In this paper, a procedure is developed for assessing the strength of brick masonry based on homogenization theory. The approach invokes a lower bound analysis whereby plastically admissible stress fields are constructed in the constituents involved, subject to periodic boundary conditions and static equilibrium requirements. The critical load is obtained by solving a constrained optimization problem. The analysis employs a set of specific loading histories such as axial tension, pure shear and biaxial tension-compression at different orientations of bed joints. The performance of this approach is verified against numerical solutions based on finite element analysis. In the second part of this paper, a methodology is outlined for identification of a macroscopic failure criterion that incorporates a critical plane approach. A quantitative verification of this criterion is carried out for different loading conditions and the results are compared with the experimental data available in the literature.

The paper examines three-dimensional (3D) analyses of the load bearing capacity of square and strip footings on a spatially variable cohesive-frictional (c-u) soil. Embedded, rigid and smooth footings are considered. Cohesion and friction angle are modelled using random fields. The vertical scale of fluctuation (SOF) is based on earlier studies of natural soils. For the square footing problem, the horizontal SOF is the subject of a parametric study. For the strip footing, only one value of the horizontal SOF is assumed, and the parametric study concerns the modelled length of the foundation. To generate the fields of strength parameters, the Fourier series method is employed. For both problems analyzed, the influence of the parameters on the probabilistic characteristics of the bearing capacity of the soil is investigated. For the square footing problem, both the mean value of bearing capacity and its coefficient of variation increase with an increasing horizontal fluctuation scale, but they stabilize at higher values of SOF. For the strip footing problem, it appears that 2D modelling is a very conservative approach, and for the precise assessment of the probability of foundation failure, the footing should be modelled in 3D. Keywords FLAC3D Á Random field Á Reliability index Á Scale of fluctuation List of symbols Roman a Lower bound of bounded interval b Upper bound of bounded interval CoV Coefficient of variation c Cohesion

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