On the Stability of Masonry Arches Through Limit Analysis and a Nonlinear Finite Element-Based Method

A comparison between limit analysis and a nonlinear finite element approach is proposed to assess the stability of masonry arches subjected to both vertical and horizontal loads. The limit analysis code discretizes the arch by means of infinitely resistant voussoirs and mortar joints reduced to interfaces. It is based on the lower bound theorem and is mathematically formulated using linear programming, where the objective function to maximize is the collapse multiplier, equality constraints are represented by equilibrium equations and inequalities rely on the material admissibility imposed on mortar joints. The finite element-based method discretizes the arch in a heterogeneous fashion, where voussoirs are meshed with classic four-node elastic elements in plane strain and joints are modelled by means of orthotropic shell elements coupled with elastic perfectly fragile cutoff bars. In this way the nonlinearities are handled adopting the simplest finite element available in any commercial software, and in particular the cutoff bars are displayed perpendicular with respect to the joint allowing the failure of the structure in mode I. To benchmark the proposed models, an arch of the main nave of the San Bassiano Church (Pizzighettone, northern Italy) is analyzed. After a deep analysis of the results obtained in terms of failure mechanism and global behavior, the efficacy and the robustness of both approaches proposed are assessed.