Probabilistic Calibration of Unreinforced Masonry Wall Properties: From Constitutive Material Models to Structural Performance

Abstract

Unreinforced masonry walls are structural elements consisting of brick units and mortar layers, which show brittle and nonlinear inelastic response with regards to their mechanical behavior. Brick and mortar components show large variations in their mechanical responses, which are attributed to variabilities in the processing conditions, compositions and types of constituents, and testing methods. The mechanical responses of brick and mortar ‘components’ strongly influence the performance and load bearing capabilities of masonry walls thought as ‘systems’. Thus, developing appropriate constitutive models and calibration of material parameters in the constitutive models are important tasks for scientists in order to generate accurate model-based predictions. Determining material parameters of a constitutive model for a nonlinear inelastic response, while being a key factor to predict its mechanical response, is a tedious task. This difficulty is due to the limited experimental tests that can be performed. Thus, a proper determination of these material parameters is necessary to improve the predictions of the overall response of masonry walls. A Bayesian probabilistic calibration is conducted to investigate the effects of the uncertainty of concrete damage plasticity model parameters in masonry wall components, i.e., brick, mortar, and concrete. For this purpose, experimental tests are simulated using finite element method (FEM) and their responses are integrated to the probabilistic calibration algorithm. Markov Chain Monte-Carlo and Metropolis-Hastings algorithms are used to integrate the material parameters using random variables. A Neural Network Optimization algorithm is proposed to identify and characterize the material parameters for describing the mechanical response of unreinforced masonry walls. Unreinforced masonry wall models are validated using the optimal material parameters that provide the best fitting between the simulation results of a masonry prism and the corresponding experimental data taken from the literature. From the tangential shear stress and normal stress distributions between brick units and mortar layers during lateral loading and vertical compression stress, potential failure modes along with their failure criteria are determined. The influence of vertical compressive stress, length-to-height “aspect ratio”, and material parametric sensitivity (e.g., flexural tensile strength, compressive strength, coefficient of friction and cohesion stress) is investigated.