ABSTRACT

ABSTRACT: The method was developed to compute stress, strain, sliding and opening of rock blocks; rigid body movement and deformation occur simultaneously. Input data consist of block geometry loading forces, the deformability constants E and v, and the restraint or boundary conditions of the block system. Output data give the movements, deformations, stresses and strains of each block, and the sliding, and detachment or rejoining of blocks. The forces acting on each block, from external loading or contact with other blocks, satisfy the equilibrium equations. Equilibrium is also achieved between external forces and the block stresses. Furthermore, this analysis fulfills constraints of no tension between blocks and no penetration of one block into another. In addition to rock block systems, this same model can be used for other block structures. Examples are masonry walls and arches, multilithic gravity dams, and even crustal plates.

1 Introduction

The numerical model considers both statics and dynamics. For dynamic problems, an implicit algorithm is used and the graphic output shows the time-ordered process of deformation and failure. For statics, the loading increments are applied and the graphic output shows block movements and block deformations after each loading increment. The discontinuous deformation analysis method parallels finite element method. It solves a finite element type of mesh where all the elements are real isolated blocks, bounded by preexisting discontinuities. However it is more general. Whereas, the elements or blocks used by the DDA method can be of any convex or concave shape or even multi-connected polygons with holes. Furthermore, in the DDA method, when blocks are in contact, Coulomb's law applies to the contact interface, and the simultaneous equilibrium equations are selected and solved for each loading or time increment. In the case of the finite element method, the number of unknowns is the sum of the degrees of freedoms of all nodes. In the case of the DDA method the number of unknowns is the sum of the degrees of freedoms of all the blocks.

2 Variables of Block Deformations

Assuming each block has constant stresses and constant strains throughout, the displacement (u,v) of any point (x,y) of a block can be represented by six displacement Variables. (available in full paper)

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