Correspondence to: Arindam Dey, Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati-

781039, Assam, India

Tel: +91 361 2582421

Email: arindamdeyiitk@gmail.com ‡ Assistant Professor; †Post Graduate Student; *Research Scholar

Received Jan. 19, 2017 ; Accepted: Aug. 9, 2017

A time-domain nonlinear effective-stress non-Masing approach of 1

ground response analysis of Guwahati city, India 2

Arindam Dey‡, Devdeep Basu†, Madhulatha Boga* 3

4

Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India 5

6

Abstract: The response of subsoil strata subjected to seismic excitations plays an important role in governing 7 the response of the overlying superstructures at any site. Ground response analysis (GRA) helps to assess the 8 influence of soil characteristics on the propagating seismic stress waves from the bedrock level to the ground 9 surface during an earthquake. For the northeastern region of India, located in the highest seismic zone in the 10 country, conducting an extensive GRA study is of prime importance. Conventionally, most of the GRA studies 11 are carried out using the equivalent linear method, which, being a simplistic approach, cannot capture the 12 nonlinear behavior of soil during seismic shaking. This paper presents the outcomes of a one-dimensional 13 effective stress based nonlinear GRA conducted for Guwahati city (located in northeast India) incorporating 14 the non-Masing load/unload/reload characteristics. The various ground response parameters evaluated from 15 this study help in assessing the ground shaking, soil amplification, and site responses expected in this region. 16 2D contour maps, which are representative of the distribution of some of these parameters throughout 17 Guwahati city, are also developed. The results presented herein can serve as guidelines for the design of 18 foundations and superstructures in this region. 19

Key words: Ground response analysis, Nonlinear effective stress approach, Non-Masing criteria, Ground 20 response parameters, Soil amplification 21

22

1. Introduction 23

The evaluation of ground response, subjected to earthquakes of varying magnitudes, is an important task, as it 24 governs the safety of structures located in seismically prone areas. The local soil geology (Kanai et al., 1959; 25 Bielak et al., 2000; Stewart and Liu, 2000; Grasso and Maugeri, 2014; Castelli et al., 2016; Ferraro et al., 26 2016) and site topography (Housner and Jennings, 1972; Cavallaro et al., 2012; Grasso and Maugeri, 2012; 27 Hongshuai et al., 2016) play an important role in governing the ground response. These parameters alters the 28 intensity and frequency content of the incoming seismic waves as they propagate through the soil strata, 29 thereby magnifying the importance of performing site-specific ground response analysis (GRA) studies. 1D 30 GRA can be performed either in the time domain (nonlinear total and effective stress approaches) or in the 31 frequency domain (linear and equivalent linear total stress approaches). However, owing to the inherent 32 nonlinearity in soil behavior, a time-domain nonlinear GRA can model the soil response, during an actual 33 earthquake, more accurately than any frequency domain GRA method. 34

Guwahati, the largest city in northeast India, is located in the most active seismic zone in the country, 35 categorized under seismic zone V (IS:1893 Part-1, 2002). As per GSI (2000), the seismic vulnerability of 36 Guwahati city is due to four major active faults crisscrossing this region: (1) a NE-SW trending fault across 37

Deepor Beel, running along Chotanagar-Maligaon area; (2) a N 10 E - S 10 W trending fault running between 38 Kalapahar and Fatasil hills for about 10 km; (3) a N 40 E - S 40 W trending fault along Tapar Beel, that runs 39

for about 20 km from the southern foot hill to the Brahmaputra river; and, (4) an E-W trending fault running 40 from near Khanapara to Deepor Beel. Some of the notable seismic events which have occurred in northeast 41 India in the past are the 1869 Cachar earthquake (Mw 7.5), the 1897 Rongjoli earthquake (Ms 8.7), the 1923 42 Meghalaya earthquake (Ms 7.1), the 1930 Dhubri earthquake (Ms 7.1), the 1950 Assam-Tibet earthquake (Mw 43 8.6) and the 1984 Silchar earthquake (Mw 6). Severe devastations in the form of structural damage, landslides, 44 liquefaction and sand vents were reported (Oldham, 1882; Oldham, 1899; Poddar, 1950) in many important 45 cities due to these seismic events. Thus, performing extensive GRA studies for the city of Guwahati is a task of 46 utmost necessity to have a better understanding of the site responses towards weak and strong ground motions. 47 Such GRA studies for this region using the equivalent linear approach have been reported in previous literature 48 (Raghukanth et al., 2008; Kumar and Murali Krishna, 2013). Equivalent linear analysis, being a total stress 49 based analysis approach, fails to address the development and subsequent dissipation of the developed pore-50 pressure, if applicable, and the development of nonlinearity in the propagating medium in case of strong 51 motions. 52

This study, conducted for Guwahati city, focusses on 1D effective stress nonlinear GRA incorporating pore-53 water pressure generation/dissipation and non-Masing load/unload/reload criteria. The results are presented in 54 terms of ground response parameters like peak horizontal acceleration (PHA), peak ground acceleration 55 (PGA), amplification factor and normalized spectral acceleration. The variation of ground response parameters 56 due to weak and strong ground motions for entire Guwahati city has been presented in the form of 2D contour 57 maps. The free field responses obtained for different locations of Guwahati, from the present study, can 58 provide a scientific estimation of the responses of the overlying super-structures. 59

60

2. Nonlinear time domain GRA: Scientific understanding 61

In the nonlinear time domain GRA approach, the stratified soil profile is represented using a multiple degree of 62 freedom lumped parameter model consisting of spring-mass-dashpot systems. Subsequently, by solving the 63 dynamic equation of motion, Eq. (1), using incremental-time based numerical integration, nonlinear response 64 of the model is analyzed. 65

guIMuKuCuM (1) 66

where M is the mass matrix, C is the viscous damping matrix, K is the stiffness matrix, u is the nodal 67 relative acceleration vector, u is the nodal relative velocity vector, u is the nodal relative displacement 68 vector, gu is the acceleration at the base of soil column and I is an unit vector. The dynamic equation of 69

motion, Eq. (1), is solved using the Newmark β method (1959). This approach utilizes any nonlinear stress-70 strain model (Stewart et al., 2008), incorporating either Masing (1926) or non-Masing characteristics, which is 71 representative of the constitutive soil behavior. At the beginning of each time step, the dynamic soil properties 72 (shear stiffness and damping) to be used in that particular time step are obtained by referring to the stress-strain 73 relationship. The hyperbolic stress-strain model (Kondner and Zelasko, 1963), or some of its modified forms 74 (Matasovic and Vucetic, 1993; Hashash and Park, 2001), is generally used to describe the backbone curve for 75 the hysteretic behavior of soil during cyclic shaking. The dynamic response of the soil for the first cycle is 76 estimated using the initial small strain based shear stiffness and damping ratio of the soil. For the subsequent 77 cycles, the stress-strain behavior is obtained by modeling the stiffness degradation of soil (represented by the 78 strain-dependent modulus reduction and damping ratio), along with the modeling of the pore-water pressure 79 that develops during the cyclic loading to represent its strength reduction. The nonlinear MRDF model 80 incorporating hysteretic damping and non-Masing rules (Phillips and Hashash, 2009) is commonly 81 implemented in site response codes for performing nonlinear non-Masing GRA. Pore-water pressure 82 dissipation is modeled using Terzaghi’s one-dimensional consolidation theory (1925). The stress-strain curves 83 are obtained using Eqs. (2) and (3), which represent the loading and unloading/reloading conditions, 84 respectively. 85

s

r

G

1

0 (2) 86

revsrm

rev

srm

rev

srrev

revm

GGGF

)(1

)(

)(1

)(

)2/)((1

)2/)((2 000 (3) 87

where is the given shear strain, r is the reference shear strain, and s are dimensionless curve-fitting 88

constants, rev is the reversal shear strain, is the shear stress, rev is the reversal shear stress, m is the 89

maximum shear strain, )( mF is the reduction factor, and 0G is the initial tangent shear modulus. 90

Various researchers (Hardin and Drnevich, 1972; Shibata and Soelarno, 1975; Laird and Stokoe, 1993) have 91 suggested the dependency of reference strain and small strain damping ratio on the confining pressure. The 92 formulations of reference strain and small strain damping ratio, as a function of confining pressure, are 93 illustrated in Eqs. (4) and (5), respectively. 94

b

refr a

(4) 95

dc

(5) 96

where a, b, c and d are curve fitting parameters, is the effective confining pressure, and ref is a reference 97

confining pressure of 0.18 MPa. The values of b and d are taken as zero when the reference strain and small 98 strain damping ratio are considered to be independent of the confining pressure. 99

100

3. Regional geology and soil data 101

Guwahati city, situated on the banks of river Brahmaputra, has a diverse soil geology. There are stretches of 102 plain land alongside the Brahmaputra river bank which mainly comprises alluvial/fluvial soil deposits. In 103 between these plain lands, there are small hillocks comprising hard soil or rock outcrop. The subsurface 104 geology profile mostly ranges from inter-bedded layers of sands, silts, clays, silty clays and silty sands. 105

For the present study, 90 boreholes (multiple boreholes around each site) are selected in the entire Guwahati 106 city. Figure 1 illustrates some of the landmark locations (referenced by their site numbers) in the city, which 107 has been considered for the present study. Soil data are obtained from the reported field investigation tests. The 108 location of water table varies drastically from one part of the city to another. It is within 2 m of the existing 109 ground level in most locations, while it is as deep as 15 m below the ground surface in a few regions. Table 1 110 enumerates the investigated locations in the area, along with their site class (as per IBC 2000) and the average 111 depth of the water table in those locations. Shear wave velocities (Vs) for soil layers are evaluated based on the 112 measured SPT-N values utilizing the standard correlations (Ohsaki and Iwasaki, 1973; Ohta and Goto, 1978; 113 Imai and Tonouchi, 1982; Iyisan, 1996; Hasancebi and Ulusay, 2007). Note that site-specific estimation of Vs 114 should be preferred whenever possible, rather than determination using empirical correlations as these indirect 115 methods may incur a greater degree of uncertainty. It is usually recommended to use multiple indirect methods 116 (Wair et al., 2012; Stewart et al., 2014) to determine Vs when direct measurement is not possible. Figure 2 117 illustrates the Vs profiles obtained from SPT-N using different indirect methods at site S1. It can be seen that 118 the median of the Vs profile does not have a large scatter as compared to the other profiles. The Ohta and Goto 119 (1978) and the Imai and Tonouchi (1982) Vs profiles are seen to closely resemble the median Vs profile. Owing 120 to the wide-range versatile nature of the Imai and Tonouchi (1982) relationship, the same has been used in this 121 present study. 122

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Table 1 Summary of site locations, the corresponding site class (as per IBC 2000) and the depth of water table 124 at each location 125

Site number Location Site class Water table depth (m)

S1 Pan Bazar D 18

S2 Maligaon E 0.4

S3 IIT Guwahati E 1.5

S4 Deepor Beel D 3

S5 Chachal C 4.5

S6 Kalapahar E 1

S7 Amingaon D 1.5

S8 Ulubari D 0.7

S9 Zoo Road E 0.5

S10 Geetanagar E 0.5

S11 Ahomgaon D 1.2

S12 Christian Basti D 1

S13 Dispur E 0.6

S14 Rajgarh E 0.5

S15 Beltola E 0.6

S16 Bhangagarh D 1

S17 Bongaon D 1

S18 Bharalumukh E 3

S19 Bhetapara E 1

S20 Boragaon D 0.5

S21 Kahilipara D 3

S22 Ghoramara D 1

S23 Guwahati Club D 1.5

S24 Dwarkanagar D 2.5

S25 Dhirenpara D 1.2

S26 Hengrabari D 2

S27 Narikal Basti D 1

S28 Chandmari C 15

S29 Paltan Bazar D 1

S30 Lokhara C 2

126

127

Figure 1 Map revealing the study site locations in Guwahati city 128

129

130

Figure 2 Shear wave velocity profiles at site S1 estimated using different empirical correlations 131

132

The diverse soil geology of Guwahati is well reflected from the six typical shear wave velocity profiles shown 133 in Figure 3. There are some sites (S1, S3 and likewise) which exhibit a gradual and continuous increase of Vs 134 with depth. Some sites (S3, S5 and likewise) manifest the existence of a very soft soil stratum at the top. Some 135 sites (S5, S1 and likewise) have a very stiff soil stratum present at large depths. The depth at which the 136 bedrock is encountered varies from one site to another, as can be mostly inferred from the difference in 137 termination lengths of the boreholes. Some sites (S1, S3 and likewise) have bedrock located at deeper levels, 138

whereas some sites (S6, S4 and likewise) have extremely shallower depth of bedrock. Based on the borehole 139 data, it can be stated that almost the entire city of Guwahati has a shallow basin with very few sites having a 140 bedrock depth higher than 60m. It must be stated that the effect of basin depth plays an important role in 141 governing the site response. In the case of deep basins (bedrock encountered at high depth), soils at a deeper 142 level considerably affect the amplification of seismic waves. Thus, in those cases, merely considering the soil 143 data up to 30 m depth for site response analysis may yield results quite different from the actual scenario. 144 Moreover, the dependence of spectral accelerations and ground motion amplifications on frequency (or period) 145 is different for shallow and deep basins (Semblat et al., 2002; Poovarodom and Jirasakjamroonsri, 2014), and 146 should be duly accommodated when the deep basin effect is prevalent; however, that is not the case for the 147 present study. 148

149

150

Figure 3 Shear wave velocity profiles of six typical sites in Guwahati city highlighting the variation in shear 151 wave velocity and depth of bedrock profile 152

153

4. Site classification 154

Standard penetration tests were carried out at intervals of 1.5 m for each of the borehole sites. The borehole 155 sites are characterized in accordance to international practices based on the average standard penetration 156 resistance ( N ) value computed using the expression (Eq. 6) given in IBC (2000). 157

n

iii

n

ii

Nd

dN

1

1

)/(

(6) 158

where di is the soil layer thickness, Ni is the SPT-N value of the soil layer, and n is the total number of soil 159 layers. 160

Out of the 90 borehole profiles considered in the study, 30 profiles are classified as Site Class E ( N < 15), 52 161 profiles are classified as Site Class D (15 < N < 50), and the remaining eight profiles are classified as Site 162 Class C ( N > 50). Table 1 lists the site classification identification for each of the locations. 163

164

5. Methodology 165

5.1 Modeling of soil profile 166

The shear wave velocity profiles for each of the soil columns are computed from the measured SPT-N values, 167 using the empirical correlation developed by Imai and Tonouchi (1982). Based on the formulation developed 168 by Ishibashi and Zhang (1993), the modulus reduction and damping curves for each of the soil layers are 169 obtained. This formulation incorporates soil properties like plasticity index, overconsolidation ratio, confining 170 pressure and angle of internal friction. These obtained curves were subsequently fitted using the MRDF fitting 171 procedure (Phillips and Hashash, 2009) to define the parameters (β and s ) for the nonlinear stress-strain 172 model. The effect of confining pressure on the reference strain and small strain damping ratio is not considered 173 (confining pressure independent) in this particular study for simplifying the material complexity of the 174 analysis. The soil profiles are assumed to be underlain by an elastic bedrock, having a shear wave velocity of 175 5000 m/s. 176

5.2 Description of seismic loading 177

The present study is carried out using strong motion records from four major earthquakes that have occurred 178 around northeast India in the recent past. Two strong motion records, corresponding to the 1995 Indo-Burma 179 earthquake (Mw 6.4, hypocentral distance from Guwahati = 450 kms) and the 2016 Imphal earthquake (Mw 6.7, 180 hypocentral distance from Guwahati = 410 kms) have a peak bedrock level acceleration (PBRA) of 0.08g. The 181 other two recorded components, corresponding to the 2011 Sikkim earthquake (Mw 6.9, hypocentral distance 182 from Guwahati = 520 kms) and the recent 2015 Nepal earthquake (Mw 7.8, hypocentral distance from 183 Guwahati = 770 kms), which caused severe damages (Xie et al., 2017), have a PBRA of 0.18g. All the four 184 motion components were recorded on rock outcrop sites near the corresponding earthquake’s hypocenter. Each 185 of the motion components have different frequency content. Table 2 lists the strong motion parameters of these 186 four chosen motions. It is observed that the bandwidth of the Indo-Burma seismic motion is largely different 187 from the other three motions. GRA study is conducted using the four above mentioned strong motions that can 188 be divided into two sets: one set of motions having a higher peak bedrock level amplitude (0.18g) and the other 189 set having a lesser peak bedrock level amplitude (0.08g). Figure 4 illustrates the acceleration time histories of 190 these four seismic motions. 191

(a) 192

(b) 193

(c) 194

(d) 195

Figure 4 Acceleration time histories of: (a) Imphal earthquake (Mw 6.7) (b) Indo-Burma earthquake (Mw 6.4) 196 (c) Sikkim earthquake (Mw 6.9) (d) Nepal earthquake (Mw 7.8) 197

Table 2 Strong motion parameters of the chosen seismic records 198

Seismic record Peak acceleration (g) Bracketed

duration (s)

Predominant period (s) Bandwidth (Hz)

Imphal 0.08 21.2 5.35 0.10 - 0.21

Indo-Burma 0.08 6 0.5 1.7 - 4.7

Sikkim 0.18 30.2 3.4 0.21 - 0.61

Nepal 0.18 32.6 4.2 0.12 - 0.27

199

6. Results and discussion from GRA studies 200

6.1 Peak horizontal acceleration (PHA) 201

For six typical borehole sites in Guwahati city (S1-S6), Figure 5 illustrates the variation of PHA with depth, 202 for the Imphal and Indo-Burma earthquakes (having the same PBRA of 0.08g). For the Imphal motion, the 203 PGA (i.e. the PHA at ground level) obtained for all five sites (except S1) is below 0.2g, whereas for site S1, 204 the PGA is observed to be considerably higher (about 0.35g). This can be accounted for by the difference in 205 location of the water table at S1 as compared to the others. The water table is located within 4 m from the 206 ground surface for all the sites except S1, where the water table is situated at a depth of almost 18 m. Note that 207 the PHA at a particular depth in a soil profile is calculated from the effective stress developed at that 208 corresponding depth. Thus, owing to the deeper water table at site S1, the pore water pressures (PWPs) 209 developed within the top 18 m of soil will be negligible (almost zero), resulting in higher effective stresses as 210 compared to the other five sites. The same logic explains the high PGA value observed at S1 corresponding to 211 the Indo-Burma seismic motion. At all the sites except S6, amplification of ground motion (i.e. PGA > PBRA) 212 is observed in the soil profile. 213

214

(a) (b) 215

Figure 5 PHA profiles at six typical sites in Guwahati city for: (a) Imphal motion (b) Indo-Burma motion 216

217

Comparison of the PHS obtained from both the seismic motions (Imphal and Indo-Burma) exhibit that the 218 PGA value obtained at any site (except S4) is similar. For site S4, the Indo-Burma motion produces a 219 considerably higher PGA as compared to the Imphal motion. This observation can be explained based on the 220 computed natural frequencies of the soil profiles (Table 3) and the frequency contents of the two motions 221 (Figure 6). The natural frequency of the layered soil deposits are computed using the average shear wave 222

velocity of the soil profile, which, in turn, is computed using N (Eqn. 6). As shown in Figure 6, the Indo-223 Burma motion has higher Fourier amplitudes at high frequency (at around 4 - 5 Hz) as compared to the Imphal 224 motion. Thus, for the site S4, which has a higher natural frequency (4.56 Hz) as compared to the other five 225 profiles (whose natural frequencies lie within a narrow band of 2.05-2.84 Hz), a higher amplification of ground 226 motion is observed for the Indo-Burma motion on account of near resonance phenomena. 227

228

Table 3 Natural frequencies of soil deposits at six typical sites in Guwahati city 229

Location of soil profile Natural frequency (Hz)

S1 2.19

S2 2.34

S3 2.05

S4 4.56

S5 2.84

S6 2.56

230

231

(a) (b) 232

Figure 6 Smoothened Fourier amplitude spectra for: (a) Imphal motion (b) Indo-Burma motion 233

234

Figure 7 shows the PHA profiles obtained for Nepal and Sikkim motions, both of which have a PBRA of 235 0.18g. It is observed that, for both the motions, the soil site S1 exhibits a considerably higher PGA as 236 compared to the other sites. The reason for a similar observation has been stated earlier in the same section. 237 For both the motions, amplification of ground motion (PGA > PBRA) is observed for sites S1, S2, S3, S4 and 238 S5, whereas attenuation (PGA < PBRA) is observed for the site S6. This attenuation can be explained on the 239 basis of ground shaking and its effect on hysteretic damping characteristics. Moving from the bottom to the top 240 of the soil profile at site S6, it can be seen that the shear wave velocity reduces sharply beyond 7 m, with a 241 very low shear wave velocity (about 50 m/s) in the topmost layer. This indicates the presence of a very loose 242 top stratum. Thus, for a ground motion with considerable intensity (0.18g PBRA), large shaking takes place 243 initially in the topmost layer, thereby inducing large strains and subsequently, larger hysteretic damping. 244 Higher hysteretic damping inhibits the soil shaking and eventually a drop in PHA is observed in the topmost 245 stratum. 246

247

(a) (b) 248

Figure 7 PHA profiles at six typical sites in Guwahati city for: (a) Sikkim motion (b) Nepal motion 249

250

6.2 Peak ground acceleration (PGA) contour maps 251

Based on the GRA study carried out for the 90 borehole profiles of Guwahati, the distribution of PGA 252 estimates all around the city are presented in the form of contour maps as illustrated in Figures 8, 9, 10 and 11. 253 From these maps, specific regions are identified where the highest PGAs are expected to develop for each of 254 the four seismic motions. High ground shaking is expected in sites like S1, S4 S20, S23 and near S5. Damage 255 in many buildings around sites S1 have been reported by Oldham (1899) for the 1897 Shillong plateau 256 earthquake. For the 2011 Sikkim earthquake, cracks in a few buildings located near to site S5 have been 257 reported by Bapat (2011). The regions around sites S2, S6, S16 and S25 are comparatively safer with less 258 values of PGA observed. 259

260

261

Figure 8 Contour map of PGA (in g) in Guwahati city for Imphal earthquake (PBRA=0.08g) 262

263

264

Figure 9 Contour map of PGA (in g) in Guwahati city for Indo-Burma earthquake (PBRA=0.08g) 265

266

267

Figure 10 Contour map of PGA (in g) in Guwahati city for Sikkim earthquake (PBRA=0.18g) 268

269

270

Figure 11 Contour map of PGA (in g) in Guwahati city for Nepal earthquake (PBRA=0.18g) 271

272

6.3 Amplification factor (AF) contour maps 273

Figures 12, 13, 14 and 15 exhibit the contour maps of the amplification factor (AF), which is the ratio of PGA 274 to PBRA at any site, across Guwahati city for the four chosen seismic motions. The amplification factor gives 275 an idea about the amplification/attenuation of ground accelerations as the stress waves propagate through the 276 soil medium. This is indicative of the damage expected at a particular location. The AF maps identify the 277 regions in Guwahati city where high amplification of ground accelerations are expected. High AF is observed 278 in sites like S1, S4, S20, S23 and near S5, whereas, least ground motion amplification is seen in regions around 279 sites S4, S6, S16 and S25 for all the four seismic motions considered in this study. 280

281

282

Figure 12 Contour map of AF in Guwahati city for Imphal earthquake (PBRA=0.08g) 283

284

285

Figure 13 Contour map of AF in Guwahati city for Indo-Burma earthquake (PBRA=0.08g) 286

287

288

Figure 14 Contour map of AF in Guwahati city for Sikkim earthquake (PBRA=0.18g) 289

290

291

Figure 15 Contour map of AF in Guwahati city for Nepal earthquake (PBRA=0.18g) 292

293

This study also highlights a decrease in AF with the increase in the PBRA of input seismic motion. This 294 characteristic has also been reported in previous literature (Warnitchai and Lisantono, 1996; Ashford et al., 295 2000; Stewart et al., 2014; Kumar et al., 2015), and it can be attributed to hysteretic damping induced during 296 shaking. Higher PBRA seismic motions induce larger strains, and subsequently higher hysteretic damping, 297 which causes lesser amplification (might even cause attenuation in some cases) of the bedrock motion as it 298 reaches the ground surface. The hysteresis curves of the topmost stratum for a borehole profile at site S15 is 299

shown in Figure 16. Larger shear strains are evident in the soil profile when it is subjected to motions with 300 higher PBRA (Sikkim and Nepal earthquake motion). Figure 17 shows the AF for the four seismic motions at 301 two sites in Guwahati. 302

303

304

(a) (b) 305

306

(c) (d) 307

Figure 16 Stress-strain loops obtained for the topmost layer at site S15 corresponding to four input motions: (a) 308 Imphal motion (b) Indo-Burma motion (c) Sikkim motion (d) Nepal motion 309 310

311

312

313

(a) (b) 314

Figure 17 Amplification factor (AF) for motions having different PBRA at sites: (a) S17 (b) S1 315

316

6.4 Uncertainty in site amplification 317

Site amplification is expressed in terms of the mean amplification factor, which is represented by a nonlinear 318 expression relating the median peak ground acceleration and the factors governing the standard deviation of 319 the site amplification (Seyhan and Stewart, 2014; Afshari and Stewart, 2015). The mean amplification can be 320 determined either from the generic models providing the ergodic site response estimate (Chiou and Youngs, 321 2008; Lin et al., 2011; Rodriguez-Marek et al., 2011; Kaklamanos et al., 2013), or from a suite of site-specific 322 ground response analysis providing the non-ergodic estimates based on random realizations of input 323 parameters (Bazzurro et al., 2004; Kwok et al., 2008; Rathje et al., 2010; Li and Assimaki, 2011). In the 324 absence of any direct site measurements for the present study, the latter technique of ground response 325 simulations is adopted to reflect the uncertainty in the site amplification. The outcome of the study is provided 326 in terms of the standard deviation of the period dependent site amplification estimates (ϕlnY) obtained for 327 different site locations and input motion variability, and is shown in Figure 18. The range of ϕlnY obtained from 328 the data-based studies (0.23-0.30) (as per Stewart et al., 2014) is also highlighted. It can be observed that most 329 of the site amplification estimated falls within this band for short and medium periods. However, for the higher 330 periods, most of the sites exhibit underestimation of ϕlnY, specifically beyond the natural periods of the site. 331 Similar observation has also been reported by Stewart et al. (2014). 332

333

Figure 18 Typical representation of ϕlnY based on the GRA simulations and data-based studies 334

335

6.5 Normalized response spectra 336

Response spectrum describes the maximum response of a single-degree-of-freedom (SDOF) system, subjected 337 to a particular input motion, as a function of the natural period (or natural frequency) and the damping ratio of 338 the system (Kramer, 1996). It is an important tool in characterizing strong ground motion. For any particular 339 site, the 5% damped surface spectral acceleration plot can be obtained based on the GRA study. Since the 340 magnitude of the spectral acceleration at a site changes with strong motion characteristics, it is important to 341 remove the dependency of the results on the input motion characteristics. Thus, normalization of the spectral 342 acceleration curves is carried out. A normalized response spectrum at any site can be obtained by dividing the 343 computed spectral acceleration values with respect to the PGA obtained from the GRA of substrata, subjected 344 to a particular bedrock input motion. For the Imphal seismic motion, Figure 19 illustrates the response 345 spectrum and the normalized response spectrum, respectively, for site S2. The normalization of the response 346 spectra has been carried out considering the PGA (= 0.21g) obtained at the site S2 due to the Imphal motion. If 347 the GRA study has been conducted using a number of bedrock input motions, then for any particular site, the 348 normalized response spectrum plot can be obtained by taking the median curve, as shown in Figure 20, for the 349 analysis conducted for site S2. 350

351

352

353

354

(a) (b) 355

Figure 19 (a) Response spectrum, and (b) normalized response spectrum, for site S2 subjected to Imphal 356 motion 357

358

359

Figure 20. Median response spectrum obtained at site S2 for four input motions 360

361

In this present study, average normalized response spectra (Figure 21) are derived from the site response study 362 for three classes of soil sites (classified on the basis of IBC, 2000) observed in Guwahati city. The average 363 normalized response spectrum for each class of soil site is obtained by taking the arithmetic average of the 364 normalized response spectra curves for multiple soil profiles belonging to the same site class. The design 365 spectra as per NEHRP Provisions (Part 1: 2003) for three classes of soil sites are also shown. Code based 366 design spectra are developed by combining different groups of soil profiles together so that their provisions 367

may apply to a broad range of soil conditions. Usually, the design spectra offer a more conservative seismic 368 guideline as compared to site-specific response spectra, which is evident from Figure 21 for different classes of 369 soil sites. Figure 21 illustrates that, at longer periods, the spectral acceleration increases with decreasing 370 subsurface stiffness, and greater long period spectral accelerations are associated with the softer soil deposits 371 (Site Class E). The effects are apparent at periods greater than 1 s. This observation tallies with the results of 372 earlier literature (Seed et al., 1976; Newmark and Hall, 1982). For long period structures like bridges and tall 373 buildings which are found on soft deposits, this effect can be very significant, and should be taken into 374 account. 375

376

377

378

Figure 21 Average normalized response spectra (5% damped) for Guwahati city 379

380

7. Conclusions 381

A nonlinear GRA study of Guwahati city has been presented for seismic motion components recorded during 382 the past four major earthquake occurrences in northeast India. The dependency of ground response parameters 383 on the soil properties like shear wave velocity, depth of water table as well as on the input motion 384 characteristics like peak bedrock level acceleration amplitude and frequency content have been illustrated. 385 Amplification/de-amplification of bedrock motion for various soil sites all across Guwahati has been studied, 386 and the uncertainty of site amplification (based on site and input motion variability) has been highlighted. It 387 has been observed that the amplification factor decreases with an increase in the input motion PBRA. PGA and 388 AF contour maps have been obtained which provide a good idea about the expected ground level accelerations 389 and the amplification characteristics of soil substrata at different locations in the city. The average normalized 390 response spectra for three different classes of soil sites observed in Guwahati have also been obtained. The 391 response parameters obtained in this study can serve as guidelines for the seismic design of new structures. To 392 minimize the seismic vulnerability of important existing structures, they may be retrofitted in accordance to the 393 findings of this research. Special consideration should be given to designing new foundations and structures in 394 the parts of the city where high ground accelerations are expected. 395

396

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