is the identification of model parameters, with these all being shown to be identifiable and computable based on standard tests on concrete. Behaviour of the model is assessed against experimental data on concrete. Copyright © 2007 John Wiley & Sons, Ltd.