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.     

裂隙化硬岩洞室围岩失稳分析方法

根据岩体的力学介质分类和块体理论及赤平投影,结合工程实例,推导了滑动方向的计算公式,研究了裂隙化岩体地下采空区围岩的稳定性分析方法。利用该方法分析了华北某大型地下采空区围岩的稳定性,展示了该模型的实用性。     

差异风化型危岩力学模型及破坏机制研究

差异风化型危岩多形成于由砂岩和泥岩等软、硬岩性组成的互层陡倾岩质边坡中,其崩塌破坏属地质灾害中的常见形态。以普洱渡危岩高边坡为例,推导出差异风化型危岩岩腔后壁泥岩压应力随岩腔深度增加而增大的计算公式。据普洱渡危岩高边坡地形地貌和地质构造特征建立了两类4种差异风化型危岩力学模型：第1类为主控结构面贯通率等于1时的泥岩基座压裂破坏型和转动破坏型危岩;第2类为主控结构面贯通率小于1时的坠落型和倾倒型危岩。利用岩石强度理论推导出研究区砂岩的二次抛物线型摩尔强度包络方程,以极限平衡理论和摩尔强度理论推导了4种危岩体在自重、地震力和裂隙水压力共同作用下的崩塌破坏判别表达式,并由此反演出危岩体的临界崩塌边界方程,得出危岩体崩塌边界（岩腔深度、危岩体厚度和高度、主控裂隙深度）之间的关系,为现场预测和判别危岩体的稳定性和崩落时序提供简便可靠的依据。     

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。     

块系岩体非协调动力响应特征试验研究

岩体在块系构造状态下的动力传播存在块体和块体间软弱介质的非协调变形现象，对岩体结构的动力稳定产生重要影响。目前块系岩体的非协调动力传播响应研究尚不充分，导致不能进行有效的动力响应特征识别。通过试验对块系岩体非协调动力传播过程岩块动力响应特征进行研究，分别从动力传播速度、岩块加速度振幅衰减、岩块振动位移响应、岩块振动持续时间、块体动能显现、块体振动频域响应特性等方面对比纵波传播，给出块系岩体非协调动力传播的特征分析。通过分析可知，块系介质非协调变形运动产生的动力传播现象相比于纵波传播是一种低频低速波，并伴随着岩块的大位移运动，同时岩块振动持续时间较长，蕴含着动能与势能的相互转换过程，这些现象构成了块系岩体非协调动力传播的重要特征。该研究将为识别岩体非协调动力传播特征及块系岩体的冲击预警波动特征识别提供参考。     

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.     

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 generalized procedure to identify three‐dimensional rock blocks around complex excavations

This paper presents a generalized procedure for the identification of rock blocks formed by finite‐sized fractures around complex excavations. It was assumed that the study domain could be partitioned into a finite number of subdomains, where each either was, or could be, approximated by a convex polyhedron, and the fractures were finite in size and disc shaped and were defined using the location of the disc center, orientation, radius, cohesion coefficient, and friction angle. These may be either deterministic fractures obtained from a field survey or random fractures generated by stochastic modeling. In addition, the rock mass could be heterogeneous; i.e. the rock matrix and individual fractures could have different parameters in different parts. The procedure included: (1) partitioning of the model domain into convex subdomains; (2) removing noncontributive fractures. A fracture was deemed contributive when it played a part in block formation; i.e. it formed at least one surface with some of the blocks; (3) decomposing the subdomains into element blocks with fractures; (4) restoring the infinite fractures to finite discs; and (5) assembling the modeling domain. Our procedure facilitates robust computational programming, and is flexible in dealing with the problem of a complex study domain and with rock heterogeneity. A computer code was developed based on the algorithm developed in this study. The algorithm and computer program were verified using an analytical method, and were used to solve the problem of block prediction around the underground powerhouse of the Three Gorges Project. Copyright © 2008 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.     

冲击载荷下块系岩体摆型波传播特性的试验研究

摆型波现象是深部开采中块系岩体固有的动力学特征之一。为研究深部块系岩体摆型波传播规律,采用理论分析与室内试验相结合的方法,研究了在冲击载荷作用下摆型波的传播特性。该试验采用12块花岗岩和橡胶夹层材料建立了模型,采用TST5915动态数据采集系统进行信号监测,分别获得了在均质夹层和部分夹层介质增厚情况下的加速度响应曲线,并运用摆型波动力模型理论进行分析。结果表明,摆型波在块体间传播过程中,频率大小不受能量大小的影响,而能量大小决定了波的衰减时间。当块体间介质黏性增加时,加速度幅值均有所下降,但对加速度衰减周期没有影响,而影响加速度衰减的主要因素是冲击载荷的能量大小。此次试验研究将为今后进一步研究摆型波动力传播特性提供一定的基础。     

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。     

层状岩体开挖洞室围岩块体稳定分析及锚固方法

由于层状岩体的稳定性受层面控制,在该类岩体中进行开挖常常导致块体的失稳,给工程建设带来巨大的危害。本文从层面与结构面组合形成的块体系统稳定性分析入手,运用改进的块体理论,进行了块体稳定分析程序的开发,对定位、半定位块体的系统稳定性分析方法进行了探讨。以西龙池抽水蓄能电站地下厂房为例,对围岩中的块体进行了系统稳定分析。通过实际开挖验证,表明了分析结果的合理性,开发的程序可供同类工程参考使用。本文所提出的方法可为地下工程施工期的超前预报、围岩的系统锚固支护设计提供重要依据。     

Estimation of Block Sizes for Rock Masses with Non-persistent Joints

Summary  Discontinuities or joints in the rock mass have various shapes and sizes. Along with the joint orientation and spacing, the joint persistence, or the relative size of the joint, is one of the most important factors in determining the block sizes of jointed rock masses. Although the importance of joint persistence on the overall rock mass strength has long been identified, the impact of persistence on rock strength is in most current rock mass classification systems underrepresented. If joints are assumed to be persistent, as is the case in most designs, the sizes of the rock blocks tend to be underestimated. This can lead to more removable blocks than actually exist in-situ. In addition, a poor understanding of the rock bridge strength may lead to lower rock mass strengths, and consequently, to excessive expenditure on rock support. In this study, we suggest and verify a method for the determination of the block sizes considering joint persistence. The idea emerges from a quantitative approach to apply the GSI system for rock mass classification, in which the accurate block size is required. There is a need to statistically analyze how the distribution of rock bridges according to the combination of joint orientation, spacing, and persistence will affect the actual size of each individual block. For this purpose, we generate various combinations of joints with different geometric conditions by the orthogonal arrays using the distinct element analysis tools of UDEC and 3DEC. Equivalent block sizes (areas in 2D and volumes in 3D) and their distributions are obtained from the numerical simulation. Correlation analysis is then performed to relate the block sizes predicted by the empirical equation to those obtained from the numerical model simulation. The results support the concept of equivalent block size proposed by Cai et al. (2004, Int. J. Rock Mech. Min. Sci., 41(1), 3–19).     

A discontinuous numerical model to simulate rock failure process

Due to the difficulty of the classical fracture mechanics in dealing with multicrack coalescence, the simulation of jointed rock failure has remained a worldwide problem since the middle of the last century. Through a nearly 10-year effort, we have developed a novel but simple discontinuum-based approach, namely DDARF (discontinuous deformation analysis for rock failure), to simulate the progressive failure process of jointed rock mass. In the proposed method, by adopting the FE adaptive mesh generation technique—the advanced front method, the computational model of triangular DDA block system is automatically established. Also, the randomly distributed mechanical parameters statistically satisfying Weibull’s law are assigned to the blocks to simulate the heterogeneity of rock mass. In the generating process of the block system, numerous artificial joints come into being. These artificial joints provide the potential paths along which the cracks generate and propagate. The two blocks beside an artificial joint are glued together through adhesive algorithm, and if the glue is invalid, the artificial joint will break and turn into a real crack. In this way, the rock fragmentation process can be simulated. The results of several verification examples indicate that the DDARF method can simulate the whole process of rock fragmentation, and is suitable for cases of intact rock, rock mass with non-penetrative joints, and even blocky rock.     

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。     

浅埋煤层长壁开采顶板岩层灾害控制研究

根据浅埋煤层顶板岩层的赋存特点和长壁开采时基岩老顶的断裂下沉特征,应用初始后屈曲理论和突变理论探讨了初次来压期间基岩老顶的灾害机制和灾害控制,补充了基岩老顶破断后控制岩块滑落失稳的充分条件和岩块触矸前后台阶下沉的判据,确定了台阶下沉量,给出了控制台阶下沉和维持顶板稳定的支护力计算公式,并以神东矿区大柳塔1203工作面为例给出了工程实例。研究发现,顶板破断后岩块处于不平衡状态,台阶下沉的机制是结构的滑落失稳;岩块触矸前后的台阶下沉分别与断裂下沉和开采高度之间存在着确定的关系;顶板强烈来压主要是由结构滑落失稳造成的,控制台阶下沉的实质是控制岩块沿煤壁的滑落失稳。研究结果表明,综合应用初始后屈曲理论和突变理论,可根据顶板结构的赋存状况和结构特征,确定基岩老顶触矸前是否会出现全厚度切落;根据工作面的开采高度和采空区有效充填厚度等,可确定基岩老顶触矸后岩块的运动形式;根据顶板的破断步距、断裂下沉量和岩块摩擦因数等,可确定岩块触矸前后控制台阶下沉的支护力     

裂隙岩体变形模量尺寸效应研究Ⅱ:解析法

通过分开考虑岩块和裂隙对岩体变形的贡献,研究了任意裂隙分布岩体等效变形模量的解析计算方法,并用正交裂隙岩体对该方法进行了验证,得到的结果和经典解析解完全一致。此外,通过该方法对锦屏Ⅱ级电站辅助洞中段随机裂隙岩体进行不同尺寸、不同方位下等效变形模量的计算,计算结果显示,随着岩体尺寸的增大,不同方位的变形模量值趋于稳定,该裂隙岩体变形模量的特征单元对(REV)尺寸为8 m,和有限元计算结果一致。结果表明该方法可以用来研究裂隙岩体等效变形模量尺寸效应和各向异性特性,研究成果对于裂隙岩体等效变形参数取值具有重要意义。     

A Morphological Visualization Method for Removability Analysis of Blocks in Discontinuous Rock Masses

Block theory has been successfully applied to solve practical problems in rock engineering associated with the stability of discontinuous rock masses. Traditional methods of block theory, which have not proposed detailed schemes for characterizing geometric features of arbitrary blocks with complex geometries, are difficult to simultaneously visualize the locations of blocks. To overcome the shortcomings of these traditional methods, this paper introduces the concept of block morphology to systematically represent the morphological characteristics of blocks. Morphological visualization analysis involves the classification, characterization and visualization of various blocks and the determination of their removability using the stereo-analytical method. The proposed morphological visualization method provides a basis for computer modeling and mechanical calculations of large-scale rock mass systems. Furthermore, examples are presented in this paper to verify the validity and demonstrate the exceptional performance of this method.     

裂隙岩体块体化程度评价方法的若干问题修正

块体化程度是评价岩体完整性的一种新指标,能从三维角度表征岩体破碎程度,但目前该方法仍存在未充分考虑岩体切割程度及块体规模、未限定基础应用条件、块体化程度等级划分不合理等缺陷。针对上述缺陷,深入分析了其产生原因,并借鉴岩体切割程度、三维块度模数、体积RQD等计算原理,限定了块体体积百分比相关概念,提出了考虑岩体完整性块度尺寸效应的块体体积综合百分比计算方法,确立了块体化程度等级及分级指标取值依据,建立了修正的块体化程度评价方法。通过对比块体化程度评价修正方法、岩土工程规范对岩体完整性的划分结果,分析了修正方法的合理性。分别以广西铜坑矿锌多金属矿体、乌东德水电工程的块体研究数据为基础,开展了修正块体化程度评价方法的实例验证,结果表明：利用修正块体化程度评价方法计算的铜坑矿+255 m中段4#试验区岩体块体体积百分比为11.18%,属轻度块状化岩体;乌东德水电站PD49-1平硐、PD4支硐块体体积百分比分别为12.847%、10.168%,均属于轻度块状化岩体,岩体完整性程度为较完整级别。与现有块体化程度评价方法比较,修正方法计算的块体体积百分比能够更准确地从三维角度表征真实岩体的完整性。研究成果对精确刻画岩体三维完整性具有重要意义。     

基于软硬石模板库的土石混合体细观损伤与力学特性分析

为了探究含软、硬两种岩性碎块石土石混合体的变形破坏过程与力学性质,发展了一种基于软硬石模板库的土石混合体建模方法。通过在PFC2D中建立符合原位结构特征的软硬石模板库,利用此模板库生成了不同含石量土石混合体颗粒流模型,对土石混合体进行了单轴压缩颗粒流模拟。结果表明：土石混合体破坏始于土-石接触面,土石介质分离大多因剪切破坏导致,加载前期微裂纹迅速增长,中、后期微裂纹增长速率减缓,但宏观变形渐趋显著;随着含石量的增加,土石混合体单轴抗压强度逐渐降低,块石的转动与侧向移动会加剧土石混合体的整体破坏;相同含石量下,随着软石比例的增加,单轴抗压强度呈下降趋势,试验后试样破裂率与单个软石颗粒的破裂程度均保持在较高水平,软石颗粒破裂是引起土石混合体单轴抗压强度降低的重要原因。