非连续子母块体理论模型研究(Ⅰ):基本理论

对节理岩体的非连续变形与破坏失稳的数值模拟分析是目前岩土力学与工程领域中的前沿课题之一,岩体由节理裂隙以及由其切割而成岩石块体组成,介于连续与非连续之间,由于其内部结构的不确定性造成了其宏观力学行为的复杂性。在讨论了岩体破坏失稳的研究尺度的基础上,从多尺度耦合的角度出发,同时考虑连续问题、非连续问题以及连续问题向非连续问题转化,提出了非连续子母块体理论模型。在非连续子母块体理论模型中,假定岩体与岩体内部被层理、节理等结构面所切割而成的岩石块体均属于宏观尺度,把宏观的岩石块体定义为母块体,用假想的人工节理将其继续分为若干更小的块体,更小的块体称为子块体,子块体为各向同性的均质体,并且在计算中不再发生破坏分解为更小的块体,作为计算分析的基本单元,子块体的研究尺度属于细观尺度。模型也重新定义了子块体间的接触,并将其划分为连续接触与非连续接触两种类型,连续接触在一定条件下发生破坏转化为非连续接触;采用增广拉格朗日乘子法对子块体间的接触进行处理,能够计算出准确的弹簧接触力。     

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。     

基于凹体凸化的全空间块体识别方法

采用结构面切割多面体再合并的方法可以实现有限结构面间的块体识别,但切割的对象必须为凸体,而实际工程中的岩体模型并不局限于凸体。为了解决这一问题,提出一种凹体凸化方法,用于将凹体模型分解为凸体子区。首先,通过面单元法建立岩体模型,并设置可包裹模型的长方体;其次,以平面对凸多面体的切割算法为基础,利用面单元所在平面将所设置的长方体切割为若干子区;最后,通过判断子区与原模型的位置关系而实现凸化,并对凸化过程中的关键算法进行说明。针对切割过程中结构面与多面体的接触性判断问题,给出了从粗略到精确的判断方法,有效地减少了计算量。结合两个具有代表性的算例,给出所提块体识别方法的过程和结果,结果显示,所识别出的块体形态及数量不受限制,从而证明了本方法用于凹体模型的适用性与有效性。     

论岩体稳定之“关键块体”问题

正"关键块体"是指在地下工程岩体稳定、边坡工程岩体稳定和地基工程岩体稳定中起关键抗滑阻挡作用,一旦失稳将引起整个工程岩体结构系统破坏,造成地下工程围岩垮塌、岩质边坡开裂滑移乃至发生滑坡或地(坝)基岩体楔形剪出的层状或块状岩体。简言之,"关键块体"即岩体结构体系中对整体稳定性起到关键作用的地质块体。岩体是在地质历史发展过程中形成的地质体,由各种成因的地质界面(岩层面、节理、裂隙或断层     

某水电站引水洞进口侧山体边坡块体识别

某水电站进口侧山体边坡岩体为完整性较差的中--薄层状灰岩,岩体中主要发育3 条断层、1 组岩脉和4 组优势节理,严重影响了该山体边坡的稳定性。根据结构面分布,采取块体理论搜索边坡上的关键块体,通过赤平投影法找出边坡上所有的非空裂隙锥,将这些非空裂隙锥与临空面组合,从而获得所有可动块体; 利用矢量法计算不同运动形式下块体JP 编号、净滑力即可获得关键块体。结果表明: 该水电站引水洞进口侧山体边坡有4 块关键块体( JP 编号为00010111、00110111、10110111、 10111011) ,为该边坡稳定性的进一步研究提供了基础。     

节理岩体关键块体稳定的概率分析

基于地下岩体受节理面的控制,节理面的几何和力学参数随机分布,从而导致岩体系统具有高度不确定性,提出以关键块体理论为基础,考虑节理几何和力学参数随机性的岩体开挖可靠度分析方法,并给出了块体稳定的总失效概率评价模型。以澳大利亚阿德莱德地区一铜矿地质条件为例,以节理面倾角、倾向、摩擦系数和黏聚力为随机变量,通过Monte Carlo模拟和概率图方法,进行了岩体可靠度和失效概率的计算。最后,采用条件概率的分析方法,计算了单面滑动块体的总失效概率。计算结果表明,块体沿单面滑动并且出现的概率为11.0%,总的失效概率为3.85%,超过一般岩体工程可允许的风险水平,认为该方法可以作为评价块体可靠性的依据。     

一种新的节理裂隙岩体弹塑性模型

提出一种节理裂隙岩体弹塑性模型,将结构划分为块体单元和缝单元,其中缝单元可以是实际节理裂隙,也可以是人为缝单元。以块体单元形心的刚体位移和块体的平均应变作为基本未知量。该模型能充分考虑节理裂隙材料和块体材料的本构关系,计算量不大,是一种位移不协调单元。该模型特别适合节理裂隙岩体的数值分析。     

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。     

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+25 5 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。研究成果对精确刻划岩体三维完整性具有重要意义。     

基于三维裂隙网络模拟的有限块体面积判断法

水工建筑物深开挖边坡中大量出现的随机楔体,他们是由广泛分布于裂隙岩体中的结构面切割而成。首先应用随机不连续面三维网络模拟技术建立不连续的概率模型,在此基础上,搜索出临空面迹线上所有的闭合凸多变形,根据文中提出的“面积判断”法,判断块体是否为有限块体。工程实例模拟的结果说明了该方法的合理性。     

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。     

基于布尔运算的复杂块体几何形态分析一般方法

提出采用布尔运算进行三维复杂块体形态分析的一般方法,并采用C++语言编写了相应的程序。块体布尔运算是将参与运算的主块体和客块体进行交、并或差运算,得到形态更加复杂的块体。为描述块体内部非贯通结构面,在块体数据结构中引入退化有向壳,允许块体中混合维度模型的存在。将主块体各面分别与客块体各面进行面-面求交线运算,通过环路分析得到各块体分割后的面。根据具体采用的布尔运算方法,确定有效面和无效面,并将有效面进行搜索得到新的壳和块体。选取3个算例和1个典型工程实例来验证该方法的可行性和应用性。计算结果表明,该方法可以生成形态更加复杂的块体,可以很方便地处理块体中的结构面,具有普遍性和适应性,并具有广泛的实际应用价值。     

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。     

Probabilistic prediction of the spatial distribution of potential key blocks during tunnel surrounding rock excavation

Jointed network simulations tend to be more random in nature due to the uncertainty of rock mass structures. In this paper, a series of jointed network models can be established in batches using Monte Carlo simulation (MSC) and loop iteration. Taking the joints, tunnel profile and their intersections as the edges E and vertices V of graph G, the jointed network model can serve as an unweighted undigraph. Then, the breadth-first search is introduced to search the closed paths around the tunnel profile, such as the potential key blocks. With batch simulation of network models, the spatial distribution characteristics and probability distribution rules of blocks can be automatically analysed during the search process. For comparison, the Laohushan tunnel of the Jinan Belt Expressway in China has been analysed using the breadth-first search, discontinuous deformation analysis method and procedure of “Finding the Key Blocks-Unrolled Tunnel Joint Trace Maps”. Each simulation starts from the same probabilistic model of geometrical parameters of joints but develops differently with different outcomes. The spatial distribution rule of potential key blocks simulated by the aforementioned batch jointed network models is essentially identical to the actual rockfall during tunnel excavation.

     

大型地下厂房块体稳定性简便分析方法

块体是结构控制型岩体中常见的潜在危险源之一。利用极限平衡法及强度折减法两种方法计算了某在建特大型水电站地下厂房开挖揭露的部分块体的安全系数,并根据计算结果提出一种利用块体几何及力学参数判断其稳定性的简便图解方法,经现场监测数据验证计算结果可靠性可满足工程要求。研究表明,对同一块体而言,极限平衡法和强度折减法得到的安全系数以及对其稳定性的总体判别结果并不一致。强度折减法受软件算法及网格尺寸影响,结果偏于保守。简单块体的安全系数计算应以极限平衡法为主,而复杂形态块体的安全系数用强度折减法计算较为方便。利用垂向地应力、块体体积、最大角点深度及结构面等效强度等4个指标并结合块体稳定性判别分区图,可满足快速判断块体稳定性的需要。对于判别为不稳定的块体,应及时支护并考虑加强支护。研究成果可用于类似工程块体稳定性的快速分析。     

The key‐group method

This paper proposes an extension to the key‐block method, called ‘key‐group method’, that considers not only individual key blocks but also groups of collapsable blocks into an iterative and progressive analysis of the stability of discontinuous rock slopes. The basics of the key‐block method are recalled herein and then used to prove how key groups can be identified. We reveal that a key group must contain at least one basic key block, yet this condition is not entirely sufficient. The second block candidate for grouping must be another key block or a block whose movement‐preventing faces are common to one or more single key blocks. We also show that the proposed method yields more realistic results than the basic key‐block method and a comparison with results obtained using a distinct element analysis demonstrates the ability of this new method. Copyright © 2003 John Wiley & Sons, Ltd.     

Block theory on the complex combinations of free planes

The core problem of block theory is to determine the finiteness, removability and mechanical stability of various blocks under different engineering structures based on dip angles, dip direction angles of discontinuities, frictional angles and the direction of the active resultant force. The practices of the classical block theory focus mainly on the convex blocks, assuming that joint surfaces and excavation faces are planar and extended infinitely in the rock mass. However, in practical engineering structures, the concave combinations of free planes (natural of excavated surfaces) are common. For example, the non-convex blocks usually exist in underground edges, corners and portals, and some of them are quite dangerous. In this paper, the characteristics of the non-convex blocks with complex combinations of free planes are analysed deeply based on the classical block theory. First, a non-convex block is seen as a combination of a series of convex blocks, then the criteria for finiteness and removability of the non-convex blocks are proposed, and finally, the identification algorithm is designed and validated by some cases. The results show that the method is effective and feasible and has important theoretical significance and practical value.     

Physical Modeling of Landslide Mechanism in Oblique Thick-Bedded Rock Slope: A Case Study

The Jiweishan landslide illustrates the failure pattern of an apparent dip slide of an oblique thick-bedded rockslide. Centrifugal modeling was performed using a model slope consisting of four sets of joints to investigate the landslide initiation mechanism. Crack strain gauges pasted between the slide blocks and the base failed in sequence from the rear to the front as the centrifugal acceleration increased. When the acceleration reached 16.3g, the instantaneous failure of the key block in the front triggered the apparent dip slide of all blocks. The physical modeling results and previous studies suggest that the strength reduction in the weak layer and the failure of the key block are the main reasons for the Jiweishan landslide. The centrifuge experiment validated the previously proposed driving-blocks–key-block model of apparent dip slide in oblique with inclined bedding rock slopes. In addition, the results from limit equilibrium method and centrifuge test suggest that even though the failure of the key block in the front is instantaneous, a progressive stable–unstable transition exists.     

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.