Numerical analysis of block stone displacements in ancient masonry structures: A new method to estimate historic ground motions

An innovative approach is presented, in which the discontinuous deformation analysis (DDA) method is used to estimate historic ground motions by back analysis of unique structural failures in archaeological sites. Two archaeological sites in Israel are investigated using this new approach and results are presented in terms of displacement evolution of selected structural elements in the studied masonry structure. The response of the structure is studied up to the point of incipient failure, in a mechanism similar to the one observed in the field. Structural response is found to be very sensitive to dynamic parameters of the loading function such as amplitude and frequency. Prior to back analysis of case studies, two validations are presented. Both compare the performance of DDA with analytical solutions and present strong agreement between the two. Using comprehensive sensitivity analyses, the most likely peak ground acceleration (PGA) and frequency that must have driven the observed block displacements are found for the two case studies - the Nabatean city of Mamshit and the medieval fortress of Nimrod in southern and northern Israel, respectively. It is found that horizontal peak ground accelerations (HPGA) of 0.5g and 1g were required to generate the observed deformations in Mamshit and Nimrod, respectively. Although these might seem too high, considering structural and topographic amplifications it is concluded that the analyses suggest ground motions of 0.2g at a frequency of 1.5 Hz for Mamshit and up to 0.4g at a frequency of 1 Hz for Nimrod. These values provide constraints on the seismic risk associated with these regions as appears in the local building code using a completely independent approach.