Accounting for ground motion directionality and building orientations in urban seismic risk analysis

Regional seismic risk analysis methods are used to estimate the loss of a group of buildings subjected to earthquakes. Buildings usually have two perpendicular horizontal principal orientations, which tend to be similar among buildings within the same city due to the grid-like nature of street layouts. Current regional seismic risk analysis methods do not consider these building orientations to estimate losses because they usually consider orientation-independent measures of horizontal ground motion intensity. However, horizontal ground motions present directionality, meaning that their intensities vary with horizontal orientation. Thus, the response of a building depends on its orientation relative to the orientation of the ground motion. This work studies the effect of building orientations and ground motion directionality on groups of buildings within a city. A testbed group of buildings subjected to an example earthquake is used to estimate losses in terms of the aggregate repair cost of the buildings. The variance of these output losses is shown to be maximized when all buildings share the same principal orientations and minimized when these orientations are fully randomized. A variance-based sensitivity analysis is then performed to compare the contribution to the output variance of ground motion directionality with that of some other sources of uncertainty usually considered in regional seismic risk analyses. When buildings share the same principal orientations and the median ground motion intensities from all orientations are fixed, ground motion directionality is found to be an important source of uncertainty, and its importance increases as more buildings are considered in the analysis. These results suggest that considering ground motion directionality and building orientations could be important for future urban seismic risk analyses and that, under the same seismic hazard, the seismic risk of cities with regular orthogonal street arrangements is larger than that of cities with more irregular street layouts.