三维离散块体边-边接触模拟

任意形状块体的接触模拟是发展三维不连续变形分析方法（3D-DDA）的关键问题。提出了三维离散块体单元的 边-边接触模型,并给出了边-边接触进入面的判定方法和嵌入准则。基于矢量分析和罚函数法,推导了接触子矩阵的表达式,算例分析结果表明了该模型的有效性。     

Three-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithm

This paper presents a new contact calculating algorithm for contacts between two polyhedra with planar boundaries in the three-dimensional discontinuous deformation analysis (3-D DDA). In this algorithm, all six type contacts in 3-D (vertex-to-face, vertex-to-edge, vertex-to-vertex, face-to-face, edge-to-edge, and edge-to-face) are simply transformed into the form of point-to-face contacts. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. In this paper, formulations of normal contact, shear contact and frictional force submatrices based on the new method are derived and the algorithm has been programmed in VC⁺⁺. Examples are provided to demonstrate the new contact rule between two blocks.     

A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis

Summary The key to three-dimensional discontinuous deformation analysis (3D DDA) is a rigorous contact theory that governs the interaction of many three-dimensional blocks. This theory must provide algorithms to judge contact types and locations and the appropriate state of each contact, which can be open, sliding or locked. This paper presents a point-to-face contact model, which forms a part of the contact theory, to be used in 3D DDA. Normal spring, shear spring and frictional force submatrices are derived by vector analysis and the penalty method. Also given are the open-close iteration criteria and operations performed for different changes in contact state. Sliding at a contact can occur in any direction parallel to the contact face, as opposed to one of two directions in two-dimensional DDA. This point-to-face contact model has been implemented into a 3D DDA computer program, and numerical results from several test cases demonstrate the validity of the model and the capability of the program.     

Application of discontinuous deformation analysis on stability analysis of slopes and underground power houses

Continuous computation and limit equilibrium computation are the two independent computations for practical rock engineering. For global stability analysis, limit equilibrium is still the fundamental method. For any numerical method, reaching limit equilibrium requires large displacements, discontinuous contacts, precise friction law, multistep computation and stabilised time-step dynamic computation. Therefore three convergences are unavoidable: convergence of equilibrium equations, convergence of open-close iterations for contacts and convergence of the contact forces of dynamic computations. This paper utilises mainly two dimensional discontinuous deformation analysis (DDA) and an available simple version of three dimensional DDA. The applications show DDA has the ability to reach the limit equilibrium of block systems.     

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。     

基于三维非连续变形分析的巨石崩塌运动研究

巨石作为一种大体积、大质量的滚石,其崩塌失稳及高速、高能远程运动往往导致沿途建筑物和交通线路的毁灭性灾难。以西藏自治区G318国道K4580典型滑坡为工程背景,基于三维非连续变形分析（three-dimensional discontinuous deformation analysis,简称3D-DDA）方法研究巨石崩塌失稳及运动全过程的特征与现象。分别建立该边坡未滑坡、浅层滑坡后和深层滑坡后3种坡形的巨石崩塌3D-DDA数值模型。采用滚石运动横向偏移经验模型,验证3D-DDA巨石运动模拟的准确性。在此基础上,分析巨石崩塌失稳机制及破坏后沿3种不同坡形边坡的运动轨迹和动能演进等运动特征。结果表明,3D-DDA能够有效模拟巨石崩塌失稳、运动发展、剧烈冲击碰撞直至最终静止等整个动力学过程。巨石崩塌表现为滑动→倾倒?滑动→倾倒→翻转?下落的失稳模式转换;巨石运动表现为碰撞、弹跳、飞跃、滚动、滑动等多种运动形式以及横向偏移、侧向偏转等三维空间运动特征,经过道路并与高架桥发生碰撞,引发巨石灾害。不同坡面几何特征下的巨石运动偏移量、弹跳高度、运动至坡底碰撞时间、最终稳定时间等均随着未滑坡、浅层滑坡后、深层滑坡后3种坡形变化而减小。通过3D-DDA巨石崩塌运动分析,预测巨石运动全过程、影响范围、冲击能量、停积位置等,可为巨石防灾减灾对策或措施制定提供依据。     

New point-to-face contact algorithm for 3-D contact problems using the augmented Lagrangian method in 3-D DDA

This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the ‘Common-Plane’ method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well.     

碎石土古滑坡弹塑性接触有限元稳定性分析

为了准确评价碎石土古滑坡的稳定性,通过资料搜集整理和分析、现场工程地质调查与勘探和室内外的物理力学试验,采用三维大变形弹塑性接触有限元算法,结合复活碎石土古滑坡工程实例,提出利用三维计算结果计算二维剖面稳定性系数的方法,分析了滑坡的稳定性。结果表明,采用三维大变形弹塑性接触有限元算法分析滑坡稳定性可以考虑滑坡体的空间效应,使计算结果更加符合实际。新方法可以更准确分析碎石土滑坡的稳定性和获得该类型滑坡所处的实际状态,为滑坡治理提供准确的科学信患。     

Sphere-boundary edge and sphere-boundary corner contacts model in DDA for simulating particulate media in 3-D

In modelling particulate media, such as soils, using 3-D DDA, there are four types of contacts: sphere to sphere, sphere to boundary face, sphere to boundary edge, and sphere to boundary corner contacts. The first two were studied by the authors in a previous work (Beyabanaki and Bagtzoglou 2012). In this paper, we present a new contact model for sphere-boundary edge and sphere-boundary corner contacts in sphere-based 3-D DDA. The model includes a new algorithm to search for contacts, detect the contact types and calculate contact points. Moreover, formulas for contact sub-matrices are derived. The proposed contact model has been implemented into a sphere-based 3-D DDA program and three test cases are studied in order to verify the workability of the new contact model. The numerical results obtained demonstrate the capability of the model to deal with sphere-boundary interaction in particulate media.     

Generalized contact model for polyhedra in three‐dimensional discontinuous deformation analysis

We present a generalized contact computation model for arbitrarily shaped polyhedra to simplify the contact analysis in discontinuous deformation analysis. A list of generalized contact constraints can be established for contacting polyhedra during contact detection. Each contact constraint contains information for 2 contact points, unique contact plane, and related contact modes (open, locked, or sliding). Computational aspects of the generalized contact model include identification of contact positions and contact modes, uniform penalty formulation of generalized contact constraint, and uniform updating of contact modes and contact planes in the open‐close iteration. Compared with previous strategies, the generalized contact computation model has a simpler data structure and fewer memory requirements. Meanwhile, it simplifies the penalty formulation and facilitates the open‐close iteration check while producing enough accuracy. Illustrative examples show the ability of the method to handle the full range of polyhedral shapes.     

三维距离势离散单元法

通过定义距离势函数,提出一种适用于空间任意凸多面体单元的三维距离势函数离散单元法。该方法采用归一化的计算方式,将势函数表征为接触体间的距离函数,并基于此建立接触力计算方程,明确了势函数的物理意义,使接触力计算更加合理,无需对各种可能的接触形式进行差异化处理。新方法克服了原有势函数物理意义不明、接触力计算受单元形式影响等重要缺陷,并突破了四面体单元的限制,可采用空间任意凸多面体单元。通过若干算例说明新方法的正确性和有效性。数值模拟结果表明新方法能够很好处理空间任意多面体单元复杂接触变换过程,准确处理复杂非连续介质的运动过程。     

非线性接触力学模型在地基-基础相互作用弹性分析中的应用

针对多体相互作用体系的非连续变形分析问题和接触问题,采用Mohr-Coulomb屈服准则和关联流动法则以及接触界面上的非线性应力分布模式,考虑接触界面特性提出了非线性接触力元模型,以结点位移和界面相互接触应力同时作为独立未知变量,建立了离散系统的总体控制方程.进而,通过数值求解能够直接确定变形体内的应力与变形、界面上的接触应力与离散体的位移与运动.将这种以接触力元为基础的多体系统分析方法具体应用于基础与地基相互作用分析,通过数值计算与分析探讨了地基与基础的相对刚度、荷载大小及其偏心距、地基与基础间界面力学参数对接触界面的应力分布和地基变形的影响,所得结果为工程中考虑基础与地基相互作用影响的设计与分析提供了参考依据.     

Analytical and numerical investigation of uniqueness and localization in saturated porous media

This paper presents first the applications of uniqueness and strain localization analysis of saturated porous media, where localization of deformation into well defined narrow zones in a saturated porous medium is studied in terms of discontinuous bifurcation theory. A generalized plasticity constitutive model and a Mohr–Coulomb model are used in both the theoretical and numerical analyses of shear band formations. The critical hardening moduli and shear band angle for localization are computed, and quantitative results are given for both constitutive models. Numerical results previously obtained and new ones are confirmed by this analytical and numerical investigation. Copyright © 2002 John Wiley & Sons, Ltd.     

基于线性互补的非连续变形分析

非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。     

Application of Numerical Method to Soil Mechanics

This is a summing-up report based on 48 papers on the applications of numerical method to soil mechanics. Recently, there is a new development of coupling of finite element with other numerical ones in soil mechanics. The dynamic numerical analyses have found further application to nonlinear stress-strain relationship, effective stress, and three dimensional problems. The suitable contact element or conjunct element could be used for contact conditions in finite element calculation. It is an important direction to combine usual numerical method with probabilistic method, which has been used in evaluations of consolidation effect, slope stability, dam, seepage, deformation calculation, interaction, and the performance analyses of pole and foundation.     

数值计算方法在土力学中的应用

本文是对48篇有关数值方法在土力学方面应用的论文进行综述的报告。近年来,在土力学方面有限元和其它数值方法的耦合有了新的发展,动力分析在非线性应力应变关系、三维问题和有效应力分析中得到了进一步的应用,接触单元或连接单元可用来处理有限元计算时的接触条件。数值方法和概率方法的结合是一个值得重视的发展方向。这些方法可应用于估计固结效应、土坡稳定、土石坝、渗流、变形计算、共同作用、桩和地基性状分析等方面。     

A simple three‐dimensional distinct element modeling of the mechanical behavior of bonded sands

This paper presents a simple three‐dimensional (3D) Distinct Element Method (DEM) for numerical simulation of the mechanical behavior of bonded sands. First, a series of micro‐mechanical tests on a pair of aluminum rods glued together by cement with different bond sizes were performed to obtain the contact mechanical responses of ideally bonded granular material. Second, a 3D bond contact model, which takes into account the influences of bond sizes, was established by extending the obtained 2D experimental results to 3D case. Then, a DEM incorporating the new contact model was employed to perform a set of drained triaxial compression tests on the DEM bonded specimens with different cement contents under different confining pressures. Finally, the mechanical behavior of the bonded specimens was compared with the available experimental results. The results show that the DEM incorporating the simple 3D bond contact model is able to capture the main mechanical behavior of bonded sands. The bonded specimen with higher cement content under lower confining pressure exhibits more pronounced strain softening and shear dilatancy. The peak and residual strengths, the apparent cohesion and peak/residual friction angles, and the position and slope of the critical state line increase with increase in cement content. Microscopically, bond breakage starts when the system starts to dilate and the maximum rate of bond breakage coincides with the maximum rate of dilation. Bond breakage is primarily due to tension‐shear failure and the percentage of such failures is independent of both confining pressure and cement content. Copyright © 2015 John Wiley & Sons, Ltd.     

黏性碎屑流坡面运动过程数值模拟与检验

由无黏粗颗粒与黏性泥浆组成的黏性碎屑流,其运动过程会产生不连续变形,基于连续介质假定的流体理论无法描述。根据散体材料理论,在考虑黏性泥浆影响情况下,以PFC3D为平台,编写黏性碎屑坡面运动数值模型试验程序,根据泥浆（成都黏土,密度1.413 g/cm3）室内拉伸试验和旋转剪切试验结果,设置数值模型参数,开展黏性碎屑流坡面运动数值模型试验,再现黏性碎屑坡面运动过程及运动过程中不连续变形现象,并通过同尺寸黏性碎屑坡面运动物理模型试验进行验证。结果表明：基于散体材料理论的PFC3D离散单元法能很好地再现黏性碎屑坡面运动过程及运动过程中不连续变形现象,为深入分析黏性泥浆介质影响下黏性碎屑坡面运动过程提供新的途径。     

黏性土固结不排水剪切的滑动损伤模型研究

在工程荷载范围内,不计骨架颗粒的变形,骨架的变形实际是颗粒接触面变形的总和。当剪应力达到某个临界值时,黏性土骨架中有一部分颗粒接触面开始滑动,随着剪应力的增大,出现滑动的颗粒接触面的取向范围也会扩大。将这种颗粒接触面的滑动视为一种损伤。在损伤阶段,黏性土骨架中既有未滑动的接触面,也有已滑动的接触面,宏观剪切模量是这两种接触面的剪切模量的加权平均。在 平面中,根据应力圆与颗粒起始滑动包络线的相对位置,计算出已出现了滑动的颗粒接触面的取向范围,并定义该取向范围与其所能达到的最大值（由破坏时的应力圆计算）之比为骨架的损伤比。按损伤比进行加权平均得到骨架的整体剪切模量。模型中的参数完全可以根据常规三轴试验确定,模型的形式简单,可适用于复杂的应力路径。对试验结果的拟合表明,该模型能较好地反映黏性土在固结不排水条件下剪切变形的主要特征。     

模拟摩擦接触问题的新型无网格数值方法

针对摩擦接触问题,给出一种新型的无网格数值方法。该方法基于单位分解思想,在标准无网格Galerkin法的位移模式中嵌入不连续函数和裂尖奇异函数,分别反映接触面的不连续性和接触面端点的奇异性;结合接触摩擦定律,继而构造出求解摩擦接触问题的无网格线性互补模型。在该方法中,接触面方程使用接触点对离散,全局离散系统方程则转化为标准的线性互补问题,可以很方便地使用Lemke算法求解。算例分析证明,本文方法的正确性和有效性。