Identification of Shear Modulus Reduction and Damping Curve for Deep and Shallow Sites: Kik-Net Data

ABSTRACT Study aims at selecting the suitable shear modulus reduction and damping curve for broad classification of soil, i.e., rock, gravel, sand, and clay. For this purpose, surface and bedrock ground motion recordings from KiK-Net downhole array for both deep and shallow soil sites have been used. Total stress one-dimensional non-linear site-response analysis has been carried out by varying the available curves for a corresponding soil type. Input parameters for few curves have been determined using parametric study. Linear mixed-effect models on residuals from predicted and recorded surface spectra have been used in suggesting the suitable curve for corresponding soil.


Introduction
Estimation of site amplification due to the local soil is an indispensable part to estimate the level of seismic hazard due to the potential earthquake.Milne [1898] observed the modification in seismic waves as it propagates from the soil stratum.1987, Mexico earthquake; 1989, the Loma Prieta earthquake; 1995 Kobe earthquake; 2001 Bhuj earthquake: and 2010 Canterbury earthquake are the classic examples that emphasize the influence of site amplification due to the local site effect.Estimation of the dynamic property of in-situ soil deposits is the most significant part in studying the response of soil and structure built on these sites.
Most of the researchers [e.g., Bakir et al., 2002;Hough et al., 2011;Bradley and Cubrinovski, 2011] have concluded that softer materials near the free surface govern the damage pattern at short distances.Various projects (NGA WEST GMPEs project) incorporated site effects using the time average shear wave velocity at 30 m depth.Whereas, in important projects, detailed site-response analysis of the site is performed.In addition to the shear wave velocity profile, strain-dependent shear modulus reduction and damping ratio curves are an essential input parameter to estimate the soil non-linearity response.In the absence of site-specific shear modulus reduction (G=G max ) and damping ratio, various authors [e.g., Mahajan et al., 2007;Anbazhagan and Sitharam, 2008;Kumar et al., 2012;Karastathis et al., 2010] have carried out site-response analysis by inputting the worldwide available curves and estimated the site amplification.Barani et al. [2013] studied the effect of G=G max and damping curve and concluded that the selection of curve has an influence in determining the site amplification.However, the less uncertain site-response study in specific cases is fundamentally dependent on inclusion of representative soil property [Seed et al., 1986;Bradley, 2011;Thompson et al., 2012] and standardization of the numerical scheme used.Hence the identification of characteristic G=G max and damping curves are of prime importance for any reliable site-response analysis.
Downhole array provides valuable data for evaluating the assumptions and capabilities of siteresponse analysis programs.Aydan et al. [2008] and Aydan [2015aAydan [ , 2015b] ] have studied the ground motion of important earthquakes recorded in KiK-net stations.Various authors [Thompson et al., 2012;Kaklamanos et al., 2013Kaklamanos et al., , 2015] ] have used KiK-Net (Kiban-Kyoshin Network) for studying the different parameters and assumption in non-linear and equivalent linear total stress site-response.Anbazhagan et al. [2017] used the KiK-Net database for the identification of appropriate G=G max and damping curve for rock, gravel and clay layers in the shallow bedrock sites.However, the study did not consider curves developed by Darendeli [2001] and Zhang et al. [2005], which were assumed to be suitable by Kaklamanos et al. [2015] for siteresponse analysis of KiK-Net sites.Akeju et al. [2017] explained the procedure for selecting and constructing the most appropriate curve for the normalized modulus reduction curve of soils.
This study aims at selecting the most representative shear modulus reduction and damping curve for deep as well as shallow sites having layers of rock, gravel, sand, and clay.Recorded ground motions are available at both bedrock and surface level with soil layering details in the KiK-Net database.Soil profiles have been further grouped based on the soil thickness and type.For the selected soil profiles, non-linear site-response analysis has been carried out using the pair of rock recorded ground motions as input.Predicted response spectra of the surface have been compared with the recorded surface spectra by considering the various available G=G max and damping curve for all the four sites.Linear mixed-effect model has been used on residuals calculated from predicted and surface recorded amplification spectra.Determined bias and standard deviation for all the input curves have been compared and the best representative shear modulus reduction and damping curve has been suggested.G=G max and damping curve suggested in this study can be used for the sites where no site-specific curves are available.

Ground Motions and Sites Selected for Analysis
The profiles used in this study have been obtained from the Kiban-Kyoshin network (KiK-Net, K-Net, http://www.kyoshin.bosai.go.jp/).The KiK-Net array consists of more than 1,000 observation stations, of which 700 have downhole and surface high-quality seismographs.Sites have been selected by considering Thompson et al. [2012] and Kaklamanos et al. [2013] studies, and database were obtained from KiK-net recorded station that has (1) the recorded ground motions with surface peak acceleration value greater than 0.05 g and ( 2) have at least 10 recorded motions where minimum signal to noise ratio is more than 5 for the 0.5-20 Hz passband.Selection criteria resulted in 580 ground motions for 23 deep soil profiles.Collected ground motions were processed as per the methodology proposed by Dawood et al. [2016], and a high-pass fourthorder acausal Butterworth filter was applied as per Boore and Bommer [2005] using the Boore Fortran Programs (TSSP).The corner frequencies were selected through the procedure given by Dawood et al. [2016], acquired from the corresponding NEES flat file for all the KiK-Net sites.Thompson et al. [2012] used 100 sites with 4,862 ground motions recorded from 1,573 earthquakes with surface acceleration less than 0.1 g for studying the KiK-Net downhole array.Out of 100 sites, 16 were identified as suitable fit for one-dimensional (1D) horizontally polarized shear wave propagation (1D SH) and 53 were identified as poor fit for 1D SH assumption (LP).Out of 100 profiles used by Thompson et al. [2012], for only 16 profiles, the depth of bedrock is more than 70 m as defined by Kaklamanos [2012].Out of 16, only 15 profiles were considered as NGNH18 and was classified as HP site.Out of 15 profiles, 10 are classified as LP profiles [Thompson et al., 2012].Most of the profiles considered by Thompson et al. [2012] were either having sand or gravel as a predominant soil type, i.e., laying over a rock.Hence, another eight profiles having clay and silt as their predominant soil type are also selected in the present study.These profiles have low intra-event variability, therefore requires non-linear site-response analysis.
Out of 23 profiles, 10 profiles have clay/silt as a predominant soil type (e.g., AICH05, YMTH06).However, 10 and 16 profiles are having sand (e.g., SZOH42, KSRH04) and gravel (e.g., KMMH14, KSRH06) as predominant soil type, respectively.Minimum rock depth is available at 70 m depth (MIEH10), and maximum rock depth is available at 364 m depth (AICH05).Summary of all the sites considered in this study along with predominant type is given in Table 1.
Addition to deep profiles, shallow profiles are also considered for selecting the shear modulus reduction and damping curves.Four rock sites (i.e., IWTH05, FKSH18, IWTH08, IWTH27); one gravel site (i.e., FKSH11); and two sand sites (FKSH08, TCGH15) were considered as shallow profiles.Details of these sites are given in Anbazhagan et al. [2017].Three clay predominant sites (IWTH02, SITH11, KSRH10) and two gravel predominant sites (FKSH11, IBRH18) are also considered, and detail of these sites can be referred from Yang et al. [2017].Summary of these shallow sites is given in Table 2. Thompson et al. [2012] observed the difference in V s structure while comparing the V s profiles determined through spectral analysis of surface waves and KiK-Net database.However, to address this issue, Monte Carlo simulations have been used for varying the V s structure and comprehensive linear site response has been performed at LP sites using low amplitude ground motions (PGA~0.05g).For all the simulated profiles, response spectra are obtained and compared with the geometric mean of the recorded response spectra at the top of the deposit.Pearson's correlation coefficient (R 2 ) is used in ranking the profiles.V s profile which is comparable to the seed profile obtained from KiK-Net database and having high R 2 is considered further.Small strain damping values are varied in each layer of the simulated profiles obtained from Monte Carlo simulations.Like Kaklamanos et al. [2013], average small strain damping value for respective V s profile is provided as the seed value of the small strain damping.
Numerous studies [e.g., Grelle and Guadagno, 2009] have found that P-wave velocity (V P ) of 1,000-2,000 m/s are characteristic of saturated soil.Hence, ground motion table is assumed where V P first surpasses 1,500 m/s [Kaklamanos et al., 2015].The coefficient of lateral earth pressure at rest (K o ) is computed using the theoretical relationship between K o and Poisson's ratio (ν), i.e., Other model parameters used in this study are described further.In-situ density of each layer has been estimated using relationship developed by Anbazhagan et al. [2016] with AE 1σ.

Methodology
Site-response analysis has been performed using DEEPSOIL [Hashash et al., 2017).Both equivalent linear total stress and non-linear analysis have been used for finally identifying shear wave velocity profiles.STRATA [Kottke et al., 2018] has been used to perform linear site response and Monte Carlo trials for calibrating LP sites.The non-linear behavior of soil is captured through the pressure-dependent hyperbolic model for the backbone curve, developed by Konder and Zelasko [1963], modified by Matasovic [1993].The unloading and reloading formulations are based on the extended Masing rules [Hashash et al., 2017], and within boundary condition has been used.The shear modulus reduction and damping curves have been used to fit the modified hyperbolic model using the MRDF-UIUC procedure developed by Phillips and Hashash [2009].Many authors including Hashash et al. [2010] and Stewart and Kwok [2009] have proposed modifications to the hyperbolic relationship to obtain reasonable estimates of shear strength post-fitting the model.Groholski et al. [2015] proposes a generalized quadratic/hyperbolic strength-controlled model to address this issue, and the module has been implemented in DEEPSOIL.This new constitutive model satisfies both the small strain and large strain modeling of the backbone curve of soils which exhibit strain-hardening behavior.This constitutive model was developed from fundamental principles of general quadratic equations considering a bounding behavior of an elastic-perfectly plastic response and resulting in a hyperbolic model.Detail regarding DEEPSOIL and model can be found in Hashash et al. [2017] and Groholski et al. [2015].
In the present study, the formulation proposed by Hashash et al. [2010] is used to obtain estimates of shear strength.Since, in downhole arrays, the static shear strength is not known beforehand, correlations between the shear wave velocity and undrained shear strength suggested by Dickenson [1994] are used.Frequency-independent Rayleigh damping is used to model the small strain damping as suggested by Phillips and Hashash [2009].Dependence of overburden pressure on the behavior of the modulus reduction curve and small strain damping is modeled through two coefficients in DEEPSOIL.
For determining the goodness-of-fit for different G=G max and damping curves, the observed response spectra at surface, SA obs T ð Þ is compared with the predicted response spectra at surface, SA pred T ð Þ from site-response study using DEEPSOIL.The residual between the observed and obtained SA (5% damping) is a natural logarithm space as: where the geometric mean is used to combine the two orthogonal horizontal components of the recorded ground motion.Negative and positive residuals, respectively, indicate overpredictions and underpredictions.For properly acquiring the statistical significance of different G=G max and damping curves, dependency between multiple recordings at single site need to be evaluated.Mixed-effect regression [Pinheiro and Bates, 2000] is a statistical procedure that helps in evaluating the repeatable bias and variance when the data are grouped with one or more classification factors.Using mixed-effect regression models, the parameter at a specific spectral period, T can be modeled as: here α is the population mean of SA resid T ð Þ, i.e., fixed effect, which represents the average bias in shear modulus and damping curves along with ground motions; η si and i;j are the inter-site and intra-site residuals, respectively.η si and i;j , respectively, represent the deviation from the population mean of the mean residual for the ith site and deviation of ground motion observation j at site i from the mean residual at site i.Both inter, and intra-site residuals are normally distributed with zero mean random variable and τ s and σ o are respective standard deviations.This mixed-effect model was used in examining the precision and bias in G=G max and damping curves used in site-response analysis.A typical flow chart explaining about the selection of these curves is illustrated as Fig. 1.

Overview of Shear Modulus Reduction and Damping Curves Used
Various researchers have developed several G=G max and damping curve with different shear strain values and for different materials.For all the available G=G max and damping curves for soil in the literature, a set of curves are widely used by researchers in site-response analysis.G=G max and damping curves presented by Seed and Idriss [1970], Seed et al. [1986], Sun et al. [1988], Vucetic and Dobry [1991], EPRI [1993], Ishibashi and Zhang [1993], Rollins et al.
For site-response study of shallow profiles, the available G=G max and damping curves in the literature do not require complex input parameters.However, in case of deeper soil profiles, various researchers [Hardin and Drnevich, 1972;Hashash and Park, 2001;Kokusho, 1980] acknowledged the effect of confining pressure on dynamic soil property, especially for granular profiles.Hashash and Park [2001] concluded the influence of pressure-dependent behavior is significant even for 100 m thick soil column, and larger amplitudes for shorter periods are observed in case of pressure-dependent model.Soil type, plasticity index (PI), mean effective confining stress (σ 0 m ), and strain (γ) have been reported as the most significant factors that affect the ratio of shear modulus by Zhang et al. [2005].Other factors such as grain characteristics, over-consolidation ratio, frequency of loading, void ratio, and degree of saturation also effects G=G max but the effect is not much significant [Darendeli, 2001;Zhang et al., 2005].However, σ 0 m , γ, PI, soil type, number of loading cycles and frequency of loading are the most influencing factor for damping ratio ().

Selection of Curves for Rock Sites
One pressure-dependent [i.e., EPRI, 1993] and two pressure-independent [i.e., Schnabel, 1973;Choi, 2008] and geology dependent [Zhang et al., 2005] have been used to study the non-linear behavior of rock sites.The details of these sites used have been given in Tables 1  and 2. A typical plot of the variation of recorded and obtained response spectra for both shallow (i.e., IWTH05) and deep (i.e., KSRH05) rock predominant sites is given as Fig. 2a,b, respectively.The typical variation of residual (combined from all GMs) for different time periods considering all the recorded GMs for these two sites is given as Fig. 2c,d.Choi [2008] curves are significantly underpredicting the spectral acceleration values for different time periods, while Schnabel [1973] curves are overpredicting for longer time periods (see Fig. 2 (a)).However, in case of deep site (KSRH05), both Schnabel [1973] and Choi [2008] are overpredicting the spectral acceleration value for a particular GM.The presence of low V s and density a weathered rock in case of KSRH05 till 100 m is the reason for overpredicting spectral acceleration instead of underpredicting as in case of IWTH05.This low-velocity rock is further treated as gravel and residuals are compared.Bias in case of Zhang et al. [2005] curve is less as compared to EPRI [1993] (see Fig. 2c,d).The bias has been calculated in two ways: (a) using site as random variable and (b) using curve as random variable.In both the cases data is grouped according to residual calculated for different spectral periods.Using Equation 2, (a) fixed effect, α; (b) intra-site/curve standard deviation, σ o ; (c) inter-site/curve, τ s ; and (d) total standard deviation, σ Y have been calculated using the mixed-effect regression model.
The distribution of actual residuals and η si for both site and curve is given in Fig. 3. Zhang et al. [2005] is performing better for (IWTH08 and FKSH18), whereas EPRI [1993] and Schnabel [1973] is having less bias value in case of both IWTH05 and IWTH27 (see Fig. 3).The residual values are more in case of Choi [2008] as compared to the other curves (see Fig. 3b).Presence of high shear wave velocity (V s ) within 5 m in case of IWTH27 may be the reason for pressure-independent Schnabel [1973] curves are performing better.However, based on the equivalent linear and non-linear analysis, Anbazhagan et al. [2017] suggested EPRI [1993] curves for site-response analysis in case of rock predominant sites.In the present study, Zhang et al. [2005] is having less bias as compared to EPRI [1993].The fixed effect in case of Zhang et al. [2005] is −0.037 and EPRI [1993] is 0.0113, i.e., the average ratio SA obs =SA pred for all the sites over the time periods, respectively, is 0.96 and 1.011.However, based on the bias, it is difficult to conclude either Zhang et al. [2005] or EPRI [1993] or both the curves can be used in the case of rock sites.Hence, σ o , τ s , and σ Y have been studied by considering sites as random variable.It can be seen that σ Y in case of Zhang et al. [2005] is less as compared to EPRI [1993] (see Table 3).
Figs. 4 and 5 show the distribution of actual residuals and η si for both site and curve, respectively, for deep sites.Zhang et al. [2005] curves are performing comparatively better for all the three sites (see Fig. 4a) and having less bias value.However, in case of KMMH03, all the    four curves are under predicting the spectral acceleration for all the time periods, which may be due to the sudden change in V s value from 30 to 80 m.Choi [2008] and EPRI [1993] curves are predicting well in case of YMTH04, which may be due to the presence of low V s mud tuff.However, Zhang et al. [2005], EPRI [1993] and Schnabel [1973] curves are performing well in case of KSRH05, which may be due to the constant high V s layer within the first 50 m (i.e., less impedance ratio).Since concluding about the suitable curve is difficult, σ o , τ s , and σ Y for all the spectral periods are also studied.It is observed that EPRI [1993] curves have less σ Y as compared to other curves (see Table 2).In all the three profiles, low-velocity tuff and gravel are also present; hence, these profiles are also analyzed using the gravel curves.Based on the analysis, it is observed that Zhang et al. [2005] and Roblee and Chiou [2004] curves are performing better as compared to other gravel curves (see Fig. E2).Further, the standard deviation and bias with respect to different time periods have been studied.It is noted that the bias and total standard deviation value of EPRI [1993] curves are less as compared to Zhang et al. [2005] curves.Fig. 6a shows the variation of average bias determined using a particular cure with spectral period.All the curves have positive bias (underprediction of ground motions) at spectra period less than 0.2 s.Except Choi [2008], all the three curves have almost zero bias for shorter spectral period and long periods, i.e., after 1 s.Bias in case of both Zhang et al. [2005] and EPRI [1993] curves is less as compared to Roblee and Chiou [2004] and Choi [2008] curves.Fig. 6b-d characterizes the variability of different curves residuals.For all the curves, intra-site standard deviation has been varied within the range of 0.25-0.35natural log units and less erratic as compared to inter-site standard deviation, τ s .The total standard deviation in case of EPRI [1993] is more constant as compared to the other three curves.However, major difference in all the curves is observed in fixed effect as compared to intra-site standard deviation.
Based on the overall analysis of both shallow as well as deep profiles, it can be suggested that if the geological age of the rock deposition is known then Zhang et al. [2005] curves can be used, else EPRI [1993].Zhang et al. [2005] and EPRI [1993] curves are performing similarly in case of Quaternary deposits.However, EPRI [1993] curves are performing better in case of high-velocity rock deposition at deeper sites as compared to Zhang et al. [2005] curves.For deep sites, if tuff (V s 300 m/s) is present, Choi [2008] curves can also be used.Conclusively, for site-response analysis in case of rock predominant sites, EPRI [1993] and Zhang et al. [2005] curves can be used for rock sites, V s !800 m/s and V s < 800 m/s, respectively, for Quaternary deposits.

Selection of Curves for Gravel Sites
For gravel, two pressure-independent [Seed et al., 1986;Rollins et al., 1998] and two overburden pressure dependent (i.e., Roblee and Chiou, 2004;Menq, 2003] and one geological age-dependent [Zhang et al., 2005] G=G max and damping ratio curves have been used.The details of the gravel predominant sites used in the analysis are given in Tables 1 and 2. Fig. 7a,b shows the variation of actual residuals considering curve and site as a random variable, respectively.Except for Menq [2003], rest all the four curves are under predicting the spectral acceleration values in case of NIGH12 and FKSH11.Whereas, in case of IBRH18, bias is less for all the five curves.Calculated bias is identical in case of Rollins et al. [1998], Roblee and Chiou [2004] and Zhang et al. [2005] and minimum in case of Menq [2003] (see Fig. E6).Similarly, σ Y is maximum in case of Seed et al. [1986] and minimum in case of Menq [2003] (see Table 3).For NIGH12 and FKSH11, significant difference is observed between calculated and observed spectral acceleration values between the period ranges of 0.08-0.14s and 0.18-0.22s.However, the bias is less in case of Menq [2003] for all the spectral periods as compared to other curves.Anbazhagan et al. [2017] concluded that Rollins et al. [1998] (-SD) and Roblee and Chiou [2004] curves can be used to define the non-linear behavior of the gravel predominant sites.However, in the present study, Menq [2003] curves are providing reliable estimate of ground response for all the spectral periods.The overall sigma in case of Menq [2003], Rollins et al. [1998] (-SD) and Roblee and Chiou [2004] is 0.066, 0.103, 0.09, respectively, while considering time periods as fixed and random variable.Menq [2003] curves are having less bias value as compared to other curves, except in case of KMMH14, where Zhang et al. [2005] curves are having less bias value (see Fig. E7a,b).Zhang et al. [2005] curves are mostly underpredicting, and Seed et al. [1986] and Rollins et al. [1998] (UL) are overpredicting the SA values for all the spectral period range (see Fig. E8).σ o is less in case of Rollins et al. [1998] (M) as compared to Zhang et al. [2005] and Roblee and Chiou [2004].However, σ Y is maximum in case of Rollins et al. [1998] (UL), i.e., 0.398 and minimum is case of Menq [2003], i.e., 0.063 (see Table 3).
All the curves have positive bias (underprediction of ground motions) except for the spectral period ranging from 0.15 to 0.35 (see Fig. 8a).All curves have almost zero bias for longer periods, i.e., after 1 s.Bias in case of Menq [2003] curves is less as compared to other curves, however, after 0.35 s, bias in the case of Zhang et al. [2005] and Menq [2003] curves is almost equal.Fig. 8b-d characterizes the variability of different curves residuals.Bias and standard deviation in case of  Roblee and Chiou [2004] are not significantly different from Zhang et al. [2005].For all the curves, intra-site standard deviation is varied within the range of 0.25-0.35natural log units and less erratic as compared to inter-site standard deviation, τ s .The total standard deviation of Menq [2003] is less as compared to the other three curves.However, the major difference in all the curve is observed in fixed effect as compared to intra-site standard deviation.
The reason for Menq [2003] curves having less bias and standard deviation value is because in addition to overburden pressure these curves are depending on the particle size as compared to Zhang et al. [2005] and Roblee and Chiou [2004].Most of the available sites used in the analysis are a combination of gravel with either sand or clay or fine particles (e.g., TCGH10).Hence coefficient of uniformity (C u ) and median grain size (D 50 ) are important inputs in Menq [2003].In this present study, which is varied based on density calculated and the type of soil available.For example, in case of TKCH08, D 50 has been varied from 0.11 to 17.4 mm; and C u from 1.1 to 15.9 and Menq [2003] curves are performing better than other curves with D 50 ranged from 0.5 to 3 mm (increasing with density) and C u from 1.1 to 5. Menq [2003] is performing better for 0:2 D 50 < 5 and 1:1 C u < 10 while considering all gravel profiles, based on the density of the deposition.However, in most of the cases, the value of D 50 and C u is not available.In such case, varying these values may not be workable, depending upon the project.Hence, bias and standard deviation have been calculated and compared for three curves, i.e., Menq [2003], Zhang et al. [2005], and Roblee and Chiou [2004] for both deep and shallow profiles.Significant variation is observed in bias value in all the three curves till 0.1 s, however, after 1 s no such variation in bias value is observed.In case of deep profiles, Zhang et al. [2005] is having less standard deviation, i.e., 0.112 as compared to Roblee and Chiou [2004], i.e., 0.201 while considering time periods as fixed variable.
Hence if the particle size is available, Menq [2003] curves can be used for gravel layers, otherwise Roblee and Chiou [2004] curves in case of shallow site and Zhang et al. [2005] curves for site-response analysis of deep gravel profiles.

Selection of Curves for Sand Sites
One pressure-independent [i.e., Seed and Idriss, 1984] and four pressure-dependent [Darendeli, 2001;Roblee and Chiou, 2004;EPRI, 1993;Menq, 2003] and one geological age-dependent [Zhang et al., 2005] curves have been used for evaluating the non-linear behavior of sand deposits.In case of Darendeli [2001], over-consolidation ratio is reasonably assumed as unity, number of loading cycles and loading frequency are, respectively, assumed as 1 Hz and 10 [Darendeli, 2001;Kaklamanos et al., 2015].The details of these sites are given in Tables 1 and 2. Using mixed-effect models, α, σ o , τ s , and σ Y have been calculated.Menq [2003] and Zhang et al. [2005] curves are performing better for deep sites (see Fig. 9a,b).For most of the sites, EPRI [1993] curves are over predicting and Seed and Idriss [1970] (M) curves are under predicting the spectral acceleration values.Overall residuals are less in case of Menq [2003] and Zhang et al. [2005] and more in case of Seed and Idriss [1970].Menq [2003] curves are performing better in case of AOMH17, SZOH43 and SZOH42.However, Zhang et al. [2005] curves are performing better in case of IBRH17, KSRH04, KSRH07 and NMRH04.In case of NMRH04, most of the curves are underpredicting except Zhang et al. [2005] which may be due to the presence of low-velocity soil deposition for deeper depth also.Fig. E9 shows the variation of actual residual and bias in all five G=G max and damping ratio curves.The bias value is   maximum for Seed and Idriss [1970] (M) and minimum for Zhang et al. [2005] curves.Negative bias is observed for Menq [2003] and EPRI [1993].σ Y is maximum (i.e., 0.23) in case of Seed and Idriss [1970] (UL) and Seed and Idriss [1970] (M) and minimum (i.e., 0.065) in case of Zhang et al. [2005] curves.Hence, Zhang et al. [2005] and Menq [2003] are performing better for sand deposits.Further bias value at different spectral periods have been studied for these five curves.Bias is less in case of Zhang et al. [2005] curves till 0.1 s and after 1.0 s both the curves have almost equal bias, tending toward zero.However, negative bias is observed for 0.08-0.14s which may be due to not considering pore-pressure rise in the analysis.Menq [2003] is performing better for all the three shallow sites and that may be due to the presence of sand-gravel mixture in all the sites (Fig. E10a,b).In case of FKSH08, except Menq [2003] and Zhang et al. [2005], almost all the curves are overpredicting bias values.Whereas KSRH03 and TCGH15 profiles are showing less bias for all the six curves.Bias value is almost zero expect for Zhang et al. [2005] and Seed and Idriss [1970] (UL) (see Fig. E11) curves.σ Y is maximum (i.e., 0.028) in case of Darendeli [2001] and Seed and Idriss [1970] (UL) and minimum (i.e., 0.019) in case of Menq [2003] curves (see Table 3).It can be concluded that Menq [2003], Zhang et al. [2005] and Seed and Idriss [1970] (LL) are performing better in case of shallow sand deposits.Further bias value at different spectral periods is studied for these five curves.The overall sigma in case of EPRI [1993], Menq [2003], Seed and Idriss [1970] (LL), Seed and Idriss [1970] (UL) and Zhang et al. [2005] is 0.034, 0.028, 0.035, 0.032, 0.030, respectively, while considering time periods as fixed and random variable.
All the curves have positive bias (underprediction of ground motions) except for the spectral period ranging from 0.15 to 0.75 (Fig. 10a).All curves have almost zero bias for longer periods, i.e., after 1 s, except EPRI [1993] and Seed and Idriss [1970] (M) curves.Bias in case of Zhang et al. [2005] and Menq [2003] curves is less as compared to other curves.However, after 0.15 s, bias in case of Zhang et al. [2005] and Menq [2003] is almost equal.Significant variability in bias value is observed for the short spectral period ranging from 0.03 to 0.1 s.Bias and standard deviation in case of Roblee and Chiou [2004] are not significantly different from Darendeli [2001] (see Fig. 10b-d).For all the curves, intra-site standard deviation is varying within the range of 0.30-0.40natural log units and less erratic as compared to inter-site standard deviation, τ s .The total standard deviation of Zhang et al. [2005] is less as compared to the other curves and not significantly different from Menq [2003].However, major difference in all the curves have been observed in fixed effect as compared to intra-site standard deviation.Menq [2003] curves are performing better for the shallow profiles and Zhang et al.
[2005] curves are performing better for deep soil deposits.However, if proper soil properties are not available instead of Menq [2003] either Zhang et al. [2005] or Roblee and Chiou [2004] can be used.

Selection of Curves for Clay and Silt Sites
Two pressure-independent curves [i.e., Vucetic and Dobry, 1991;Yamada et al., 2008] and two pressure-dependent [i.e., Darendeli, 2001;Roblee and Chiou, 2004] curves have been used for evaluating the non-linear behavior of clay deposits along with Zhang et al. [2005].The details of the sites considered are given in Tables 1 and 2.
All the clay curves are mostly dependent on soil plasticity.It is important to see the non-linear behavior of clay profiles with varying PI values.Hence, parametric study has been carried out to select the most representative PI values, so that the residual will be less between the observed and recorded SA at the surface.The PI value varies from 0 to 100 for all G=G max and damping ratio curves for both shallow and deep profiles.For example, in case of KSRH10 for the first 35 m, PI values vary from 0,10,15,20,30,40,50,75, 100 for all the cases.Vucetic and Dobry [1991], Darendeli [2001], Zhang et al. [2005], and Yamada et al. [2008] curves are predicting less bias for PI range for 15 PI < 20, 40 PI < 50, 20 PI < 30 and 20 PI < 30, respectively.Similarly, in case of AICH05, Vucetic and Dobry [1991], Darendeli [2001], Zhang et al. [2005], and Yamada et al. [2008] curves are predicting less bias for PI range for 20 PI < 30, 50 PI < 75, 20 PI < 40 and 40 PI < 50, respectively.Among all the sites, curve having less bias for corresponding PI is selected for further site-response analysis and selection of proper curves.The selection of the best representative curves for clayey sites is explained further.
All the curves have positive bias (underprediction of ground motions) except for the spectral period ranging from 0.40 to 0.75 (see Fig. 11a).All curves have almost zero bias for longer periods, i.e., after 1 s.Bias in case of Darendeli [2001] is less as compared to other curves, however, after 1.0 s, bias in case of Zhang et al. [2005] and Darendeli [2001] curves is almost equal.Roblee and Chiou [2004] and Yamada et al. [2008] curves are significantly underpredicting the spectral acceleration values for spectral period range 0.05-0.25 s.This may be due to PI independency in case of Roblee and Chiou [2004] and overburden pressure-independency in case of Yamada et al. [2008].Significant variability in bias value was observed for the short spectral period ranging from 0.01 to 0.1 s.Fig. 11b-d characterizes the variability of different curves residuals.Bias and standard deviation in case of Zhang et al. [2005] curves are not significantly different from Darendeli [2001] curves.For all the curves, intra-site standard deviation is varying within the range of 0.25-0.40natural log units and less erratic as compared to inter-site standard deviation, τ s .The total standard deviation of Darendeli [2001] curves is less as compared to the other curves and not significantly different from Zhang et al. [2005].However, the major difference in all the curves is observed in fixed effect as compared to intrasite standard deviation.
Only Darendeli [2001] is available for silt sites.Hence, only one site (i.e., MIEH10) has been tested to find the suitable PI value.PI values vary as 0, 5, 10, 15, 20, 25, 30, 50.It can be seen that in case of 20 PI < 30, the bias value is less as compared to other PI value.At PI more than 30, there is a significant increase in bias and standard deviation value.
Hence, Darendeli [2001] and Zhang et al. [2005] curves are performing better in case of shallow profiles and Darendeli [2001] curves are performing better in case of deep soil deposits.Additionally, Darendeli [2001] curves are performing better for PI range 40-75 in case of deep deposits and 30-50 in case of shallow clay deposits.For PI range from 20 to 30, Darendeli [2001] curves are representing better in case of silt deposits.

Limitation and Assumption of Current Study
In this study, non-linear 1D site-response model has been considered for selecting the representative curve for different soil types.As the grain size distribution is not available, hence, a qualitative estimate is used for soil classification.Sites are selected according to Thompson et al. [2012] based on poor and good fit for 1D wave propagation assumption, i.e., LP and LG sites.For LP sites, vertical incidence is not presumed as a source of error.The results derived from the present study may not be suitable for sites that are classified as HP and HG as per Thompson et al. [2012].Difference in small strain damping ratio and shear wave velocity is used for attributing this error.Using the Monte Carlo simulations and linear 1D site-response analysis, shear wave velocity profiles have been estimated and used further in the analysis.Various developed shear modulus reduction and damping ratio curves demand different parameters which are difficult to obtain without soil sampling.Hence those curves are not used in the analysis.1D site-response model that assumes horizontally polarized shear wave propagation assuming vertical incidence has been used for analysis.Due to lack of non-linear material data and pore-pressure data for KiK-net sites, complicated non-linear constitute models could not be used.If the same selected curves are to be used for different sites other than Japanese sites, uncertainty must be taken into consideration.Additionally, it can be noted that these curves can only be used as an initial estimate to predict the surface amplification spectra for the sites where information about the soil deposit is not available.

Conclusion
This study aims at identifying and selecting shear modulus reduction and damping curves for the soils by dividing it into rock, gravel, sand, and clay part of KiK-Net downhole array network.1D site-response analysis and Monte Carlo simulations are carried out for the sites which are not good for 1D wave propagation assumptions.Using the selected profiles, non-linear onedimension total stress site-response analysis is carried out, by giving the rock recorded ground motions as input parameter.Both shallow and deep soil sites available are considered for selecting the representative G=G max and damping ratio curves for the corresponding soil profile.Using the mixed-effect models, the residuals are calculated from recorded and predicted surface amplification spectra.Based on the results obtained, fixed effect bias and standard deviation, representing curves are selected.G=G max and damping ratio curves given by Darendeli [2001] are found to perform better for PI range 40-75 in case of deep deposits, and 30-50 in case of shallow clay deposits.For PI range from 20 to 30, Darendeli [2001] curves represent better in case of silt deposits.G=G max and damping ratio curves of Menq [2003] curves are found to perform better in case of shallow sites, and Zhang et al. [2005] curves are found to perform better in case of deep sites with dominant sand layers.Menq [2003] G=G max and damping ratio curves are found to perform better in gravel dominated sites.In case of non-availability of proper soil sampling, G=G max and damping ratio curves of Zhang et al. [2005] and Roblee and Chiou [2004] can be used for sand and gravel dominated sites.Limited G=G max and damping ratio curves are available for rock sites, however, curves given by EPRI [1993] are found to be more suitable as compared to other curves available in the literature.For few gravel and sand deposit profiles, pore-pressure rise and effective stress behavior significantly changes the predominant period of soil columns.The recommended G=G max and damping ratio curves can be used in the site-response analysis for the sites where site-specific curves are not available.

Figure 1 .
Figure 1.Flow chart showing the methodology used in selecting G=G max and damping curve.

Figure 2 .
Figure 2. Variation of response spectra for different G=G max and damping curve of (a) shallow site IWTH05 and (b) deep site KSRH05 and spectral (i.e., combined all GMs) residual for (c) shallow site IWTH05 and (d) deep site KSRH05.

Figure 3 .
Figure 3. (a-c) Variation of actual residual for four shallow sites considering (a) curve and (b) site as random variable for all the time periods.Top of (a) is showing the bias and bottom is showing the intra-site residual for different curves used in the analysis of rock sites.(c) Variation of actual residuals considering sites as random variable.Red line indicates the fixed bias.

Figure 4 .
Figure 4. Variation of actual residual for three deep rock sites considering (a) rock specific curve and (b) gravel specific curve as random variable for all the time periods.Variation of residuals using (c) rock specific and (d) gravel specific curve considering site as random variable.Top of (a,b) is showing the bias and bottom is showing the intra-site residual for different curves used in the analysis of rock sites.

Figure 5 .
Figure 5. Variation of actual residuals using (a) rock and (b) gravel specific curve considering sites as random variable.Red line indicates the fixed bias.

Figure 6 .
Figure 6.Period dependence of the parameters of the linear mixed-effects regression model for rock sites: (a) fixed effect, a; (b) intra-site standard deviation, σ 0 ; (c) inter-site standard deviation, τ S ; and (d) total standard deviation, σ Y .

Figure 7 .
Figure 7. Variation of actual residual for three shallow gravel sites considering (a) curve and (b) site as random variable for all the time periods.Top of (a) is showing the bias and bottom is showing the intra-site residual for different curves used in the analysis of rock sites.

Figure 8 .
Figure 8. Period dependence of the parameters of the linear mixed-effects regression model for gravel sites: (a) fixed effect, a; (b) intra-site standard deviation, σ 0 ; (c) inter-site standard deviation, τ S ; and (d) total standard deviation, σ Y .

Figure 9 .
Figure 9. Variation of actual residuals for seven deep sites considering (a) curve and (b) site as random variable for all the time periods.Top of (a) is showing the bias and bottom is showing the intra-site residual for different curves used in the analysis of rock sites.

Figure 10 .
Figure 10.Period dependence of the parameters of the linear mixed-effects regression model for sand sites: (a) fixed effect, a; (b) intra-site standard deviation, σ 0 ; (c) inter-site standard deviation, τ S ; and (d) total standard deviation, σ Y .

Figure 11 .
Figure 11.Period dependence of the parameters of the linear mixed-effects regression model for clay sites: (a) fixed effect, a; (b) intra-site standard deviation, σ 0 ; (c) inter-site standard deviation, τ S and (d) total standard deviation, σ Y .

Table 1
Description of deep soil profile used in this study.

Table 2
Description of shallow soil profile used in this study.

Table 3
Bias and standard deviation calculated using linear mixed-effect models for different curves.The numbers cited in the test is in square bracket.