Seismic numerical analysis of an Inca stone wall in Sacsayhuaman using rigid body dynamics within a finite element framework

The study and conservation of the stone heritage is a global concern, mainly when the buildings are in seismic zones. Stone structures can be very simple or considerably complex, depending on their style and form of construction. A clear example is the Inca architecture in Peru, which has different and complex typologies due to its cultural diversity. Inca structures of remarkable heritage value are in Cusco, an area of active cortical faults that might produce a seismic event at any time. The main objective of this research is to contribute to the knowledge of the seismic vulnerability analysis of Inca's stone walls by using the dynamics of rigid bodies (within the finite element method) to evaluate the possible out-of-plane failure mechanisms. This methodology allows for reducing the high number of degrees of freedom usually considered when modelling an entire irregular large stone wall by other approaches, such as continuum models. A wall section from the archaeological site of Sacsayhuaman (Cusco, Peru) is analysed as a case study. Each stone is discretised and modelled as a rigid body, and the interaction among blocks is evaluated within a finite element numerical framework. The structure's predominant frequencies are evaluated using updated methods such as white noise and sinusoidal signals. Then, a non-linear dynamic analysis of the studied wall is performed considering three Peruvian seismic records. The analyses show that the structure could suffer significant damage and endanger its structural stability for cortical earthquakes with a Peak Ground Acceleration (PGA) greater than 0.2 g. Considering the historical significance of these structures, the analysis of Inca stone walls' seismic safety accounts for potential residual movements between individual stones.