Computation of ground motion amplification in Kolkata megacity (India) using finite-difference method for seismic microzonation

Acta Geophysica DOI: 10.2478/s11600-013-0169-2

________________________________________________ © 2013 Institute of Geophysics, Polish Academy of Sciences

Computation of Ground Motion Amplification in Kolkata Megacity (India) Using

Finite-Difference Method for Seismic Microzonation

Amit SHIULY, Vinay KUMAR, and Jay P. NARAYAN

Department of Earthquake Engineering, Indian Institute of Technology Roorkee, Roorkee, India; e-mail: [email protected]

A b s t r a c t

This paper presents the ground motion amplification scenario along with fundamental frequency (F0) of sedimentary deposit for the seismic microzonation of Kolkata City, situated on the world’s largest delta is-land with very soft soil deposit. A 4th order accurate SH-wave visco-elastic finite-difference algorithm is used for computation of response of 1D model for each borehole location. Different maps, such as for F0, am-plification at F0, average spectral amplification (ASA) in the different frequency bandwidth of earthquake engineering interest are developed for a variety of end-users communities. The obtained ASA of the order of 3-6 at most of the borehole locations in a frequency range of 0.25-10.0 Hz reveals that Kolkata City may suffer severe damage even during a moderate earthquake. Further, unexpected severe damage to collapse of multi-storey buildings may occur in localities near Hoogly River and Salt Lake area due to double resonance effects during distant large earth-quakes.

Key words: viscoelastic damping, finite-difference method, ground mo-tion amplification, fundamental frequency, seismic microzonation.

1. INTRODUCTION The year by year increase of human and economic losses due to earthquakes calls for seismic microzonation to predict the seismic hazard at the micro-level for earthquake disaster mitigation and risk assessment. Local geology

A. SHIULY et al.

largely affects the ground motion characteristics and plays an important role in damage distribution during an earthquake (Oprsal et al. 2005, Narayan 2005, 2010, 2012, Narayan and Singh 2006). Severe damage, even at large epicentral distances, can occur due to the local site effects and double reso-nance (double resonance is the resonance of body wave frequency with F0 of soil and then again resonance with the natural frequency of structures). For example, selective damages to structures in Mexico City during Michoacan earthquake of 1985 (Romo and Seed 1986) and in Ahmedabad City during Bhuj, India, earthquake of 2001 (Narayan et al. 2002). The current practice of seismic microzonation in most of the countries is to transfer the bedrock motion to the surface using the 1D S-wave response of a soil column. The prediction of fundamental frequency (F0) of soil deposit is a very important task since earthquake engineers generally keep the natural frequency of structures below the F0 to avoid double resonance during earthquake. Soil amplification is studied using different approaches for site-specific ground motion prediction and seismic microzonation in the past (Romo and Seed 1986, Campillo et al. 1988, Boatwright et al. 1991, Atkinson and Cassidy 2000, Anbazhagan and Sitharam 2008, Kumar and Narayan 2008, Singh 2009). Recently, Vaccari et al. (2011) computed the site-specific ground mo-tion and computed 2D soil amplification along few lines in Kolkata City.

Our study area, the Kolkata Megacity and the capital of West Bengal, is situated in Bengal Basin in the eastern part of India (Fig. 1). Originally Kol-kata City has grown in north-south direction along the Hoogly River towards the eastern bank. In Bengal Basin, the range of thickness of sedimentary de-posit from west to east is 1.2 to 20 km (Nandy 2001). But below the Kolkata City the depth of basement is around 7.0 km and the variation of basement depth is smooth (Murty et al. 2008). There are three rivers, namely Ganga, Brahmaputra, and Barak, flowing in Bengal Basin. The historical Kolkata City has many old buildings, bridges, subways, multi-storied buildings, huge shopping malls, etc. The Kolkata City lies on the border of seismic zones III and IV as per the seismic zoning map of India incorporated in Indian stand-ard criteria for earthquake resistant design of structures (IS-1893 (2002)). According to the census report of 2001, the population of Kolkata City is about 13 millions. Because of very large population of Kolkata City and fur-ther increase year by year, the swampy and marshy lands are being filled for construction buildings in an unplanned way (Nandy 2007).

Figure 2 depicts the seismotectonic map for Kolkata City. This map shows the major tectonic features and earthquakes which have occurred in and around the Kolkata City in a more than 300 km in radius. The major fault systems in this region are Garhomoyana–Khandaghosh Fault (GKF), Jangipur–Gaibandha Fault (JGF), Pingla Fault (PF), Eocene Hinge Zone (EHZ), Debagram Bogra Fault (DBF), Kulsi Fault (KF), Dhubri Fault (DHF),

SOIL AMPLIFICATION IN KOLKATA CITY

Fig. 1. Map showing important features, places, BH-locations in Kolkata City. Col-our version of this figure is available in electronic edition only.

Sylhet Fault (SF), and Rajmahal Fault (RF) (GSI 2000). The Kolkata City has experienced the shaking during both local and regional earthquakes. The intensity of shaking in Kolkata during 15 April 1964, Calcutta earthquake (M = 5.2; epicentral distance 106 km) was of the order of VII on MMI scale

(Jhingran et al. 1969, GSI 2000). Similarly, the shaking was of the order of VIII on MMI scale during the great 1897 Assam earthquake (M = 8.7), although epicentral distance was more than 470 km (Seeber and Armbruster 1981). The city has also felt many large and distant earthquakes, like 1918 Srimangal earthquake, 1930 Dubhri earthquake, 1934 Bihar Nepal earth-quake, etc. The research work presented in this paper has four important as-pects, namely prediction of F0 of sedimentary deposit at different borehole locations in Kolkata City, amplification factor at F0, average spectral ampli-fication in the frequency range of 0.25-10.0 Hz and average spectral amplifi-cations in different smaller frequency bands (0.25-1, 1-2, 2-5, and 5-10 Hz).

Borehole sites

Stream

Lake

Open field

River

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Fig. 2. Seismotectonic map for Kolkata City and surrounding region (major tectonic features are Garhomoyana–Khandaghosh Fault (GKF), Jangipur–Gaibandha Fault (JGF), Pingla Fault (PF), Eocene Hinge Zone (EHZ), Debagram Bogra Fault (DBF), Kulsi Fault (KF), Dhubri Fault (DHF), Sylhet Fault (SF), and Rajmahal Fault (RF); after GSI (2000)). Colour version of this figure is available in electronic edition only.

2. BENGAL BASIN AND ADJOINING REGION The Bengal Basin encompasses Ganga, Brahmaputra, and Barak basins. Near the Indo–Bangladesh border, Farakka barrage diverts the Ganga water to the Hooghly River to increase and maintain adequate depth of flow for navigation and operation of Kolkata port. The sediments transported by Ganges–Brahmaputra have formed world’s largest delta island in southern part of Bengal Basin. The Bengal Basin consists of three structural features, namely western scrap zone, middle shelf zone, and eastern deeper basin part. The western part of the Bengal Basin is bounded by the basin margin fault zone to the west and northwest and by the Eocene Hinge Zone (EHZ) to the east and southwest and constitutes a broad shelf zone (Salt et al. 1986). In the shelf zone, the Tertiary sediment dips homogeneously toward the south-east with a sudden flexure along the EHZ. EHZ extends NE to SW direction with a width of 25 km and a length of 550 km (Fig. 2). This hinge zone marks a zone of differential thickening and subsidence rate of Oligocene and Miocene section (Salt et al. 1986).


3. GEOTECHNICAL DATA The geotechnical data for the study area were collected from several agen-cies, like C.E. Testing Company Pvt. Ltd., S. Ghosh & Associates, etc. Geo-technical data from around 85 borehole locations (BH) were obtained. The data include SPT values, density, plasticity index, finer content, etc. Finally, data of only 44 borehole locations, shown in Fig. 1 and Table 1, were

Table 1 Borehole (BH) locations, fundamental frequency, amplification at F0,

and Average Amplification Factors in different frequency bands

BH No.

Long. [°N]

Lat. [°E] Locality name F0 Ampl.

Average Amplification Factors (AAF) [Hz]

.25-10 .25-1 1-2 2-5 5-10 1 22.5413 88.3679 91, Park St., Kolkata 1.73 6.07 4.24 3.18 1.47 2.77 5.14

2 22.5752 88.3886 33/1A, Upendra Banerjee Rd. 1.83 6.25 5.45 2.53 4.85 2.70 7.78

3 22.5134 88.3559 89, Southern Av. 1.73 7.00 3.81 6.03 4.73 1.92 0.35

4 22.5237 88.3808 42/197/1, Bediadanga 2nd Lane 1.73 7.00 4.28 3.08 5.69 4.81 3.82

5 22.5182 88.3269 15B/1A, Raja Santosh Rd. 1.73 7.21 4.41 3.09 5.44 3.24 5.14

6 22.5772 88.4313 DN-1, Sector-5, Salt Lake, Kolkata 1.87 6.54 4.36 3.18 4.93 3.39 5.02

7 22.5442 88.3533 3A Upper, Wood St., Kolkata 1.73 8.89 4.54 3.22 6.55 3.53 4.99

8 22.5775 88.3810 1, Radhagovinda Nath Sarani, Tollygunge 1.73 6.46 3.69 3.18 4.95 3.32 3.77

9 22.5333 88.3569 Ballygunge Circular Rd.,Kolkata 1.73 7.51 3.88 3.31 5.68 3.11 4.10

10 22.5176 88.3568 121, Rash Bihari Av.,Kolkata 1.73 6.70 6.85 3.23 5.20 3.12 9.98

11 22.5176 88.3642 68, Hindusthan Park,Kolkata 1.87 6.08 4.52 3.13 4.63 3.22 5.50

12 22.5300 88.3084 K.K. Roy Choudhury Rd,Behala, Kolkata 1.87 6.61 4.53 3.19 5.00 3.30 5.39

13 22.4806 88.3300 8/5/1, Alipore Rd., Kolkata 1.73 5.95 4.67 3.19 4.75 2.35 6.29

14 22.4964 88.3195 31, James Long Sarani,Behala, Kolkata 1.60 6.31 4.09 3.54 5.16 4.09 3.94

15 22.5144 88.3252 53, Haraprasad Shastri Sarani, New Alipore 1.73 8.28 3.70 3.10 6.02 3.04 3.76

16 22.5683 88.3510 18, British India St., Kolkata 1.87 5.91 4.78 3.17 4.69 2.39 6.50

17 22.5342 88.3745 72, Tiljala Rd., Kolkata 1.20 14.38 2.66 4.50 9.19 1.42 1.92 to be continued

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Table 1 (continuation)

BH No.

Long. [°N]

Lat. [°E] Locality name F0 Ampl.

Average Amplification Factors (AAF) [Hz]

.25-10 .25-1 1-2 2-5 5-10

18 22.5332 88.3460 18b, Ashutosh Mukherjee Rd., Kolkata 1.73 6.85 4.92 3.30 5.52 2.15 6.75

19 22.5218 88.3492 14/1b, Manohar Pukur Rd., Kolkata 2.53 7.15 4.28 2.79 4.72 5.51 3.62

20 22.5020 88.3565 375, Prince Anwar Shah Rd., Kolkata 1.73 6.96 3.72 3.26 5.41 2.99 3.92

21 22.5822 88.3948 41 & 46, Canal Circular Rd. 1.73 6.04 4.35 3.22 4.86 1.97 5.88

22 22.5416 88.3494 20, Lee Rd., Kolkata 1.73 7.34 3.64 3.25 5.53 3.46 3.46

23 22.5191 88.3400 20/1, Chetla Rd., Kolkata 1.73 5.88 3.60 3.18 4.74 2.55 4.09

24 22.5654 88.3988 134b, Beliaghata Rd., Kolkata 1.60 7.40 3.98 3.41 6.05 2.80 4.41

25 22.5387 88.3978 E.M. Bypass, Kolkata 1.73 7.58 4.37 3.29 5.77 2.88 5.18

26 22.5437 88.3812 1/3, Mahendra Roy Lane, Kolkata 1.73 8.06 3.48 3.12 6.06 2.67 3.56

27 22.5041 88.3317 45, Buroshibtala Main Rd., Behala, Kolkata 1.60 8.18 4.77 3.51 6.37 4.01 5.64

28 22.5634 88.3534 Prop.Topsel Toyota at Kolkata 1.73 5.92 4.53 3.51 6.37 3.18 5.64

29 22.6413 88.3821 Prop. M.B.D. Airport Hotel at Kolkata 1.60 3.92 2.68 0.85 1.68 1.83 2.68

30 22.5376 88.4144 83/3 & 84/3 at Topsia Rd., Kolkata 1.73 8.03 3.57 3.23 4.83 2.96 3.51

31 22.5946 88.3549 Nimtala Burning Ghat 1.73 3.64 3.15 0.70 2.15 2.20 4.32 32 22.5727 88.4144 Ib Salt Lake 1.33 14.83 5.28 4.05 10.61 3.52 5.56 33 22.6404 88.372 Baranagar Isi 0.80 13.77 4.16 8.76 3.26 2.12 4.83 34 22.5878 88.4448 Substation New Town 1.60 11.06 4.22 3.45 8.36 3.36 4.11 35 22.5801 88.4096 Sector 3 Fc 1.73 10.29 4.20 2.89 7.75 3.52 4.16 36 22.5705 88.4216 Nicopark 1.87 6.38 4.96 3.21 5.00 3.04 6.38 37 22.5729 88.3641 Sealdah, Ultadanga 1.73 7.63 3.79 3.31 3.77 5.60 3.85

38 22.4521 88.3046 Diamond Park, Joka, Kolkata 1.73 8.30 4.76 3.35 6.19 3.15 5.69

39 22.5230 88.2870 Garden Reach 1.60 15.63 6.91 4.27 14.04 5.18 6.82

40 22.6550 88.3870 4, M.M. Feedar Rd., Kolkata 0.80 14.50 3.90 10.13 3.36 3.76 3.42

41 22.6150 88.3940 8, Mall Rd., Kolkata 1.60 6.69 3.75 3.29 5.57 4.67 2.92

42 22.5174 88.4051 E.M. Bypass, Plot No. 3794 1.87 6.86 4.12 3.17 5.02 3.55 4.45

43 22.5174 88.4051 16/1a, Gardenrich Rd. 1.62 13.34 6.70 4.15 13.04 4.18 6.52 44 22.5174 88.4051 20/2, Hestings Sarani 1.60 13.05 6.51 3.95 12.53 5.08 6.72


i,j i+1, j

i,j+1 i+1,j+1

: V, ρ

: , , , ; 1,... ...,xy xy xyxy u l lY l mσ μ χ =

: , , , ; 1,... ...,zy zy zyzy u l lY l mσ μ χ =

considered for the study, keeping in view that data should be widely distrib-uted in the study area as well as at the same time to avoid the clustering of data points. The number of sedimentary layers in the upper 50 m deposit var-ies from 3 to 8. The correction factors, namely overburden correction, dila-tancy correction, and correction due to finer content, are applied on N values (Sitharam et al. 2007). After applying the correction factors, N values have been used for obtaining the shear wave velocity in different layers down to a depth of 50 m using the formula Vs = 51.5 N0.516 (Iyisan 1996). The shear wave velocity for layers deeper than 50 m is derived from the velocity struc-ture at Bishnupur (south of the study area shown in Fig. 1), which falls on the Gopali–Port Canning seismic refraction profile (Reddy et al. 1998). There are two common layers for all the considered BH locations having thickness of 23 m (50-70 m depth) and 627 m (73-700 m depth), and a ve-locity of 740 and 1048 m/s, respectively. The velocity of the order of 1890 m/s for the basement at a depth of 700 m is also derived from the ve-locity structure at Bishnupur (Fig. 8 of Reddy et al. 1998).

4. SALIENT ASPECTS OF THE USED COMPUTER PROGRAM A computer program developed by Narayan and Kumar (2012) which is based on staggered grid second order in time and fourth order in space finite-difference approximation of viscoelastic SH-wave equation for heterogene-ous medium is used. In this subsection, the incorporation of frequency de-pendent damping in time domain FD simulation is described in brief (details are given in Narayan and Kumar (2012)). Figure 3 shows the staggering technique, where the particle velocity and density are defined at the nodes and the shear stresses, unrelaxed modulus of rigidity, anelastic coefficients

Fig. 3. Staggering technique for SH-wave modeling with fourth order spatial accura-cy. Particle velocity and density are defined at grid nodes and shear stress compo-nents and relaxed modulus of rigidity, anelastic coefficients, and anelastic functions are defined at the midway between two adjacent grid points.

A. SHIULY et al.

and anelastic functions are defined at the midway between the two adjacent grid points. The viscoelastic SH-wave equation for heterogeneous medium in the xz plane is given by Kristek and Moczo (2003) and Moczo et al. (2004).

,xy zyVt x z

σ σρ

∂ ∂∂= +

∂ ∂ ∂ (1)

( )12

1

, 1,2,..., ,m nxy xy xy xy

u l ll

V Y l mt xσ

μ χ+

=

⎛ ⎞∂ ∂ ⎟⎜= − =⎟⎜ ⎟⎜⎝ ⎠∂ ∂ ∑ (2)

( )12

1

, 1,2,..., ,m nzy zy zy zy

u l ll

V Y l mt zσ

μ χ+

=

⎛ ⎞∂ ∂ ⎟⎜= − =⎟⎜ ⎟⎜⎝ ⎠∂ ∂ ∑ (3)

where V is the particle velocity in the y direction, σxy and σzy are the stress components, ρ is the density, χ is the anelastic function, and uμ and lY are the modified modulus of rigidity and anelatic coefficients, respectively. ∂/∂x, ∂/∂z and ∂/∂t are the differential operators. Parameter m is the number of re-laxation frequencies used (the value of m in the present study is 4). Super-script n denotes the time index.

The anelastic function (χl) is given by the following equations (Moczo et al. 2004)

( ) ( )1 12 2

2 2 , 1,2,..., ,2 2

n nl lxy xyl l

l l

t t V l mt t xω ω

χ χω ω

+ −−Δ Δ ∂= + =

+Δ +Δ ∂ (4)

( ) ( )1 12 2

2 2 , 1, 2,..., .2 2

n nl lzy zyl l

l l

t t V l mt t zω ω

χ χω ω

+ −−Δ Δ ∂= + =

+Δ +Δ ∂ (5)

The modified modulus of rigidity, xyuμ and zy

uμ , can be computed using the following relations

1

1

11

1 , 1,2,..., ,

1 , 1,2,..., .

mxy xy xyu u l l

l

mzy zy zyu u l l

l

G Y l m

G Y l m

μ μ

μ μ

=

=

⎡ ⎤⎢ ⎥= + =⎢ ⎥⎣ ⎦⎡ ⎤⎢ ⎥= + =⎢ ⎥⎣ ⎦

∑

∑ (6)

Similarly, the modified anelastic coefficients xylY and zy

lY can be com-puted using the following relations

2

2

2 , 1, 2,..., ,2 , 1,2,..., ,

xy xyl u ll

zy zyl u ll

Y G Y l mY G Y l m

μ

μ

= =

= = (7)

where Yl are anelastic coefficients, μu is the unrelaxed modulus, and the con-stants G1l and G2l are given by


1 22and , 1, 2,..., .

2 2l

l ll l

tG G l mt tωω ω

Δ= = =

−Δ −Δ (8)

The effective values of the modulus of rigidity, xyuμ and zy

uμ at the mid-ways between the two adjacent grid points, are obtained using harmonic mean of μu at the node points in order to incorporate the material discontinui-ty (Moczo et al. 2002).

1 1

1 1, ,, 1, , , 12 2

1 1 1 1 1 1( ) and ( ) .2 ( ) ( ) 2 ( ) ( )

xy zyu ui j i j

u i j u i j u i j u i jμ μ

μ μ μ μ

− −

+ ++ +

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜⎢ ⎥ ⎢ ⎥⎟ ⎟= + = +⎜ ⎜⎟ ⎟⎢ ⎥ ⎢ ⎥⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ (9)

Further, the unrelaxed modulus μu has been obtained using phase veloci-ty of S wave ,( )rSV ω at a reference frequency (Fr = 1.0 Hz) and the following equations (Moczo et al. 1997).

12 2 21 2, 2

, where ,2ru S

RV RRω

ϑμ ρ ϑ ϑ

+= = + (10)

( ) ( )

1 22 21 1

11 , , 1,2,..., .1 1

m mr l

l ll lr l r l

Y Y l mω ωϑ ϑ

ω ω ω ω= =

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= − = =⎢ ⎥ ⎢ ⎥

+ +⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦∑ ∑ (11)

An elastic coefficients Yl, l = 1, 2, …, m have been computed with the help of following equation using Futterman’s equation (Futterman 1962) and least square technique.

( )21

12 2

1

( ) , 1,2,..., , 1, 2,..., 2 1.m

l k k lk l

l l k

QQ Y l m k mω ω ω ωω

ω ω

−−

=

+= = = −

+∑ (12)

The logarithmically distributed considered values of relaxation frequen-cies ω1, ω2, ω3, and ω4 are 0.3141, 3.141, 31.41, and 314.1, respectively. The

( )kQ ω values obtained using the Q at reference frequency and Futterman’s equation has been used for optimization. The ωk values are also logarithmi-cally distributed. ωk is defined at ωl as well as at the mid of two consecutive ωl values. Further, ωk=1 = ωl=1 and ωk=2m–1 = ωl=m.

In Eqs. 1-5, the time derivative was replaced by second order accurate central difference FD operator and space derivatives were replaced by a fourth order staggered grid FD operator (Levander 1988, Graves 1996, Moczo et al. 2000, Narayan 2001, Narayan and Kumar 2012). Both the sponge boundary (Israeli and Orszag 1981) and A1 absorbing boundary (Clayton and Engquist 1977) conditions were implemented on the model edges to avoid the edge reflections. In order to avoid the thickness discrep-

A. SHIULY et al.

ancy of the first soil layer, which causes a larger value of numerically com-puted F0, VGR-stress imaging technique developed by Narayan and Kumar (2008) was used. The use of staggered grid along with stress-images across the free surface causes soil-thickness discrepancy of half grid size in the ver-tical direction (Details of soil-thickness discrepancy is discussed in Narayan and Kumar (2008)). Variable grid size in vertical direction is used in order to accommodate the thickness of different soil layers and to reduce the re-quirement of computational memory and time (Narayan and Kumar 2008).

4.1 Validation of implementation of viscoelastic damping The accuracy of implementation of viscoelastic damping in time domain, FD simulation is validated by comparing the numerically computed spectral am-plitude damping in homogeneous half-space model with the same computed analytically.

4.1.1 Homogeneous half-space model First, seismic responses of a homogeneous half-space model were computed with and without damping. The phase velocity and quality factor for homo-geneous half-space model were taken as 1890.2 m/s and 189 at reference frequency 1.0 Hz. The density was taken as 2340 Kg/m3. The S-wave veloc-ity at reference frequency was used to compute the unrelaxed shear modulus using Eqs. 9-11. The anelastic coefficients were also computed using the quality factor at reference frequency. The response was computed at free sur-face using a horizontal plane wave front at a depth of 3.25 km. A horizontal wave front was inserted into the numerical grid using many point sources at the same depth. A Ricker wavelet with 4.0 Hz dominant frequency and con-siderable spectral amplitude in frequency range of 0.25 to 10.0 Hz was used as an excitation function for generating the point sources. Now, the computa-tion of response using a horizontal plane wave front is 1D response in nature using 2D FD algorithm. The ratio of spectra of responses with and without damping was computed to find out the spectral damping (please note that the spectra in case of no damping is equivalent to spectra at the source position (A0) since a plane-horizontal wave front is used in simulation). The analyti-cal spectral amplitude ratio Ax/A0 in the frequency range of 0.25 to 10.0 Hz was also computed using x = 3.25 km (the source-receiver distance) and the following well known equation.

0

.x xA eA

α−= (13)

Figure 4a shows the comparison of numerically and analytically comput-ed spectral amplitude ratios for a distance travelled as 3.25 km. The excellent


Fig. 4. Comparison of analytical (continuous line) and numerical (dotted line) spec-tral amplitude ratio (a), and soil amplification (b).

matching of analytical and numerical spectral amplitude ratios validates the accuracy of procedure of implementation of viscoelastic damping in time domain SH-wave finite-difference algorithm.

4.1.2 Soil layer overlying the half-space model In order to further validate the accuracy of implementation of viscoelastic damping in time domain FD simulation, seismic response of a horizontal soil layer overlying the half-space was used to compute the spectral amplifica-tion at F0. The parameters for soil layer were taken as VS = 223.5 m/s, den-sity = 1810 Kg/m3, quality factor = 24.86, and thickness = 30 m. Similarly, the parameters for half-space were taken as VS = 1890.2 m/s, density = 2340 Kg/m3, and quality factor = 158.2. The other parameters were the same as in the previous case. The simulated seismic responses with and without soil layer above the half-space were used for the computation of spectral amplification at F0. Figure 4b depicts that the spectral amplification factor at F0 is of the order of 7.87. The spectral amplification factor com-puted at F0 using the following analytical relationship is 7.91 (Bard and Riepl-Thomas 2000).

(a)

(b)

A. SHIULY et al.

01spectral amplification at ,

1 0.5πIC

Fξ

=+

(14)

where IC is impedance contrast and ξ is damping. The excellent matching of spectral amplification factor at F0 obtained analytically and numerically further validates the accuracy of implementation of viscoelastic damping in time domain finite-difference SH-wave algorithm.

5. COMPUTATION OF SPECTRAL AMPLIFICATION The deepest information in the study area from borehole (BH) data is only down to a depth of 50 m. Further, Information down to a depth of 30 m is available at all the BH locations. Two horizontal sedimentary layers with ex-tent from 50-73 m (thickness 23 m) and 73 to 700 m (thickness 627 m) above the considered seismic basement are common for all the BH locations. Where there is no information between 30 to 50 m depth, the known parame-ters of the deepest layer are extrapolated/interpolated down to a depth of 50 m. The shear wave velocity (1890 m/s) and density (2340 Kg/m3) for seismic basement are derived from the published data by Reddy et al. (1998). The quality factor (189) for seismic basement was taken as 10% of VS.

In this Section, first, details of development of 1D model for borehole location No. 4 (BH4) are given for the computation of spectral soil amplifi-cation. Thickness, N value, density, and other essential parameters for each soil layer are obtained from borehole log (Fig. 5) and table provided by the soil testing agency. There are three soil layers down to a depth of 30 m at BH4; the fourth layer parameters are derived from the surrounding BH loca-tion where information down to a depth of 50 m is available. As discussed earlier, two sedimentary layers are considered to be common for all the BH locations. So, finally, there are six sedimentary layers above the basement at BH4. The shear wave velocity, density, thicknesses, and quality factors for different layers are given in Table 2. The quality factor for layers having S-wave velocity between 175 to 610 m/s was computed using the relation Q = 0.08 VS + 6.99 (Iyisan 1996) and it was 10% of VS, where VS was larger than 610 m/s. In order to incorporate the different layers with their exact thicknesses in FD-grid as well as to avoid grid dispersion and to reduce the requirement of computational memory and time, variable grid size in vertical direction was used. The grid size in X direction was taken as 1.5 m. In case of 1D model for BH4, the grid sizes in vertical direction from top to bottom were taken as 2.1, 1.95, 2, 2, 4.6, and 10.45 m, respectively. The vertical grid size in the basement was taken as 10.45 m.


Table 2 The thickness, S-wave velocity, quality factor and density

of different sedimentary layers as well as bedrock for 1D model corresponding to BH4 location

Layers Thickness [m]

Vs [m/s]

Quality factor

Density [g/cc]

1 4.2 223.5 24.9 1.81 2 7.8 297.8 30.8 1.60 3 18 368.1 36.4 1.90 4 20 399.5 38.9 1.95 5 23 704.0 70.4 2.02 6 627 1048.3 104.8 2.03

Bedrock – 1890.0 189.0 2.34

Fig. 5. Boreholedetails of site BH4(after C.E. TestingCompany Pvt. Ltd.).

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Fig. 6. Seismic responses (a), spectral amplitude (b), and amplification factors (c).

Seismic responses of 1D model corresponding to BH4 were computed with and without considering the sedimentary layers above the basement us-ing a line source at a depth of 1.0 km. The time domain responses without and with sediment layers are shown in Fig. 6a. The maximum amplitude in case of model having sediment layers is about 4.4 times larger than that without sediment layers. The spectral amplification caused by sediments above the bedrock was computed just by taking the ratio of spectra shown in Fig. 6b. Figure 6c shows the spectral amplification factors in a frequency bandwidth of 0.25 to 10 Hz. The fundamental frequency and the correspond-ing spectral amplification factor were obtained as 1.73 Hz and 7.0, respec-tively. The obtained average amplification factors (AAF) in the frequency band of 0.25-10.0, 0.25-1.0, 1.0-2.0, 2.0-5.0, and 5.0-10.0 Hz are 4.28, 3.08, 5.69, 4.81, and 3.82, respectively. AAFs are highly variable from band to band and highest (5.69) is in frequency band of 1.0-2.0 Hz.


6. RESULTS AND CONCLUSIONS In a similar way, as given in previous section, 1D models for all the BH lo-cations were developed for the computation of seismic responses and spec-tral amplification factors. The fundamental frequencies (F0), amplification at F0, AAF in the considered frequency bandwidth as well as in other smaller frequency bands for the rest of BH locations were computed. Prepared maps of F0, AAF in different frequency bands and amplification factors at F0 may be very useful for a variety of end-users of communities, including structural and geotechnical engineers, building officials, emergency managers, land-use planners, private business, and general public. The map can be directly used for the seismic hazard assessment and seismic microzonation purposes, if basement motion is known.

6.1 Fundamental frequency and amplification factor The variation of fundamental frequency of sediment deposit above the con-sidered basement in Kolkata City is given in Fig. 7 and Table 1. The

Fig. 7. Map showing fundamental frequency of sedimentary deposit in Kolkata City at different BH-locations. Colour version of this figure is available in electronic edi-tion only.

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lowest value of F0 of the order to 0.8 Hz is obtained in Baranagar area (BH33 and BH40), very near to the Hoogly River. F0 of the order of 1.6 Hz is obtained at BH44, BH43, and BH39, very near the Hoogly River in the southwestern part of study area, in Nagar Bazar area (BH29) and Kolkata airport region (BH41). Small patches of low F0 of sediment deposit are also present sporadically in the study area. For example, F0 of the order of 1.2 Hz at Tiljala Road (BH17) and 1.33 Hz in IB Salt Lake area (BH32 and BH34). But the large F0 (1.73 Hz) obtained in Nimlata region (BH31) maybe due to a very thin surficial soft soil layer. The largest value of F0 = 2.53 Hz was obtained in Manohar Pukur Road area (BH19). This may be due to higher S-wave velocity in the surficial soil layers. At most of the BH locations, F0 was between 1.73 and 1.86 Hz.

Figure 8 depicts the amplification factor at F0. Very large spectral ampli-fication at F0, of the order of 13-15, is obtained near the Hoogly River (BH40, BH33, BH44, BH43, and BH39) except in Nimtala area (BH31). Small patches of very high spectral amplification at F0 are also observed in Salt Lake area (BH32, BH34, and BH35) and on Tiljala Road area (BH17).

Fig. 8. Map showing the amplification factors at fundamental frequencies. Colour version of this figure is available in electronic edition only.


Very low spectral amplification of the order of 3.6 to 3.9 is obtained in Nazar Bazar area (BH29) and Nimtala area (BH31). The very low spectral amplification at BH29 and BH31 may be due to the presence of a thick low velocity layer at some depth with considerable impedance contract at both the upper and lower interfaces, as was reported by Kumar and Narayan (2008). In rest of the study area, spectral amplifications at F0 are between 4 and 8.

6.2 Average amplification factor (AAF) Average amplification factor (AAF) in the frequency range of 0.25-10 Hz is shown in Fig. 9. This frequency range covers the natural frequency of almost all the engineering structures (single to multi-storey buildings) existing in Kolkata City. Very high AAF, of the order of 5-7, is obtained in southwest-ern part of the study area, very near the Hoogly River (BH39, BH43, and BH44). Small patches of large AAF are also observed at BH32 (Salt Lake area), BH10 (Rash Bihari Avenue), and BH2 (Upendra Banerjee Road area). Figure 9 also depicts very low AAF (< 3) in Nager Bazar area (BH29) and

Fig. 9. Map showing average amplification factors in frequency range of 0.25-10 Hz. Colour version of this figure is available in electronic edition only.

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Tiljala Road area (BH17). Obtained AAF of the order of 3 to 5 at most of the BH locations reveals that Kolkata City may suffer a severe damage even during a moderate earthquake. Very large AAF, of the order of 10 in fre-quency range of 0.1-5 Hz, was also reported by Singh (2009) in Roorkee situated in Ganga Basin.

6.3 Average amplification factors in different discrete frequency bands The average amplification factors in different frequency bands are also pre-sented in the form of table and contour maps, so that they can be used for cost effective earthquake engineering purposes.

6.3.1 AAF in frequency band of 0.25-1 Hz Figure 10 depicts the AAF in the frequency range of 0.25 to 1.0 Hz. In this frequency range, the high-rise buildings having storey greater than 10 and less than 40 may be affected due to resonance. Largest AAF, of the order of 8-10, is obtained in Baranagar area (BH33 and BH40). The cause of large AAF in low frequency band may be due to the very soft surficial soil layers.

Fig. 10. Map showing average amplification factors in frequency range of 0.25-1 Hz. Colour version of this figure is available in electronic edition only.


Larger AAF, of the order of 4, is also observed in southwestern part of the city, very near the Hoogly River (BH39, BH43, and BH44). Distant and large earthquakes may cause unexpected severe damage to high rise build-ings situated in areas very near the Hoogly River due to occurrence of dou-ble resonance, excluding Nimtala region (Narayan et al. 2002). The obtained large AAF (6.03) in southern avenue region (BH3) may be due to the pres-ence of Rabindra Sarobor (Lake). Higher AAF is also obtained at BH17 and BH32. AAF less than 1.0 at BH29 (Nager Bazar) and BH31 (Nimtala area) reveals that the high-rise buildings may be safer in these regions. The de-ampli-fication in the frequency range 0.25-1.0 Hz in Nimtala area and Nager Bazar may be due to the presence of a thick low velocity layer at depth with considerable impedance contract at both the upper and lower interfaces. Similar effect was also reported by Kumar and Narayan (2008). The AAF lies between 2.5 to 3.5 at most of BH locations in the study area.

6.3.2 AAF in frequency band of 1-2 Hz In this frequency band, the spectral amplification is larger as compared to other frequency bands. Similar observation was also reported by Vaccari et

Fig. 11. Map showing average amplification factors in frequency range of 1-2 Hz. Colour version of this figure is available in electronic edition only.

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al. (2011). The natural frequency of 5 to 10 storey buildings falls in this fre-quency range, which may be more affected during an earthquake due to dou-ble resonance under favorable condition. The AAF in the frequency band of 1.0-2.0 Hz is shown in Fig. 11. This figure depicts that in most of the study area AAF is in the range of 4-7. Largest AAF, of the order of 12-14 was ob-tained in Gardenreach area and beside the Hoogly River in the southwestern part of the study area (BH39, BH43, and BH44). Large AAF (8-10) was also obtained in entire Salt Lake and Newtown area and in Tiljala area (BH17). In the Salt Lake area, marshy low land is filled with soil. Figure 11 depicts lowest AAF (< 2) in Nager Bazar area (BH29) and Park Street area (BH1).

6.3.3 AAF in frequency band of 2-5 Hz In this frequency band, AAF is relatively lower as compared to other consid-ered frequency bands. The AAF in the frequency band of 2.0-5.0 Hz is shown in Fig. 12. In this frequency band, natural frequency of 2 to 4 storey buildings fall. AAF is of the order of 3-4 at most of the BH locations in the study area. The largest AAF, of order of 5.6, is obtained in Sealdah region



(BH37). Larger AAF, of the order of 4-5, is obtained in southwestern part of the study area (Gardenreach area; BH39, BH43, BH44). Larger AAF (4-5) is also obtained in small patches at BH41 (Kolkata airport area), BH19, and BH4 locations. There are few borehole locations where AAF is less than 2 (BH3, BH17, BH21, and BH29). Two to four storey buildings may suffer relatively more damage in Sealdah area and Manohar Pukur Road area (BH19) during an earthquake.

6.3.4 AAF in frequency band of 5-10 Hz Figure 13 depicts AAF in the frequency band of 5.0-10.0 Hz. One and two storey buildings have natural frequency in this frequency range. The ob-tained AAF even less than 1 (0.35) in South Avenue area (BH3) reveals that 1-2 storey buildings may suffer relatively less damage during an earthquake. Again, the de-amplification at BH3 in the considered frequency band may be due to the presence of low velocity layer at depth. The largest AAF of the order of 10 is obtained in Rash Bihari Avenue area (BH10), nearby Rabindra Sarovor Lake. This may be due to very soft soil deposit in surficial layers.


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Large AAF of the order of 7.8 is also obtained in Sealdah area (BH2). Large AAF of the order of 6-7 appeared in southwestern region of study area along the Hoogly River (BH39, BH43, BH44, BH13, BH18). Similar range of AAF is also obtained in small patches in Nicco Park area (BH36). AAF is of the order of 3-5 at most of the borehole locations in the study area. In this frequency range, AAF is also low (2.68) in Nager Bazar area (BH29).

7. DISCUSSION Highly populated Kolkata City is situated on the world’s largest delta-island. Being the main socio-political and economic nerve in the eastern part of In-dia, it needs special attention to be paid by planners, engineers, and decision makers for earthquake disaster preparedness. The computed soil amplifica-tion factors in different frequency bands revealed that the Kolkata City is very much prone to severe damage even during a moderate earthquake. It has already been reflected in terms of unexpected intensity of the order of VII during 15 April 1964, Kolkata earthquake (M = 5.2 and epicentral dis-tance of 106 km) and intensity VIII during Assam earthquake of 1897 (M = 8.7 and epicentral distance > 470 km) (Jhingran et al. 1969, Seeber and Armbruster 1981, GSI 2000). Sometimes, unexpected severe damage to collapse of mutli-storey buildings occur due to double resonance during a large and distant earthquake, as observed in Ahmedabad City during Bhuj (India) earthquake of 2001 (Narayan et al. 2002) and in Mexico City during Mexico earthquake of 1985 (Romo and Seed 1986). It means, unexpected damage to 10-20 storey buildings in Baranagar area (BH33, BH40) and 5-10 storey buildings in Gardenreach area (BH39, BH43, BH44) and Salt Lake area (BH32, BH34, BH35) may occur even during distant and large earth-quakes due to double resonance. The obtained very large AAF, of the order of 5-10 in the frequency range of 1-2 Hz, corroborates the findings of Vac-cari et al. (2011). Very large AAF, of the order of 10 in a frequency band of 0.1 to 5.0 Hz, was also reported by Singh (2009) at Roorkee in Ganga Basin, India.

It seems that the Nager Bazar area (BH29) and Nimtala area (BH31) are the safest areas from an earthquake point of view since in these areas AAF is very low in all the considered frequency bands and there is even de-ampli-fication in the frequency range of 0.25-1.0 Hz. This may be due to the pres-ence of thick low velocity sedimentary layer at deeper horizon with a con-siderable IC on both the upper and lower interfaces. A similar, low velocity effect on ground motion de-amplification was also reported by Kumar and Narayan (2008). It can be inferred that all sorts of structures in the Garden-reach area, near the Hoogly River (BH39, BH43, BH44) may suffer severe damage since AAF is very large in all the considered frequency bands. In certain areas/localities very selective damage may occur during earthquake.


For example multi-storey buildings (> 5) may suffer more damage as com-pared to few-storey buildings (< 5) in Southern Avenue area (BH3) and Tijala Road area (BH17). In Salt Lake area (BH32, BH34, BH35), 5-10 sto-rey buildings may suffer more damage. Similarly, in Baranagar area (BH33 and BH40) high-rise buildings (> 10 storey) may suffer more damage as compared to other structures. The 1-2 storey buildings in Rash Bihari Ave-nue area (BH10, BH21) may suffer more damage as compared to other buildings.

Acknowledgemen t . The authors are grateful to two unknown re-viewers for valuable comments and suggestions, which led to great im-provement in the original manuscript. Authors are also thankful to the Ministry of Earth Sciences (MoES), New Delhi for the financial assistance as well as C.E. Testing Company Pvt. Ltd., Kolkata and S. Ghosh & Associ-ates, Kolkata for providing the borehole data.

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Received 2 May 2012 Received in revised form 9 October 2012

Accepted 13 November 2012

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Computation of ground motion amplification in Kolkata megacity (India) using finite-difference method for seismic microzonation