A Genetic Algorithm adaptive homogeneous approach for evaluating settlement-induced cracks in masonry walls

This paper presents a Genetic Algorithm adaptive homogeneous approach aiming at representing the crack patterns induced by ground settlements on masonry walls. This type of damage is a critical issue since it affects all masonry buildings, including those that are not located in seismic-prone areas. The GA-adaptive homogeneous approach here proposed is meant as a tool that overcomes the usual high computational costs requested by the traditional heterogeneous and homogeneous approaches. Here, the considered masonry wall is discretized into a low number of 2D polygonal elements; its displacement field is then determined through a linear programming problem. The actual position of cracks induced by the applied settlement is identified by modifying the initial mesh through an iterative mesh adaptation procedure performed with a Genetic Algorithm (GA); the iterations are carried on until the absolute minimum of the work performed by the reaction forces is attained. In this way, the computational effort needed for identifying the actual crack patterns is dramatically decreased due to the very few unknowns of the problem. The reliability of the GA-adaptive homogeneous approach here proposed is validated against selected benchmarks that come from experimental and numerical results, and is also compared with the traditional heterogeneous and homogeneous approaches. In all the three benchmarks, the GA-adaptive approach offers a satisfying computational efficiency and identifies the actual crack patterns with good accuracy, despite the low number of elements employed in the discretization of the masonry wall. This may pave the way for a broader use of this approach in the analysis of complex masonry structures affected by settlement-induced damages.