The joint polygons and block systems are three-dimensional. Most of joints are not perpendicular to a given two dimensional cross section. Therefore, the two-dimensional computations of jointed rocks or block systems are of limited reliability and accuracy. The three-dimensional analyses of block systems are important. Three-dimensional discontinuous deformation analysis (3-D DDA) forms blocks directly from general polygons and The blocks can be convex or concave. Also, the blocks can have any numbers of polygonal faces.

The 3-D DDA program computes three-dimensional deformable block systems. In the current version, there are 12 degrees of freedom per block: displacements on X, Y, Z directions, rotations around axis X, Y, Z and six 3-D strains. The block displacements are complete linear functions of the coordinates. Each block is assumed to have constant stresses and strains.

The discontinuous contacts between 3-D blocks are the main part of 3-D DDA algorithms. There are more ways for blocks to contact in three-dimensions compared with two-dimensional block contacts. For the friction law, the two-dimensional sliding directions form a line, while the three-dimensional sliding directions form a plane. This paper present the 3-D block matrices such as mass matrix, stiffness matrix, point load matrix, body load matrix, initial stress matrix and fixed point matrix.

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