Analysis of the Effective Compliance. Homogenization analysis of multi joint set problem by the Stress Compensation-Displacement Discontinuity Method(SC-DDM). (2nd Report).

Theory and practice for the effective compliance analysis are presented and discussed, along with successful case examples, in order to make clear that the Stress Compensation-Displacement Discontinuity Method (SC-DDM) is an useful tool available for the homogenization problem of multi joint sets.The fundamental concept of the homogenization of joint sets and the SC-DDM, proposed in the previous paper, are firstly summarized, and it is shown that an infinite structure of rock mass is homogenized using a unit cell which is a representative structure of microscopic, and that the macroscopic characteristics is able to be defined and analyzed using the fundamental response of the unit cell computed numerically by the Displacement Discontinuity Method. Subsequently the stress compensation scheme available for the analysis of the effective compliance is proposed, showing successful case studies using a latticed model and an alternative model of a single open joint set. It is shown how the restrict stress acting on the unit cell can be removed to compensate the boundary stress condition required, and how the macroscopic strain of the unit cell can be computed from the displacement distribution on the sides of a representative unit cell. Additionally, the relation between the joint density and the effective compliance is discussed, comparing with the approximation by a parallel pillar model.