New formulation and validation of the three-dimensional extension of a static relaxation method

This paper presents the new formulation and validation of three-dimensional extension of a static relaxation method for modeling large displacement of jointed rock masses. By relating the contact forces with the relative displacements on the contact interface of two contacting blocks, the 6×6 stiffness matrix of the relaxed block is derived, and the equilibrium equations may then be set up. Because large displacements come from the accumulation of small displacement increments, an iteration procedure is adopted in the calculation. Within each iteration cycle, one-by-one relaxation consequence is capitalized on. The C++ computer program developed by the authors previously is updated based on the current algorithm, and two illustrative examples are computed to verify the new formulation and to demonstrate the ability of the three-dimensional model.