Application of the third medium method for frictionless contact problems in geomechanics

Traditional approaches in contact mechanics demand complicated search algorithms at the interface between the contacting bodies. Recently, a new contact method based on the concept of a third medium has been developed, which overcomes the drawbacks of conventional contact mechanics techniques. This new scheme is based on a space filling mesh, in which the contacting bodies can move and interact. The ability and accuracy of this method in predicting displacements, as well as the contact forces, is validated by solving selected numerical examples. The potential merits of this method for analysing geotechnical problems by the finite element method are addressed.     

三维油藏中应力与渗流的摄动-有限元分析

提出了一个较为实际的石油油藏的三维力学模型。以已有的三维介质中应力与渗流耦合问题的变分原理为基础,用摄动法证明了光油藏厚度变化为小量时,三维问题或简化为平面应变问题,并可采用不同厚度的平面应变单元进行有限元分析,所得到的解即是该三维问题的零阶摄动解。给出了摄动法的推导和有限元格式,计算了一个水驱法进行油田二次开发的算例并给出了计算结果。     

地下水流二维、准三维及三维模型模拟结果比较

本文为三种简单的由多个含水层和弱透水层组成的越流含水系统建立了二维、准三维和三维数学模型,并对它们的解进行了比较分析.三种水流系统的二维、准三维及三维数学模型计算结果相互间的偏差随抽水时间的延长而增大,随井距的增大而减小;二维与准三维数学模型计算结果间的偏差随弱透水层越流系数的减小而减小;两种准三维数学模型计算结果间的偏差随抽水含水层与弱透水层间贮水系数比值的增大而减小;考虑弱透水层弹性释水的准三维模型与三维模型的解最为接近,它们之间的水头差当贮水系数比值一定时,随抽水含水层与弱透水层间渗透系数比值增大而减小,且随各向异性比值的增大而增大.     

Comparative analysis of some geomechanics problems using finite and infinite element methods

Four classical geomechanics problems involving semi-infinite linear elastic media have been solved numerically using recently developed mapped infinite elements coupled to finite elements.The effect of the remoteness of the truncated boundary and the location of infinite element coupling on solution accuracy has been studied. The results of conventional analyses using finite elements over a relatively large but restricted region are compared to the coupled analyses. Comparison of the results shows that for the same number of degrees of freedom the performance of the coupled solutions is superior to the conventional approach with respect to accuracy of solution and computational efficiency. Finally, some general guidelines are proposed for the efficient numerical solution of these types of problems using the coupled finite/infinite element approach.     

Large strain analysis of some geomechanics problems by the finite element method

This paper presents a rational approach to the finite strain analysis of elastic-plastic materials. An updated incremental finite element technique was applied to problems of shallow foundations of homogeneous as well as multilayer soils. This was based on a variational principle which is suitable for such problems.     

The significance of trace elements in solving petrogenetic problems and controversies

In contrast to the cases of interpolation, in the cases of extrapolation trace elements and trace-element ratios can be used as evidence in solving petrogenetic problems. Despite of the many instances of successful employment of trace elements in solving genetic problems and in differentiating cases, on the whole trace elements should only be used as contributory evidence, together with geological, structural and textural data.     

Dynamic stress analysis of a class of geomechanics problems by the boundary element method

This paper presents the application of an advanced BEM for periodic and transient dynamic stress analyses of a class of geomechanics problems. For transient dynamic analysis, the problem is first solved in the Laplace transform space, which happens to be similar to the periodic dynamic analysis, and then the time domain solution is obtained by numerical inversion of transform domain solutions. The numerical implementation of the BEM used to present the results in this paper is complete and most general available to date. It is capable of treating very large, multi-layered problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring, capability problems related to layered media and soil–structure interaction have been analysed. A number of examples are presented and through comparisons with available analytical and numerical results, the applicability and usefulness of the present analysis to real geomechanical problems are established.     

From discrete to continuum modelling of boundary value problems in geomechanics: An integrated FEM-DEM approach

Double-scale numerical methods constitute an effective tool for simultaneously representing the complex nature of geomaterials and treating real-scale engineering problems such as a tunnel excavation or a pressuremetre at a reasonable numerical cost. This paper presents an approach coupling discrete elements (DEM) at the microscale with finite elements (FEM) at the macroscale. In this approach, a DEM-based numerical constitutive law is embedded into a standard FEM formulation. In this regard, an exhaustive discussion is presented on how a 2D/3D granular assembly can be used to generate, step by step along the overall computation process, a consistent Numerically Homogenised Law. The paper also focuses on some recent developments including a comprehensive discussion of the efficiency of Newton-like operators, the introduction of a regularisation technique at the macroscale by means of a second gradient framework, and the development of parallelisation techniques to alleviate the computational cost of the proposed approach. Some real-scale problems taking into account the material spatial variability are illustrated, proving the numerical efficiency of the proposed approach and the benefit of a particle-based strategy.     

Image‐based modelling and analysis of microstructures for two‐scale problems in geomechanics

This paper focuses on the geometry modelling and numerical analysis of microstructures of geomaterials employing the concept of image‐based engineering. The novel modelling and analysis techniques with digital images are incorporated with the mathematical homogenization method to study the interaction between individual phases, each of whose shape and spatial distribution are irregular. Owing to the distinctive features of these computational techniques, the evaluation of homogenized properties for geomaterials provides the reliable information about the micro‐ or macroscopic mechanical behaviours for engineering practice. It is, naturally, inevitable that engineers' demands on safety and efficient design place emphasis on quantitative estimates for these values. Thus, calibration accompanied with actual measurements comes within the scope of this study so that these properties would be realistic and practical from the engineering viewpoints. Copyright © 2002 John Wiley & Sons, Ltd.     

Visualization of material stiffness in geomechanics analysis

This paper presents novel visualization techniques to simplify representation of the fourth‐order material stiffness tensor as a set of three‐dimensional geometric objects. Stiffness visualization aids in understanding the complex stiffness characteristics of highly non‐linear constitutive models including modelled material anisotropy and loading path dependent stiffness variation. Stiffness visualization is relevant for understanding the relationship of material stiffness to global behaviour in the analysis of a boundary value problem. The spherical pulse stiffness visualization method, developed in the acoustics field, is extended to visualize stiffness of geomaterials using three three‐dimensional objects. This method is limited to relatively simple constitutive models with symmetric stiffness matrices insensitive to loading magnitude and direction. A strain dependent stiffness visualization method is developed that allows the examination of material stiffness for a range of loading directions and is suitable for highly non‐linear and path dependent material models. The proposed stiffness visualization can be represented as 3‐D, 2‐D and 1‐D objects. The visualization technique is used to represent material stiffness and its evolution during simulated soil laboratory tests and deep excavation construction. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiscale modeling of large deformation in geomechanics

Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain-scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small-strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil-pipe interaction, and soil column collapse.     

煤样三维渗透率应力敏感性试验研究

目前国内三维渗透率测试研究处于起步阶段,利用自主研发的煤样三维渗透率测试仪,可以模拟实现真实三向应力状态下流体通过立方体煤样孔隙的三维渗流,并进行真实三向应力条件下煤样渗透率应力敏感性试验研究。试验结果表明,真实三向应力作用下煤样水平最大主应力对煤样水平方向渗透性的影响程度大于水平最小主应力;煤样三维渗透率对三向应力的敏感程度不同,对垂直应力的敏感性最强,水平最大主应力次之,水平最小主应力最小。     

运用遗传算法求解土钉支护结构的整体稳定性系数

以土钉支护结构整体稳定性计算的圆弧滑动简单条分法为基础,运用遗传算法对北京某大厦基坑的土钉支护结构最危险滑移面的位置进行了动态搜索与确定,并计算了其稳定系数。结果表明基坑边坡在实施土钉支护后,其最危险滑移面将后移,同时表明遗传算法能够较准确地确定土钉支护结构最危险滑动面及其相应的整体稳定性系数,且可在优化设计中避免陷入局部最小值,证明了该方法的有效性和准确性。     

The development of logging methods in solving hydrogeological problems at the Aleksandrovka research base

This paper presents the results of the development of a digital logging system and its implementation into everyday practice, at a well of Moscow State University. Complex data interpretation in relation to problems of hydrogeology is discussed. New developments, such as a video well-logging device and a highfrequency induction probe (HFIL) for plastic-cased wells, are used in the system in addition to the obligatory logging types (GL, RL, SP, CL, and temperature measurement).     

三维黏弹性介质人工边界研究

为了得到适于分析非线性结构-地基相互作用问题的人工边界,结合弹性波理论与黏弹性理论,推导出了适于模拟三维黏弹性远场介质辐射阻尼的人工边界,并对其模拟远场地基辐射阻尼的性能及相应地震波动输入方法进行了研究。结果表明：在结构-地基动力相互作用问题中,得到的黏弹性人工边界模拟计算域外远场黏弹性介质的辐射阻尼具有理想精度;不论是简谐波还是非简谐波,地震波动输入都取得了理想结果;在黏弹性介质条件下自由地表处的总场位移幅值n是输入波幅值的 倍。     

三维高密度电法用于工程勘查的试验

国内三维高密度电法在工程上的应用,大都采用二维数据反演,通过三维成图软件把视电阻率剖面连成三维视电阻率分布立体图,而很少将三维数据拼接在一起,通过三维软件反演。结合管线探测,对真三维高密度电法进行了探测试验,并取得了良好的勘探效果,为三维高密度电阻率法的进一步推广提供了宝贵的实践经验。     

Analysis of iterative ensemble smoothers for solving inverse problems

This paper examines the properties of the Iterated Ensemble Smoother (IES) and the Multiple Data Assimilation Ensemble Smoother (ES–MDA) for solving the history matching problem. The iterative methods are compared with the standard Ensemble Smoother (ES) to improve the understanding of the similarities and differences between them. We derive the three smoothers from Bayes’ theorem for a scalar case which allows us to compare the equations solved by the three methods, and we can better understand which assumptions are applied and their consequences. When working with a scalar model, it is possible to use a vast ensemble size, and we can construct the sample distributions for both priors and posteriors, as well as intermediate iterates. For a linear model, all three methods give the same result. For a nonlinear model, the iterative methods improve on the ES result, but the two iterative methods converge to different solutions, and it is not clear which should be the preferred choice. It is clear that the ensemble of cost functions used to define the IES solution does not represent an exact sampling of the posterior-Bayes’ probability density function. Also, the use of an ensemble representation for the gradient in IES introduces an additional approximation compared to using an exact analytic gradient. For ES–MDA, the convergence, as a function of increasing number of uniform update steps, is studied for a huge ensemble size. We illustrate that ES–MDA converges to a solution that differs from the Bayesian posterior. The convergence is also examined using a realistic sample size to study the impact of the number of realizations relative to the number of update steps. We have run multiple ES–MDA experiments to examine the impact of using different schemes for choosing the lengths of the update steps, and we have tried to understand which properties of the inverse problem imply that a non-uniform update step length is beneficial. Finally, we have examined the smoother methods with a highly nonlinear model to examine their properties and limitations in more extreme situations.     

The theory of the recoverable linear strain sensor and its application in geomechanics

Summary After introducing the new linear strain sensors and the theory behind their modus operandi, the paper discusses in general the performance characteristics as well as the potential value of their application in geomechanics. Application features and effects of application environments are then outlined and examples of practical applications are given.