Time-history analysis of slender masonry towers: a parametric study on the reliability of a simplified Bouc and Wen approach

The assessment of existing masonry structures under seismic loading requires reliable and expedite numerical modelling approaches. These approaches should take into account both the specific non-linear behaviour of the material (f.i. the small tensile strength) and, in case of time-history analysis, the hereditary nature of the restoring forces that describe the masonry mechanical behaviour. The paper, considering the need of simplified but effective methods to assess the seismic response of masonry towers, proposes an expeditious approach based on an equivalent Bouc and Wen model. The model, that has been extensively employed to describe a wide range of hysteretic behaviours like degradation of stiffness and strength, has the advantage of the computational simplicity since only one auxiliary non-linear differential equation is needed to describe the hysteretic behaviour. As a prototype of masonry towers, a cantilever masonry beam is analysed and the non-linear Bouc and Wen model is employed to reproduce the system hysteretic response assuming that the first mode shape governs the dynamic behaviour. A two-steps identification procedure is proposed. Static non-linear analyses are employed to assess a few of the Bouc and Wen model parameters; remaining ones are assessed in order to minimize the error between the estimated displacement and the one obtained in a reference finite element model of the structure. Within the paper, the identification of the parameters needed to build the single-degree-of-freedom oscillator is analysed in depth analysing the effects of four different seismic natural records. The results of the identification procedure show a general trend concerning the values to be selected for the Bouc and Wen parameters.