Non-linear modulation of site response: Sensitivity to various surface ground-motion intensity measures and site-condition proxies using a neural network approach

The impact of non-linear soil behavior on site response may be described by the non-linear to linear site response ratio RSRNL introduced in Regnier et al. (2013). This ratio most often exhibits a typical shape with an amplitude above one below a site-specific frequency f(NL), and an amplitude below one beyond f(NL). This paper presents an investigation of the correlation between this RSRNL ratio and various parameters used to characterize the site (Site Condition Proxies: SCPs) and the seismic loading level (Ground Motion Intensity Measures: GMIMs). The data used in this analysis come from sites of the Japanese Kiban-Kyoshin (KiK-net) network, for which the nonlinear to linear site-response ratio (RSRNL) is obtained by comparing the surface/down-hole Fourier spectral ratio for strong events and for weak events. The five SCPs are Vs30, the minimum velocity of the soil profile(Vs(m)(in)), an index of the velocity gradient over the top 30 m (B-30), the fundamental frequency f(OHv), as measured from the H/V earthquake ratio, and the corresponding amplitude Amw. The seven GMIMs are PGA, PGV, PGV/V-s30 (peak strain proxy), I-A (Arias Intensity), CAV (Cumulative Absolute Velocity), a(rms), (Root Mean Square Acceleration) and Trifunac-Brady Duration (D-T). The original data set consists of a total of 2927 RSRNL derived from KiK-net recordings at 132 sites. To assign an equal weight to each site, and to avoid any bias linked to sites with many recordings, for each GMIM, this original data set is grouped in 15 different intervals corresponding to fixed fractiles of the statistical distribution of the considered GMIM (every 10% from F10 to F50, and every 5% from F55 to F100). In each group, the average RSRNL Gm for each site is computed. For each of these seven advanced data sets, a neural network approach is used to predict the behavior of RSRNL Gm as a function of the corresponding GMIM, and one or two SCPs. The performance of each model is quantified through the average variance reduction coefficient mu(Rc) in a fixed frequency range. This sensitivity study is performed in the normalized frequency (f/f NL ) domain to identify the best combinations (GMIM, SCPs) providing the largest variance reduction, and then in the absolute frequency domain for the final optimal combination. The optimal combinations [GMIM, two-SCPs] are triplets [PGV/V-s30, V-s30 f(0HV); mu(Rc) = 18.6%], [PGV/V-s30, V-s30 A(0HV); mu(Rc) = 18.16%], [PGV, V-s30 -f(0HV); mu(Rc) = 17.3%] and [PGA, B-30 -A(0HV); mu(Rc) = 17.2%]. The final absolute frequency model with the best triplet makes it possible to predict the non-linear response of a given site knowing its linear, weak-motion response, and two site proxy parameters, for wide ranges of the considered ground motion parameters.