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。     

基于布尔交运算的三维流形单元生成研究

三维流形单元的生成是进行三维数值流形分析的首要问题之一。详细研究了三维流形单元的生成过程,并采用C++语言编写了相应的程序。借鉴二维流形单元的形成技术,基于拓扑学的“有向性”原理,将点、有向边、有向环、有向面和有向壳等作为三维块体的基本数据结构。将材料体和数学网格进行布尔交运算,并对形成的流形块体进行有效性检测,满足要求后即形成新的三维流形单元。每个数学网格的顶点作为新流形单元的数学覆盖,再对数学覆盖进行细分,形成流形单元的物理覆盖。分别选取凹形体、空心体和包含有限结构面的材料体与数学网格进行布尔交运算,并选取一个典型工程来检查该方法和程序的可行性。计算结果表明,该方法可以对复杂块体（凹形体、空心体和包含有限结构面的体）进行处理,为今后进行复杂结构计算和分析奠定基础,具有较强的适应性和可靠性。     

基于线框架模型的三维地质断层结构模型及其构建技术

基于地质断层构造的特点,文中提出了一种适合三维断层模拟的数据模型——线框架模型,并基于该数据模型详细描述三维断层结构模型的构建方法,实现了从层面结构的地质模型向块体结构的地质模型进行自动转换的关键算法。线框架模型以方向线框架来表达地质模型的骨架,以方向TIN网来表达地质模型的血肉,具备地质断层结构模型所要表达的各种几何元素与拓扑关系。基于线框架模型的三维地质断层构模技术将地质界面之间的交切在地质界面三角网形成之前就进行处理,将面与面之间的切割操作简化为线与线之间的操作,这种方法不仅能有效地减轻断层地质体构模的复杂程度,而且可以将线与线之间的交线作为地质界面三角网构建时的约束边,从而有效地保证了地质界面之间交切关系的正确性。     

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。     

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。     

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。     

多结构面三维块体极限稳定新方法探讨

对复杂块体进行简单切分后,根据块体基本理论与刚体分块极限平衡原理,探讨多结构面三维复杂块体稳定分析新方法,研制适应性较强的三维极限稳定分析程序,在龙滩水电站右岸坝肩高边坡等工程中取得成功应用。     

坐标投影作图法在川藏线宿瓦卡岩质边坡稳定性分析中的应用

边坡稳定性问题是川藏线工程建设面临的重要问题。野外调查发现基岩边坡失稳一般表现为块体塌落或滑动。基于岩体结构控制理论,作者以川藏线西藏境内宿瓦卡附近的人工高边坡为例,进行了块体边坡稳定性分析。对比现有理论方法的优缺点,采用坐标投影作图法及其计算机化程序CPH。坐标投影作图法是一种以正投影为基础,以分析岩体结构面的几何关系及由其切割出来的块体的稳定性为目的的图解方法。根据现场量测取得的数据,采用CPH程序确定了块体边坡的结构面方程,从而求出各结构面产状。在此基础上建立水平切面图,并求得各块体顶点坐标,计算出块体的表面积及体积。根据极限平衡理论,运用CPH程序进行块体稳定性分析,并求出块体的稳定性系数。通过分析可知,坐标投影作图法及其计算机化的CPH程序在块体边坡稳定性分析中有着很好的应用效果。     

位场建模中的曲面切割方法

给出了将构造图表示的地质模型向块体模型转化的曲面切割计算流程。用Ｄｅｌａｕｎａｙ三角形、约束Ｄｅｌａｕｎａｙ三角形和投影等,解决了曲面切割所遇到的交线求取、交线插入、交线三角形的搜索和沿交线断开等方法问题,并给出了实际模型的计算实例。     

主TIN模式下面向拓扑的三维地质块体构建方法

当前普遍采用主TIN模式对层状地质体进行三维结构建模,然而在地质块体的构建方面还有所欠缺。考虑到由于尖灭、出露等现象引起的各地质块体间空间位置关系的复杂性,根据主TIN建模的特点,处理完地层相交与高程调整之后,通过对地层面中某个区域内的三角网与上下地层中对应区域内的三角网的重叠次数的不同,设置子面类型标记,从而分离出一个地层面中不同类型的子面。依据子面的类型可以快速建立地质块体与被引用的各子面之间的对应关系,最终自动分离出地层中的各个地质块体,并保证相邻块体在邻接处有唯一的公共子面,由此可建立各地质块体间的空间拓扑关系。     

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。     

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.     

弹粘塑性块体单元法在龙滩水电站右坝肩边坡稳定分析中的应用

介绍了三维弹粘塑性块体单元法的基本原理。该方法假定岩石块体为刚体,只考虑结构面的变形和强度特性。在建立块体系统的平衡方程、结构面的变形与块体位移的几何相容方程以及结构面上的弹粘塑性本构方程的基础上,出块体系统位移与稳定的基本方程。针对龙滩水电站右坝肩边坡地质条件复杂,块体稳定问题较为突出的情况,采用块体单元法计算了边坡中典型结构面切割形成的特定块体在不同工况下的强度储备安全系数,并针对结构面的几何参数和力学参数等重要影响因素进行了敏感性分析,为工程设计提供了依据。应用表明,作为一种新型的水工结构数值方法,块体单元法应用于复杂地质条件下的岩石高边坡的稳定和变形分析具有准确、适用和简便的特点。     

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.     

Modeling branched and intersecting faults in reservoir-geomechanics models with the extended finite element method

Faults are geological entities with thickness several orders of magnitude smaller than the grid blocks typically used to discretize geological formations. On using the extended finite element method (X-FEM), a structured mesh suffices and the faults can arbitrarily cut the elements in the mesh. Modeling branched and intersecting faults is a challenge, in particular when the faults work as internal fluid flow conduits that allow fluid flow in the faults as well as to enter/leave the faults. By appropriately selecting the enrichment function and the nodes to be enriched, we are able to capture the special characteristics of the solution in the vicinity of the fault. We compare different enrichment schemes for strong discontinuities and develop new continuous enrichment functions with discontinuous derivatives to model branched and intersecting weak discontinuities. Symmetric fluid flows within the regions embedded by branched, coplanar intersecting, and noncoplanar intersecting faults are considered to verify the effectiveness of the proposed enrichment scheme. For a complex fault consisting of branched and intersecting faults, the accuracy and efficiency of the X-FEM is compared with the FEM. We also demonstrate different slipping scenarios for branched and intersecting faults with the same friction coefficient. In addition, fault slipping triggered by an injection pressure and three-dimensional fluid flows are modeled to show the versatility of the proposed enrichment scheme for branched and intersecting weak discontinuities.     

乌东德水电站右岸地下厂房随机块体特征研究

随机块体的几何特征和稳定性是水利水电工程中地下厂房支护设计的重要依据。对乌东德水电站右岸地下厂房随机块体的特征进行了深入研究。对研究区域内实测的裂隙参数进行了分组统计,确定了各组裂隙产状、迹长等参数的分布形式和大小。利用逆建模方法建立了三维裂隙网络模型,获取了各组裂隙的直径和三维密度。采用一般块体方法对地下厂房进行随机块体的识别和稳定性分析,利用GeneralBlock软件进行了10次随机实现,对10次计算结果进行了统计分析和讨论。研究结果表明,结构面与开挖面形成的随机块体集中在地下厂房的顶拱部位,10次随机实现中,地下厂房全长范围内平均每次形成的随机块体为414个;随机块体的平均体积为2.9 m³,最大块体的体积达152.0 m³;可移动块体中,大部分为稳定块体,不稳定块体均以坠落形式破坏;构成可移动块体的结构面多为3~4条,最多可达12条,其中倾W向的中等倾角裂隙是构成块体并可能造成块体失稳的最危险结构面;随机块体的平均深度为1.2 m,最大深度为8.8 m。建议支护锚杆应尽量穿透倾W向中等倾角的长大裂隙,且锚杆支护长度大于8.8 m。     

Kinematic and Block Theory Analyses for Shiplock Slopes of the Three Gorges Dam Site in China

The granitic rock mass that exists in the shiplock region of the Three Gorges dam site contains a number of major discontinuities and about four sets of minor discontinuities. One hundred and thirty three major discontinuities have been mapped around the shiplock covering an area of 1740×600 m. These major discontinuities were used to perform rock slope kinematic and block theory analyses. Kinematic analyses were performed under the following two cases: (1) assuming all the mapped discontinuities cross the shiplock; (2) using only discontinuities that actually intersect the shiplock. Under case (1) and case (2) the shiplock faces in the proposed permanent shiplock region in fresh rock were found to be stable up to a cut slope of about 45° and 58°, respectively. Block theory was applied to identify different block types that exist on the shiplock faces and to estimate the maximum safe slope angles on the shiplock faces. The orientations of the major discontinuities that actually intersect the shiplocks were considered in this analysis. The total length of the shiplock (1750 m) was divided into 50 m segments. From the stereo-plots, the key blocks (Type I) and/or potential key blocks (Type II) were found for only five segments of the shiplock slopes. It was found that the dip of the cut slope should be less than about 60° to avoid creation of a key block on the proposed shiplock slopes. However, it is important to keep in mind that these conclusions are based on the kinematic analyses performed using only the major discontinuities. Further kinematic as well as kinetic analyses are recommended incorporating minor discontinuities, water forces, earthquake forces etc. before making the final conclusions about the maximum safe slope angle for the shiplock region.     

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.     

弯曲结构面几何条件的图解方法及其应用

分析岩体和山体稳定性的主要问题也就是确定结构面及临空面之间的相对位置关系及组合方式。坐标投影作图法是一种以正投影为基础,以分析岩石工程中结构面的几何关系及由其切割出来的块体的稳定性为目的的图解方法。对于弯曲结构面,采用“以直代曲”的原理,将其简化为有限个小平面的集合体进行分析。以蛇蟠岛国际旅游度假村清风洞室群1号洞为例,采用坐标投影作图法对弯曲结构面进行分析,来解决弯曲结构面几何条件的描述和确定问题。