裂隙岩体一般块体理论初步

本文在前人工作的基础上提出了一种通用方法解决任意大小裂隙、任意形状工程岩体的岩石块体识别及稳定性计算问题。在这一方法中裂隙既可以是实测裂隙也可以是通过随机模拟方法生成的随机裂隙,工程岩体可以是任意由多面体组合成的形状,如复杂边坡或地下洞室,而且岩体和裂隙面可以是非均质的。这一通用过程被称为一般块体理论。它克服了关键块体理论(或楔形体法)中存在的弱点:即把裂隙假设为无限大的不连续面,因此无法预测岩石块体的数量和位置,而且一般只能识别出简单形状的凸形体。它在块体识别的同时将复杂的块体分解为几个简单的凸形块体,从而使复杂块体的几何描述、体积及重力计算、力学分析、可视化表示等一系列问题大大简化。在对一公路边坡的裂隙进行了详细观测之后,利用本文的方法进行了块体识别和稳定性分析,对本文的研究进行初步的验证。     

一般块体方法理论解验证

裂隙岩体一般块体方法能够解决任意大小裂隙、任意形状工程岩体的岩石块体识别及稳定性计算问题。它在块体识别的过程中,将复杂的块体分解为若干个简单的凸形块体,从而使复杂块体的一系列问题大大简化。边坡和地下硐室是野外最常见的岩体建筑物,本文分别选择了一个边坡和一个地下硐室,从块体识别、块体规模、下滑力、摩擦力、粘滞力、稳定性系数等角度对该方法进行了验证。通过解析的方法求得上述两种模型中各个物理量的解,然后把求得的这些解析解与一般块体算法和程序的求解结果进行了比较。结果表明,一般块体方法的算法与程序是正确的。     

A new stereo‐analytical method for determination of removal blocks in discontinuous rock masses

The paper provides a new stereo‐analytical method, which is a combination of the stereographic method and analytical methods, to separate finite removable blocks from the infinite and tapered blocks in discontinuous rock masses. The methodology has applicability to both convex and concave blocks. Application of the methodology is illustrated through examples. Addition of this method to the existing block theory procedures available in the literature improves the capability of block theory in solving practical problems in rock engineering. Copyright © 2003 John Wiley & Sons, Ltd.     

Developing an algorithm for reconstruction blocky systems in discontinuous media: three‐dimensional analysis

Block detection is one of the important steps in all discontinuous methods of analysis such as discontinuous deformation analysis and discrete element method. It is in fact a pre‐processing step for these methods. This paper describes a new approach to the problem of geometrically defining polyhedral rock blocks created by the intersection of planar discontinuities in a rock mass. An approach is developed based on the concept of using matrices with integer elements that mostly represent vertices, edges, or face numbers and their connections. Using square matrices with integer elements and performing edge/face regularization reduce the size of the matrices because of elimination of unnecessary faces, edges, and vertices; speed and accuracy of block tracing operation will be increased. This algorithm is able to trace and identify all kinds of blocks including convex and concave blocks formed by limited or unlimited fractures. The simplicity of the procedure makes it very attractive. The algorithm was programmed in C#.Net by over 8100 code lines; several examples are presented to show application of the algorithm in different situations. Copyright © 2011 John Wiley & Sons, Ltd.     

Developing an algorithm for reconstruction of blocky systems in discontinuous media: two-dimensional analysis

Block detection is one of the most important steps in all discontinuous methods of analysis like Discontinuous Deformation Analysis (DDA) and Discrete Element Method (DEM). This is in fact a pre-processing step for those methods. In this study, a comprehensive computational algorithm, for tracing rock block created by discontinuities, has been developed. Using square matrices with integer elements and performing edge regularization step, reduce the size of the matrices due to elimination of unnecessary edges and vertices. Therefore speed and accuracy of block tracing operation will be increased. This algorithm is able to trace and identify all kind of blocks including convex and concave blocks formed by limited or unlimited fractures. The algorithm was programmed in C#.Net by over 3400 code lines and some cases were modeled by the code as example.     

考虑岩桥破坏的块体稳定性分析方法

经典块体理论在进行块体可移动性分析和稳定性计算时是分步独立进行的,默认不可移动块体是稳定的,对不可移动块体不再进行稳定性分析。实际工程中,某些阻碍岩石块体运动的“岩桥”可能发生破坏,使得不可移动块体发生滑动。当块体的规模比较大时,在重力作用下破坏局部岩桥的可能性会增高。文中提出一种考虑岩桥破坏的块体稳定性分析方法,不再默认不可移动块体绝对稳定,计算块体稳定系数时,将阻碍块体移动的岩桥的抗剪切力纳入到块体的抗滑力中。该方法首先找出块体所有可能的滑动面和裂隙交线,识别块体沿每一个方向运动时需要破坏的岩桥,基于摩尔-库仑强度准则计算出块体沿每个方向运动时的稳定系数,然后,选取最小的稳定系数作为块体的实际稳定系数,最小稳定系数对应的方向即为块体最有可能的运动方向。     

基于有限结构面的三维复杂块体切割研究

岩体的块体结构和结构面网络模型生成,是进行各种力学分析和场分析的基础。详细研究了有限结构面进行复杂块体切割的过程,提出了相应的算法,并采用C++语言编写了相应的程序。为描述块体切割后的复连通特性,在块体数据结构中添加了有向壳的概念。结构面可以为简单的凸多边形,也可采用形态更加复杂的凹多边形。通过面-面求交线、交线环路搜索形成有向环、有向环包含关系分析形成有向面、有向面拓扑搜索形成有向壳和有向壳包含关系分析形成块体等过程,将有限结构面分别与各块体进行切割运算,形成进行块体切割的一般方法。在切割过程中将得到的有向环,有向面、有向壳和块体分别进行拓扑有效性校核,满足要求后得到最终的块体和结构面网络模型。选取4个算例来验证该方法的可行性。计算结果表明,该方法可以对复杂块体进行有效地切割,结构面可以选择包括凹形面在内的复杂多边形,方法具有普遍意义。     

基于自由面上环路对应节理无限切割的关键块体搜索

关键块体理论在评价工程裂隙岩体稳定性中得到了广泛应用。然而,一方面岩体中节理数量众多,关键块体的搜索将耗费较多机时;另一方面,极少数偶然出现的块体识别也会极大地增加计算量。因此,开发有针对性和灵活的关键块体搜索方法就非常重要。首先将研究区域分解成凸子区域,找出自由面上的闭合环路,然后利用环路的组成节理以及与其相交节理进行空间无限切割来识别该环路是否对应关键块体。该方法针对性强,能较好地适应人为规定的判别条件,如搜索楔形体以及后缘切割限定等,并能顺利实现凹面体的关键块体搜索,且编程实现简单。以某挂帮矿的顶柱为实例进行关键块体的搜索,验证了上述方法的可行性。     

Analytical formulas for the geometric and inertia quantities of the largest removable blocks around tunnels

This paper presents algorithms for determining the vertices of the maximum removable block (MB) created by a joint pyramid (JP) around a tunnel when discontinuities are fully persistent. It is shown that an MB cannot be formed by more than 4 discontinuities and this drastically limits the proliferation of rock blocks that need to be analysed. The non‐convex block obtained after the MB is tunnelled through (real maximum block, RMB) is partitioned into a set of tetrahedra, and procedures are given for determining the vertices of these tetrahedra. Geometric and inertia quantities needed for stability analysis and support/reinforcement design are determined as functions of the calculated vertices' co‐ordinates. These quantities are: RMB's volume, face areas, perimeter of the excavated surface, centroid and inertia tensor. The algorithms for their calculation are at least two times faster than other algorithms previously proposed in other applications. It is shown that the formulations presented by Goodman and Shi for translational analysis and by Tonon for rotatability analysis can be used to analyse the RMBs using the geometric quantities presented. A numerical example is presented among those used to verify these analytical procedures and their implementation. Copyright © 2006 John Wiley & Sons, Ltd.     

3D key‐group method for slope stability analysis

Because of the simplicity and the speed of execution, methods used in static stability analyses have yet remained relevant. The key‐block method, which is the most famous of them, is used for the stability analysis of fractured rock masses. The KBM method is just based on finding key blocks, and if no such blocks are found to be unstable, it is concluded that the whole of the rock mass is stable. Literally, though groups of ‘stable’ blocks are taken together into account, in some cases, it may prove to be unstable. An iterative and progressive stability analysis of the discontinuous rock slopes can be performed using the key‐group method, in which groups of collapsible blocks are combined. This method is literally a two‐dimensional (2D) limit equilibrium approach. Because of the normally conservational results of 2D analysis, a three‐dimensional (3D) analysis seems to be necessary. In this paper, the 2D key‐group method is developed into three dimensions so that a more literal analysis of a fractured rock mass can be performed. Using Mathematica software, a computer program was prepared to implement the proposed methodology on a real case. Then, in order to assess the proposed 3D procedure, its implementation results are compared with the outcomes of the 2D key‐group method. Finally, tectonic block No.2 of Choghart open pit mine was investigated as a case study using the proposed 3D methodology. Results of the comparison revealed that the outcomes of the 3D analysis of this block conform to the reality and the results of 2D analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Propriétés fractales de la fragmentation et processus stochastiques de fracturation : approche géométrique 3D à l'aide du modèle ObsifracFractal properties of fragmentation and stochastic fracturing processes: geometrical 3D approach by OBSIFRAC model

A numerical rock fragmentation model was elaborated, producing a 3D puzzle of convex polyhedra, geometrically described in a database. In the first scenario, a constant proportion of blocks are fragmented at each step of the process and leads to fractal distribution. In the second scenario, division affects one random block at each stage of the process, and produces a Weibull volume distribution law. Imposing a minimal distance between the fractures, the third scenario reveals a power law. The inhibition of new fractures in the neighbourhood of existing discontinuities could be responsible for fractal properties in rock mass fragmentation. To cite this article: L. Empereur-Mot, T. Villemin, C. R. Geoscience 334 (2002) 127–133.     

某电站地下厂房裂隙发育规律及其对围岩稳定性的影响

裂隙岩体内的洞室围岩块体稳定问题是抽水蓄能电站地下厂房建设中要解决的重要工程地质问题。为了在厂房开挖之前较准确地预测不稳定块体的发育位置,本文以某抽水蓄能电站为例,对厂房探洞内的裂隙进行统计分析,结合厂房区构造断层的发育情况,确定了裂隙发育规律;根据裂隙发育规律将厂房区岩体划分为A、B、C、D、E 5个构造分区;并利用Unwedge程序,以各分区裂隙组合为基础,确定可能形成的块体位置,评价了其稳定性状况。研究结果表明,裂隙受多期构造控制,在一定范围内具有方向性,A、E区优势裂隙与构造产状接近,B、C、D区优势裂隙与构造产状斜交;裂隙在厂房上、下游侧边墙各形成6处潜在不稳定块体,顶拱处形成10处潜在不稳定块体,右端墙处形成1处潜在不稳定块体。     

节理粗糙度对岩块体积的影响规律研究

岩体结构直接控制着岩体力学、水力学特性,岩块体积分布规律可直接反映岩体结构特征。目前研究多将节理面简化为平面,忽略了粗糙度对岩块体积的影响。利用Hurst指数H和高度均方根R_q表征节理粗糙度,研究了节理粗糙度对岩块数量和体积分布规律的影响。结果表明：(1)H、R_q控制节理的粗糙起伏形态,粗糙度随着R_q的增大而增大、随着H的增大而减小;(2)块体的数量总体上与节理粗糙度正相关,即随着粗糙度的增大而增加;(3)R_q和H对岩块体积分布的影响,主要通过改变小体积块体所占比例实现,块体的平均体积和中位体积随着粗糙度的增大而减小;(4)当节理正交且间距相近时,块体数量随粗糙度的变化可以分为3个阶段,即稳定阶段、初始增长阶段和快速增长阶段,R_q和H共同控制着各区间的相对分布范围。最后,基于摄影测量采集的数据建立了岩体节理模型,对大连某公路边坡的岩块体积分布进行了研究,验证了上述结论的准确性。     

An analysis of the action of dowels on the stabilization of rock blocks on underground excavation walls

Summary  Underground excavation in fractured rock masses can lead to instability of rock blocks on its perimeter. Among the stabilization measures that are often used, dowels or passive bolts play an important role. These passive reinforcement measures cannot, however, be easily considered in simplified calculation techniques based on the Limit Equilibrium Method (LEM). The analysis of such elements cannot be separated from rock-dowel interaction following the displacement of the block. A new simplified calculation procedure is presented in this paper for the analysis of the interaction between rock and dowels on walls of an underground excavation where potentially sliding rock blocks are present. The assumed interaction scheme is, however, partial in that dowel reinforcement is only activated by a small displacement, while this displacement does not induce a destressing of the rock block. Such a procedure allows a fast dimensioning of the dowels, considering the maximum stabilizing force that they are able to apply to the block without reaching a critical condition with reference to dowel failure or to its connection to the rock. Correspondence: Dr. Pierpaolo Oreste, Politecnico di Torino, DITAG, C. so Duca degli Abruzzi 24, 10129 Torino, Italy     

Failure mechanism in an extremely slow rock slide at Bitchu-Matsuyama castle site (Japan)

One of the specific problems related to historical structures is the fact that they are prone to damage caused by even very small deformations acting over a long period of time, such as creep or extremely small rock displacements. If any damage has already occurred, the determination of the rock slope failure mechanism is one of the prerequisites for successful mitigation technique selection. In this study a medieval castle in central Japan, suffering damage caused by deformation of the rock mass in the subgrade of the castle, was investigated using a combination of field investigation, high-precision monitoring and physical modeling experiments. Using these techniques an attempt to determine the failure mechanism of the rock slope was made. Based on the field investigation a toe-slope failure seemed to be the main triggering factor activating the deformations in the upper slope area, right below the defense walls of the castle. The displacement monitoring of the surface rock blocks revealed a slumping failure with the backward rotational component prevailing over the sliding in the immediate vicinity of the castle wall. This was in accordance with the expectations obtained from the structural analysis of the rock mass carried out during the field investigation. The displacements obtained during the rock block monitoring, especially from the crack gauges, were not sufficient for drawing a satisfactory conclusions about the failure mechanism of the blocks located in the central part of the slope. Therefore, the failure mechanisms of rock blocks inferred from their displacements obtained from the monitoring were correlated with the results of modeling experiments carried out on the scaled slope model. The physical modeling revealed a possibility of toppling failure of rock blocks in the central area of the slope caused mainly by block interlocking, which was supported by the data from surface tilt meters installed additionally in the field. Furthermore, the possibility of the occurrence of forward and backward rock block rotations in the same sliding body at given conditions was supported by the physical modeling experiments.     

三维随机裂隙岩体渗流分析的块体单元法

岩体中的裂隙分布具有随机性,且渗流主要通过裂隙面进行。运用蒙特卡罗法模拟生成岩体中的随机裂隙面,基于矢体的概念,实现了包括凹块体和多连通体在内的三维随机裂隙岩体的块体单元自动识别。假定岩块不透水、渗流仅通过裂隙面进行,建立了三维随机裂隙岩体渗流分析的块体单元法。通过算例分析,验证了所提方法的准确性和有效性。     

A mixed solution for two-dimensional unsteady flow in fractured porous media

A mixed finite element–boundary element solution for the analysis of two-dimensional flow in porous media composed of rock blocks and discrete fractures is described. The rock blocks are modelled implicitly by using boundary elements whereas finite elements are adopted to model the discrete fractures. The computational procedure has been implemented in a hybrid code which has been validated first by comparing the numerical results with the closed-form solution for flow in a porous aquifer intercepted by a vertical fracture only. Then, a more complex problem has been solved where a pervious, homogeneous and isotropic matrix containing a net of fractures is considered. The results obtained are shown to describe satisfactorily the main features of the flow problem under study. © 1997 by John Wiley & Sons, Ltd.     

Constructing boundary structures of rock blocks

Determining rock-block structures is important for modeling jointed rock masses. This paper presents a method to construct the boundary structures of complex blocks by eliminating fictitious surfaces. The planes involved in forming a complex block are retrieved, and the boundary polygons on each plane are determined using a series of Boolean operations. A regulation method is used to adjust the resulting polygons so that the regulated outer boundary structures can be used directly in the contact-detection algorithms. The interior fracture boundaries that are not explicitly associated with the formation of blocks are also constructed. These boundary surfaces are valued in hydraulic models to provide conductive channels of fluids in rock masses. The proposed method extends previous developments on block-identification algorithms, and the constructed boundary structures can be used directly in the modeling process of most discrete models. The program implemented based on this method has been used to study the stability and morphology of blocks in the Three Gorges Project, and several examples are given to further demonstrate the ability and performance of the proposed method.     

亚洲大陆主要活动块体的现今构造应力数值模拟

亚洲大陆晚新生代和现代构造变形以活动地块为主要特征,表现为在统一构造格局下不同地块间具有不同的运动方式和速度。为了研究这些具有不同运动学性质块体间的相互作用以及构造变形特征,基于亚洲大陆的总体构造格局构建了二维有限元模型。根据模拟结果,对比已知GPS数据、震源机制解以及地质调查数据等,定量分析了大陆内部主要活动地块构造应力场的分布特征,并探讨了影响亚洲大陆现今构造变形特征的主要因素。结果表明：在我国的西部陆块内,由于周边一系列近EW向弧形活动构造带的存在,导致其内部次级块体运动速率的衰减,从而进一步导致应力环境的变化,由青藏中部的挤压-拉张环境逐渐转变为塔里木、天山地区的完全挤压环境;在西伯利亚地块和印度板块的联合挤压作用下,华北地块上地壳的应力表现为较弱的挤压环境,而在该种应力环境下块体内部伸展构造的成因很可能与其深部的动力学环境有关;华南地块的运动方向与台湾造山带相反,从而形成一个秦岭-大别造山带以南的较强烈的挤压-拉张区;在印度-澳大利亚板块和菲律宾俯冲板块的联合挤压作用下,巽他地块作为华南地块和印支地块的逃逸窗口,表现出以婆罗洲、南海为中心近圆弧形的弱挤压区以及环绕挤压区外缘挤压-拉张区的应力分布特征。     

随机裂隙岩体渗流-应力耦合分析的块体单元法

视岩石裂隙为一种“充填介质”,进而将有填充物和无填充物的裂隙统一处理,推导了裂隙面的刚度系数、导水系数和法向应力之间的关系式。在此基础上,根据块体单元法的应力、渗流分析的基本原理,即认为岩块为刚体、变形集中发生于裂隙面,假定岩块不透水、渗流仅通过裂隙面进行,并考虑了法向应力和裂隙面刚度、导水系数的关系式,运用两场交叉迭代法,提出了三维随机裂隙岩体渗流与应力耦合分析的块体单元模型。编写了相应的Fortran程序,该程序将块体元的应力、渗流两个分析模块整合在一起,计算效率较高。该模型的最大优势是能考虑大规模复杂的节理、裂隙,且前、后处理简单。通过沙沱重力坝的分析,验证了方法的准确性和有效性