Reliability Design of a New Masonry Bridge: An Approach Based on RBDO and Rigid Block Analysis

The objective of this study is to establish a reliability-based design framework for new masonry arch bridges, providing a rational alternative to the empirical rules that traditionally governed their construction. The proposed methodology integrates Reliability-Based Design Optimization (RBDO) with the rigid block limit analysis method to optimize key geometric parameters under uncertain loading conditions. The probabilistic formulation incorporates the variability of geometric and load parameters, which are identified as the dominant sources of uncertainty during the design phase of new masonry bridges. Two RBDO strategies are employed: the Performance Measure Approach (PMA) and Sequential Optimization with Reliability Assessment (SORA), both coupled with a linear programming formulation of equilibrium and yield constraints. The approach is applied to the reconstruction of the historical Dar El Makina bridge in Fes, Morocco, to determine the optimal geometric configuration that satisfies target reliability requirements. The results indicate that the optimized design achieves a 27% reduction in arch thickness and a 13% increase in rise compared to the existing structure, leading to a safer and more material-efficient configuration. Compared with classical empirical formulas, the proposed approach provides a rational and quantitative basis for the design of masonry bridges, combining structural safety, material efficiency, and heritage preservation.