A rigorous solution for the stability of polyhedral rock blocks

Block theory has been widely applied to stability analysis of rock engineering due to its clear concept and elegant geometrical theory. For a general block with multiple discontinuity planes, it is assumed that contact is only maintained on a single plane (single-plane sliding) or two intersecting planes (double-plane sliding) in block theory analysis. Since the normal forces and shear resistances acting on the other discontinuity planes are omitted, it can cause unreasonable estimations of block failure modes and incorrect calculation of factors of safety. In this study, a new method is presented that permits to consider the contribution of the normal forces and shear resistances acting on each discontinuity plane to the block stability. The proposed method meets all of the force-equilibrium and moment-equilibrium conditions and provides a rigorous solution for stability of general blocks with any number of faces and any shape. Some typical polyhedral blocks in rock slopes are analyzed using block theory and the proposed method. The results indicate that the traditional block theory may give a misleading conclusion for the predictions of stability and sliding direction of rock blocks when contact occurs on more than two discontinuity planes.     

岩体结构稳定分析原理和方法

工程实践表明,在边坡、地基或地下工程岩体中几组地质结构面和临空面的组合往往构成可能失稳的岩石结构体、存在向临空面运动的可能性、影响到工程岩体的稳定性。这时必须针对这种可能失稳的结构体进行分析,采取必要的加固或处理。关于岩石结构体的稳定分析,文献中已有一些报导,但偏重于图解和计算方法、一般是针对特定单一块体的解析,仅应用于边坡工程。     

岩体化学风化的非连续性及其科学意义

岩体化学风化在空间上具有高度的非连续性,这种非连续性广泛存在于从宏观、细观到微观的所有尺度。宏观结构面是化学风化最主要的发生场所;风化岩体内,新鲜岩块被沿结构面内法线方向发育的腐蚀带包围,呈斑点状分散于腐岩中。微缝等细观损伤普遍存在于各类岩石中;化学风化从岩块内不同空间位置的水力有效空隙向三维空间扩展,决定了细观尺度上化学风化的非连续性。矿物溶解是在晶体中具有过剩表面能的缺陷位置优先发生的,因而具有显著的微观非连续性。由于非连续特性,化学风化可增大水岩界面,提升矿物溶解反应的规模及速率。通过对既有损伤的扩展及在损伤空间堆积残余物,化学风化具有分离—裂化岩体、岩块及造岩矿物的重要作用,这种作用可使以新鲜岩石为主的岩体大规模脱离母岩,而堆积于坡脚的岩石块体在化学风化的继续作用下,可裂解为更小的岩屑或矿物碎屑,为向水体搬运创造条件,从而极大地促进斜坡夷平及地貌重塑进程。     

Influence of Stochastic Discontinuity Network Parameters on the Formation of Removable Blocks in Rock Slopes

Summary  We study the effects of discontinuity network parameters on the formation of removable wedges in rock slopes. Discontinuities are simulated using the Poisson disk model, and removable wedges are identified using block theory. The formation of removable wedges of different sizes is assumed to follow a Poisson process. Poisson regression and Monte Carlo simulation are then used to identify statistically relevant parameters of the model, and to study the effects that variations in their values have on formation of removable blocks. The sensitivity of the results as a function of the mean orientations of the discontinuity sets forming the blocks is also studied by means of a parametric study. The volumetric intensity of discontinuities in the rock mass is found to have a significant impact on the computed estimates of removable block formation. As predicted by theory, our results indicate that, everything else being equal, the expected rate of formation of removable wedges is proportional to the square of the intensity measure. Estimates are also sensitive to changes in discontinuity size, especially in cases in which discontinuities are smaller than one to two times the height of the slope. The interaction between the mean size of discontinuities and the coefficient of variation of discontinuity sizes is found to be significant as well. Finally, results of our sensitivity analysis suggest that the orientation of discontinuity sets significantly affects the rate of formation of removable blocks in rock slopes. Author’s address: Dr. Rafael Jimenez-Rodriguez, ETS Ing. de Caminos, Canales y Puertos. Universidad Politecnica de Madrid, Spain     

Evaluating rock mass geometry from photographic images

Summary The importance of discontinuities in controlling rock mass behaviour in any engineering project involving excavations calls for a sound and spatial characterization of the discontinuity structure present. Such a characterization necessitates field work that requires sufficient rock exposures in order to obtain an adequate number of data, time and considerable cost. Photoanalysis techniques can help in overcoming the above difficulties equally well or better than other techniques. This paper refers to simple photographic techniques and their implementation for computer aided analyses for the characterization of the rock mass fracturing features. In particular attention is focused on scale problems and on reconstruction of fracture density stereoplots on the basis of data collected from one or two images according to different lithologies and outcropping conditions. The methodology for evaluating the volumetric fracture intensity follows in a slightly modified way a technique previously suggested in the literature. Certain reported examples allow to validate the photoanalytical technique used and the proposed method of analysis. Furthermore, analyses on planar density, spacing, frequency, terminations in solid rock or against other discontinuities and spatial correlation have been implemented in a software to yield a more complete rock mass characterization. At the same time input data and analysis results are produced in data files available as input for numerical analyses.     

Determining the size and shape of blocks from linear sampling for geotechnical rock mass classification and assessment

Classifying and assessing geotechnical aspects of rock masses involves combining parameters in various ways, guided by empirical considerations, to derive quantitative geotechnical parameters. Geological structures and the deformation history of rocks underpin the nature of rock masses. The kinematics of a deforming rock mass may occur as sliding along throughgoing discontinuities or as distributed sliding on block faces. Distributed sliding will tend to disrupt the continuity of planar structures such that data on the size and shape of blocks is needed, rather than relying on discontinuity orientation data alone. Orientation and spacing data can be combined to provide a geometric analysis of block systems from linear samples, such as drill core. Dihedral angles and spacing of sequential pairs of discontinuities provides a sample of the size and shape of blocks that can be interpreted stereologically. Further detail can be derived by combining neighbouring intersections that enclose or partially enclose individual blocks. The shape and size of a block can be represented on a stereograph with the enclosing faces shown as poles and their perpendicular distance from an arbitrary point inside the block shown as a number. Identifying the size and shape of specific blocks rather than relying on statistical methods is beneficial to critical aspects of design such as analysing keyblocks that would be exposed during excavations. The detailed characterization of block size and shape is also a step toward interpreting the kinematics of rock mass deformation and the analysis of rock masses as ultra-close packed dilatant granular systems.     

用三维激光成像技术调查高陡边坡岩体结构

论文针对“罗盘 皮尺”传统模式调查高陡边坡岩体结构中的缺点,提出了三维激光成像技术调查高陡边坡岩体结构的新方法。利用三维激光成像技术可获得完全实景的数字模型,并在该数字模型上可直接量取点、线、面和三维实体空间坐标,从而进行结构面产状、迹长与连通率、间距等岩体结构特征参数计算和地质剖面切图。最后,以营盘山陡崖边坡为例,详细阐述了三维激光成像技术调查高陡边坡岩体结构特征参数方法及过程。结果表明,利用三维激光成像技术所得的结构面产状、间距等岩体结构特征参数要优于传统的“罗盘 皮尺”量测结果。因此,三维激光成像技术的引入,必将引发岩体结构特征参数测试技术革新性的发展。     

Three-dimensional slope stability analysis of South Peak, Crowsnest Pass, Alberta, Canada

South Peak is a 7-Mm³ potentially unstable rock mass located adjacent to the 1903 Frank Slide on Turtle Mountain, Alberta. This paper presents three-dimensional numerical rock slope stability models and compares them with a previous conceptual slope instability model based on discontinuity surfaces identified using an airborne LiDAR digital elevation model (DEM). Rock mass conditions at South Peak are described using the Geological Strength Index and point load tests, whilst the mean discontinuity set orientations and characteristics are based on approximately 500 field measurements. A kinematic analysis was first conducted to evaluate probable simple discontinuity-controlled failure modes. The potential for wedge failure was further assessed by considering the orientation of wedge intersections over the airborne LiDAR DEM and through a limit equilibrium combination analysis. Block theory was used to evaluate the finiteness and removability of blocks in the rock mass. Finally, the complex interaction between discontinuity sets and the topography within South Peak was investigated through three-dimensional distinct element models using the code 3DEC. The influence of individual discontinuity sets, scale effects, friction angle and the persistence along the discontinuity surfaces on the slope stability conditions were all investigated using this code.     

Analysis of tetrahedral and pentahedral key blocks in underground excavations

This paper presents a study the non-pyramidal key blocks of the rock mass. After a review of the Key Blocks Method (KBM), the study focuses on the analysis of key blocks formed by three and four discontinuity planes in underground excavations. The concept of non-pyramidal key blocks is described and their generation from a geometric operation called dislocation, thus determining the pentahedral key blocks that may be formed. To do so, the software program ASTUR (Analysis of the Support of Tunnels in Rock) was used, which develops a ubiquitous approach and allows the analysis of both pyramidal and non-pyramidal tetrahedral and pentahedral blocks.     

基于结构面网络模拟的桥基岩体空间状态分析

分析结构面在岩体中的分布和组合特征是研究岩体稳定性的前提。根据结构面网络随机模拟方法,通过对岩体表面结构面的测量,可以建立岩体结构面空间分布的概率统计模型,从而确立了岩体结构面的网络结构模型。在此基础上分析了局部临空块体的空间几何形态,指出了块体的可能破坏形式,从宏观角度对块体系统整体稳定性进行了预测。     

Probabilistic key block analysis of a mine ventilation shaft stability – a case study

In this study, the probabilistic key block analysis was applied to evaluate the stability of a mine ventilation shaft developed in a rock mass of granite. The key blocks were identified based on the block theory. The variations of discontinuity orientations were fitted with the Beta distribution and taken into consideration. The key block forming probabilities were analyzed. For simplification of calculations the first-order second-moment (FOSM) approximation was employed for probability estimation. With the considerations of the rock properties as random variables and applications of several statistical analysis tools, the key block failure probabilities, the probabilistic distribution of safety factors, and the probabilistic distribution of potential maximum key block volumes were analyzed. The analysis indicated that although the safety factor calculated based on the mean values of the variables was above 1.0 for the stability of the most critical key block, the block had a considerable probability of failure with a significant rock volume due to variations in discontinuity orientations and rock properties. Without promptly applying supports to the rock excavation, the shaft had a significant likelihood of failure.     

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。     

阳泉矿区瓦斯抽放方式及优选原则

针对阳泉矿区瓦斯赋存特点,通过对比分析各类瓦斯抽放方式指标,从而得出经济、技术可行的最优抽放方式;阳泉矿区单一煤层采用U+L型通风方式的工作面,大口径钻孔抽放方式是最佳选择和发展方向;15#煤层综放工作面采用U型通风方式和走向顶板岩巷抽放方式比较优越。      

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.     

结构面网络模拟结果后处理研究

结构面网络模拟是获取岩体结构模型的主要手段。基于网络模拟结果建立岩体力学或水力学分析模型,然后开展精细数值模拟研究,是岩石力学领域具有良好前景的发展方向。但目前尚没有成熟的分析软件能够将网络模拟结果转化为能用于力学或水力学计算的单元网格,针对这一现状,开发了一整套结构面网络模拟结果后处理程序,利用该程序,可以方便地将网络模拟结果转化为能用于水力学计算的连通水力网络,以及能用于力学分析的包含节理单元的有限元网格。并对相关的程序算法和实现过程作了详尽的介绍,希望能够对从事该领域研究工作的同行有参考价值。     

基于单个钻孔孔壁电视图像确定地下岩体结构面产状的普适数学方法

岩体结构面产状是影响岩体力学性质及工程稳定性的重要地质因素.从钻孔孔壁电视平展图上可较精确地提取结构面迹线上不共线三点的相对二维坐标(d, h),再利用空间解析几何理论确定其三维空间相对坐标(x, y, z),并求得结构面法向矢量.根据钻孔孔壁与坡面及结构面产状的空间几何关系,在保持原点不变的情况下,采用空间坐标变换的方法,将三维坐标系z轴和y轴分别转化为竖直方向z′和正北地理方向y′,并确定转化后坐标系空间的结构面法向矢量.再从结构面产状的定义出发,根据结构面法向矢量与结构面倾向、倾角的相关性,建立了一个空间几何模型,通过该模型可求得任意平直坡面上任一钻孔内局部岩体结构面的产状.      

裂隙化岩体中圆形断面调压井围岩稳定性分析

块体理论是适用于裂隙化岩体变形失稳分析的有效方法。运用块体理论赤平投影法研究某水电站超大型调压井围岩随机块体的稳定性,将圆形断面调压井开挖临空面抽象简化为八个方位的边墙加以研究,分析了井周各部位可能的关键块体及其运动形式,计算了关键块体的净滑力。分析结果对工程施工具有可靠的现实指导作用,为锚固设计和永久衬砌设计提供了依据,可供类似工程参考。     

岩体结构面网络模拟技术研究进展

主要介绍了岩体结构面网络模拟技术的研究进展，通过近期的研究，结果面网络模拟技术得到了进一步的完善与发展，特别是三维模拟技术的出现使岩体结构面网络模拟技术更加实用，表现出比二维模拟更大的优势，可以较好地解决空间岩体力学问题，具有良好的应用前景。     

A computational algorithm for rock cutting optimisation from primary blocks

Quarry yield can be increased by choosing the appropriate cutting direction for the primary blocks. This increase will reduce the extraction costs and the resulting environmental impact. This paper presents a computational approach to automatically predict and optimise the cutting of ornamental commercial rock quarry from primary blocks. Our work complements previous ones, which are focused on the primary blocks prediction, since we start with primary blocks and optimise their cutting for ornamental purposes.The developed method uses data from the three main families found in an exploited deposit and numerical procedures to calculate the appropriate advance direction for the exploitation yield optimisation. Specifically, the family system is numerically modelled to determine the maximum block to be extracted and its surrounding parallelepiped (SP). Then a 3D mesh is created for use in the rock-cutting process and to determine the optimum advance direction.Modelling the rock-cutting process permits the results for any cutting parameter and advance direction to be obtained automatically. The obtained data have allowed us to observe large variations in the exploitation yield by modifying the cutting advance direction and how the developed method automatically predicts the optimum advance direction for maximising exploitation yield. Furthermore, the developed method has been implemented in a computer tool, which presents the results graphically.The automatic prediction of the cutting output is of significant practical utility because it enables exploitation yield to increase while reducing dump size. These improvements imply economic and environmental benefits because more commercial blocks will be extracted from a single exploitation, and the disposable volume will decrease.     

Comparative study of Sarma's method and the discontinuous deformation analysis for rock slope stability analysis

This paper presents a comparative study of two methods, Sarma's method and the discontinuous deformation analysis (DDA), for rock slope stability analysis. The comparison concerns the stability analysis of two classic rock slopes. The study shows that the DDA, which accounts for the block kinematics, provides a very different factor of safety as compared with Sarma's method. More realistic reaction forces around each rock block can be obtained by the DDA, including the thrust forces between rock blocks and the forces between the base and the blocks. The DDA's result shows two possible directions for the relative movement between two contiguous blocks at the initiation of slope failure. It also indicates that the limit equilibrium condition may not occur along the interfaces of rock blocks at the initiation of slope failure. The determination of realistic interaction forces around each block will be very important in rock slope stability analysis if nonlinear failure criteria are considered.