Boundary Element based Discontinuous Deformation Analysis

Abstract

Summary A Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd.

Variational inequality‐based particle discontinuous deformation analysis

“…Over the past several decades, a great number of progresses have been made on DDA. These improvements are mostly concentrated on suppressing the false volume expansion, strengthening the deformability, scrutinizing the time integral scheme, refining the stress distribution, imposing the boundary conditions, fracturing the jointed rock mass, coupling the fluid and solid, accelerating the convergence of open‐close iteration, enhancing the contact search, optimizing the transformation of vertex‐vertex contact, and improving the calculation of contact force …”

“…Over the past several decades, a great number of progresses have been made on DDA. These improvements are mostly concentrated on suppressing the false volume expansion, [25][26][27][28][29][30][31][32] strengthening the deformability, [33][34][35][36][37][38][39] scrutinizing the time integral scheme, [40][41][42][43] refining the stress distribution, [44][45][46][47][48] imposing the boundary conditions, [49][50][51][52] fracturing the jointed rock mass, [53][54][55][56][57][58][59] coupling the fluid and solid, [60][61][62][63][64] accelerating the convergence of open-close iteration, 65,66 enhancing the contact search, [67][68][69][70][71][72]…”

Stability Analysis of Slope with Multiple Sliding Surfaces Based on Dynamic Strength‐Reduction DDA Method

“…Zheng et al [26] used the dual form of this method to solve the problem of opening and closing iterations and strong applied forces. Fu et al [27] combined the border element method with the DDA to achieve synchronous deformation modeling and displacement modeling. Fan et al [28,29] used virtual work theory to improve the accuracy of deformation and large rotation error estimation and proposed a new method to identify and analyze the contact blocks.…”

Damage to structures due to explosion by discontinuous boundary elements

“…This has been overcome by solving distribution of displacements and tractions within each particle in terms of the boundary element method, in which the lowest approximation of displacements and stresses is introduced: the uniform distribution of these variables along the boundary between adjacent elements, see (Procházka, 2019;Procházka, 2014;Procházka, 2004). Similar method was proposed in (Fu et al, 2017), where time dependent kernels were used.…”