Modelling Of Response Spectral Amplification Ratios From Slope Topography

In general, earthquake ground motion consists of source, path and site effects. The site effect has a remarkable influence on the strong ground motion, as demonstrated by many researchers, including field observation, theoretical analysis, and physical experiments. Among all the site effects, topography effect has been recognized as a significant type and the slope effect has been considered to be important. However, a large number of studies on the effect of slope provide amplification ratios in the frequency domain and these results cannot be used for engineering design. In This study, therefore, attempts were made to evaluate the topographic effects of slope on strong ground motion, and to drive a set of predictive equations for response spectral amplification ratios by using numerical simulations and statistical analyses. The models derived in the present study can then be used to modify the spectrum for a flat rock site to obtain the design spectrum at a given location on the slope for engineering designs.1) 80 numerical models for slopes with different model parameters and the corresponding one-dimension free-field models were established.2) The models were subjected to a strong-motion record from a rock site, and the ground motions at several locations of each slope model and the corresponding free-field models were computed.3) The transfer function between the ground motion from each observation point and the input ground motion was derived in the frequency domain by Fourier transform.4) Using the transfer functions derived in the last step, the strong-motion in the time domain at each observation point on the slope model can be computed for a large number of rock site strong-motion records. This approach enhanced the computing efficiency greatly.5) Response spectral amplification ratios between the computed ground motions on the slope and the corresponding free-field motion were calculated.6) A relatively simple empirical model with only four model parameters:the height of the slope, the angle of the slope, the distance from the slope edge and the shear-wave velocity of the slope materials (hard soil and rock) was established by using a systematic statistical analysis and a random effects methodology.Residual analyses were used intensively to select model parameters and to test the statistical significance of each model parameter. Residuals were separated into within-model and between-model parts. The within-model residuals are from the frequency contents of the rock site motions and the between-model residuals are from the imprecision of the simple empirical model using four parameters to describe the amplification ratios. The distributions of the two types of residuals from the final model is unbiased with respect to all model parameters in a linear scale, e.g. the slope of the straight line fitted to the residuals is zero. Results show that the standard deviations for both types of residuals are generally small and the earthquake parameters have effect mainly in short spectral periods.Two examples demonstrate that the reflected waves from the lateral energy absorption boundary may affect the estimated response spectral amplification ratios but the level of error should be acceptable in the ground-motion modeling. The final model should capture the first order effect in the response of slopes within the limit of selected model parameters.