Deriving amplification factors from simple site parameters using generalized regression neural networks: implications for relevant site proxies

Abstract

Abstract Most modern seismic codes account for site effects using an amplification factor (AF) that modifies the rock acceleration response spectra in relation to a “site condition proxy,” i.e., a parameter related to the velocity profile at the site under consideration. Therefore, for practical purposes, it is interesting to identify the site parameters that best control the frequency-dependent shape of the AF. The goal of the present study is to provide a quantitative assessment of the performance of various site condition proxies to predict the main AF features, including the often used short- and mid-period amplification factors, $$F_{a}$$ F a and $$F_{v}$$ F v , proposed by Borcherdt (in Earthq Spectra 10:617–653, 1994). In this context, the linear, viscoelastic responses of a set of 858 actual soil columns from Japan, the USA, and Europe are computed for a set of 14 real accelerograms with varying frequency contents. The correlation between the corresponding site-specific average amplification factors and several site proxies (considered alone or as multiple combinations) is analyzed using the generalized regression neural network (GRNN). The performance of each site proxy combination is assessed through the variance reduction with respect to the initial amplification factor variability of the 858 profiles. Both the whole period range and specific short- and mid-period ranges associated with the Borcherdt factors $$F_{a}$$ F a and $$F_{v}$$ F v are considered. The actual amplification factor of an arbitrary soil profile is found to be satisfactorily approximated with a limited number of site proxies (4–6). As the usual code practice implies a lower number of site proxies (generally one, sometimes two), a sensitivity analysis is conducted to identify the “best performing” site parameters. The best one is the overall velocity contrast between underlying bedrock and minimum velocity in the soil column. Because these are the most difficult and expensive parameters to measure, especially for thick deposits, other more convenient parameters are preferred, especially the couple $$\left( {V_{{{\text{s}}30}} ,f_{0} } \right)$$ V s 30 , f 0 that leads to a variance reduction in at least 60%. From a code perspective, equations and plots are provided describing the dependence of the short- and mid-period amplification factors $$F_{a}$$ F a and $$F_{v}$$ F v on these two parameters. The robustness of the results is analyzed by performing a similar analysis for two alternative sets of velocity profiles, for which the bedrock velocity is constrained to have the same value for all velocity profiles, which is not the case in the original set. Graphical abstract Performance of various site proxies (velocity contrast C v , fundamental frequency f 0, harmonic velocity average over the top 30 m V S30, total sediment thickness Depth, average corresponding velocity V Sm) to predict the short-period (top, F a ) and mid-period (bottom, F v ) amplification factors. Proxies may be considered alone, or in combination with several other proxies.

Keywords

• 1D linear site response
• Site proxies
• Amplification factors
• Neural network