Impact of mechanical properties of historical masonry bridges on fundamental vibration frequency

The fundamental frequency of a historical monument like a masonry bridge or any other structure provides a better and detailed seismic assessment of its demand to provide protection against unexpected seismic ground motion. On this basis, this paper aims to develop an empirical formulation to fit the ambient vibration frequency of historical masonry bridges using a nonlinear regression model. For this purpose, data series were collected from the literature especially focused on both ambient vibration measurement and finite element models of historical masonry bridges modeled on a full scale to get the first global natural frequency. The first approach is to forecast the natural vibration frequency by using only physical characteristics of the historical masonry bridges obtained from the literature-based experimental ambient vibration frequency data. The second approach consists of forecasting the first natural vibration frequency considering the unit weight and elasticity modulus of the dominant construction material based on the homogenization approach. In addition to mechanical characteristics, physical properties of historical masonry bridges were used, such as the length, height, width, and Main Arch Span (MAS) length of the masonry bridge, to predict the first natural vibration frequency. Among the proposed equations, a maximum accuracy of 58% was reached with the literature-based experimental approach. Moreover, an empirical formulation with 81% accuracy was proposed by using both physical characteristics and mechanical properties of the bridges on the basis of finite element model results. Also, this study highlights that this accuracy decreases to 35% if the modulus of elasticity and unit weight are ignored. In addition, the developed formulations are compared with other empirical formulations using the Mean Square Error (MSE), as a measure of the average of the squares of the errors. Consequently, the smallest MSE value of 1.95 was obtained with the proposed equation, whose accuracy was 81% in this study.