利用ICCG迭代技术加快电阻率三维正演计算

一般而言,有限差分法求解点源三维地电场正问题所形成的大型稀疏线性方程组Ａｘ＝ｂ,直接解法的计算效率极低。本文从系数矩阵Ａ的不完全Ｃｈｏｌｅｓｋｙ分解及矩阵特征值的特点等角度,说明了不完全Ｃｈｏｌｅｓｋｙ共轭梯度（ＩＣＣＧ）迭代技术可大大提高电阻率三维正演速度的内在原因。结合矩阵Ａ的稀疏存储模式,使得内存需求也大大减少。     

利用ICCCG迭代技术加快电阻率三维正演计算

一般而言,有限差分法求解点源三维地电场正问题所形成的大型稀疏线必方程组Ａｘ＝ｂ,直接解法的计算效率极低。本文从系数矩阵Ａ的不完全Ｃｈｏｌｅｓｋｙ分解及矩阵特征值的特点等角度,说明了不完全Ｃｈｏｌｅｓｋｙ共轭梯度（ＩＣＣＧ）迭代技术可大大提高电阻率三维正演速度的内在原因。结合矩阵Ａ的稀疏存储模式,使得内存需求也大大减少。     

井地直流电法三维数值模拟中若干问题研究

讨论了地下垂直线源分段计算和场叠加的方法,并实现了在套管上供直流电的三维数值模拟。讨论了大型容量矩阵的压缩存储方式,采用数组和结构体相结合的方法实现容量矩阵的一维链表式压缩存储。在求解超大型稀疏线形方程组时引入不完全Cholesky分解稳定化的双共轭梯度算法(ICBG),通过与均匀半空间垂直线源解析解的对比,证明了该算法是准确可靠的。     

有限元法中总刚动态存取及其应用

讨论了如何利用FORTRAN 90中指针和派生类型相结合构成的链表结构的方法对总刚实现动态存取、增强总刚的灵活性,从而克服了以往总刚形成和存储的一些缺点。方法不仅能方便地实现总刚矩阵内任意位置上数据的插入和删除而不影响其它数组结构的变化,而且比一般半带宽存储节约更多内存。方法特别适合岩土工程开挖与支护等大型结构的三维有限元分析,能大大提高求解效率。     

近似对称矩阵的直接解法及其应用

所谓近似对称矩阵是指矩阵中仅有极少一部分元素是非对称的,在将对角线以上的非对称元素用其对角线以下的对称元素替代后,该矩阵就变成了一个对称矩阵。在求解非线性连续介质力学问题时常常会遇到近似非对称矩阵。基于Sherman-Morrison定理,给出了一种新的近似非对称矩阵的分解算法。在确保数值稳定性的前提下,无论在求解效率还是在内存开销方面新算法都优于一般的非对称稀疏矩阵的求解器,且仅需对传统的基于LDLT分解的求解器略做修改,即可开发出适应于对称和非对称稀疏矩阵的求解器。最后用一个摩擦接触算例,显示了新算法的优越性。     

LANCZOS迭代算法及其在三维地电场数值模拟计算中的应用研究

在三维电阻率的正演计算中往往涉及到快速、准确求解大型线性方程纽Ax=b的问题。通过采用有限差分法来构造出求解点电源三维地电场的大型稀疏对称线性方程组。并引入Lanczos迭代技术，构造出三对角阵方程组，然后采用正交分解法进行求解，它是Krylov子空间方法中的一种。与传统迭代算法相比，它占用内存少，收敛速度快且稳定。针对大型稀疏矩阵及MATLAB语言的特点，采用简单记录矩阵的非零元素值及其所在行、列值的方法存储大型稀疏矩阵，可大大节省机器内存，提高运算速度。理论分析和计算实例显示，此算法是地电三维正演计算的有效方法，为下一步的反演计算打好基础。     

多自由度块行压缩存储技术及大型稀疏方程组的求解

在地球物理电磁勘探领域有限元数值模拟中,最后都会得到一个大型稀疏的复系数线性方程组,受计算机内存空间的限制,必须根据有限元刚度矩阵的稀疏性对其进行压缩存储。由于电磁场有限元计算的自由度大都在三个以上,因而提出了适合多自由度的块按行压缩稀疏存储方案,并通过存储格式的转换,把块按行压缩方式转换成流行的,大型稀疏矩阵的行压缩存储格式,以便于求解。用求解大型稀疏方程组的Krylov子空间方法中的稳定双共轭梯度（Bicgstab）方法,收敛速度快,精度高,而且稳定性好,结合ilu预处理技术,可以大大提高求解大型稀疏方程组的效率。     

稀疏矩阵快速回代的Cholesky分解法

采用一维压缩存储正演计算中的对称稀疏矩阵,进行Cholesky分解,利用分解后二个矩阵的对称性和稀疏性,对占用时间较多的回代过程采用先消去列的方法,实现快速回代.算例表明,采用该方法,对于点源场的求解与传统顺代回代求解法对比可以提高五倍的速度,对于大地电磁的正演问题,提高了二倍的速度.     

矩阵相乘的压缩存储算法

介绍了对稀疏矩阵进行压缩存储时,稀疏矩阵相乘运算的基本思想和算法.在此基础上,探讨了避免矩阵中零元素相乘的无效操作,奠定了该算法的矩阵变换基础.     

迭代法中压缩对角存储的应用框架

在许多有限元、有限差分的应用中,待解方程组的系数矩阵是大型稀疏带状阵,方程组的求解一般使用迭代法.与其它存储方式相比,压缩对角存储由于不存矩阵元素的行列索引,对内存的使用最为节省.使用压缩对角存储,沿对角线操作可以完成高效的矩阵—向量乘.由于在以往的文献中,没有提及按行、列操作的算法,压缩对角存储的应用范围受到一定的限制.用行、列、对角版的矩阵—向量乘代表普通意义的行、列、对角方向操作模式,通过等价矩阵推导和伪代码,给出了一个包括按行、列操作算法在内的应用框架.这里运用C语言实现不完全Cholesky分解共轭梯度法解方程,阐述了如何在实际编程中使用这个算法框架.经理论与实验分析表明,对角压缩存储应用于框架中是高效的,因为与使用常用的一维行索引存储格式所编程序相比,同样迭代次数的耗时减少了约25％.     

Extended Finite Element Method for the Analysis of Discontinuities in Rock Masses

The strength and deformability of rock mass primarily depend on the condition of joints and their spacing and partially on the engineering properties of rock matrix. Till today, numerical analysis of discontinuities e.g. joint, fault, shear plane and others is conducted placing an interface element in between two adjacent rock matrix elements. However, the applicability of interface elements is limited in rock mechanics problems having multiple discontinuities due to its inherent numerical difficulties often leading to non-convergent solution. Recent developments in extended finite element method (XFEM) having strong discontinuity imbedded within a regular element provide an opportunity to analyze discrete discontinuities in rock masses without any numerical difficulties. This concept is based on partition of unity principle and can be used for cohesive rock joints. This paper summarizes the mathematical frameworks for the implementation of strong discontinuities in 3 and 6 nodded triangular elements and also provides numerical examples of the application of XFEM in one and two dimensional problems with single and multiple discontinuities.     

An evaluation model of artificial neural network to predict stable width in gravel bed rivers

Regime width of alluvial channels is a vital problem in river morphology and channel design. Many equations are available in the literature to predict regime width of alluvial rivers. In general, there are many approaches to estimate regime width; however, none of them is widely accepted at present. This is due to the fact that most hypotheses have many constrains which may lead to simplify governing conditions and also lack of knowledge of some physical processes associated with channel formation and maintenance. Intelligent models are a new approach to describe complex problems one of which is artificial neural networks. In this research, initially, gravel bed rivers database was used in bankfull discharge condition to train various dimensional and non-dimensional neural-network schemes with three and four variables as input data, respectively. Then, the same database was applied to fit regression analysis to estimate regime width; this led to drive dimensional and non-dimensional equations. Finally, dimensional and non-dimensional neural-network models and regression equations were compared together based on 50% error bands with other dataset. Results show that neural network can adequately estimate the regime width in gravel bed rivers and multilayer perceptron network with one hidden layer and eight hidden neurons based on dimensional data set was selected as optimum network to predict regime width. A sensitivity analysis also shows that bankfull discharge has a greater influence on regime width of gravel bed channels than the other independent parameters in dimensional scheme of neural network.     

单轴拉伸岩样破坏过程及尺寸效应数值模拟

由于从实验及理论角度研究岩样单轴拉伸条件下的破坏全过程及尺寸效应难度都很大。因此采用拉格朗日元法来研究这些问题。在峰值强度之前后,岩石材料的本构模型分别取为线弹性及拉破坏线性应变软化模型。为了使拉伸塑性区不出现在试样的端部,在试样的两侧面中部预制了2个凹槽。数值模拟结果表明,全程拉应力-拉应变曲线分为峰前和峰后阶段。在接近峰值的峰前阶段,由于两凹槽附近具有明显的拉应力集中现象,拉伸塑性区最先出现在两凹槽附近。随着轴向拉应变的增加,发生拉伸破坏的单元的数目增加,新发生拉伸破坏的单元越来越接近试样的中心,直到两块拉伸塑性区在应变软化阶段贯通。两凹槽连线上各单元拉应力的分布呈现3个阶段,“澡盆型”（“U型”）阶段,“双峰型”（“M型”）阶段及“单峰型”（“Π型”）阶段。“澡盆型”阶段对应于全程拉应力-拉应变曲线的弹性阶段。“双峰型”阶段及“单峰型”阶段对应于全程拉应力-拉应变曲线的非弹性阶段（包括峰值强度之前的一小段,即应变硬化阶段及峰后的应变软化阶段）。增加试样高度及降低试样宽度,拉应力-拉应变曲线的软化段变得越来越陡峭,因而试样越容易发生失稳破坏。由于试样宽度较大时,试样内部的单元并非处于单向拉应力状态,因此,增加试样宽度,全程拉应力-拉应变曲线的峰值强度增加。当试样宽度较小时,从出现塑性区,到塑性区贯通所需要的时间步较小,或应变范围较窄。这说明试样的脆性较强,前兆不明显。前兆不明显的脆性破坏对应常见的是洞室岩爆、冲击地压及地震等灾害。     

Arching in Inclined and Vertical Mine Stopes

Hydraulic fills are one of the most common backfills used by mining industries to backfill the stopes (voids) created after extracting the ore. It is important to estimate the stresses within to the stope to design the drainage and barricades. Most of the existing analytical models for the estimation of stresses within the stopes consider flat rectangular elements to include the effects of arching, although a continuous compression catenary arch of principal stresses using intersections of shear lines is the reality in field situations. In this paper, a circular compression arch of principal stresses has therefore been used to derive a general expression for stress within the inclined stopes. The results have been compared with the existing analytical and numerical models for vertical stopes as well as inclined stopes. A methodology has been presented to determine the vertical stress variation along the width of stope at different depths. The variation of stresses along the width of stope is also presented graphically.     

Leveling geochemical data between map sheets

Geochemical surveys are frequently assembled into larger, regional compilations. In some cases a boundary shift in the values for one or more elements may be observed at the join of adjacent surveys. This indicates that data for the affected elements are not consistent between the surveys. Where the same sampling medium has been used, the shift may be due to different crews/organizations, who varied in their sampling techniques. However, most commonly the shift is due to imperfect calibration of the analytical method used for samples from the different surveys. For example, there may have been a lack of proper analytical standardization between survey programs. To carry out leveling, bands are established on either side of the boundary between two surveys that show a shift. It is desirable that the bands have a close match in terms of geology and physiography. A quantitative method is presented to estimate the optimum width for these bands. Quantiles of the data within each band are calculated. The quantile pairs are plotted in X–Y space and a line fitted to express the relationship between the pairs of quantiles. The equation of this line is used to correct the shift between the two surveys. This method is tested on data for Mo in stream sediments, and pH of stream water, from two National Geochemical Reconnaissance Surveys in British Columbia.     

Evolution of mineral assemblage zoning in diffusion metasomatism

Metamorphic reaction bands consist of mineral assemblage layers, that separate incompatible mineral assemblages, and grow by reaction at their contacts and by precipitation within the layer. The stoichiometry of these reactions is determined by the relative diffusion fluxes within adjacent layers. Using the local equilibrium-steady diffusion model of Fisher (1973), the stoichiometric coefficients of layer growth reactions can be computed from the mass balance at each layer contact and independent ratios of instantaneous fluxes within each layer.Model calculations in a ternary system show that (1) variation in bulk composition across a reaction band, expressed in terms of layer sequence, mineral formulae of phases that comprise monomineralic layers and modal proportions of phases in multimineralic layers is largely determined by the relative fluxes of components that diffuse in the same direction; (2) the fraction of the width of a reaction band produced by replacement of each of the initial reactant assemblages is largely determined by the relative fluxes of components that diffuse in opposite directions; (3) the fraction of the width of a layer produced by internal precipitation is determined by temperature and the relative fluxes of components that diffuse in opposite directions; (4) in a multilayer reaction band, only one layer can grow by reaction at both contacts, and that layer contains the initial contact between initial reactants; and (5) a reaction band cannot grow by constant volume replacement of both reactant assemblages, if the system is closed to diffusion beyond layer contacts with the initial reactant rock masses.     

Constitutive and numerical framework for modeling joints and faults in rock

A three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Study of Drainage Through Hydraulic Fill Stopes using Method of Fragments

A good understanding of the pore water pressure developments within the hydraulic fill stope and the discharge through the drain is essential for improving the designs of barricades and the safety in the mines. A finite difference software FLAC was used to study the drainage and pore water pressure developments within a two dimensional rectangular stope with a single drain at the bottom. Using the method of fragment, a simple solution was proposed for determining the discharge and the maximum pore water pressure within the stope, when the height of water is greater than the width of the stope. The predictions are within 1% of those obtained from FLAC.     

数字滑坡技术及其应用

“数字滑坡”技术,就是以遥感（RS）和空间定位方法为主,结合其他勘探、试验、调查手段获取数字形式的、与地理坐标配准的滑坡基本信息;并利用GIS技术存贮和管理这些数字信息;在此基础上,根据滑坡地学原理进行空间分析,研制各类模型,并服务于滑坡调查、监测、研究、滑坡灾害评价、危险预测、灾情评估、滑坡防治等。通过金龙山三维数字模型,卫星监测易贡滑坡、三峡库区重点城镇滑坡及千将坪滑坡等地的遥感调查说明数字滑坡技术的实际应用。     

A superposition scheme to obtain fundamental boundary element solutions in multi‐layered elastic media

A superposition scheme is proposed to obtain a fundamental solution for boundary elements in multi‐layered elastic media. A three‐layered elastic region is obtained by superposing two sets of bonded half‐planes and subtracting one infinite plane. Therefore, the solution for an element in a layered media can be expressed in terms of bonded half‐plane solutions and an infinite‐plane solution. The major advantages of this superposition scheme are: (1) it is unnecessary to introduce elements at the interface, (2) it can be extended to higher‐order element, and (3) it may be applicable to three dimensions easily. The accuracy and performance of the developed model is illustrated by two examples. For the problem of a pressurized two‐dimensional crack within a three‐layered system, the comparison with other numerical results shows the model is quite accurate and efficient. The model is also used for a study of a practical two‐dimensional mining problem in South Africa, i.e. stoping through a dyke with material properties different from the host rock. Copyright © 2000 John Wiley & Sons, Ltd.