2D nonlinear site response analysis of shallow bedrock sites using integrated subsurface profiles

In this study, an attempt has been made to generate the subsurface profiles using integrated geophysical approach and a site-specific 2-D nonlinear site response analysis at shallow bedrock sites in Peninsular India. The site selected for the study is Tarapur, India in which three survey lines were selected for the sub-surface mapping. The subsurface profiling of these three locations was done by an integrated geophysical approach by carrying out Multichannel Analysis of Surface Waves 2D survey, Ground Penetrating Radar survey, and conventional drilling borehole and measurement of Standard Penetration Test N values. Thirteen intraplate recordings from all around the world are selected for the site response analysis. The subsurface profiles generated by the integrated geophysical approaches are modeled in FLAC 2D nonlinear module and site response parameters are estimated. Further 1D site response analyses are carried out at selected points in 2D profiles using the program DEEPSOIL and the 2D site response results are compared. Results of site response analysis are expressed in terms of short-period amplification factor (Fc) and long period amplification factor (Fs) and the results show that the 2D geometry of sub-surface is more sensitive to the higher frequency content of ground motion especially for subsurface with more heterogeneities. Also, a parametric study has been done on a synthetic 2D profile to quantitatively evaluate the effect of different ground motion characteristics like amplitude and frequency content on 2D site response analysis. The parametric study shows that underground heterogeneity is very sensitive to the ground motions with high-frequency content and low amplitude.


Introduction
Earthquakes are one of the most destructive natural events in the world which can cause tremendous damage to the structures. Over the recent years there have been many major earthquakes that have occurred in India-Bhuj (2001;Mw 7.6), Uttarkashi (1991; ML 6.6), Jabalpur (1997; Mw 5.8), Latur (1993; Mw 6.1), Kashmir (2005; Mw 7.6), Chamoli (1999;ML 6.8) and Sikkim (2011;Mw 6.9). Even though for many years Peninsular India was considered as a "stable continental region", earthquakes like Bhuj (2001; Mw 7.6), Koyna (1967;Mw 7.6), Jabalpur (1997;Mw 5.8) and Latur (1993; Mw 6.1) occurred in this 'stable region' are demanding a seismic study at this region. Also, many researchers have noted that the seismic activity of Peninsular India has increased in recent years and cannot be considered as a stable continental region [Anbazhagan et al., 2010;Boominathan et al., 2008;Ganesha Raj and Nijagunappa, 2004]. All these studies are pointing to do a site-specific ground response analysis in Peninsular India especially for the important structures.
Site response analysis is a process of estimating the local site effects due to the ground motion propagation during an earthquake shaking and it became an important step for the geotechnical design of important structures [Roesset, 1977;Idriss, 1990;Kramer, 1996;Borja et al., 2002;Idriss and Seed 1968;Ferraro et al., 2008]. It gives the input for the soil-structure interaction analysis. Generating the representative subsurface profiles is an important step in the site response analysis as it gives the input parameters for the analysis [Panzera et al., 2016]. Most of the site response analyses carried out in Peninsular India are one dimensional Anbazhagan and Sitharam 2008;Jaya and Remmya 2010;Maheswari et al., 2008], in which the input parameters are obtained through SPT data or MASW 1-D data. These analyses were done with the assumption that the soil layers are uniform which is not completely true due to the heterogeneous soil deposits in the region. Hence these studies may not be very effective for the estimation of the actual site effect due to spatial variation of the subsurface. The application of 2D or 3D site response could result in better estimation of site response which accounts the effect of spatial variability of the subsurface [Sanchez-Sesma and Luzon 1995;Heymsfield, 2000;Kamiyama and Satoh 2002;Finn et al., 2003;Semblat et al., 2003;Capilleri et al., 2018].
The main objective of this study is to do a detailed subsurface characterization in 2D at selected locations in  -Gawthorpe et al., 1993;Jol and Bristow, 2003;Moorman et al., 2003;Neal, 2004;Urbini et al., 2001;MASW-Steeples and Miller 1993;Park et al., 1999;Leucci et al., 2007;Maheswari et al., 2008;Mahajan et al., 2007]. The subsurface profiles generated by the integrated geophysical approaches are used for the 2D nonlinear site response analysis by using the programs FLAC 2D. Also, the 2D site response results were compared with conventional 1D site response results using the program DEEPSOIL. These are the two commonly used programs in the field of site response analysis for the last two decades [DEEPSOIL -Hashash and Park, 2001;Phanikanth et al., 2011;Abhishek et al., 2013;FLAC 2D -Movahedasi and Ghayamghamian, 2015;Khanbabazadeh et al., 2016;Rayhani et al., 2007].

Methodology
The site selected for the study is Tarapur, Palghar district, Maharashtra, India. The location of the site is very near to the sea. Many boreholes were drilled with SPT (Standard Penetration Test) N measurement at the site for proposed construction. Three survey lines were selected at this location for generating the subsurface profiles for the study.
The location of the site and the survey lines are shown in Figure 1. The survey lines were selected based on the availability of space and also by connecting multiple boreholes. Geophysical surveys (GPR and MASW) were carried out over these survey lines and data were collected.
GPR is a commonly used geophysical method in the field of subsurface exploration. The identification of different subsurface layers using GPR is mainly depended upon the contrast in the dielectric properties of the materials. The dielectric constant of the material can be determined from the GPR data by knowing the velocity of penetration, depth of material and two-way travel time [Leng and Al-Qadi, 2010]  Deepu Chandran et al.
constant component of the signal in case there is one), application of an automatic gain control (AGC), band-pass filtering (to increase the signal to noise ratio) and the final GPR profile is generated. GPR data has been interpreted based on the available literature for GPR radar stratigraphy by Smith and Jol [1995], Gawthorpe et al. [1993], Jol and Bristow [2003], Moorman et al. [2003], Neal [2004] and Pellicer and Gibson [2011].
MASW is a seismic exploration technique that evaluates ground stiffness by measuring the shear wave velocity of the subsurface. In this study, MASW data were collected by 24 channel geode seismograph with a sampling interval of 1 ms. Geophones of each 4.5 Hz frequency and 24 numbers spaced at 1 m intervals were used for the survey. A software package of Surfseis has been used to process the MASW data. During data analysis, each timedomain shot was converted to the frequency domain by using the fast Fourier transform approach .
Then, from each transformed shot, a site-specific dispersion curve (a plot of phase velocity versus frequency) was generated. A 1D-Vs profile is generated from the dispersion curve by using an iterative nonlinear inversion process . The typical dispersion curve and inverted 1D velocity depth profile for the Tarapur site is shown in Figure 2. All the 1D shear wave velocity profiles along the survey line are interpolated by using a Kriging algorithm in a shot station sequential order and the final continuous 2D-Vs profile was generated. Based on the spatial variation shear wave velocity, different soil layers were identified. Previous studies in MASW by many researchers like Leucci et al. [2007], Maheswari et al. [2008], , Shaaban et al. [2013], and Mahajan et al. [2015] are used to interpret the 2D-Vs profiles.
These two geophysical test results were correlated with borehole data and the final subsurface profiles were generated in 2D. A similar kind of subsurface profiling at the Bangalore site using integrated geophysical approaches is mentioned in detail in Chandran and Anbazhagan [2017]. The final subsurface profiles were used for 2D nonlinear site response analysis using FLAC -2D program of version 7.0 [Itasca 2013] and amplification factors were generated.
1D site response analysis was also done at specific points in the survey lines using DEEPSOIL program of version 6.0 [Hashash et al., 2015] and the results were compared with the 2D site response results. Also, a parametric study has been done at the end of the study to quantitatively evaluate different ground motion parameters on 2D site response analysis.

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2D site response analysis of shallow bedrock sites

Subsurface profiling using integrated geophysical methods
GPR and MASW surveys were conducted along the selected three survey lines. Boreholes were drilled up to 20 m and SPT tests were conducted as per IS 2131 (1981) at different depths in a borehole. The details of the borehole data are shown in Table 1. The borehole data show that clayey black cotton soil with very low SPT N value is present up to a depth of 3 m and after that weathered basalt rock starts and after that compacted basalt rock begins.
The typical GPR profile generated at line 1 is shown in Figure 3 (a). Here we can distinguish two distinctive layers based on the radar sequence and their interface is marked by a yellow dotted line. The depth of the top layer varies from 2.5 to 4 m and it is very clear due to the strong GPR reflection. This top layer mostly corresponds to the clayey black cotton soil and the bottom layer corresponds to the weathered basalt rock as in the borehole data (Table 1).
The radar signal is getting attenuated after the top layer. This may be mainly because of the high clay content or salt content as all these survey lines are located very near to the sea. GPR profile shows too much of noise from a distance of 17 to 23 m. This may be due to the presence of some boulders or electric poles nearby. GPR profiles for lines 2 and 3 are also interpreted similarly and are shown in Figures 4 (a) and 5 (a) respectively. GPR profiles at these two lines also have an almost similar trend as that at line 1 in which the GPR signal is very clear in the top layer approximately up to 3 m and after that, the signal is getting attenuating. In this case, GPR seems to be very effective to delineate the top layers compared to deeper layers. Typical 2D-Vs profile at line 1 is shown in Figure 3(b). It shows three sub-surface layers that are marked using black dotted lines. The layer 1 (7-15 m thick) has a shear wave velocity of 100-550 m s -1 , whereas the layer 2 located at the depth range 25-30 m has a velocity of 550-1100 m s -1 . Layer 3 is extended up to 35 m depth and is having a velocity range of 1100-1600 m/s. Top layer 1 most likely corresponds to the clayey black cotton soil at the top and weathered basalt rock at the bottom. But the interface between this soil layer and the weathered rock is not clearly visible in Figure 3(b). Layer 2 mostly corresponds to the compacted basalt rock and layer 3 mostly corresponds to hard basalt rock with very high velocity. MASW profiles (2D-Vs profiles) for lines 2 and 3 are also interpreted similarly and are shown in Fig. 4(b) and 5(b) respectively. MASW profiles at these two lines also have a three-layered structure similar to line 1. The top layer of black cotton soil cannot distinguish clearly in line 2 and 3 similar to line 1. In this case, MASW seems to be very effective to delineate the deeper layers compared to GPR.

2D dynamic modeling
Two-dimensional dynamic analysis has been carried out by modeling three integrated profiles in FLAC -2D [Itasca, 2013]. FLAC is an explicit finite difference method that uses Lagrangian analysis to model the soil profile [Itasca, 2013]. The materials are assumed to be elastic and dry. Quiet boundaries were used at the base of the model to simulate the real situation of interaction between the bedrock and the soil [Lysmer and Kuhlemeyer, 1969]. To simulate the infiniteness of the media at sides free-field boundaries were set at the vertical boundaries [Cundall et al., 1980]. The spatial element was selected smaller than one-tenth of the wavelength associated with the highest frequency component of the wave [Kuhlemeyer and Lysmer, 1973]. Hysteretic damping is used for the energy dissipating response. The backbone curves selected are Sun et al. [1988] upper limit (UL) curve for the clay and Schnabel [1973] curve is used for the rock.

Selection of input motion
The selection of appropriate input ground motion is one of the main aspects of the site response analysis. India, it can be found that study area may have potential for a PGA (Peak ground acceleration) value of 0.05 g to 0.2 g Kumar et al., 2012;Ramanna and Dodagaodar, 2012;Raghukanth, 2011]. Hence by considering all these factors thirteen intraplate recordings from all around the world have been selected for the study from Anbazhagan et al. [2017]. Summary of selected ground motions is presented in Table 2.

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2D site response analysis of shallow bedrock sites

Site response analysis and amplification factor
Two-dimensional nonlinear site response analyses are performed by using FLAC -2D on all three locations subjected to thirteen input motions. Subsurface layer properties and backbone curves selected for the three locations are given in Table 3. The unit weight of the material corresponding to each layer is measured from the density Vs correlation [Anbazhagan et al., 2016]. Responses are recorded at the surface point of the soil profile and acceleration response spectra are generated. Response spectra were generated with a 5 % damping. The amplification factor can be calculated in many ways. Average spectral amplification factor for different ranges of a period can be calculated from the spectral amplification plots and it is an effective way of expressing the spectral amplification [Dobry et al., 2000;Hall et al., 1975]. In this study, a short period amplification factor (Fc) range from 0.01 s to 0.06 s and long period amplification factor (Fs) range from 0.05 s to 1 s are taken similar to Aditya [2014] for the intraplate earthquake data. Factors Fc and Fs can be calculated using equations as follows: (2) where, RSsoil and RSrock are response spectra on soil and rock at a given period T, and Rsoil and Rrock are the hypocentral distances of soil and rock stations. The ratio of Rsoil/Rrock was assumed to be 1.0 in this study as rock and surface spectral hypocentral distance is similar. 1D site response analysis is done at specific points in the survey lines using DEEPSOIL program.
Typical acceleration response spectra corresponding to an input motion A1-enr for line 1 is shown in Figure 6.
It shows that 2D spectral accelerations are different from 1D and it is comparatively higher than 1D. Variations of short and long period amplification factors (Fc and Fs respectively) with distance corresponding to ground motion  A1-enr are shown in Figure 7. It shows that the spectral amplification pattern in terms of Fc and Fs are differing for 1D and 2D. This difference is higher in the case of Fc and it is slighter in the case of Fs. The amplification pattern in terms of Fc and Fs for all the 13 intraplate ground motions is shown in Figure 8. It shows that 2D amplifications are different from 1D. There is a remarkable variation in the 2D amplification pattern in terms of Fc values. The 2D amplifications are higher than 1D, especially for Fc. As can be seen, the 2D geometry of the sub-surface is more sensitive to the higher frequency content of ground motion. Amplification pattern corresponds to all the ground motions in terms of long period amplification factor (Fs) shows a uniform trend and is converging to a single line especially in the case of 1D (Figure 8).

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2D site response analysis of shallow bedrock sites Figure 6. Comparison between 2D and 1D response spectra at different observation points along the survey line 1.
Similar to line 1 typical spectral acceleration plots corresponding to the input motion A1-enr for the line 2 and 3 are shown in Figures 9 and 12 respectively. Fc and Fs values corresponding to the ground motion A1-enr for lines 2 and 3 are shown in Figures 10 and 13 respectively. Amplification pattern in terms of Fc and Fs for lines 2 and 3 corresponding to all the 13 intraplate ground motions are shown in Figures 11 and 14 respectively. The amplification pattern of line 2 shows an almost similar trend of line 1 in which the 2D amplification is higher than that of 1D (Figures 9, 10 and 11). In the case of line 3, the amplification pattern shows some what a different trend compared Deepu Chandran et al.
12  to the other two lines 1 and 2. The intensity of spectral amplification is almost the same for both 1D and 2D corresponding to the ground motion A1-enr for line 3 (Figures 12 and 13). In a few cases, 1D amplification seems to be slightly higher than 2D. Amplification pattern in terms of Fc corresponding to all the 13 intraplate ground motions for line 3 (Figure 14) is not showing a remarkable variation as in the case of the other two lines 1 and 2. This is mainly because the subsurface layers are more uniform for line 3 when compared to the other two lines.
The responses (Fc and Fs) of all the thirteen ground motions expressed in terms of their Mean value and maximum standard deviation (Max SD) value and are shown in Figures 15 and 16 respectively. Now it is more clear and easy to compare the effect of 2D and 1D amplification pattern corresponding to each survey line. The results confirm the 2D amplifications are higher and more complex than 1D especially in the case of Fc. The pattern of 1D amplification almost shows a uniform trend for all the lines. Also as mentioned earlier, the 2D amplification in the case of line 3 is not showing a huge variation as in the case of the other two lines due to the higher uniformity in that profile (Line 3). This shows that actual 2D amplification is highly sensitive to the underground heterogeneity which cannot be captured through the conventional 1D model.

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2D site response analysis of shallow bedrock sites Figure 9. Comparison between 2D and 1D response spectra at different observation points along the survey line 2.

Parametric study
A parametric study has been done to quantitatively evaluate the effect of different ground motion characteristics on the 2D site response. A synthetic 2D profile of 50 m length and 30 m depth has been generated as shown in Figure 17. This synthetic profile consists of four subsurface layers with different shear wave velocities. The material properties of each layer are given in Table 4. 2D and 1D site response analysis have been done on this synthetic profile similar to the survey lines. The effects of ground motion characteristics such as amplitude and frequency in site response are mentioned below in detail.

Effect of the amplitude of ground motion
An intraplate ground motion A2enr has been selected and it is scaled to three different amplitudes of 0.01 g, 0.1 g, and 1 g through linear scaling method. It is done by applying suitable scaling factors to the amplitude axis of the record [Jaramillo 2003, Watson-Lamprey 2007. A2-enr is selected and it is scaled to three different PGA values 0.01 g, 0.1 g, and 1 g by multiplying every data of acceleration record by a scale factor of 0.01/PGA A2-enr , 0.1/PGA A2-enr and 1/PGA A2-enr respectively. The result of site response analysis is shown in Figure 18. It shows that 2D amplifications are increasing with a decrease in the amplitude of ground motion especially in the case of Fc. The rate of increase in the amplification in 2D is very much higher than that of 1D. 2D amplification pattern seems to be uniform when the intensity of ground motion increases to 1 g and it became very undulating when the amplitude decrease to 0.01 g. This shows that the underground heterogeneity has very less effect on the site response if the ground motion intensity is very high and vice versa.

Effect of the frequency content of the ground motion
Two intraplate ground motions A2-enr (predominant period, Tp = 0.1s), A7-ent (predominant period= 0.2 s) with high frequency content (see Table 2) and one interplate ground motion Diam [Loma Prieta, 1989 earthquake] (see Table 5) with relatively low frequency content (predominant period= 0.4 s) were selected for the dynamic analysis.
All three ground motions are scaled to the same PGA of 0.1 g through the linear scaling method. The response is shown in Figure 19. It shows that high-frequency motions A2-enr and A7-ent show higher amplification that the low-frequency motion Diam for both 1D and 2D. Compared to 1D amplification, the 2D amplification is very high for high-frequency motions, especially for Fc. The intensity of amplification is almost similar for 1D and 2D in the case of low-frequency ground motion Diam. 2D amplification pattern seems to be more complex corresponds to the high-frequency ground motions A2-enr and A7-ent, and the complexity is slighter in the case of low-frequency ground motion Diam. The results show that the 2D geometry is very sensitive to high-frequency ground motion.
The parametric study shows that underground heterogeneity is very sensitive to the ground motions with highfrequency content and low amplitude. All the thirteen intraplate ground motions used in this study are of high-frequency content (Predominant period, Tp < 0.2 sec) and low amplitudes (PGA < 0.2 g) (see Table 2). This is one of the reasons why the 2D amplification is very much higher than that of the 1D amplification in many cases.
2D site response analysis of shallow bedrock sites

Summary and conclusions
In this study subsurface profiling is done at three selected survey lines in Tarapur, India using integrated geophysical approaches by using GPR, MASW and drilled borehole data. GPR seems to be effective in delineating the subsurface layers at very shallow depth and MASW is effective for deeper depth. By integrating these two geophysical methods and correlating the results with the conventional SPT borehole data, the final subsurface profiles were generated.
Two-dimensional dynamic analysis was done on all the profiles using FLAC-2D through proper boundary conditions and includes hysteresis damping. Thirteen intraplate ground motions were selected for the analysis.
The results of 2D dynamic analysis were compared with 1D analysis by DEEPSOIL. Results of site response analysis were expressed in terms of short-period amplification factor (Fc) and long period amplification factor (Fs) and the results show that 2D responses can rarely be captured through 1D analysis. The results show that the 2D geometry of sub-surface is more sensitive to the higher frequency content of ground motion especially for lines 1 and 2 in which the underground heterogeneities are very high. Hence the 2D amplification patterns corresponding to all the ground motions in terms of Fc values are more complex and giving higher values than the 1D. Amplification patterns in terms of Fc for line 3 are not showing a remarkable variation as in the case of the other two lines 1 and 2. This is mainly because the subsurface layers are more uniform for line 3 when compared to the other two lines.
Amplification patterns in terms of Fs seem to be almost uniform and are converging to a single line especially in the case of 1D.
A parametric study has been carried out to quantitatively evaluate the effect of different ground motion characteristics on 2D site response analysis. A synthetic 2D profile has been generated and 2D dynamic analysis has been done on this profile by using ground motions with different amplitudes and frequency contents. The parametric study shows that the underground heterogeneity is very sensitive to the ground motions with high-frequency content and low amplitude. All the thirteen intraplate ground motions used in this study are of high-frequency content and low amplitudes. This is one of the reasons why the 2D amplification is very much higher than that of the 1D amplification in many cases.
20 Figure 19. Variation of 2D and 1D amplification pattern corresponding to three ground motions with different frequency content.