Numerical Simulations and Development of Relations for the Assessment of Ground Motion Amplifications Along the Flanks of 2D and 3D Hills

Earthquake engineers continually face challenges in how to implement ridge/hill amplification to transfer predicted peak horizontal acceleration (PHA) near the base using a ground motion prediction equation (GMPE) to the desired location on the ridge to compute the design forces. There are very few relations available for the prediction of 2D ridge amplification only, irrespective of geometry. This paper presents the development of relationships for the prediction of ridge amplification based on the numerically simulated seismic responses of the 2D triangular and elliptical and 3D conical and ellipsoidal ridge models for different shape ratios. The variation in ridge effects with the change of azimuth of a site on a hill is also considered in the development of relationships. The analysis of simulated results revealed very large amplitude and spectral amplifications as well as average spectral amplifications (ASA) in the case of 3D ridges as compared to the corresponding 2D ridges. An increase in ridge amplification with an increase in shape ratio is observed for both the 2D and 3D ridge models. An increase in the fundamental frequency of ridges with an increase in shape ratio is observed for a particular width. The analysis of snapshots of the seismic wave field reveals the need for computation of amplitude amplification and associated strain within the hill mass for a tunnel design. It is concluded that the estimated ridge amplification using earthquake records and standard spectral ratio method gives an overestimate due to the de-amplification at the reference station as well as a false fundamental frequency. The developed relations for the 2D and 3D ridges predict amplitude amplification as well as ASA for a particular value of normalised elevation and shape ratio. These relations can be conservatively used by the field earthquake engineer to predict the PHA at any location on a hill (taking into account the dimensionality and shape of the real hill mass), if the same is available at the base of that hill mass using a GMPE.