Sensitivity analysis for parameter identification in quasi‐static poroelasticity

This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd.     

Performance studies of the fixed stress split algorithm for immiscible two-phase flow coupled with linear poromechanics

In this work, we measure the performance of the fixed stress split algorithm for the immiscible water-oil flow coupled with linear poromechanics. The two-phase flow equations are solved on general hexahedral elements using the multipoint flux mixed finite element method whereas the poromechanics equations are discretized using the conforming Galerkin method. We introduce a rigorous calculation of the update in poroelastic properties during the iterative solution of the coupled system equations. The effects of the coupling parameter on the performance of the fixed stress algorithm is demonstrated in two field studies: the Frio oil reservoir and the Cranfield injection site.

     

各向异性初始应力状态下圆柱孔扩张理论弹塑性分析

传统的圆柱孔扩张理论假定初始应力为各向同性的。在城市地下管道的铺设、隧道工程等的水平掘进施工过程中,圆柱孔受到的初始竖向应力不等于初始水平应力,并不满足各向同性初始应力条件。考虑土体的各向异性初始应力条件,假定土体满足Mohr-Coulomb屈服准则,推导了各向异性初始应力状态下的圆柱孔扩张问题弹塑性解答。算例计算结果表明：土性参数一定时,在相同内压力作用下,各向异性初始应力状态下的圆柱孔扩张形成的塑性区半径大于各向同性初始应力状态下的圆柱孔扩张的塑性区半径,但前者的极限扩孔压力小于后者。     

定轴排水剪切试验中各向异性砂土的力学响应

南京云母砂主要由片状颗粒组成,具有较为明显的各向异性特性。采用香港科技大学的自动控制空心圆柱扭剪仪进行了应力主轴方向角分别为10°、30°、60°、80°的密实云母砂定轴剪切试验,研究云母砂的初始各向异性规律。为研究中主应力的影响,又对同一密度的试样在中主应力系数b＝0.1、0.5、1.0三种不同情况下进行定轴剪切试验。试验结果表明,在大主应力方向角从0°～90°的变化过程中,强度先减小后增大,且随着b值的增加强度增大;变形表现出明显的各向异性,随着b值的增加体变增大     

Convergence acceleration of iterative sequences for equilibrium chemistry computations

Computational Geosciences - The modeling of thermodynamic equilibria leads to complex nonlinear chemical systems which are often solved with the Newton-Raphson method. But this resolution can lead...     

Convergence of iterative coupling for coupled flow and geomechanics

In this paper, we study solving iteratively the coupling of flow and mechanics. We demonstrate the stability and convergence of two widely used schemes: the undrained split method and the fixed stress split method. To our knowledge, this is the first time that such results have been rigorously obtained and published in the scientific literature. In addition, we propose a new stress split method, with faster convergence rate than known schemes. These results are specially important today due to the interest in hydraulic fracturing (Dean and Schmidt SPE J. 14:707–714, 2009; Ji et al. SPE J. 14:423–430, 2009; Samier and De Gennaro 2007; Settari and Maurits SPE J. 3:219–226, 1998), in oil and gas shale reservoirs.     

Variation with depth of the stress tensor anisotropy inferred from microfault analysis

In order to study the Pyrenean tectonic phase, a quantitative method of stress analysis using microfault measurements is used on a calcareous plateau located in southern France. The method developed here allows the determination of several tectonic events and the evaluation of (with σ σ₂ σ₃).The Pyrenean compression is seen to occur in two stages, confirming previous geological studies.A recent canyon allows the study of the variation with depth of the R ratio on a vertical cross-section (300 m). With a simple model of gravity and tectonic stresses, the vertical variation of R can be used to estimate quantitatively the Pyrenean tectonic stresses. For realistic values of the parameters in this model, the horizontal tectonic stresses are obtained in the following range: 50–200 bar for the maximum horizontal principal stress, 10–25 bar for the other horizontal stress.These results seem to be consistent with in situ stress measurements, but they are much lower than those predicted by experimental rock mechanics.     

基于各向异性岩体渗透参数分析的矿区地下水环境预测

地下采矿工程势必会引起矿区周边地下水水位的变化,而地下水在岩体中渗流主要受岩体裂隙的影响,因此地下水渗流具有非均质各向异性的特点。采用统计学分析方法,根据岩体裂隙几何参数计算渗透张量,获得综合渗透系数,并与钻孔抽水试验所得渗透系数相比较,进行修正,得到渗透主值。并运用于Visual Modflow中建立地下采矿区各向异性的地下水渗流模型,进而较准确地预测采矿过程中地下水降落漏斗的影响范围及影响幅度。     

Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium

We consider an iterative scheme for solving a coupled geomechanics and flow problem in a fractured poroelastic medium. The fractures are treated as possibly non-planar interfaces. Our iterative scheme is an adaptation due to the presence of fractures of a classical fixed stress-splitting scheme. We prove that the iterative scheme is a contraction in an appropriate norm. Moreover, the solution converges to the unique weak solution of the coupled problem.     

Demonstration of spatial anisotropic deformation properties for jointed rock mass by an analytical deformation tensor

This paper develops a joint deformation tensor (JD), which considers all of the joint's mechanical and geometrical parameters that affect the deformability of the rock mass. The method based on JD (JD method) and an elastic deformation anisotropy index (EDAI) are deduced for estimating the spatial anisotropy deformation of a jointed rock mass. The numerical modeling and in situ true triaxial compressive experiments well verified the effectiveness of the EDAI and JD method for the rock mass containing one joint set, orthogonal joint sets or the rock mass containing any types of joint network with unity stiffness ratio.     

Elastic stress and strain in jointed rock masses by means of crack tensor analysis

Summary An elastic stress-strain relation is formulated in terms of crack tensors which makes it possible to take into account explicitly the effect of joints on elastic behavior of rock masses. The present study is to discuss some related topics which may be encountered in its practical application. Two problems are solved by incorporating the elastic stress-strain relation into a program for three-dimensional finite element analyses; i. e., stress concentration by surface loading and displacement by excavation of an intersecting tunnel. Validity of the results is checked by comparing them with a laboratory model test and a field test, with the following conclusions: The overall distribution of stress definitely depends on a joint stiffness ratio (i. e., normal stiffness to shear stiffness). If the ratio is chosen as unity, the stress concentration occurs mainly in the direction parallel to major joints. If the ratio is high, say 10, then the stress concentrates along the perpendicular as well as the parallel directions to major joints. It can be said, on the basis of the fairly good agreement of the calculations using the high stiffness ratio with the field and laboratory measurements, that the elastic solution by crack tensors provides a practical tool for estimating the stress and strain in strongly jointed rock masses.     

基于断层擦痕侧伏角公式的构造应力张量反演

利用Aleksandrowski推导的断层擦痕侧伏角公式,提出了一种改进的构造应力张量反演法。根据不同应力比值下构造应力与断层擦痕侧伏角的关系,利用最小二乘法,详细推导了构造应力张量的反演方法,最后利用Matlab软件编制程序实现了该计算过程。在此基础上,现场调查了江西武山铜矿北矿带的断层滑动数据,利用上述改进方法反演了该地区的构造应力张量方向特征。将上述反演结果与由震源机制解获得的最新构造应力场结果进行对比分析,并结合研究区断层的展布特征及所在的地质构造背景,获得了该地区自晚侏罗世以来的构造应力场特征,表明该地区构造应力场具有一定的稳定性。改进后的构造应力张量求解过程及工程应用表明,将Aleksandrowski的图示法和Etchecopar等的反演法结合起来反演构造应力张量,是对已有方法的改进,具有更加简单、实现容易等特点,计算结果比较符合实际。     

岩土材料应力路径无关硬化参量的构成方法

在分析砂土试验结果的基础上,揭示了基本硬化内参量（塑性体积应变、塑性剪应变）变化的应力路径相关性,提出了应力路径无关硬化参量的一般表达式。并指出了塑性功硬化参量及其提出的黏土和砂土统一硬化参量均是所提一般表达式框架下的特例。还将该统一硬化参量直接和修正剑桥模型结合,并与试验结果对比,表现出描述剪胀特性的简单性和有效性。     

Interpretation of in situ stress measurements in anisotropic rocks with the doorstopper method

Summary A correct interpretation of in situ stress measurements by means of the doorstopper technique in cross anisotropic rocks requires that 10 stress concentration factors at the bottom of the borehole be known instead of the 3 which are needed for isotropic rocks. In order to analyse the data obtained in a site investigation in a gneiss of the Alpine region, these factors were determined by a three-dimensional high-order finite-element model. The results are presented and compared with those obtained by means of first approximation methods. The feasibility of carrying out measurements in anisotropic rock by means of only 2 boreholes is discussed and it is shown that in practice 3 properly oriented boreholes are needed in this case too.     

柱状节理坝基岩体三维各向异性数值分析

在分析柱状节理不连续性和各向异性的工程特性基础上,对某拱坝及坝基的柱状节理岩体进行三维数值模拟分析。考虑河谷初始地应力场和岩体各向异性力学性质,采用各向同性本构和各向异性弹塑性本构进行对比分析。计算表明,坝基柱状节理岩体各向异性特性对工程整体应力、变形的影响比较明显,采用各向异性弹塑性模型计算更能反映柱状节理的特殊性。其结果为该坝区岩体工程各向异性力学分析提供了示例。     

二维各向异性岩土介质中渗流分析的等参有限元方法

为了建筑环境的保护,软土地区基坑围护中的坑内降水与坑外水位保持常是一对矛盾的课题.而坑内外的水位差,极易形成止水结构两侧的渗流运动.对饱和各向异性、水平延伸、厚度大致相等、且存在一、二类边界时的承压含水层中的承压水二维非稳定流渗流问题,本文推导出了二维、各向异性渗流等参有限元方程,用以进行基坑围护止水结构附近渗流场分析,并给出了算例.     

Three-dimensional finite element modelling of stress relaxation tests in anisotropic clayey medium: direct problem and back analysis

This paper deals with a new strategy for initial stress identification by stress relaxation methods, coupled with finite element calculation, and applied to the overcoring test. The back-analysis of such a test uses an inversion method which consists in the minimisation, with a gradient-based algorithm, of a cost functional of least-squares type, which quantizes the difference between measured and computed strains. The computed strains are assessed by three-dimensional finite element modellings of the overcoring test. The inversion methodology is applied to a recent in situ overcoring test performed at Mont Terri laboratory, Switzerland. The inversion gave good results and allows us to validate the inversion methodology. The constitutive law considered for this application is transverse isotropic elasticity but the inversion method developed is applicable to most constitutive laws and every kind of in situ test.     

非均匀各向异性储层地震AVAZ响应模拟及分析

基于波动理论的各向异性反射率方法能够充分考虑地震波动力学特征。对单界面理论模型、实际非均匀各向异性模型分别进行正演模拟及分析,比较Ruger理论与反射率方法模拟结果的波动力学特征。结果表明,对于界面模型两种方法均能得到相同的计算结果,但对于实际非均匀各向异性介质,基于Ruger理论的算法受时间采样率的影响,而基于波动理论的反射率方法输入实际空间域模型,计算结果不受时间采样率的限制。     

An operator‐split ALE model for large deformation analysis of geomaterials

Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd.