Stress‐driven integration strategies and m‐AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces

The paper proposes a stress‐driven integration strategy for Perzyna‐type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity‐like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m‐AGC tangent operator. This operator is combined with the stress‐prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra‐step iterations (in physical viscoplasticity), or to a variable time‐step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero‐thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed. Copyright © 2016 John Wiley & Sons, Ltd.     

New point-to-face contact algorithm for 3-D contact problems using the augmented Lagrangian method in 3-D DDA

This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the ‘Common-Plane’ method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well.     

油井开采过程中油层变形的流固耦合分析

在油气开采过程中,随着油气的不断采出,必然造成孔隙流体压力的逐渐降低,由此导致储层岩石骨架的有效应力增大,使得油层产生变形或压实。当油层产生变莆或压实时,对油气生产将造成不利影响。比如：使得油藏的渗透率降低,继而使油井的产能降低,同时,油层的变形直接影响着油井和套管的变形与破坏等等。敢开采过程中油层的变形可以描述为三维变形与三维流体流动场的耦合问题,利用可变形多孔介质中流体渗流的流固耦合有限元数值     

Applying Bayesian approach to predict deformations during tunnel construction

In this paper a fully probabilistic approach based on the Bayesian statistical method is presented to predict ground settlements in both transverse and longitudinal directions during gradual excavation of a tunnel. To that end, the convergence confinement method is adopted to give estimates of ground deformation numerically. Together with in situ measurements of the evolution of vertical deflections at selected points along the tunnel line, it allows for the construction of a likelihood function and consequently in the framework of Bayesian inference to provide posterior improved knowledge of model parameters entering the numerical analysis. In this regard, the Bayesian updating is first exploited in the material identification step and next used to yield predictions of ground settlement in sections along the tunnel line ahead of the tunnel face. This methodology thus makes it possible to improve original designs by utilizing an increasing number of data (measurements) collected in the course of tunnel construction.     

复杂电性结构大地电磁二维响应特征

为了改进计算区域离散化问题,本文利用自适应非结构化网格有限单元法求解二维地电结构下大地电磁场满足的加权余量表达式。在有限元求解电磁场的过程中,网格剖分越精细、计算精度越高,计算量也会越大。此外,结构化网格难以适应任意地形以及复杂地质构造。而自适应非结构化网格在电性变化剧烈的区域会自动加密,在电性缓变的区域则生成粗疏的网格,从而优化网格质量与数量。因此,文中引入COMSOL Multiphysics软件,以实现若干地电模型的构建及非结构化自由四边形单元网格化。将网格数据信息导入本文算法,计算大地电磁场响应,并与解析解及数值解对比。结果表明,基于非结构化网格的正演模拟精度高、适应性强,为计算区域网格化提供了新的方法。     

有限单元法三维电阻率最小二乘反演中存在问题的研究

针对有限单元法在三维电阻率最小二乘反演中关于深部单元的反演能力、反演稳定性和速度问题进行了讨论与改进.首先构造了全新的"体积因子"作为先验信息加入到电阻率反演中,使地质体赋存区域的电阻率变化更符合实际情况,提高了深度较大的地质体的分辨能力.反演计算中对实测电阻率数据和模型正演数据分别取对数,并改进迭代修正量的计算方法,将以前的加减修正量改为与修正量指数之积,这样,不但可以改进电阻率模型出现负值的缺陷,提高反演计算的稳定性,而且还可减少迭代次数;针对反演时间过长的缺陷,将三维全域反演改为三维局域反演,使每次迭代的时间由4 h减少到目前的15 min;对模型的反演计算表明,以上改进是非常有效的.     

渗流问题的三维h型自适应有限元法研究

研究了三维渗流的自适应有限元法,建立了集成网格自动剖分、渗流有限元分析、网格调整、后处理等四大模块的四面体单元h型自适应系统。给出的算例证实了系统的有效性和优越性。     

水泥土桩加固海洋土的渐进变形破坏试验与数值分析

应用一个高度非线性的三维各向异性粘弹塑性(EVP)模型及有限元法,对一水泥土桩(CDM)加固海洋土的复合地基进行数值模拟。海洋软粘土的渐进变形采用粘弹塑性模型来模拟,水泥土桩破坏前后的应力-应变关系采用一个双曲线模型来模拟,提出了一个简单且非常实用的数值分析方法来解决水泥土桩碎裂软化的数值模拟问题。将数值模拟结果与实测数据进行了比较,二者吻合较好。     

基于强度折减法的三维边坡稳定性与破坏机制

基于强度折减技术的三维弹塑性有限元法是当前较为有效的边坡稳定性评价方法,但很少应用于复杂地质环境及负载条件下的三维边坡稳定性与破坏机制分析。拓展这一方法,利用典型算例,探讨了单元尺寸、边界条件、土体强度、局部超载和地震荷载等因素对三维边坡稳定性及潜在滑动面的影响;在此基础上,着重研究含软弱夹层及地下水的复杂三维边坡在负载条件（坡顶局部超载及地震荷载）下的破坏模式及滑动机制。结果表明：随着黏聚力的增加,潜在滑坡体的剪出位置远离坡脚,滑坡后沿远离坡肩,滑坡深度加深;坡顶超载强度较低时,边坡表现为整体破坏模式,而高超载强度下表现为局部地基破坏;考虑地下水后边坡的稳定性显著下降,且潜在滑动面加深,滑坡体体积有所增大。含软弱夹层的三维边坡,其潜在滑动面呈折线型,当受超载作用时,其破坏模式和滑动机制与地震荷载作用下不同:前者为竖向剪切和水平错动的联合作用,而后者为软弱夹层水平错动起主导作用。     

Three-dimensional slope reliability and risk assessment using auxiliary random finite element method

This paper aims to propose an auxiliary random finite element method (ARFEM) for efficient three-dimensional (3-D) slope reliability analysis and risk assessment considering spatial variability of soil properties. The ARFEM mainly consists of two steps: (1) preliminary analysis using a relatively coarse finite-element model and Subset Simulation, and (2) target analysis using a detailed finite-element model and response conditioning method. The 3-D spatial variability of soil properties is explicitly modeled using the expansion optimal linear estimation approach. A 3-D soil slope example is presented to demonstrate the validity of ARFEM. Finally, a sensitivity study is carried out to explore the effect of horizontal spatial variability. The results indicate that the proposed ARFEM not only provides reasonably accurate estimates of slope failure probability and risk, but also significantly reduces the computational effort at small probability levels. 3-D slope probabilistic analysis (including both 3-D slope stability analysis and 3-D spatial variability modeling) can reflect slope failure mechanism more realistically in terms of the shape, location and length of slip surface. Horizontal spatial variability can significantly influence the failure mode, reliability and risk of 3-D slopes, especially for long slopes with relatively strong horizontal spatial variability. These effects can be properly incorporated into 3-D slope reliability analysis and risk assessment using ARFEM.     

Numerical modelling of competitive components transport with non‐linear adsorption

A characteristic finite element (CFE) algorithm for modelling contaminant transport problems coupled with non‐linear competitive adsorption is presented. An alternative algorithm, termed as the transport‐equilibrium Petrov–Galerkin (TEPG) methods in this paper, is also presented for comparison. Through analyses of a number of examples with Peclet number ranging from zero to infinity, it is shown that the CFE algorithm is very competitive with the middle–point TEPG method in terms of accuracy, stability and efficiency. The fully explicit and fully implicit TEPG methods are found to be less appropriate for transport problems coupled with non‐linear equilibrium equations. Copyright © 2000 John Wiley & Sons, Ltd.     

Displacement‐controlled method and its applications to material non‐linearity

For the analysis of non‐linear problems, the displacement‐controlled method (DCM) has a more extensive application scope and more powerful abilities than the load‐controlled method (LCM). However, difficulties of the DCM's procedure not amenable to most finite element implementations of the conventional LCM have restricted its applications in geomechanics. By means of Sherman–Morrison's theorem, the solution of DCM is improved. The improved procedure is characterized by high efficiency, good numerical stability and a programme structure similar to LCM. Two aspects of applications of DCM are illustrated. The first application is to compute the response of a structure under a given load level like the conventional finite element analysis. The second application is to trace the equilibrium path of a structure under a given load distribution type. A simple but effective algorithm is presented for automatically adjusting the step length in tracing the equilibrium path. Examples illustrate that the proposed procedures are suited for modelling complicated non‐linear problems in geomechanics. Copyright © 2005 John Wiley & Sons, Ltd.     

四节点矩形弹簧元及其特性研究

弹簧元法是一种将单元离散为一系列弹簧的数值计算方法。不同的单元具有不同的离散方式,确定相应的离散弹簧的刚度系数表达式是弹簧元法的关键。将四节点矩形单元离散为6个基本弹簧,每个基本弹簧包括法向弹簧和切向弹簧两个派生弹簧,并用泊松弹簧和纯剪弹簧描述单元的泊松效应和剪切效应,用有限元的单元刚度矩阵标定各弹簧的刚度系数,实现了一种四节点矩形弹簧元的构造形式。该单元的同类弹簧具有相同的表达形式。法向与切向弹簧的刚度表达式中分别含有法向和切向弹簧刚度待定系数。通过改变待定系数的值可使该单元分别对应于有限元的常应变、双线性及Wilson非协调单元。将上述弹簧元方法进行理论推导,并应用于基于连续介质的离散单元法（CDEM）的核心计算进行简单算例验证,证明了提出方法的正确性。通过以上研究发现,四节点矩形弹簧元有以下特点：对于相同问题,不同单元有不同的计算精度;对于梁弯曲问题,应用该单元可显著提高离散单元法的求解精度;改变待定系数的值,可得到更高或者更低精度的单元。     

岩土工程亿级单元有限元模型可扩展并行计算

讨论了亿万单元有限元模型的可扩展并行计算方法。从软件和硬件两个方面提出了前处理、并行计算方法、程序算法、后处理实现等核心问题的解决方案。采用网格加密方法生成一亿单元的有限元模型,利用对偶原始有限元撕裂内联法（FETI-DP）求解系统方程。基于图论理论建立了子区域间的通讯拓扑关系,实现了子区域间点对点通讯,避免速度慢、通信量大的全局通讯。在自主开发程序基础上,增加相应模块,采用面向对象编程技术和MPI消息传递库开发程序。对一个一亿多单元的工程实例运用5 000核并行计算,得到了超线性加速比。计算结果在专用图形工作站上进行后处理,显示和交互操作速度良好。研究在两方面实现了突破：一是将模型规模提高到了一亿多单元;二是同时调用了5 000个计算核来并行运算,并得到了很高效率。高分辨率有限元并行模拟研究成果可为岩土工程中结构特别复杂、计算区域特别大、地质情况复杂等模拟提供很好的技术方法和实现手段。     

Iterative analysis of pore‐dynamic models discretized by finite elements

This work proposes an iterative procedure to analyze dynamic linear/nonlinear fully saturated porous media considering time‐domain finite element discretization. In this iterative approach, each phase of the coupled problem is treated separately, uncoupling the governing equations of the model. Thus, simpler, smaller, and better conditioned systems of equations are obtained, rendering more attractive techniques. A relaxation parameter is introduced in order to improve the efficiency and robustness of the iterative solution, and an expression to compute optimal values for the relaxation parameter is discussed. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Strain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a micro‐crack‐based anisotropic damage model for rock‐like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well‐known mesh‐sensitivity problem in FEM. In the computation, elements with C₁ continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D‐non‐linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

三维地电断面电阻率测深有限元数值模拟

用有限单元法进行了电导率分块均匀的三维点源电场电阻率测深的数值模拟.首先给出了三维构造中点源电场的边值问题、变分问题; 然后, 用有限单元法求解变分问题, 将区域剖分成六面体单元, 在单元中进行三线性函数插值, 将变分方程化为线性代数方程组; 最后解方程组, 得各节点的电位值, 进而计算出地表的视电阻率.对几例较典型的地电模型进行试算, 结果表明本方法是行之有效的      

基于Ansys的渗流自由面计算方法

对渗流自由面计算的单元传导矩阵调整法进行了改进。在局部坐标系下,将单元离散为一系列面元（三维为体元）,根据面元或体元形心处的压力水头值来确定面元或体元的权系数,然后按加权平均确定单元的等效渗透系数,该方法既可以避免复合单元中自由面上下面积或体积的计算,面元或体元的离散密度也可以任意选择,简化了计算程序。通过预设的收敛参数来控制迭代过程,可避免相邻两次计算的渗透系数变化太大而难于收敛。以Ansys为开发平台,用APDL语言编写了相应的计算程序,扩展了Ansys的计算功能,为渗流自由面计算提供了新途径。算例表明：该方法的收敛性较好、计算精度较高,能满足工程需要。     

水沙运动一、二维分区耦合虚拟点算法

建立了一种计算具有多空间尺度水沙运动的一、二维分区耦合虚拟点算法。该算法通过在一、二维区域的交界面定义虚拟点,并利用有限元的非结构化网格与单元叠加的特点,将所有一、二维区域连接点的影响系数集成到总体阵中虚拟点的元素上,实现不同分区之间的强耦合作用。同传统的使用简单匹配条件的一、二维分区弱耦合算法相比,该方法可以提高分区耦合计算的稳定性。对算法的正确性用一河口算例进行了检验。     

三维地电断面激发极化法有限元数值模拟

用有限单元法求解三维地电断面激发极化法正演模拟算法.首先给出了三维构造中点源电场异常电位的边值问题与变分问题, 简化无穷远边界上的边界条件以提高计算速度及计算精度.以此为基础计算视电阻率对模型电阻率的偏导数矩阵, 并进行三维地电断面激发极化法正演模拟, 与等效电阻率法相比节约了计算时间.对几例较典型的地电模型进行计算, 结果表明本方法是正确可行的.