A Monte Carlo-based methodology for the seismic vulnerability assessment of masonry structures

Introduction. Historical masonry buildings constitute a significant share of architectural heritage worldwide. Their massive elements and low tensile strength make them particularly vulnerable to seismic action, while the heterogeneity of their materials and construction techniques introduces substantial uncertainty into structural assessment. Evaluating their reliability under extraordinary loading events is therefore essential for heritage preservation, requiring methodologies able to capture this uncertainty.

Methods. A probability-based reliability framework is proposed to evaluate seismic damage in existing masonry structures. Geometric and mechanical data are incorporated into a 3D finite element model, with material properties characterized by log-normal distributions derived from in-situ testing. A Monte Carlo-type analysis samples random realizations of these properties, and structural reliability is quantified through a Damage Index representing the proportion of damaged volume. The methodology is applied to a historic masonry church in Granada (Spain), a seismically active region, subjected to a seismic action defined according to the national seismic code.

Results. The methodology accurately quantifies seismic vulnerability through a Damage Index that captures the probabilistic distribution of structural damage, identifying both the overall reliability of the structure and the relative contribution of each material parameter to its seismic performance. In the case-study church, the bell tower experiences substantially greater displacements and stresses than the main body, which behaves in a quasi-rigid manner; the overall Damage Index indicates the structure remains potentially resistant, despite localized stress concentrations at the tower-nave junction. Sensitivity analysis shows that damage correlates strongly with tensile strength and Young’s modulus, with negligible dependence on compressive strength, and that certain stiffness ranges cause resonance-driven amplification of the seismic response when the structure's fundamental frequency approaches that of the earthquake input.

Conclusions. The proposed Monte Carlo-based methodology provides a robust, uncertainty-aware tool for assessing seismic vulnerability in heritage masonry structures, supporting evidence-based conservation decisions.