Template elastic‐plastic computations in geomechanics

In this paper we present a new approach to computations in elasto‐plastic geomechanics. The approach is based on the object oriented design philosophy and observations on similarity of most incremental elastic–plastic material models. This new approach to elastic–plastic computations in geomechanics allows for creation of template material models. The analysis of template material models will in turn allow for an easy implementation of other elastic–plastic material models based on the object oriented design principles. Furthermore we present some illustrative implementation details. Finally we present analysis results that emphasize features of template elastic–plastic computations in geomechanics. Copyright © 2002 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.     

Preconditioners in computational geomechanics: A survey

The finite element (FE) solution of geomechanical problems in realistic settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the linear solver efficiency may play a crucial role: 1. fully coupled consolidation and 2. faulted uncoupled consolidation. A class of general solvers becoming increasingly popular relies on the Krylov subspace (or Conjugate Gradient‐like) methods, provided that an efficient preconditioner is available. For both problems mentioned above, the possible preconditioners include the diagonal scaling (DS), the Incomplete LU decomposition (ILU), the mixed constraint preconditioning (MCP) and the multilevel incomplete factorization (MIF). The development and the performance of these algorithms have been the topic of several recent works. The present paper aims at providing a survey of the preconditioners available to date in computational geomechanics. In particular, a review and a critical discussion of DS, ILU, MCP and MIF are given along with some comparative numerical results. Copyright © 2010 John Wiley & Sons, Ltd.     

地质力学磁力模型试验中均匀梯度磁场的构建

地质力学磁力模型试验利用电磁力（场）模拟重力（场）的原理研究地质力学工程问题,采用的相似材料由铁磁材料与岩土体混合而成。铁磁材料在磁场中的受力方向和大小与所处空间的磁通密度梯度的大小和方向有关,为了模拟均匀的重力场,需要得到在一定空间范围内磁通密度梯度大小相同、方向单一的磁场。根据电磁学基本原理,构建了3种磁路形式以获得磁通密度梯度相对均匀的磁场,对磁力模型试验相似材料进行加载。对比3种磁路,在最佳试验区内开放式磁路对磁场的利用率更高,所以在电流相同条件下等到的磁通密度梯度的量值也更大。与另两种磁路形式相比,尽管半开放式磁路在重量和工作效率上的性能不及开放式和封闭式磁路,但其最佳试验空间的磁通密度梯度的均匀性最好,误差在5%以内,半开放式磁路可以作为地质力学磁力模型试验的磁场发生装置。     

Thermal reservoir modeling in petroleum geomechanics

Thermal oil recovery processes involve high pressures and temperatures, leading to large volume changes and induced stresses. These cannot be handled by traditional reservoir simulation because it does not consider coupled geomechanics effects. In this paper we present a fully coupled, thermal half‐space model using a hybrid DDFEM method. A finite element method (FEM) solution is adopted for the reservoir and the surrounding thermally affected zone, and a displacement discontinuity method is used for the surrounding elastic, non‐thermal zone. This approach analyzes stress, pressure, temperature and volume change in the reservoir; it also provides stresses and displacements around the reservoir (including transient ground surface movements) in a natural manner without introducing extra spatial discretization outside the FEM zone. To overcome spurious spatial temperature oscillations in the convection‐dominated thermal advection–diffusion problem, we place the transient problem into an advection–diffusion–reaction problem framework, which is then efficiently addressed by a stabilized finite element approach, the subgrid‐scale/gradient subgrid‐scale method. Copyright © 2008 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.     

地质力学磁力模型试验原理及其在工程中的应用

地质力学磁力模型试验借鉴土工离心模型试验中利用离心力模拟重力的思想。在均匀梯度磁场中,掺有铁磁材料的相似材料会受到均匀的磁力作用,由此可以利用均匀的磁力场模拟重力场。根据电磁学基本原理和磁路设计原理,设计并制造了一台2 000匝线圈的均匀梯度磁场发生装置。该装置在220 V电压情况下,能够产生0～16 A电流,在1.2 m×1.2 m×1.0 m试验空间内,可将磁性相似材料的重度提高10～30倍。以锦屏一级电站左岸高陡边坡为例,进行地质力学磁力模型试验。试验结果表明,在一定的电流作用下,可以使模型所受体力的提高倍数达到相似比的要求,并与数值模拟结果进行了对比,试验结果与计算结果基本一致。在增加通电电流时,试验设备可以模拟边坡的超载过程,进而可以求出边坡的超载安全系数。     

An enhanced ensemble Kalman filter scheme incorporating model error in sequential coupling between flow and geomechanics

In this work, we construct a new methodology for enhancing the predictive accuracy of sequential methods for coupling flow and geomechanics while preserving low computational cost. The new computational approach is developed within the framework of the fixed-stress split algorithm procedure in conjunction with data assimilation based on the ensemble Kalman filter (EnKF). In this context, we identify the high-fidelity model with the two-way formulation where additional source term appears in the flow equation containing the time derivative of total mean stress. The iterative scheme is then interlaced with data assimilation steps, which also incorporate the modeling error inherent to the EnKF framework. Such a procedure gives rise to an “enhanced one-way formulation,” exhibiting substantial improvement in accuracy compared with the classical one-way method. The governing equations are discretized by mixed finite elements, and numerical simulation of a 2D slab problem between injection and production wells illustrate the tremendous achievement of the method proposed herein.     

三维张量CSAMT响应特征研究

张量CSAMT(可控源音频大地电磁法)能完整地描述三维的地电信息,更适应复杂地质条件下的地质勘探。采用将总场分解为一次场和二次场的策略,用差分近似微分形成大型线性方程组,通过解方程组得到张量CSAMT三维正演结果。通过计算低阻和高阻目标体的响应,发现卡尼亚视电阻率和视阻抗相位对低阻体表现为低值异常,对高阻体表现为高值异常,视阻抗相位达到极值时的频率比视电阻率达到极值时的频率要高。张量CSAMT对低阻体比高阻体更灵敏,在同样条件下,高阻体的异常区位置相比于低阻体会上移。某工区的勘察案例表明,根据卡尼亚视电阻率异常能定性地判断地下异常体的存在,为解决地质类问题提供了依据。本研究为张量CSAMT三维反演提供了基础。     

利用全概率方法分析岩土力学数值模拟结果的变异性

提出了一种用于分析在多参数随机情况下岩土力学数值模拟结果变异性的全概率方法。以特定数值模拟结果为随机隐式响应量,根据多维高效数值求积理论,计算出响应量特定函数的均值,利用快速傅里叶变换数值概率分析方法及笔者开发的最大熵分布,求解器软件一次性求解出响应量的全概率分布,用于定量评估数值模拟结果的变异性。算例表明该法具有精度和计算效率较高的优点。     

油气模型的重力梯度张量研究

以位场数据处理中的傅里叶变换为出发点,推导出由重力异常计算梯度张量的余弦谱变换公式,进而通过离散余弦变换实现梯度张量的数值计算。对不同贮油厚度的三度体球冠模型梯度张量的研究表明:当油气含量较小时,其梯度张量与均匀三度体球冠模型所表现出的特征相似,V_xx、V_yy呈“两高夹一低”的对称特征;V_xy总体上呈现出向中心变小的趋势,在4个边缘的中部分别有4个呈两两对称的相对较高值;V_zz四周低,中间高;V_zx、V_zy呈现出西低东高和南低北高的特征。而当贮油厚度逐渐增大时,V_xx、V_yy的形态则渐变为“两低夹一高”;V_xy在四周有相对低值,中部有极大值;V_zz四周高,中间低,变化更加尖锐;V_zx及V_zy呈西高东低和南高北低的特征。对三度体球冠模型重力梯度张量的研究,可以为寻找储油背斜构造提供理论依据。     

张量CSAMT数据处理技术初步研究与示范应用

面对大深度和三维探测,标量CSAMT(controlled source audio-frequency magnetotellurics)已显力不从心,而张量CSAMT正逐渐成为研究热点。在前人研究基础上,笔者就张量CSAMT数据处理方面提出Mohr圆分析和传统坐标旋转两种处理技术,并首次创新性地使用我国自主研发的综合电法仪开展了张量CSAMT示范应用。结果表明:Mohr圆分析和传统坐标旋转法相结合应用效果良好,可定性挖掘地下地质体的纵向和横向构造特征,主轴方位的视电阻率和阻抗相位与目标体对应良好,并且电阻率反演结果与钻孔等地质资料综合分析对建立试验区的地质地球物理模型是有益的。     

Three-Dimensional Conjugate Gradient Inversion of Magnetotelluric Impedance Tensor Data

We developed a three-dimensional(3D) conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotelluric impedance tensor in 3D inversion,synthetic data were inverted using the 3D conjugate gradient inversion,and the inversion results were compared and analyzed.The results from the 3D inversion of synthetic data indicate that both the off-diagonal and the diagonal components are required in in...     

全张量重力梯度数据误差分析及补偿

针对用于航空移动平台的高精度全张量重力梯度测量系统,深入研究了梯度仪12个加速度计按3个不同旋转轴圆盘形成差分组合的结构。在确认该结构具有有效抑制运动共模加速度、减少外界环境干扰、实现高精度探测优点的同时,着重分析了重力梯度仪测量误差的来源和影响。研究表明,主要影响包括仪器固有随机噪声和外界确定性噪声。为定量描述影响程度,推导了在航空动态环境下的测量方程,并分离出加速度计的性能不匹配、平台不稳定、圆盘转速不稳定3个主要固有因素,从时间域和频率域角度定量分析固有影响因素的噪声水平。试验分析表明,通过利用Simulink仿真系统可以获得固有因素产生的噪声水平,并提出抑制方案。针对搭载环境测量误差,还分析了实测飞行中姿态和质量的改变对重力梯度测量值造成的环境影响,提出了基于点质量源的自身梯度校正方法。     

利用重力梯度张量研究黑龙江省虎林盆地的断裂构造

以重力异常为依据,利用快速傅里叶变换计算了虎林盆地的重力全梯度张量。根据Vxx和Vyy的零值线能突出场源 体的边界以及走向近似于x或y轴方向的地质体、Vzz能够圈定异常体的位置和范围以及Vzx,Vzy和Vxy能够突出显示NS, EW和NE（NW）向的断裂构造线,分析虎林盆地重力异常及其梯度张量展布特征。推断研究区存在近NE,NW,NEE,近 EW向和NS向断裂,对其中5条深大断裂进行了描述。根据重力异常及其全梯度张量和断裂展布特征,可以将虎林盆地划 分为3个隆起和2个凹陷,与迎春隆起、虎林河凹陷、虎林中央隆起、东林子凹陷和兴凯湖隆起5个构造单元存在很好的对 应关系。     

A Relative Moment Tensor Inversion Technique Applied to Seismicity Induced by Mining

Summary. Studies of source mechanisms of mining-induced seismic events play an important role in understanding the various modes of failure observed around underground excavations and enable the geometry of likely planes of failure to be determined. These planes can be mapped using conventional techniques, for example, geological fracture mapping. However, such an approach is often problematical due to limited access to the site and/or poor exposures (if any) of the failure plane. An added difficulty is that planes of failure often do not follow faults of geological origin, but are related to the geometry of the advancing stope face. For example, the development of face-parallel shear zones ahead of deep-level stope faces. In such cases, the stresses induced by mining dominate over the geological structure in the critical region close to the stope face. Seismic methods therefore have the potential of being a practical method of studying the development of seismic shear zones underground.Slip on such a failure plane generates a three dimensional elastic wave that propagates through the rockmass, carrying a wealth of information regarding the source rupture process. The ground motions caused by the passage of the wave can be recorded by arrays of sensitive instruments called seismometers. These sets of recordings (seismograms) provide the basic data that seismologists use to study these elastic waves as they propagate through the Earth. Conventional seismic analyses provide scalar measurements of the rupture size and intensity. However, through a process known as moment tensor inversion (MTI), the seismograms recorded from a seismic event can be used to calculate a moment tensor that describes the three dimensional nature of the source mechanism. Interpretation of the moment tensor gives insight into whether the rockmass failed in tension, compression or shear and indicates the direction of movement and the failure plane.Moment tensor solutions computed using conventional MTI methods are sensitive to noise and may be biased due to systematic errors in the measurements. The primary objective of this study was to develop a robust MTI method to estimate the moment tensors of clusters of seismic events recorded in the underground environment. To achieve this, three hybrid MTI methods were developed by the author. These methods involve different iterative weighting schemes designed to enhance the accuracy of the computed moment tensors by decreasing the effect of outliers (data points whose residuals lie far from the mean or median error). The additional information required for hybrid methods is obtained by considering a spatial cluster of seismic events and assuming that the waves generated by each event in the cluster follow a similar path through the rockmass and allowing a common ray-path to be assumed. Hence the unknown effect of the heterogeneous rockmass on the waveform is similar for all the events in the cluster.The final objective was to determine whether the techniques developed could be successfully applied to real data. The hybrid MTI methods using the median and the weighted mean correction were applied to a cluster of 10 events, having remarkably similar waveforms, recorded at Oryx Gold Mine. For comparative purposes, the more conventional absolute method was also applied. The solutions computed using the hybrid MTI with a median correction displayed a distinct improvement after the iterative residual correction procedure was applied, in contrast to the solutions obtained from the absolute method. The radiation patterns and fault-plane solutions from the hybrid method showed a high degree of similarity, and were probably more accurate reflections of reality. These observations are very encouraging and point towards the potential for using the hybrid MTI method with a median correction as a standard processing tool for mine seismicity.The implications of this work are that a robust method for calculating the focal mechanisms of clusters of seismic events induced by mining activities has been developed. Regular application will lead to a better understanding of rock fracture processes and to improved safety underground.     

A computational procedure for joining separate map sheets

Map sheets have been often used as a basic spatial unit for managing spatial data produced from paper maps. This often results in incompatibility between adjacent map sheets, because spatial objects do not cross the boundaries smoothly and even the boundaries themselves do not match their neighbors exactly. To solve the problem this paper proposes a computational procedure for joining separate map sheets to obtain seamless spatial data. Line objects digitized separately in different map sheets are considered, which are frequently used to represent road networks, gas pipelines, and boundaries of polygon objects. The procedure consists of three steps: (1) extraction of end nodes, (2) detection of matching nodes, and (3) transformation of the map sheet. Each step goes interactively so that unexpected errors can be avoided by human observation. To test the validity of the procedure, map sheets are combined containing the road network data of Tokyo 23-ku area, Japan. This revised version was published online in July 2006 with corrections to the Cover Date.     

计算河流动力学理论体系框架探讨

计算河流动力学重在研究河流动力的时空变化,实质上是计算流体力学、计算土力学在河流动力学中的应用,但并非简单组合,主要难点源自相间作用机理复杂性及研究对象多尺度性所导致的应用可行性问题。问题解决的过程中产生大量新的适于河流动力计算的数学模型和数值模型,但当前理论体系还缺乏系统性。综合河流动力学、计算流体力学、计算土力学理论,给出计算河流动力学的理论体系框架,明确计算河流动力学各部分内容的基本联系。基于此理论体系,可以方便地判断模型准确性、计算量和复杂性,构建最优的数学模型,并判断数学模型的发展方向。     

Glyph and hyperstreamline representation of stress and strain tensors and material constitutive response

Results of numerical analyses of boundary value problems in geomechanics include output of three‐dimensional stress and strain states. Two‐dimensional plots of stress–stress or stress–strain quantities, often used to represent such output, do not fully communicate the evolution of stress and strain states. This paper describes the use of glyphs and hyperstreamlines for the visual representation of three dimensional stress and strain tensors in geomechanics applications. Glyphs can be used to represent principal stress states as well as normal stresses at a point. The application of these glyphs is extended in this paper to represent strain states. The paper introduces a new glyph, called HWY glyph for the representation of shear tensor components. A load step‐based hyperstreamline is developed to show the evolution of a stress or strain tensor under a general state of loading. The evolution of stress–strain states from simulated laboratory tests and a general boundary value problem of a deep braced excavation are represented using these advanced visual techniques. These visual representations facilitate the understanding of complex multidimensional stress–strain soil constitutive relationships. The visual objects introduced in this paper can be applied to stress and strain tensors from general boundary value problems. Copyright © 2003 John Wiley & Sons, Ltd.