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.     

Multiscale approach to geo‐composite cellular structures subjected to rock impacts

Geo‐composite cellular structures are an efficient technological solution for various applications in civil engineering. This type of structure is particularly well adapted to resisting rockfalls and can act as a defensive structure. However, the design of such structures is for the most part empirically based; this lack of research‐based design stagnates optimization and advanced development. In this paper, the mechanical behaviour of a geo‐composite cellular structure is investigated using a multi‐scale approach, from the individual cell made up of an assembly of rocky particles contained in a wire netting cage to the entire structure composed of a regular array of cells. Based on discrete modelling of both the cell and structure scales, a computational tool has been developed for design purposes. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling dynamic breakage in rock blocks with different elongation and flatness ratios upon impact

The two crucial shape factors (elongation ratio and flatness ratio) of brittle particles may influence the dynamic breakage of brittle particles upon impact. Hence, three-dimensional discrete element method simulations of brittle rock blocks with different shapes upon normal impact were performed. The simulated results indicate that the elongation ratio, that is, ratio of width to length and flatness ratio, that is, ratio of thickness to width can significantly affect the breakage of brittle rock blocks. Three fracture mechanisms, that is, fragmentation, horizontal tensile fracture and vertical tensile fracture, were revealed, which determine the dynamic breakage of rock blocks. The fragmentation results in numerous single-sphered fragments with velocities even larger than 2 times of the initial velocities. Fragmentation can provide a buffering effect at high impact velocities of larger than 4 m/s. With an increasing elongation ratio or flatness ratio, the phenomenon of fragmentation gradually disappears. The reflection of a compression stress wave results in horizontal tensile fracture. The expansion in the plane perpendicular to the impact velocity results in vertical tensile fracture.     

三江中段两古陆铅同位素地球化学边界的厘定

根据三江中段及周边邻区火成岩铅同位素数据,确认了三江中段扬子陆块与冈瓦纳古陆的边界。两古陆的铅同位素地球化学边界为^206Pb/^204Pb=18．583、^208Pb／^204Pb=38．575和V1=60、V2=52,低于界线值的属扬子陆块,高于界线值的属冈瓦纳古陆。三江中段两古陆的铅同位素地球化学边界在地理上对应于德钦鲁春-红坡牛场一线,以东属扬子陆块,以西为冈瓦纳古陆;在构造上对应于德钦-字呷断裂带;在构造-岩浆带上对应于金沙江构造岩浆带与澜沧江构造岩浆带的分界线;在成矿上则对应于德钦羊拉-鲁春-红坡牛场铜多金属成矿带。     

A novel nonlinear solution for the polygon scaled boundary finite element method and its application to geotechnical structures

The polygon scaled boundary finite element method is semi-analytical and known for its high precision. However, the material nonlinearity cannot be maintained because this method uses an analytical solution in the radial direction. In this paper, a novel nonlinear algorithm is developed by introducing internal Gaussian points over a subdomain. The response of nonlinearity for a concrete-faced rockfill dam is modeled. The results correspond well with the results from finite element modelling, which demonstrates the method can be used to describe the nonlinear characteristics of geomaterials. Furthermore, this method offers promising flexibility for analyzing complex geometries without decreasing the precision.     

偶应力对层状岩体结构面边界层效应的影响

在压剪载荷作用下,层状岩体结构面附近的剪切变形梯度非常显著。基于偶应力理论,研究层状岩体结构面边界层效应。利用有限单元方法进行数值计算,并将偶应力理论的计算结果与经典弹性理论的结果进行比较。采用Serendipity单元（S单元）,导出S单元内的插值函数及位移插值公式。利用ANSYS进行前处理,并基于Matlab编制经典理论和偶应力理论相应的计算和后处理程序。结果表明：偶应力对层状岩体结构面剪应变有显著影响,尺度效应明显。相对于经典弹性理论,在偶应力理论中,应变量减小,并在边界层附近出现过渡区;剪应变突变现象得以改善,但剪应力不再连续。特征长度影响过渡区域的大小,但第二剪切模量、泊松比、弹性模量不改变过渡区域的大小。     

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.     

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.     

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.     

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。     

Analysis of single rock blocks for general failure modes under conservative and non‐conservative forces

After describing the kinematics of a generic rigid block subjected to large rotations and displacements, the Udwadia's General Principle of Mechanics is applied to the dynamics of a rigid block with frictional constraints to show that the reaction forces and moments are indeterminate. Thus, the paper presents an incremental‐iterative algorithm for analysing general failure modes of rock blocks subject to generic forces, including non‐conservative forces such as water forces. Consistent stiffness matrices have been developed that fully exploit the quadratic convergence of the adopted Newton–Raphson iterative scheme. The algorithm takes into account large block displacements and rotations, which together with non‐conservative forces make the stiffness matrix non‐symmetric. Also included in the algorithm are in situ stress and fracture dilatancy, which introduces non‐symmetric rank‐one modifications to the stiffness matrix. Progressive failure is captured by the algorithm, which has proven capable of detecting numerically challenging failure modes, such as rotations about only one point. Failure modes may originate from a limit point or from dynamic instability (divergence or flutter); equilibrium paths emanating from bifurcation points are followed by the algorithm. The algorithm identifies both static and dynamic failure modes. The calculation of the factor of safety comes with no overhead. Examples show the equilibrium path of a rock block that undergoes slumping failure must first pass through a bifurcation point, unless the block is laterally constrained. Rock blocks subjected to water forces (or other non‐conservative forces) may undergo flutter failure before reaching a limit point. Copyright © 2007 John Wiley & Sons, Ltd.     

工程中渗流问题的边界元算法与分析

针对河堤、水坝、高速公路档水墙等存在多孔单元介质中的定常渗流问题,将渗流Laplace方程,通过数学变换转化为边界积分方程,进而离散为线性代数方程组。采用边界元编写FORTRAN程序。计算结果表明:该法与有限元法相比,占用CPU时间短,不需要网格化分,使繁杂问题简单化,同时很好地切近实际。      

无限域横观各向同性岩体介质中折线裂纹边界元方法

岩体材料的各向异性导致其中的光滑裂纹在扩展后会变为折线裂纹。对于折线裂纹,其折线处裂纹面外法线方向不惟一,不能用连续单元离散。为此,在光滑裂纹问题方法的基础上,引入4种新的不连续单元来离散折线处裂纹面,建立了适用于折线裂纹问题的对偶边界元方法,该方法基于横观各向同性基本解。算例验证表明,该方法具有较好的精度。最后用该方法分析了横观各向同性岩体中的折线裂纹,得到了该类裂纹的应力强度因子。当裂纹面上作用法向均布力,横观各向同性岩体介质中的矩形光滑裂纹发生弯折时,折线两侧的裂纹面在张开时存在抑制效应,从而导致折线裂纹裂尖应力强度因子小于原光滑裂纹。同时还发现,随裂纹面的逐渐弯折,其裂纹面对各向同性面的倾角发生变化,因此,其裂尖断裂特性还受到岩体各向异性的影响。     

复杂岩质高边坡半确定性块体三维稳定性研究

通过工程地质学中的赤平投影原理对各个结构面产状进行统计分析,找出优势结构面组合,再对非确定位置的结构面按一定间距进行搜索,利用运动学分析方法对各个块体进行分析,确定出可能从坡体上滑出的块体。结合三维刚体极限平衡法,计算出各个可能块体组合在不同工况下的稳定系数,找出最危险滑块,进而对边坡进行稳定性评价,通过具体的工程实例进行了验证。结果表明,将工程地质学方法、运动学分析方法与刚体极限平衡法结合起来分析复杂岩质边坡可以提高边坡稳定性评价的准确性,对工程具有很好的指导意义。     

黄海深部结构与中朝-扬子块体结合带在海区位置的地球物理研究

以黄海及其邻区为研究对象 ( 32～ 4 2°N ,1 2 0～ 1 30°E) ,以研究区的空间重力异常、布格重力异常和地震层析成像数据为基础 ,在研究区中分辨出方向各异的主要断裂带并给出它们的分布。对在朝鲜半岛存在的一条近SN向分布的断裂带进行了重点讨论。根据重力数据、莫霍深度分布特点和层析成像的结果 ,认为该断裂带的两侧应属于不同的构造地质单元 ;提出该断裂带与五莲—青岛断裂带和济州岛南缘断裂带一起组成了中朝与扬子块体在黄海海区的边界结合带的认识 ;并推测在三叠纪的晚期 ,沿郯庐断裂带和该断裂带曾分别发生过左旋和右旋走滑。受SN向挤压应力的作用 ,(下 )扬子块体被平移嵌入到中朝块体之中。因此 ,两个块体在海区的结合带为一个巨大的“Z”字型的入构造     

A 2.5-D coupled FE–BE model for the dynamic interaction between saturated soil and longitudinally invariant structures

A two-and-a-half-dimensional (2.5-D) coupled finite element–boundary element (FE–BE) model is presented to simulate the three-dimensional dynamic interaction between saturated soils and structures with longitudinally invariant geometries. A regularized 2.5-D boundary integral equation for saturated porous media is derived that avoids the evaluation of singular traction integrals. The 2.5-D coupled FE–BE model is established by using the continuity conditions on the soil–structure interface. The developed model is verified through comparison with an existing semi-analytical method. Two case studies of a tunnel embedded in a poroelastic half-space and the efficiency of a vibration isolating screen are presented.     

基于坐标投影法岩质边坡块体稳定性分析及其可视化研究

块体塌落或滑动是岩质边坡工程的重要破坏形式之一,因此块体稳定性分析是岩质边坡工程中一项极为重要的内容。以浙江仙居县神仙居岩质边坡为研究背景,对块体稳定性分析及可视化进行研究。基于线性回归法和非均匀有理B样条法提出拟合结构面和临空面的新方法。基于坐标投影法提出单滑面和双滑面型块体的稳定系数计算方法,将无人机与坐标投影法结合,并基于Matlab开发出适于岩质边坡工程中平面多面体块体和曲面块体稳定性分析的CPG程序。该程序可实现结构面、临空面及不稳定块体的空间表示及可视化。工程实践表明,该研究可高效、准确地处理落石、崩塌等工程地质灾害问题。程序计算结果与坐标投影块体理论计算结果基本一致,块体稳定性分析方法可靠,开发的CPG程序可行,可大幅提高块体稳定性分析效率,具有实际工程意义。     

用无穷边界元分析半无限域问题

在边界积分方程离散的基础上,根据远场位移的特性,用衰减函数描述远场位移,阐述了自适应高斯积分算法,并结合前人成果—用解析法求出在远场上的强奇异积分,编制了适合于半无限域线弹性问题的计算机程序,并进行了事例验证,验证表明,该法比传统边界元具有更高的精度。     

岩体结构拉裂的块体单元法模拟

基于阶谱块体单元法,提出了二次覆盖的概念和一种分析岩石块体受拉开裂破坏的方法。该方法将块体及其一次覆盖在概念上细分为许多个积分子域,即二次覆盖。在二次覆盖上引入模糊裂纹模型,并把裂缝的形成视为一个粘塑性屈服流动过程,将开裂后产生的不平衡力进行转移,通过迭代使结构重新达到平衡。该方法既能考虑结构本身的不连续性,又能有效地模拟块体受拉开裂和裂纹扩展的现象。数值算例表明,计算结果基本合理。     

基于块体单元法的岩石边坡安全系数研究

岩石边坡因其结构面数量众多、块体系统及其滑动方式复杂,给危险块体组合的搜索及其安全系数计算带来很大困难。基于块体单元法,对岩石边坡中的危险块体组合搜索及其安全系数的计算方法进行了研究。首先,在块体元强度折减计算的成果下,根据屈服面贯通理论提出搜索危险块体组合的新方法;然后,对安全系数计算方法进行研究,建议在位移突变判据下采用双线性交叉法计算安全系数;最后,进行了单面、双面和多面滑动以及复杂块体系统的算例分析,并与刚体极限平衡法计算结果进行了对比。结果表明,由于块体单元法考虑了力与力矩的平衡及结构面上应力的非均匀分布,其计算结果更准确。该方法有望广泛应用于复杂岩石边坡稳定分析。