Probabilistic seismic performance of masonry towers: General procedure and a simplified implementation

A procedure for the probabilistic assessment of the seismic performance of masonry towers is developed within the general PEER framework. The ingredients identified for the whole procedure are the Intensity Measure (IM), the mechanical model, the seismic procedure, the Engineering Demand Parameter (EDP), the uncertain mechanical parameters, and the probabilistic method. For each one, a choice suitable for masonry towers is proposed. A tower is modeled as a geometrically nonlinear Timoshenko beam with no-tensile and limited-compressive strengths. The reaching of the ultimate compressive strain is assumed as main failure criterion. Pushover analyses are carried out and a performance measure based on the seismic displacement capacity and demand is used as EDP. The conditional probability of exceedance of the EDP given the peak bedrock acceleration, used as IM, is computed through Monte Carlo simulations by considering as random variables the mechanical parameters representative of inertia, stiffness, strength, and ductility of the masonry. The calculations are then developed with reference to a case study. The dispersion of the displacement capacity is recognized as the main source of uncertainty. As to the mechanical parameters, the compressive strength and the strain ductility play the most critical roles, as also highlighted by a sensitivity analysis. These parameters are the most uncertain as destructive tests, usually not allowed in historical monumental buildings, would be required for their assessment. The effects of static load patterns for nonlinear static analysis and the comparison with incremental dynamic analysis are also briefly discussed.