Fragility curves for masonry structures submitted to permanent ground displacements and earthquakes

Usually, the vulnerability of structures is treated considering only one single hazard, for example either seismic hazard or ground instability. However, historical monuments, cultural heritage structures or old masonry structures can be affected, over the past centuries of existence, by a succession of different hazards. The objective of this paper was to quantify the changes in the seismic vulnerability of a given structure previously damaged by quasi-static differential settlements. In view of this, a soil-structure model of the masonry building is constructed using TREMURI software by putting springs at the base of the building to account for the soil behaviour. Classical empirical relationships are used for setting the mechanical properties of these foundation springs. The chosen equations are valid for both static and dynamic situations. The soil-structure model is first submitted to differential settlements with maximum magnitudes ranging from 5 to 25 cm. Then, the damaged structures are submitted to a set of time-histories. Fragility curves taking into consideration permanent differential settlements are finally obtained, using a modified regression technique accounting for the presence of residual drift due to the prior static loading.