隧道开挖的双重介质水力耦合模型有限元分析

基于混合物理论孔隙-裂隙岩体的双重孔隙介质水力耦合计算的微分方程,利用伽辽金有限元法提出了相应的有限元公式,并基于岩体分类指标（RQD,RMR）提出了与岩体应变状态相关的渗透系数计算公式。编制了裂隙岩体双重介质流固耦合的2-D有限元程序,给出的验证算例表明,该程序是合理和实用的。同时将该程序用于隧道开挖的模拟计算,探讨渗流效应对开挖隧道围岩变形与渗流场的影响。计算结果表明,在隧道设计中不考虑渗流的影响是偏于不安全的。     

岩体渗流场与温度场耦合的连续介质模型

孔隙型岩体、密集裂隙型岩体以及孔隙—密集裂隙型岩体的渗流问题均可视为连续介质或等效连续介质渗流问题。本文从理论上分析了这种类型岩体渗流场与温度场相互影响、相互作用的机理，提出了岩体渗流场与温度场耦合分析的连续介质数学模型，并讨论了该数学模型的有限元数值求解方法。     

岩体结构与岩体水力耦合计算模型

水力耦合作用是岩体中力学过程与渗流过程相互作用的物理过程。水力耦合机理的理解是水力耦合分析的关键问题,其耦合机理是由岩体结构特性决定的。在分析岩体水力耦合过程基础上,根据岩体的基本结构及代表性单元体（REV）是否存在提出了建立水力耦合模型的方法。当裂隙岩体中不存在代表性单元体（REV）时,提出了裂隙岩体多重介质流固耦合分析的全耦合数学模型,给出流固耦合模型数值方法求解的数学模型及有限元计算表达式。程序编制和验证工作正在进行中。     

塑性扩容梯度对孔隙介质岩体中T-H-M耦合作用的二维有限元分析

由双重孔隙-裂隙介质热-水-应力耦合模型退化为单一孔隙介质模型,将其与岩体扩容梯度引入笔者所研制的二维有限元程序中,使用Mohr-Coulomb准则,计入塑性扩容对岩体孔隙率及渗透系数的影响,针对一个假设的实验室尺度且位于饱和孔隙介质岩体中的高放废物地质处置库模型,拟定不同扩容梯度值的5种工况,进行4年处置时段的数值模拟,考察了岩体中的温度、正应力、塑性区、孔隙率及渗透系数、孔隙水压力和地下水流速的变化、分布情况。结果主要显示,相比于不考虑扩容梯度的工况,考虑扩容梯度工况的正应力、孔隙率及渗透系数、孔隙水压力和地下水流速等的分布与塑性区的分布有明显的对应关系,呈现了某种"剪切带效应";正应力量值、塑性区面积、孔隙率及渗透系数、孔隙水压力、地下水流速等均随所取扩容梯度值的变大而增加。     

多空隙组合地质单元渗流理论分析与试验

岩体通常是以孔隙岩石为基质并包含各种成因的裂隙和溶隙的复杂多空隙组合地质材料。为研究孔隙-裂隙-溶隙多空隙组合介质的渗流特性,在简要介绍多孔介质渗流Darcy定律、平板窄缝流Poiseuille定律和圆形管道流Darcy-Weibach理论的基础上,分析了几种孔隙-裂隙-溶隙组合情况的多空隙介质渗流特性,推导出相应组合的等效渗透系数KE,给出了描述多空隙组合介质KE的一般表达式,讨论了影响各种空隙组合KE的主要因素。以普通砖模拟岩石基质,通过砖身钻孔填充及砖间缝隙填充,试验模拟了岩溶岩体和裂隙岩体中溶孔和裂隙填充后的渗透情况。试验结果与所推求理论公式计算出的KE在同一量级且误差很小,很好地验证了所推导的多空隙组合介质渗透系数表达式的有效性。     

岩体弹粘塑性显式波动有限元分析

真实反映地震动传播特性的分析方法是准确描述岩体地震反应的基础。基于显式波动有限元,采用能够考虑应变率影响的弹粘塑性本构模型,提出了一种用于分析岩体地震反应的新方法,编制了相应的计算程序。以均质岩石边坡为例,计算了EL-CENTRO波输入下边坡的位移和应力反应,并将计算结果与采用粘弹性本构模型的结果进行了比较,初步验证了程序的可靠性。计算结果表明,所提出的新方法能够较合理地计算出地震作用下边坡的永久位移和残余应力。     

岩体介质的随机固流热耦合模型

考虑岩体介质是由基质岩块与裂缝组成的结构体,采用岩体结构力学的研究方法,针对岩石矿物组分及其分布的不同,将物理力学参数作为随机介质,建立了岩体介质的三维随机非均质固流热耦合数学模型,介绍了随机有限元计算方法,深入分析了随机固流热耦合模型的特点,该模型是经典固流热耦合数学模型的扩展,为岩石热破裂数值实验的研究提供了理论基础及其方法。     

岩体三维非稳定渗流模型及数值模拟

地下水是导致地质灾害发生的重要因素之一。岩体本身的复杂性及地下水在岩体内随时间而变化造成地下水在岩体内运动机理的复杂性。文章采用数值模拟方法探索地下水在岩体内的运动规律,了解其致灾机理。以岩体结构力学为基础,运用现代分形理论,建立主干裂隙分形网络;根据裂隙发育规模与工程尺度关系将岩体看作拟连续介质与块裂介质混合介质,并根据两类介质接触处水头相等及节点流量相等建立合理的三维非稳定渗流模型;给出渗流模型的有限元解法,开发出相应的有限元软件;给出算例,计算结果体现了主干裂隙在渗流中的强导水作用及网络状裂隙的贮水功能与渗流滞后效应;强调根据裂隙发育规模与工程尺度关系确定合理渗流模型的重要性。     

裂隙刚度随应力变化对双重孔隙介质热-水-应力耦合影响的有限元分析

引入并修正了变刚度的连续屈服节理模型,同时考虑应力拉压和压力（化学）溶解对裂隙开度的综合影响,对所建立的双重孔隙-裂隙介质热-水-应力耦合有限元计算程序作了改进。通过一个假定的高放废物地质处置库的数值模拟,就岩体裂隙刚度变化的2种工况,分析了岩体中的温度、裂隙刚度、正应力、孔（裂）隙水压力和地下水流速的变化、分布情况。结果显示：与裂隙刚度是常数时相比,裂隙刚度是法向应力的函数时计算域中温度较低;岩体应力的大小也有一定不同,其分布与裂隙刚度“场”有明显的相似性;并且负孔（裂）隙水压力的绝对值要略小一点,约是常数时的98%。     

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。     

Finite element modeling of hydraulic fracturing in 3D

A procedure based on the finite element method is suggested for modeling of 3D hydraulic fracturing in the subsurface. The proposed formulation partitions the stress field into the initial stress state and an additional stress state caused by pressure buildup. The additional stress is obtained as a solution of the Biot equations for coupled fluid flow and deformations in the rock. The fluid flow in the fracture is represented on a regular finite element grid by means of “fracture” porosity, which is the volume fraction of the fracture. The use of the fracture porosity allows for a uniform finite element formulation for the fracture and the rock, both with respect to fluid pressure and displacement. It is demonstrated how the fracture aperture is obtained from the displacement field. The model has a fracture criterion by means of a strain limit in each element. It is shown how this criterion scales with the element size. Fracturing becomes an intermittent process, and each event is followed by a pressure drop. A procedure is suggested for the computation of the pressure drop. Two examples of hydraulic fracturing are given, when the pressure buildup is from fluid injection by a well. One case is of a homogeneous rock, and the other case is an inhomogeneous rock. The fracture geometry, well pressure, new fracture area, and elastic energy released in each event are computed. The fracture geometry is three orthogonal fracture planes in the homogeneous case, and it is a branched fracture in the inhomogeneous case.     

A new locally conservative numerical method for two-phase flow in heterogeneous poroelastic media

We construct a new class of locally conservative numerical methods for two-phase immiscible flow in heterogeneous poroelastic media. Within the framework of the so-called iteratively coupled methods and fixed-stress split algorithm we develop mixed finite element methods for the flow and geomechanics subsystems which furnish locally conservative Darcy velocity and transient porosity input fields for the transport problem for the water saturation. Such hyperbolic equation is decomposed within an operator splitting technique based on a predictor–corrector scheme with the predictor step discretized by a higher-order non-oscillatory finite volume central scheme. The proposed scheme adopts an inhomogeneous dual mesh with variable cell size ruled by the local wave speed of propagation to compute numerical fluxes at cell edges. In the limit of small time steps the central scheme gives rise to a semidiscrete formulation for the water saturation capable of incorporating heterogeneous porosity fields and generalized flux functions including the water transport due to the solid phase velocity. Numerical simulations of a water-flooding problem in secondary oil recovery are presented for different realizations of the input random fields (permeability, Young modulus and initial porosity). Comparison between the accuracies of the proposed approach and the traditional one-way coupled hydro-geomechanical formulation are presented. The effects of the cross-correlation between the input random fields and compaction drive mechanism upon finger growth and breakthrough curves are also analyzed. A notable feature of the formulation proposed herein is the accurate prediction of the influence of geomechanical effects upon the unstable movement of the water front, whose evolution is dictated by rock heterogeneity and unfavorable viscosity ratio, without deteriorating the local conservative character of the numerical schemes.     

A 2D coupled finite element and boundary element scheme to simulate the elastic behaviour of jointed rocks

In this paper a coupled finite and boundary element formulation is developed for the analysis of excavation in jointed rock. The presence of joints in the rock mass has been included implicitly by treating it as an appropriate anisotropic elastic continuum. The boundary element formulation for an anisotropic medium is briefly discussed. Good agreement has been found between numerical and analytical solutions for several example problems, demonstrating the accuracy of the present formulation. Numerical solutions are also presented for the problems of a deep circular tunnel and a basement excavated in a variety of jointed rock masses.     

矿井通风对多年冻土井筒围岩热影响的数值分析 (Ⅱ): 多年冻土井筒围岩温度的变化规律

在多年冻土区进行煤矿地下开采, 通风作用改变了井筒围岩的热平衡条件, 从而引起了多年冻土上限及其井筒周围冻土季节融化层的变化, 有可能影响到井筒支护结构的稳定性. 因此, 研究在矿井通风作用下, 多年冻土温度场分布及随季节的变化趋势是有意义的. 基于ANSYS有限元分析软件, 针对多年冻土区某煤矿的赋存条件、 试验采场位置以及通风作用对冻土的影响范围, 建立了二维数值计算模型, 利用焓式有限元方法对多年冻土井筒围岩的温度特性进行了数值模拟, 分析了矿井通风对多年冻土井筒围岩的热影响程度, 其计算方法和结果为下一步多年冻土煤矿地下开采井筒支护设计提供参考依据.     

Analysis of rock reinforcement using finite difference methods

Large-scale rock reinforcement offers the prospect of flexible and effective control of rock displacements aroud large open mine excavations. Although the technology of rock reinforcement is well developed, reinforcement analysis and design methods are not. Analysis is presented here for the mechanics of two models of rock reinforcement, one based on local action of a reinforcing element at a slipping joint, the other on spatially-extensive action in rock subject to diffuse deformation. The principles of some finite difference methods of analysis of stress and displacement are outlined. The performance of a code modeling spatially-extensive reinforcement is examined in a parameter study of stope hangingwall reinforcement using long, grouted cables.     

Prediction of dilation and permeability changes in rock salt

A numerical procedure has been developed for predicting dilation (porosity) and gas permeability changes in rock salt. The hierarchical single-surface constitutive model of Desai and co-workers is used a finite element program to calculate the state of stress and strain surrounding excavations in rock salt. The elastoplastic constitutive model accounts for strain hardening, a non-associative volumetric response and stress-path-dependent behaviour. The calculated stress and strain fields are used in a flow model based on the equivalent channel concept to predict permeability. Parameters for both the mechanical and permeability models are developed from laboratory test results. Two field experiments adjacent to underground excavations are modelled. The extent of the dilated rock zone around the excavation is predicted well, but the magnitude of the porosity and gas permeability is underpredicted very near the excavations. This discrepancy is attributed to model parameters derived from loading-only laboratory tests, whereas significant unloading occurs in the field. The shape of the yield surface was found to be an important factor in dilation and permeability predictions. Similar stress, strain and permeability fields were obtained with different model types (plane strain or axisymmetric) and initial stress states, and with instantaneous and progressive excavation.     

Capacity and limits of the finite element method in applying it to geotechnical problems

The capacity of numerical methods is very large. It covers complex geomtries, nonlinear material laws, excavating phases in tunnelling. The finite element methods has been developed from continuum theory. Hence, the method is readily applicable for materials like steel, salt-rock, fluids, sands, clays but less suitable for concrete, jointed rocks, discontinua. Real failure modes during excavation in rock are scarcely covered by the finite element approach but satisfactory results are obtained if stresses and deformations under working loads are of interest. Problems arising when results obtained by sophisticated analysis have to be interpreted by engineers not familiar with the method are discussed (“black box”).     

Numerical modelling of transient contaminant migration problems in infinite porous fractured media using finite/infinite element technique. Part I: Theory

The leakage effect in porous fissured media has been considered in a general sense by introducing a new expression of the leakage term in this paper. The double porosity concept is employed and the related expressions are formulated using the upwind finite element approach. Considering the infinite extension of the problem domain, a mapped transient infinite element has been presented to simulate the far field of the infinite medium. Since the mass transfer function of the present mapped transient infinite element is dependent on both space and time variables, the mechanism of transient contaminant migration problems in infinite porous fractured media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest. By comparing the current numerical results with the analytical ones, the accuracy, correctness and effectiveness of the present method have been established. Three different time discretization schemes were examined and it was found that either the central difference or the backward difference approximation is suitable for the upwind finite element simulation of transient contaminant migration problems.