Empirical predictive model for the vmax/amax ratio of strong ground motions using genetic programming

Earthquake-induced deformation of structures is strongly influenced by the frequency content of input motion. Nevertheless, state-of-the-practice studies commonly use the intensity measures such as peak ground acceleration (PGA), which are not frequency dependent. The vmax/amax ratio of strong ground motions can be used in seismic hazard studies as a parameter that captures the influence of frequency content. In the present study, genetic programming (GP) is employed to develop a new empirical predictive equation for the vmax/amax ratio of the shallow crustal strong ground motions recorded at free field sites. The proposed model is a function of earthquake magnitude, closest distance from source to site (Rclstd), faulting mechanism, and average shear wave velocity over the top 30 m of site (Vs30). A wide-ranging database of strong ground motion released by Pacific Earthquake Engineering Research Center (PEER) was utilized. It is demonstrated that residuals of the final equation show insignificant bias against the variations of the predictive parameters. The results indicate that vmax/amax increases through increasing earthquake magnitude and source-to-site distance while magnitude dependency is considerably more than distance dependency. In addition, the proposed model predicts higher vmax/amax ratio at softer sites that possess higher fundamental periods. Consequently, as an instance for the application of the proposed model, its reasonable performance in liquefaction potential assessment of sands and silty sands is presented.