As historic monuments become more vulnerable to seismic hazard with time, it becomes essential to be able to assess the seismic hazard in a quantifiable manner. For soft soil foundations, a computer program such as SHAKE may be utilized. For stiff rocks comprised of layers and joints a discontinuous approach must be utilized. This approach can be extended to masonry structures, so as to find by means of numerical analysis the peak ground acceleration and frequency at which the historic monument is most vulnerable and to predict the anticipated failure modes. The numerical, discrete element discontinuous deformation analysis (DDA) method is used here for this purpose. We begin by demonstrating DDA's ability to model wave propagation through layered media using a theoretical example and a real case study. We proceed with comparing between thermally and seismically induced irreversible block displacements in jointed rock slopes at the foundation of Masada world heritage site, and finally we present two case studies of masonry structures in Israel that are prone to seismically induced deterioration due to their proximity to the active Dead Sea rift.


We model here the vulnerability of historic monuments in rocks to earthquake hazards using the numerical, discrete element, discontinuous deformation analysis (DDA) method (Shi 1993). The basic principles of DDA are relatively well known and will not be reviewed here, for the sake of brevity. Interested readers are referred to review papers and text books that describe the theory, its verification, and application (Jing & Stephansson 2007, Jing 1998, Jing 2003, Yagoda Biran & Hatzor 2016, Ohnishi et al. 2006). To demonstrate the applicability of DDA for modeling wave propagation through discontinuous media we shall begin with checking the accuracy of DDA in modeling P and S wave propagation in an elastic bar and a stack of layers, respectively. We shall check the ability of DDA to compute accurately two-dimensional site response in masonry structures by comparing between DDA and a field scale site response study performed on a historic multi-drum column founded on stiff rock foundation. We will demonstrate the applicability of the approach in historic monuments that are prone to seismically induced damage due to their proximity to the active Dead Sea rift:

  1. the rock slopes of Masada world heritage site, and

  2. Byzantine period cathedrals in Mamshit and Susita, located in the southern and northern segments of the Dead Sea rift.

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