Stability analysis of underground space with discontinuous planes using a four-node iso-parametric element numerical manifold method with rigid body rotation

Abstract

In a large-scale rock structure with discontinuous planes in a rock mass, the pattern of the discontinuous planes strongly influences the deformation and stress distribution behaviors along the structure. A jointed rock mass, however, is generally assumed to be partially and imperfectly connected rather than completely discontinuous. Earlier the authors presented an elastic-plastic analysis of a discontinuous model of a jointed rock mass using a four-node iso-parametric manifold method (Sasaki and Ohnishi, 2001). The authors adapted Drucker-Prager’s elastic-plastic yield criterion, the Jaumann co-rotational derivative to determine the objectivity of stresses for rotation, and a rock-bolting element.In discontinuous models such as the original numerical manifold method (NMM), however, rigid rotation is not introduced in the degrees of freedom in the manner seen in the conventional finite element method (FEM). This paper describes the co-rotational formulation theory (Crisfield and Moita, 1996) introduced for a four-node iso-parametric NMM, along with examples of a model of rockfall activity in underground space. The results compare very well with the values obtained without a rigid body rotation analysis, especially those obtained for block shapes with large rotations.