2-D Orthotropic failure criteria for masonry

Abstract

The proposed phenomenological masonry failure criteria are intended for use in numerical calculations based on models where the masonry is considered as an orthotropic homogeneous material. The failure criteria are presented geometrically, in the form of a three-dimensional failure surface that defines the absolute values of the limit tangential stresses (τ as a function of the normal stresses which act perpendicularly (σn) and in parallel (σp) to the masonry mortar bed interface. The different limit relations between the principal stresses, which were determined experimentally by different authors, were used in determining the geometry of the failure surface. It is supposed that this surface is composed of 5 parts, which correspond to the failure modes depending on different combinations of the normal and tangential stresses in the masonry wall. These parts of the failure surface have the shape of planes, conical surfaces, and one part has the shape of a convexo-convex surface. One horizontal and three vertical sections, which are named for main vertical sections, are used for the construction of the failure surface of the masonry. The configuration of the horizontal section (τ=0) is taken in the form of the closed convex octagon. The main vertical sections are located along the coordinate axes and the bisector of the angle between them. The geometry of the failure surface is determined by means of three of its intersections by the use of the three vertical planes. These are termed as the principal sections. Two principal sections are located along the coordinate axes and the third one – along the bisector of the angle between them. The lines of intersection between the failure surface and the principal section planes have a cap model shape, comprising of two linear segments and a curvilinear segment which is a part of an elliptical arc. The initial data for constructing the failure surface are the strength properties of the masonry which are listed in the design norms of masonry structures, as well as some additional characteristics for which the empirical formulae are proposed. The failure criteria and the method of approximate determination of the initial data for the calculation are developed for masonry with solid masonry units (without cavities). Good correspondence was established between the proposed criteria and the experimental results.