Estimating Mean and Variance of In-Plane Resistance of Masonry Walls Using Inaccurate Design-Code Models and Limited High-Fidelity Data

Analyzing uncertainty or estimating statistics of load resistance of structures is crucial for reliability-based code calibrations, forming the foundation for modern limit state design. While design-code models can be used to estimate the load resistance of masonry walls against in-plane (IP) loading, it is widely recognized that these models are inherently inaccurate due to their simplifications, assumptions, or empirical features. Therefore, employing them for uncertainty analysis or statistics estimation can be challenging. On the other hand, detailed mechanics-based finite-element (FE) models and physical experimental tests are typically more accurate. Nevertheless, their application for uncertainty analysis or statistic estimation is often impractical due to their high computational or economic cost. To address this challenge, this study introduces improved estimators for mean and variance of the IP resistance of masonry walls after considering parameter uncertainties, by leveraging efficient design-code models and limited high-fidelity data generated from detailed FE models. In the proposed estimators, a large number of design-code model evaluations are introduced to improve computational efficiency, while only a limited number of FE model evaluations are integrated to ensure accuracy. Three case studies are presented to illustrate the applicability of the proposed estimators: one on unreinforced masonry (URM) walls and two on reinforced masonry (RM) walls. The results indicate that design-code model-based estimators exhibit large bias, and compared to the estimators that solely rely on the FE model, the proposed estimators achieve higher accuracy given the same computational budget.