Elastic–plastic discontinuous deformation analysis using Mohr–Coulomb model

The original (i.e. first order) discontinuous deformation analysis (DDA) formulation has two main shortcomings. First, a linear function is used to represent the displacement field in the blocks. This formulation implies that the state of stress (and strain) within each block is constant. Second, the material within each block is assumed as linear elastic. These two major limitations can often render the original DDA analysis method unrealistic and significantly inaccurate. In the modified DDA approach introduced in this study, these two limitations have been addressed. The authors have used the finite element method (FEM) to discretise each block in the DDA formulation using an automatic mesh generation algorithm to determine the distributions of stress and strain within each block to a desired accuracy. In addition, the Mohr–Coulomb elastic–plastic yield criterion is incorporated within the modified DDA analysis method using a time marching algorithm to account for the possibility of material failure. This allows the plastic behaviour (i.e. yielding) of the material within each block be included in the analysis, which is a significant improvement over the original DDA method. The numerical implementation of the Mohr–Coulomb criterion involves trials using initial elastic stress increment and comparisons with the yield criterion within each element. The proposed DDA formulation including the Mohr–Coulomb failure criterion (termed here as the MC-DDA method) is validated against selected analytical solutions, numerical solutions from FLAC verification problems and field measurements.