Contents lists available at ScienceDirect International Journal of Rock Mechanics and Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms Probabilistic performance-based approaches to the static and seismic assessment of rock cavities Filomena de Silva a,b, ⁎ , Anna Scotto di Santolo a a Università Telematica Pegaso, Italy b Università degli Studi di Napoli Federico II, Italy ARTICLEINFO Keywords: Rock cavity Performance-based seismic assessment Modal analysis 3-D numerical analysis Resilience ABSTRACT Thispaperdemonstratestheapplicabilityofaprobabilisticperformance-basedapproachtoassessthestabilityof rock cavities under gravity and seismic loads, with reference to the case study of a Neapolitan room and pillar cave,locatedinsidearockyhill.Anadvanced3Dmodelwasgenerated,importinginthenumericalcodethedata acquiredduringalaserscanning-basedgeometricalsurvey.Thecarefulreproductionoftheon-sitegeometrywas found to improve the reliability of the results of static and dynamic analyses; because (i) the load eccentricity induced by the irregular shape of the hill reduces the stability of pillars, (ii) the localization of the roof crack dependsontheshapeoftheceiling,and,furthermore,(iii)theglobaldynamicbehaviourofthehillisafectedby topographic efects. The safety factors of rooms and pillars computed after the seismic analyses were compared to their values before earthquake to highlight earthquake-induced modifcations of the static equilibrium under gravity loads. Some considerations on the resilience of the cavity are reported based on the latter comparison. 1. Introduction Rock hills and shallow rock layers are usually crossed by complex systems of cavities resulting from the past quarrying activity. With the passing of time, the shape of the caves was transformed by natural events and their function was modifed by human actions into necro- polises, cemeteries, houses, or aqueducts. 1 Due to their resilience, some of them are preserved as world heritage sites; some of the most famous examples are the necropolis of Cerveteri and Tarquinia near Rome, the aqueduct below the Sassi of Matera in the south of Italy, the city of Petra in Giordania, the Hypogeum in Malta, the Cappadocia Region in Turkey, and so on. The increasing interest of tourists highlights the urgency to evaluate the static and seismic safety of cavities to ensure their preservation and safe fruition. Guessing the behaviour under gravity and dynamic loads becomes difcult because of irregular geo- metry, history of loads and spatial variability of rock stifness, stress and strength. The most widespread approach was conceived for room-and-pillar in coal mines and is based on the separate assessment of pillar and roof stability. A huge number of papers have been published on the esti- mation of the bearing capacity of a single pillar under vertical load through empirically-based 2 or analytical formulas 3 validated on nu- merical analyses that include the efect of overburden stifness 4 or rock discontinuity. 5 Suchowerska et al. 6 have provided successful comparisons between empirical, analytical and numerical methods predicting the roof stability of a rectangular room. Limit equilibrium and limit analyses have been proposed to individuate the ultimate conditions of rectangular 7–9 or circular 10 rooms under gravity loads. Accurate fnite elements, fnite diference and distinct element analyses have been performed on static condition of some case studies, as the man-made caves cut in the weak sandstone in Nottingham, 11 the an- cient caverns of the Bet-Guvrin National Park in Israel, 12 the coal mines in USA, 13 the Sandaozhuang molybdenum mine in China. 14 Mostofthestudiesonthestabilityofcavitiesunderdynamicactions concerntheefectsinducedbyvibrationmachinesorblasting. 14,15 With reference to earthquake, the modifcation of the seismic ground motion induced by the presence of underground cavities in a linear homo- geneous soil was widely analysed through pioneering solutions 16,17 and more recent theoretical approaches 18 as well as numerical investiga- tions. 19–23 All the referenced studies focus on the amplifcation of the seismic hazard due to the presence of cavities and neglect the seismic vulnerability of the cavity itself. Only few seismic response analyses of specifc case studies are integrated with evaluations on the stability under seismic actions. 24,250 In the analyses of case studies under gravity or seismic loads, the shape of the cave is generally fattened (rendered smoother) and the overburden is assumed to be uniform, due to the lack of an accurate geometrical survey. Such approximation reduces the reliability of https://doi.org/10.1016/j.ijrmms.2018.10.028 Received 28 May 2018; Received in revised form 15 October 2018; Accepted 19 October 2018 ⁎ Corresponding author. E-mail address: flomena.desilva@unina.it (F. de Silva). International Journal of Rock Mechanics and Mining Sciences 112 (2018) 354–368 1365-1609/ © 2018 Elsevier Ltd. All rights reserved. T