Homogenised limit analysis of masonry walls, Part I: Failure surfaces

A simple micro-mechanical model for the homogenised limit analysis of in-plane loaded masonry is proposed. Assuming brickwork under plane stress condition and adopting a polynomial expansion for the 2D stress field, a linear optimisation problem is derived on the elementary cell in order to recover the homogenised failure surface of the brickwork. Different models of higher accuracy are obtained by increasing the degree of the polynomial approximation. Several cases of technical interest are treated in detail, varying both the geometrical characteristics of the cell and the mechanical properties of the components. The model is validated through comparisons with experimental data and kinematic approaches; the comparison with experimental data has the aim to reproduce in a qualitative way the shape of the failure surface, since 3D effects and brittle behaviour of bricks can not be taken into consideration with the model proposed.In an accompanying paper, the homogenised failure surfaces here obtained are implemented in a finite element limit analysis code and relevant structural examples are treated both with a lower and an upper bound approach.