水利水电工程外文翻译—基于离散单元法的砌石重力坝安全分析工具

外文翻译专业水利水电工程基于离散单元法的砌石重力坝安全分析工具摘要介绍一种基于离散单元法的砌石重力坝分析数值模型。

大坝和岩基用3到4节点的基本块组成的块集合表示。

复杂的块形状通过把基本块整合到宏模块来得到，允许模型应用在从等效连续到完全不连续分析的各种情形。

开发了一个接触面公式，能够根据基本块之间建立的接触面，基于一种精确的边边方法表示宏模块之间的相互作用。

描述了模型的主要数值方面，特别介绍了接触面的创建和更新步骤以及一个支持一种高效且能够得到明显结果的算法的数值设备。

讨论了一个现有的砌石坝的安全评价的应用，包括结构的应力分析和涉及大坝岩石界面附近不同路径的滑动失效机制的评估。

关键词砌石坝；离散元；应力分析；失效机制1 简介结构分析必须使用适当的手段来实现它的最终目的。

这些手段必须能够：（1）模拟建筑物的几何和物理特征，尤其是不连续的和共有的特征；（2）用一套完整的方法来模拟荷载，能够考虑所涉及的不同现象间的相互影响；（3）评价非线性作用，特别是能够界定失效结构。

砌石重力坝应该被理解为一个包含坝体本身，水库，岩石基础的系统。

坝体和岩石是不均匀且不连续的介质。

坝体和围岩的交界面也是不连续的，需要特别注意。

不连续面控制着砌石坝的强度，因为它们是薄弱面，决定着主要失效机制。

另外，大坝所受的各种不同的荷载需要一套完整的方法来处理，因为它们之间相互关联。

这些独特的特点使得大1多数的数值工具，无论商业的还是科学的，都不能完全适合地模拟浆砌石重力坝。

在这种背景下，新的数值工具的发展就显得尤为重要。

本文将描述一种为砌石重力坝的静力、动力及流体力学的分析量身定做的数值工具，离散单元法。

离散单元法最初是为了处理岩石力学问题而提出的替代有限元法的方法。

离散单元法的基本原理是将不连续介质看作受力作用不同的块的集合，因此不同于将其看作同一单元的有限元法。

这些数值处理方法也被广泛地应用于砖石结构。

在Cundall所开发的产品的基础上发展起来的二维编码通用离散元程序（UDEC），已经被用于包括混凝土坝的地基等方面的研究中，主要用于尝试通过岩石评估失效机理。

Taone等人做了一个在坝体与岩石交界面上的滑移离散单元法分析，充分地考虑了交界面的不规则几何形状及应力集中。

离散单元法的代码通常通过将应变块离散成三角形均匀应变单元的内部网格来代表应变块。

指令“离散有限单元法”通常被用于编码块单元的允许破坏量来模拟渐进破坏过程。

本文所介绍的模型是基于离散单元法，满足三个设计要求，在一个完全由作者自己开发的新型软件工具里实施的。

首先，本模型要将浆砌石坝和岩石基础用一套完整的方法做成块系统的部件；其次，软件工具需要提供一种可实现的方法来用同一网格表示等效的连续介质和块状模型；最后，该工具需要包含大坝工程分析的所有要素，比如水流量及接头处和加强部位的压力，比如主动或被动锚固，以及应用在静力分析和地震分析中涉及到的荷载的方法。

所有这些部分通过一个兼容的数据结构相互作用。

因此，本模型在一个更普遍的框架下结合了标准离散单元法的能力，该框架可以满足实际应用的兼顾刚性块和应变块，连续网格和离散单元的要求。

此外，还采用了一个基于边界间相互作用的非传统接触面公式，能够得出一个更精确的交界面压力。

新的系统与离散单元法一样有按照预先设定好的路径模拟一个连续体碎裂成块的能力，但是采用了一种基于联合刚度和适合砌石和岩石构成规律的表示接触面的方法，这点不同于后者，例如Munjiza 的接触力公式。

有关应力计算的方面将在下面的部分详细讨论，本文将介绍一个砌石坝的安全评价在实际中的应用的例子。

大坝与岩石基础的23水工分析以及最新开发的分析工具，将在另一篇论文中被介绍。

图1 砌石坝和岩石基础形成的不连续介质图2 宏模块构成的连续和不连续模型2 模型离散化和接触面本数值工具旨在模拟如图1所示的浆砌石坝与岩石基础所组成的系统。

根据设计惯例以及大坝安全规范，结构的保守假设是二维假设，其中的实际原因是：以往大坝都设计成重力坝，无法保证其拱效应，而且这样的计算模型更容易理解。

结构离散化的基本要素是具有三或四个边界的块，可以是刚性的或可变形的，并且可以计划性地在同一模型中使用。

块的选择应由结构，特征以及分析的目的来决定。

在性能方面，由于刚性块只在单元的质心处建立运动方程，减少了模型自由度，所以刚性块的计算速度更快。

刚性块的计算优势是只在显动态分析时有实质性作用，因为其静态的结果通常可以迅速得到。

在大坝工程中，结构应力分析和地基应力分析通常是必须的，所以应变块是首选。

每个应变块在这里都被假定为一个具有完全高斯积分的等参非线性有限元。

一般形状的块可以通过将3和4节点的块整合成宏模块来创建。

这是模拟如砌石坝和岩石基础这类不连续介质的重要特征。

这样等效连续表示整个或部分系统，其中每个块正是有限元网格的一个单元。

一个宏模块就是一个块的排列，相应块的顶点相互重合，组成一张连续的网络。

在同一宏模块的不同块之间没有相对位移，所以没有接触压力。

宏模块类似于有限元网格，但是有一个明确的结果，因为整体刚度矩阵的组合并不会发生。

图2a展示了一个有点个单独模块组成的不连续模型。

图2b表示的是一个类似但是连续的模型，它是由一个宏模块构成的。

另一个与有限元网格相似的连续模型在图2c展示。

图2d表示一个由两个宏模块构成的混合模型，在这两个宏模块之间有一个明显而重要的联接。

宏模块有一个包含一系列块和一系列由一个主节点和多个从节点构成的宏节点的数据结构。

宏节点与独立节点有着相同的自由度，所有数值操作只能在主节点上进行。

在计算循环中，所有从节点的力必须集中在主节点上，在新坐标上计算完成后，从节点从各自的主节点中更新数据。

尽管步骤较多，利用宏模块还是有减少接触面和自由读数目的优点。

同一个模型可能有几个宏模块，且每个宏模块可以有不同材质的块。

4A DEM Based Tool for the Safety Analysis ofMasonry Gravity DamsABSTRCTA numerical model for analysis of masonry gravity dams based on the Discrete Element Method is presented. The dam and the rock foundation are represented as block assemblies, using elementary 3- and 4-node blocks. Complex block shapes are obtained by assembling the elementary blocks into macro-blocks, allowing the model to be applied in various situations ranging from equivalent continuum to fully discontinuum analysis. A contact formulation was developed, which represents the interaction between macro-blocks in terms of contacts established between elementary blocks, based on an accurate edge–edge approach. The main numerical aspects of the model are described, addressing in particular the contact creation and update procedures, and the numerical devices that support an efficient explicit solution algorithm. An application to the safety evaluation of an existing masonry dam is discussed, including stress analysis in the structure, and the assessment of sliding failure mechanisms, involving different paths in the vicinity of the dam–rock interface.1 IntroductionStructural analysis must use appropriate methods to achieve its final purposes. These methods should be capable of (i) modeling the geometrical and physical characteristics of the structure, in particular5the discontinuities and joints, (ii) modelling the loads in an integrated manner, taking into account the interaction between the relevant phenomena involved, and (iii) evaluating the non-linear behaviour, particularly allowing the definition of failure mechanisms. Masonry gravity dams should be understood as a system composed of the dam itself, the reservoir, and the rock mass foundation. The dam and the rock mass are heterogeneous and discontinuous media. The dam–rock interface is also a discontinuity which requires particular attention. The discontinuity surfaces control the behaviour of masonry dams, because they are weakness planes that determine the main mechanisms of failure. In addition, dams are subject to a wide variety of loads requiring an integrated approach since they are often correlated. These particular features make the majority of the available numerical tools, both commercial and scientific, not entirely suitable for modeling masonry gravity dams. In this context, the development of new analysis tools is required. Here, a tailored numerical implementation of the Discrete Element Method (DEM) for static, dynamic and hydromechanical analysis of masonry gravity dams is described.The Discrete Element Method was initially proposed as an alternative to the Finite Element Method (FEM) to address Rock Mechanics problems [1]. DEM was based on the representation of the discontinuous media as an assembly of blocks in mechanical interaction, thus differing from the standard FEM approach based on joint elements [2,3]. These numerical approaches have also been widely applied to masonry structures [e.g. 4]. The 2D code UDEC [5], which evolved from Cundall’s pioneering work, has been used in several studies involving concrete dam foundations, mostly intending to assess failure mechanisms through the rock mass [e.g.6–8]. Tatone et al. [9] performed a DEM analysis of sliding on the dam–rock6interface, considering a detailed representation of the irregular geometry of this surface and the ensuing stress concentrations. Discrete Element Method codes usually represent deformable blocks by discretizing them into an internal mesh of triangular uniform strain elements (e.g., [5]). The designation ‘‘discrete finite element method’’ [10,17] is often applied to codes that allow the breakage of the block elements to simulate progressive failure processes. The model presented in this paper is based on DEM and was devised with three main requirements, implemented in a novel software tool fully developed by the authors. Firstly, it is intended to model in an integrated manner both the masonry dam and the rock foundation as components of a blocky system. Secondly, the software tool should provide a practical means to address both equivalent continuum and blocky models, using the same mesh. Finally, the tool needs to include all the features required in dam engineering analysis, such as water flow and pressures in the joints, reinforcement elements, such as passive or active anchors,and the means to apply the loads involved in static and seismic analysis. All these components interact through a compatible data structure. Therefore, the present model combines the standard DEM capabilities in a more general framework, which allows combining rigid and deformable blocks, continuum meshes and discrete components, as required by the application. Moreover, a non-traditional contact formulation is adopted, based on edge–edge interaction, which provides a more accurate stress representation in the interface. The new code shares with DEM the capability to simulate fracturing of a continuum into blocks through predefined paths, but adopts a representation of contact based on the joint stiffnesses and constitutive laws appropriate for masonry and rock, not following, for example, Munjiza’s formulation of contact force potentials [17]. The aspects related to the mechanical calculation will be discussed in detail78in the following sections, and an example of application to the safety assessment of a masonry dam in operation will be presented. The hydraulic analysis of the dam and rock foundation, also incorporated in the newly developed analysis tool, was described in a different paper[11].2 Model discretization and contactsThe numerical tool is intended to model systems composed of a masonry dam and its rock foundation, as shown schematically in Fig. 1. Two-dimensional analysis is conservatively assumed for these structures, following common design practices and dam safety codes[e.g. 12–14], for practical reasons: historically, masonry damsweredesigned as gravity dams; arching effects cannot be guaranteed; and, the computational model is simpler to understand. The fundamental element of discretization of the structure is the block with three or four edges, which may be rigid or deformable, and can be used simultaneously in the same model. The structure, characteristics and objectives of the analysis should dictate the choice of blocks. In terms of performance, the calculation is faster for the rigid blocks because the equation of motion is established only in the centroid of the element, thus reducing the degrees of freedom of the model. The computational advantage of rigid blocks is only relevant in explicit dynamic analysis, since static solutions are usually very fast to obtain. In dam engineering, stress analysis in the structure and foundation is usually required, so deformable blocks are preferred. In case of deformable blocks, each block is assumed here as an isoparametric linear finite element with full Gauss integration.Blocks of general shapes may be created by assembling the 3 and 4 node blocks into macroblocks. This is an important feature to model discontinuous media, such as masonry dams and rock mass foundations. In this way, it is possible to adopt an equivalent continuum representation of the whole system, or part of the system, in which each block is just an element of the FEM mesh.A macroblock is a combination of blocks, forming a continuous mesh, in which the vertices are coincident. Between the blocks of the same macroblock, relative movement is not permitted, so there are no contact forces. The macroblock is similar to a finite element (FE) mesh but with an explicit solution because the assemblage of a global stiffness matrix does not take place. Fig. 2a shows a discontinuous model composed by two individual blocks. A similar model, but continuous, composed by one macroblock, is presented in Fig. 2b. Another continuum model, similar to a FE mesh is showed in Fig. 2c. A9hybrid model, composed by two macroblocks, is presented in Fig. 2d, with an explicit joint considered between the two macroblocks.The macroblock has a data structure containing a list of blocks and a list of macronodes, with a master node and several slave nodes. The macronode has the same degrees of freedom of any individual node, and all numerical operations can focus only on the master node. During the calculation cycle, all forces from the slave nodes must be concentrated in the master node, and after calculation of new coordinates, slave nodes are updated from the respective master node. Despite these procedures, the use of macroblocks has the advantage of reducing the number of contacts and the number of degrees of freedom. The same model may have several macroblocks and each macroblock can have blocks with different materials.10References[1] Cundall PA. A computer model for simulating progressive largescale movements in blocky rock systems. In: Rock fracture (ISRM), Nancy; 1971.[2] Goodman RE, Taylor RL, Brekke TL. A model for the mechanics ofjointed rock. J Soil Mech Found Div ASCE 1968;94(3):637–59. [3] Wittke W. Rock mechanics. Theory and applications with casehistories. Berlin: Springer-Verlag; 1990.[4] Louren PB. Computations of historical masonry constructions. ProgStruct Eng Mater 2002;4:301–19.[5] Itasca, Universal Distinct Element Code (UDEC) –version 5.0,Minneapolis; 2011.[6] Lemos JV. Discrete element analysis of dam foundations. In:Sharma VM, Saxena KR, Woods RD, editors. Distinct element modelling in geomechanics, Balkema, Rotterdam; 1999. p. 89–115.[7] Barla G, Bonini M, Cammarata G. Stress and seepage analyses fora gravity dam on a jointed granitic rock mass. In: 1st InternationalUDEC/3DEC symposium, Bochum; 2004. p. 263–8.[8] Gimenes E, Fernández G. Hydromechanical analysis of flowbehavior in concrete gravity dam foundations. Can Geotech J 2006;43(3):244–59.[9] Tatone BSA, Lisjak A, Mahabadi OK, Grasselli G, Donnelly CR. Apreliminary evaluation of the combined finite element-discrete element method as a tool to assess gravity dam stability. In: CDA annual conference, Niagara Falls; 2010.[10]Petrinic N. Aspects of discrete element modelling involvingfacet-to-face contact detection and interaction, PhD thesis.University of Wales, Cardiff; 1996.11[11]Bretas EM, Lemos JV, Lourenco PB. Hydromechanical analysis ofmasonry gravity dams and their foundations. Rock Mech Rock Eng 2012.[12]FERC (Federal Energy Regulatory Commission). Engineeringguidelines for evaluation of hydropower projects –gravity dams.Federal Energy Regulatory Commission, Office of Hydropower Licensing. Report no. FERC 0119-2, Washington, DC, USA; 1991 [Chapter III].[13]USACE (US Army Corps of Engineers). Engineering and design:gravity dam design. Report EM 1110-2-2000, Washington, DC;1995.[14]USBR (United States Bureau of Reclamation). Design of smalldams, Denver, Colorado; 1987.[15]Cundall PA. Formulation of a three-dimensional distinct elementmodel –part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech Abstr 1988;25(3):107–16.[16]Williams JR, O’Connor R. Discrete element simulation and thecontact problem. Arch Comput Methods Eng 1999;6(4):279–304.[17]Munjiza A. The combined finite-discrete element method. WestSussex: Wiley; 2004.12。