Abstract

The non-linear analysis of historic masonry structures can be difficult to perform due to the highly irregular geometric features, the inherent variability within the materials, as well as the limited amount of experimental data available. The present work details a specific methodology and result for the analysis of the compressive strength of the masonry found in walls of St. Ann’s Church in the Czech Republic. A multi-scale 2D finite element modelling approach was adopted. In a mesoscale-level representation of masonry, “small stones” were grouped in with the mortar and treated as a matrix component with homogenized properties, while large stones were treated as discrete inhomogeneities. To characterize this matrix component, microscale-level models were used, in which only the “small stones” and mortar were represented. By simulating uniaxial compression and tension tests on multiple microscalelevel models, statistical distributions for compressive and tensile strength, stiffness, and fracture energy were determined. On the mesoscale-level, overall stiffness and compressive strength were determined by simulating uniaxial compression tests on models involving only the large stones embedded in the homogenized matrix. The matrix was considered either as spatially uniform or variable. In the latter case, it was modeled with random fields based on the properties’ distributions obtained from the micro-scale model analyses. Furthermore, the multi-scale study was performed for two different threshold sizes defining the “small stones” to compare differences. Approximate qualitative methods were utilized to validate the results. Overall, decreasing compressive strength was observed from the plain mortar to the microscale model of mortar with “small stones” to the meso-scale model of masonry. Models where matrix variability was represented with random fields exhibited similar failure mechanisms but with strengths 5-6% lower than models with a uniform matrix. Therefore, the effect of the spatial variability of the matrix properties was deemed insignificant.