Validation of dynamic block displacement analysis and modification of edge-to-edge contact constraints in 3-D DDA

Abstract

The validity of three-dimensional discontinuous deformation analysis (3-D DDA) is examined by comparing its solution for dynamic block displacement with an analytical solution. Displacement of a single block on inclined planes subjected to dynamic loadings is studied for analytical solutions derived with respect to the frictional resistance offered by the planes. 3-D DDA predicts accurately the analytical displacements, and the results were found sensitive to the maximum displacement ratio, and the size of the time step, which are defined by the user. Best results were achieved when the actual displacements were approximately equal to the assumed maximum displacements per time step. Furthermore, edge-to-edge contact constraints have been improved by using the augmented Lagrangian method instead of the penalty method. Using the augmented Lagrangian method to enforce contact restraints retains the simplicity of the penalty method, and reduces its disadvantages. The new formulation of edge-to-edge contact using the augmented Lagrangian method is implemented in 3-D DDA and has been programmed in VC++. Finally two illustrative examples are presented for demonstrating this new approach. Crown Copyright © 2008.