Lower bound limit analysis of unreinforced masonry shear walls

This paper describes a new technique for computing the lower bound limit loads in unreinforced masonry shear walls under conditions of plane strain. From a macroscopic point of view, masonry displays similar behaviour to jointed rock or reinforced earth, which have already been successfully modelled using the lower bound theorem. The overall behaviour of the masonry shear wall is controlled by the mechanical properties of the intact unit (brick/block) and the discontinuities or joints, as well as the relative positions and orientation of the joint sets. As a result, masonry needs to be treated as an anisotropic, inhomogeneous material. In order to make use of the lower bound theorem of classical plasticity, two basic assumptions have to be made. Firstly, the material exhibits perfect plasticity, and obeys an associated flow rule without strain hardening or softening. Secondly, the body is assumed to undergo only small deformation at the limit load, and so the geometric description of the body at collapse remains unchanged. Both of these assumptions are reasonable in the case of unreinforced masonry shear walls. In the present paper, the yield surfaces of the intact brick units and of the head and bed joints are expressed separately. By using a Mohr-Coulomb approximation of the yield surfaces, the proposed numerical procedure computes a statically admissible stress field via linear programming and finite elements. The stress field is modelled using linear three-noded triangular elements and allowing statically admissible stress discontinuities at the edges of each triangle. By imposing equilibrium, yield criterion and stress boundary conditions, an expression of the collapse load is formed, which can be maximized subject to a large number of linear constraints on the nodal stresses. Because all the requirements are met for a statically admissible stress field, the solution obtained is a rigorous lower bound on the actual collapse load. The numerical solutions obtained from the lower bound formulation are compared with available experimental and finite element results from the literature. The lower bound approach developed in the present paper is shown to give good approximations to the ultimate collapse load for the two examples presented. (C) 2001 Elsevier Science Ltd. All rights reserved.