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Engineering, Technology & Applied Science Research Vol. 12, No. 6, 2022, 9471-9476 9471 
 

www.etasr.com Thakur & Roy: Soil Liquefaction Potential in Different Seismic Zones of Bihar, India 

 

Soil Liquefaction Potential in Different Seismic 

Zones of Bihar, India 
 

Ishwar Chandra Thakur 

Civil Engineering Department 

National Institute of Technology Patna  

Patna, India 

ishwart.phd20.ce@nitp.ac.in 

L. B. Roy 

Civil Engineering Department 

National Institute of Technology Patna  

Patna, India 

lbroy@nitp.ac.in 
 

Received: 28 August 2022 | Revised: 8 September 2022 | Accepted: 9 September 2022 

 

Abstract-Liquefaction potential analysis for the liquefiable as 

well as non-liquefiable soils of Bihar state has been performed in 

this paper based on the actual field data from three seismic zones, 

i.e. zone III, zone IV, and zone V. The analysis has been 

performed following the simplified procedure given in [1] and 

later modified in [2]. The results show that districts under seismic 

zone III are comparatively more resistant to liquefaction in most 

cases, districts of zone IV are relatively more prone to 

liquefaction up to a few depths, and districts of zone V are most 

liquefiable. Liquefaction resistance is primarily depending upon 

the fine content of soil and SPT N-values.  

Keywords-standard penetration test; cyclic stress ratio; cyclic 

resistance ratio; soil liquefaction 

I. INTRODUCTION  

Liquefaction is the phenomenon in which the strength and 
stiffness of the soil are reduced by earthquake shaking and/or 
another dynamic loading. When an earthquake of suitable 
intensity shakes a deposit of loose saturated coarse-grained 
cohesionless soils, then the grain structures are triggered 
towards a more compact packing. However, it is not possible to 
drain off the pore water because it does not have sufficient time 
to do so during an earthquake. The pore water pressure then 
shoots outward because the applied stresses are taken up by the 
incompressible water and the effective stresses approach zero: 

� � = � − �    (1) 
where � �  is the effective stress, � is the total stress, and �  is 
pore water pressure. 

In the case of cohesionless soil (� = 0), shear strength (�) 
reduces to zero when effective stress approaches zero. 

� = � + σ� tan � �    (2) 
where � � is the effective internal resistance of the soil. 

Liquefaction is one of the most disastrous seismic hazards. 
India has experienced the world’s greatest earthquakes in the 
last few decades which lead to soil liquefaction and 
consequential damages.  

Authors in [1] presented a simplified procedure for the 
evaluation of the liquefaction potential of soil using the 

assemblage of available field data of liquefied or non-liquefied 
soil during earthquakes. The author in [3] studied the field data 
from different countries for the evaluation of the liquefaction 
potential of soil in earthquake magnitude Mw = 7.5 and the 
result was then extended to earthquakes of other magnitudes 
and for silty soil. Authors in [4] presented a critical review of 
sandy soil deposits. It was found that the sand that has more 
than 10% fine content has a much higher resistance to 
liquefaction than clean sand having the same SPT N value. For 
clean sands with SPT N1 values greater than 25, silty sands 
containing more than 10% fines with SPT N values greater than 
20, or sandy silts with more than 20% clay will not undergo 
any extensive damage. Sands containing gravel particles have 
lower resistance than the clean sands without gravel for the 
same SPT N-values. Authors in [5] presented the influence of 
SPT procedures in the evaluation of liquefaction resistance. 
They also proposed the curve of liquefaction resistance for 
sands with the variations of SPT N-values and fines content. 
Authors in [6] proposed a simple correction factor to counteract 
the effect of overburden pressure on the results of the Standard 
Penetration Test (SPT) performed in sands. Authors in [7] 
studied the possible frequency of earthquakes in India and 
found that India has relatively higher frequencies of great 
earthquakes and lower frequencies of moderate earthquakes. 
Authors in [8] studied the liquefaction potential as per the case 
history of the Bihar-Nepal Earthquake on 21 August 1988. 
Based on three prevailing approaches, they found the 
differences with regard to relative density and depth of 
liquefaction potential and suggested further research. Authors 
in [9] studied the mechanism of liquefaction and soil failure 
during the 1994 Northridge earthquake with detailed 
subsurface investigations. They found that the variation of the 
Ground Water Table (GWT) in combination with the 
heterogeneous nature of alluvial fan sediments is responsible 
for complex patterns of ground deformation. Authors in [10] 
found that clay particles are mainly responsible for the 
liquefaction characteristics of the soil. Authors in [2] convened 
a workshop sponsored by the National Center for Earthquake 
Engineering Research (NCEER) with 20 experts to review 
developments in the field of liquefaction in the past. They have 
given many updates and augmentations to the simplified 
procedure proposed in [1]. Authors in [11] studied the 

Corresponding author: Ishwar Chandra Thakur 



Engineering, Technology & Applied Science Research Vol. 12, No. 6, 2022, 9471-9476 9472 
 

www.etasr.com Thakur & Roy: Soil Liquefaction Potential in Different Seismic Zones of Bihar, India 

 

likelihood of the initiation of soil liquefaction by SPT-based 
probabilistic and deterministic correlations. Authors in [12] 
closely studied the possible factor of the Bhuj 2001 earthquake 
and found that deep fluid inflow plays a crucial role in the 
intensity of disasters. Authors in [13] studied the Liquefaction 
Potential Index (LPI) of Mumbai city. They evaluated the 
factors of safety to predict the liquefaction potential along the 
depths of soil with a 2% probability of exceedance in 50 years 
using an SPT-based simplified procedure. Authors in [14] 
described the influence of earthquake ground motion on the 
liquefaction resistance of the soil. Authors in [15] investigated 
the paleoliquefaction from four sites in north Bihar and one site 
in eastern Uttar Pradesh. Based on the available data, they 
found the recurrence interval of 124 ± 63 years for great 
earthquakes like the 1934 earthquake in Bihar. They also 
concluded that the Plains of Bihar are most vulnerable to the 
seismic activity originating from the Himalayas as well as the 
terai Plains of Nepal. Authors in [16] studied the quality of 
groundwater in Bihar. Authors in [17] studied the post-
earthquake effect in Kathmandu valley after Gorkha, Nepal 
earthquake on 25 April 2015. They found seven locations of 
sand blows based on geotechnical investigation records. 
Authors in [18] reinterpreted the dynamic behavior of sandy 
soils subjected to recent historical earthquakes in Japan and 
demonstrated that the aged soils have higher resistance towards 
liquefaction than that suggested by their current design code. 
Authors in [19] studied four districts of Bihar, i.e. Samastipur, 
Darbhanga, West-Champaran, and Araria based on reliability 
techniques for the prediction of seismic liquefaction. Authors 
in [20-26] described stability methods for the soil types in 
Bihar. Authors in [27] evaluated the effect of plasticity on the 
liquefaction potential of fine-grained soil in the seismically 
active regions of Bihar based on Multi-Linear Regression 
(MLR) analysis and reliability analysis, i.e. First Order Second 
Moment (FOSM), and established a co-relation between the 
factor of safety against liquefaction, reliability index, and 
liquefaction probability.  

According to the literature survey, Bihar is one of the most 
vulnerable states concerning seismic activities. Tremendous 
work has been conducted in the field of liquefaction, but little 
in the region. This study has been done to overcome this 
shortcoming and to have more accurate predictions of 
liquefaction in the seismic zones of Bihar, i.e. zone III, zone 
IV, and zone V and their relative vulnerability towards 
liquefaction. Here, a general correlation between liquefaction 
potential, depth, fines content, and SPT-N value has been 
established to be used as a handy tool. The method adopted 
here for the analysis is the method recommended by Indian 
Standard which is originally based on the simplified empirical 
method of [1] and later on modified by different researchers in 
this field.  

II. METHODOLOGY 

The prime concern is to know whether the soil is 
susceptible to liquefaction or not, so that suitable measures can 
be adopted in advance if required. For this purpose, the Factor 
Of Safety (FOS) against liquefaction is estimated according to 
the method described in Annex F of Indian Standard code [28] 
IS 1893 (Part 1): 2016, which is based on the Simplified 

Procedure proposed in [1] and later modified in [2]. The 
proneness of soil towards liquefaction is assured by estimating 
the FOS at different depths below Natural Ground Level 
(NGL). The FOS is estimated by dividing the Cyclic 
Resistance Ratio (CRR) required to induce liquefaction in the 
soil by the Cyclic Stress Ratio (CSR) produced by an 
earthquake.  

FOS = ������     (3) 
A. Evaluation of CSR 

Authors in [1] formulated the following expression for the 
calculation of (CSR): 

CSR = 0.65 ������  �
!"#
!"#$

 %&     (4) 
where '(�) = Peak Ground Acceleration (PGA) at the ground 
surface, * = gravity acceleration, �,- = total vertical stress at 
the point of interest, �,-� = effective vertical stress at the same 
point, and %& =    %eduction factor. 

The value of the reduction factor was initially given in [1] 
which was later approximated in [29]: 

%& = ..///0/.1..23
4.56/./1/7836/.//.9723:.5

..///0/.1.9934.56/./798;30/.//<8/73 :.56/.//.8./3=    (5) 

IS 1893 (part 1):2016 recommends using the ratio  
('(�) /*) equal to seismic zone factor if the value of PGA is 
not available.  

TABLE I.  SEISMIC ZONE FACTOR 

Seismic zone factor II III IV V 

Z 0.10 0.16 0.24 0.36 

 

B. Evaluation of CRR 

CRR = ABB9.7(CDE)F! FG     (6) 
where ABB9.7 =  CCR for earthquake magnitude Mw = 7.5, 
MSF, F! , and FG are the correction factors for earthquake 
magnitude other than 7.5 (commonly known as magnitude 
scaling factor), overburden stress, and static shear stress 
respectively. 

Authors in [2] re-evaluated the 1982’s data set to get the 
revised MSF given by:  

MSF = 108.81 ∕ CK8⋅7<     (7) 
The high overburden correction factor is required for a 

depth greater than 15m is [30]: 

F! = (�,-� ∕ M� )N0.    (8) 
where M�  is the atmospheric pressure measured in the same unit 
as effective overburden pressure ( �,-� )  and the value of O 
depends on relative density (PQ ): 

O=   R 0.8~0.7            for PQ  =  40% to 60% 0.7~0.6            for PQ =    60% to 80%    (9) 
As per the report correction for static shear stress [28], FG, 

is required only for sloping ground which may be assumed to 
be in routine practice. 



Engineering, Technology & Applied Science Research Vol. 12, No. 6, 2022, 9471-9476 9473 
 

www.etasr.com Thakur & Roy: Soil Liquefaction Potential in Different Seismic Zones of Bihar, India 

 

The SPT N-value measured in the field is corrected for the 
60% hammer efficiency and standardized equipment using the 
expression: 

[</ = [A</     (10) 
where A</ = A\] ∗ A\_ ∗ A`` ∗ Aab ∗ Acd  and A\] , A\_ , A`` , 
Aab , and Acd  are the correction factors for the height of fall, 
hammer weight, sampler setup, rod length, and borehole 
diameter respectively. 

The N60 value computed is normalized to approximately 
100kPa effective overburden pressure as suggested in [6]: 

([.)</ = Ae [</    (11) 
where: 

Ae = (M� /�,-� )/.7 ≤ 1.7    (12) 
Authors in [22] developed an equation for counteracting the 

effect of fines content to get an equivalent clean sand value 
([.)</fg: 

([.)</fg = h + i([.)</    (13) 
where: 

2

190 1.5
[1.76 ]

0                1                      for 5%

    0.99    for 5% 35%
1000

0.5             1.2                   for 35%

FC

a FC

FC
a e FC

a FC









  

    

  

    (14) 

An expression for cyclic resistance ratio for a 7.5 
magnitude earthquake was formulated in [31] based on a clean 
sand base curve plot originally proposed in [5]: 

ABB9.7 = .210(e:)j4kl +
(e:)j4kl

.27 +
7/

m./×(e:)j4kl617o=
− .8//    (15) 

This expression is valid for ([.)</ < 30. For ([.)</ ≥ 30, 
soils are too dense and non-liquefiable. 

III. DATA ANALYSIS 

Analysis has been done based on the big input data set 
which includes the depth of strata, its dry density, moisture 
content, fineness content, and SPT N-values. The rotary 
method of boring was adopted with a borehole diameter of 
150mm throughout the project. For the analysis of the whole 
project the magnitude of the earthquake, Mw, was taken as 7.5. 
Three major district data from seismic zone III, five from 
seismic zone IV, and three from seismic zone V are 
summarized here in Tables II-IV for representation. The other 
districts from that zones show almost similar results. The soil 
of Nawada and Buxar districts has initially lower resistance to 
liquefaction which is almost near to the FOS-1 line but at 3m 
depth there is a sudden increase in the FOS of Buxar due to the 
increase in SPT N-value. Bhojpur has comparatively higher 
resistance against liquefaction in seismic zone III.  

 

 
Fig. 1.  Variation of the factor of safety with depth in seismic zone III 

TABLE II.  LIQUEFACTION ANALYSIS OF ZONE III (PGA: 0.16, MSF: 1, KA: 1) 

District 
Depth 

(m) 

ϒ 

(kN/m
3
) 

FC N-value 
σv 

(kPa) 

σ´v 

(kPa) 
rd CSR C60 N60 CN (N1)60 (N1)60CS Kσ CRR7.5 CRR FOS 

Buxar 

GWT: 1.10m 

1.50 19.62 95.20 10 29.43 25.51 0.990 0.12 0.65 6.50 1.70 11.04 13.75 1.00 0.15 0.15 1.24 

3.00 19.91 97.20 22 59.74 41.10 0.979 0.15 0.69 15.25 1.56 23.78 29.04 1.00 0.41 0.41 2.78 

4.50 19.72 97.20 14 88.73 55.38 0.969 0.16 0.74 10.31 1.34 13.85 17.12 1.00 0.18 0.18 1.13 

6.00 19.82 94.10 18 118.90 70.83 0.958 0.17 0.82 14.81 1.19 17.60 21.62 1.00 0.24 0.24 1.42 

7.50 19.82 94.20 20 148.62 85.84 0.943 0.17 0.82 16.46 1.08 17.76 21.82 1.00 0.24 0.24 1.41 

9.00 19.91 96.40 21 179.23 101.73 0.923 0.17 0.82 17.28 0.99 17.13 21.06 1.00 0.23 0.23 1.35 

10.50 19.91 96.60 23 209.10 116.89 0.894 0.17 0.87 19.92 0.92 18.43 22.61 1.00 0.25 0.25 1.51 

Nawada 

GWT: 3.50m 

1.50 18.64 3.20 9 27.96 27.96 0.990 0.10 0.65 5.85 1.70 9.94 9.94 1.00 0.11 0.11 1.09 

3.00 18.64 4.30 11 55.92 55.92 0.979 0.10 0.69 7.62 1.34 10.19 10.19 1.00 0.11 0.11 1.13 

4.50 18.34 5.00 22 82.55 72.74 0.969 0.11 0.74 16.20 1.17 18.99 18.99 1.00 0.20 0.20 1.78 

6.00 18.25 6.80 26 109.48 84.95 0.958 0.13 0.82 21.40 1.08 23.21 23.49 1.00 0.26 0.26 2.06 

7.50 18.25 2.70 25 136.85 97.61 0.943 0.14 0.82 20.57 1.01 20.82 20.82 1.00 0.23 0.23 1.64 

9.00 18.25 3.00 26 164.22 110.26 0.923 0.14 0.82 21.40 0.95 20.38 20.38 1.00 0.22 0.22 1.54 

10.50 18.25 6.30 28 191.59 122.92 0.894 0.14 0.87 24.26 0.90 21.88 22.05 1.00 0.24 0.24 1.67 

12.00 18.15 7.00 31 217.78 134.40 0.857 0.14 0.87 26.85 0.86 23.16 23.48 1.00 0.26 0.26 1.83 

13.50 18.05 3.10 35 243.68 145.58 0.811 0.14 0.87 30.32 0.83 25.13 25.13 1.00 0.29 0.29 2.09 

15.00 18.05 3.50 39 270.76 157.94 0.761 0.14 0.87 33.78 0.80 26.88 26.88 0.87 0.34 0.29 2.15 

Bhojpur 

GWT: 6.90m 

1.50 19.72 74.30 11 29.58 29.58 0.990 0.10 0.65 7.15 1.70 12.15 15.08 1.00 0.16 0.16 1.56 

3.00 19.72 84.60 12 59.15 59.15 0.979 0.10 0.69 8.32 1.30 10.81 13.47 1.00 0.15 0.15 1.42 

4.50 19.72 85.50 14 88.73 88.73 0.969 0.10 0.74 10.31 1.06 10.94 13.63 1.00 0.15 0.15 1.45 

6.00 19.82 79.30 17 118.90 118.90 0.958 0.10 0.82 13.99 0.92 12.83 15.90 1.00 0.17 0.17 1.70 

7.50 19.82 80.30 19 148.62 142.74 0.943 0.10 0.82 15.64 0.84 13.09 16.20 1.00 0.17 0.17 1.69 

9.00 19.91 77.40 23 179.23 158.63 0.923 0.11 0.82 18.93 0.79 15.03 18.53 1.00 0.20 0.20 1.82 

10.50 19.91 78.40 25 209.10 173.78 0.894 0.11 0.87 21.66 0.76 16.43 20.21 1.00 0.22 0.22 1.95 



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TABLE III.  LIQUEFACTION ANALYSIS OF ZONE IV (PGA: 0.246, MSF: 1, KA: 1) 

District 
Depth 

(m) 

ϒ 

(kN/m
3
) 

FC 
N-

value 

σv 

(kPa) 

σ´v 

(kPa) 
rd CSR C60 N60 CN (N1)60 (N1)60CS Kσ CRR7.5 CRR FOS 

Nalanda 
GWT: 

3.85m 

1.50 18.25 92.95 5 27.37 27.37 0.990 0.15 0.65 3.25 1.70 5.52 7.13 1.00 0.09 0.09 0.57 

3.00 18.25 93.75 6 54.74 54.74 0.979 0.15 0.69 4.16 1.35 5.62 7.24 1.00 0.09 0.09 0.59 

4.50 18.34 90.95 11 82.55 76.17 0.969 0.16 0.74 8.10 1.15 9.28 11.64 1.00 0.13 0.13 0.78 

6.00 18.34 88.92 14 110.07 88.98 0.958 0.18 0.82 11.52 1.06 12.21 15.16 1.00 0.16 0.16 0.87 

7.50 18.44 91.32 17 138.32 102.51 0.943 0.20 0.82 13.99 0.99 13.82 17.08 1.00 0.18 0.18 0.91 

9.00 18.44 90.44 21 165.99 115.46 0.923 0.21 0.82 17.28 0.93 16.08 19.80 1.00 0.21 0.21 1.03 

10.50 18.44 92.59 24 193.65 128.41 0.894 0.21 0.87 20.79 0.88 18.35 22.52 1.00 0.25 0.25 1.19 

12.00 18.44 90.09 29 221.31 141.36 0.857 0.21 0.87 25.12 0.84 21.13 25.85 1.00 0.31 0.31 1.48 

13.50 18.74 91.20 30 252.95 158.28 0.811 0.20 0.87 25.99 0.79 20.66 25.29 1.00 0.30 0.30 1.47 

15.00 18.74 89.77 31 281.06 171.68 0.761 0.19 0.87 26.85 0.76 20.50 25.09 0.85 0.29 0.25 1.29 

Patna 
GWT: 

4.50m 

1.50 19.33 90.90 7 28.99 28.99 0.990 0.15 0.65 4.55 1.70 7.73 9.78 1.00 0.11 0.11 0.72 

3.00 19.52 90.90 9 58.57 58.57 0.979 0.15 0.69 6.24 1.31 8.15 10.28 1.00 0.12 0.12 0.76 

4.50 19.62 90.90 12 88.29 88.29 0.969 0.15 0.74 8.84 1.06 9.40 11.78 1.00 0.13 0.13 0.85 

6.00 19.72 91.70 16 118.31 103.59 0.958 0.17 0.82 13.17 0.98 12.94 16.02 1.00 0.17 0.17 1.00 

7.50 19.72 91.70 20 147.89 118.46 0.943 0.18 0.82 16.46 0.92 15.12 18.65 1.00 0.20 0.20 1.08 

9.00 19.91 91.70 23 179.23 135.08 0.923 0.19 0.82 18.93 0.86 16.29 20.04 1.00 0.22 0.22 1.13 

10.50 19.91 92.90 24 209.10 150.24 0.894 0.19 0.87 20.79 0.82 16.96 20.85 1.00 0.23 0.23 1.17 

12.00 20.01 92.90 28 240.15 166.57 0.857 0.19 0.87 24.26 0.77 18.79 23.05 1.00 0.26 0.26 1.34 

13.50 20.01 92.90 30 270.17 181.88 0.811 0.19 0.87 25.99 0.74 19.27 23.62 1.00 0.27 0.27 1.42 

15.00 20.11 90.90 33 301.66 198.65 0.761 0.18 0.87 28.59 0.71 20.28 24.84 0.81 0.29 0.23 1.30 

Saran 
GWT: 

2.00m 

1.50 19.23 92.70 6 28.84 28.84 0.990 0.15 0.65 3.90 1.70 6.63 8.45 1.00 0.10 0.10 0.65 

3.00 19.52 92.70 9 58.57 48.76 0.979 0.18 0.69 6.24 1.43 8.93 11.22 1.00 0.12 0.12 0.68 

4.50 19.62 92.70 10 88.29 63.77 0.969 0.21 0.74 7.36 1.25 9.22 11.57 1.00 0.13 0.13 0.61 

6.00 19.23 91.90 12 115.37 76.13 0.958 0.23 0.82 9.88 1.15 11.32 14.08 1.00 0.15 0.15 0.67 

7.50 19.23 91.90 15 144.21 90.25 0.943 0.24 0.82 12.34 1.05 12.99 16.09 1.00 0.17 0.17 0.73 

9.00 19.33 91.90 18 173.93 105.26 0.923 0.24 0.82 14.81 0.97 14.44 17.83 1.00 0.19 0.19 0.80 

10.50 19.33 93.00 23 202.92 119.53 0.894 0.24 0.87 19.92 0.91 18.22 22.37 1.00 0.25 0.25 1.04 

12.00 19.62 93.00 26 235.44 137.34 0.857 0.23 0.87 22.52 0.85 19.22 23.56 1.00 0.27 0.27 1.16 

13.50 19.62 93.00 28 264.87 152.06 0.811 0.22 0.87 24.26 0.81 19.67 24.10 1.00 0.28 0.28 1.25 

15.00 19.72 91.70 30 295.77 168.24 0.761 0.21 0.87 25.99 0.77 20.04 24.54 0.86 0.28 0.24 1.16 

West 

Champaran 

GWT: 

5.10m 

1.50 19.13 94.90 28 28.69 28.69 0.990 0.15 0.65 18.19 1.70 30.93 37.61 1.00 0.00 0.00 0.00 

3.00 19.03 96.50 7 57.09 57.09 0.979 0.15 0.69 4.85 1.32 6.42 8.20 1.00 0.10 0.10 0.64 

4.50 19.03 96.60 6 85.64 85.64 0.969 0.15 0.74 4.42 1.08 4.77 6.23 1.00 0.08 0.08 0.54 

6.00 19.03 95.10 12 114.19 105.36 0.958 0.16 0.82 9.88 0.97 9.62 12.04 1.00 0.13 0.13 0.81 

7.50 19.23 95.30 23 144.21 120.66 0.943 0.18 0.82 18.93 0.91 17.23 21.18 1.00 0.23 0.23 1.31 

9.00 19.23 95.30 25 173.05 134.79 0.923 0.18 0.82 20.57 0.86 17.72 21.76 1.00 0.24 0.24 1.29 

10.50 19.33 95.40 28 202.92 149.95 0.894 0.19 0.87 24.26 0.82 19.81 24.27 1.00 0.28 0.28 1.47 

Begusarai 
GWT: 

4.00m 

1.50 19.52 84.30 9 29.28 29.28 0.990 0.15 0.65 5.85 1.70 9.94 12.43 1.00 0.14 0.14 0.87 

3.00 19.52 84.30 11 58.57 58.57 0.979 0.15 0.69 7.62 1.31 9.96 12.45 1.00 0.14 0.14 0.89 

4.50 19.91 84.30 19 89.61 84.71 0.969 0.16 0.74 13.99 1.09 15.20 18.74 1.00 0.20 0.20 1.25 

6.00 19.91 84.30 23 119.49 99.87 0.958 0.18 0.82 18.93 1.00 18.94 23.23 1.00 0.26 0.26 1.46 

7.50 19.91 87.20 25 149.36 115.02 0.943 0.19 0.82 20.57 0.93 19.18 23.52 1.00 0.27 0.27 1.39 

9.00 19.91 87.20 26 179.23 130.18 0.923 0.20 0.82 21.40 0.88 18.75 23.00 1.00 0.26 0.26 1.30 

10.50 20.01 79.40 28 210.13 146.37 0.894 0.20 0.87 24.26 0.83 20.05 24.56 1.00 0.28 0.28 1.41 

12.00 20.01 79.40 30 240.15 161.67 0.857 0.20 0.87 25.99 0.79 20.44 25.03 1.00 0.29 0.29 1.47 

13.50 20.11 82.40 32 271.49 178.30 0.811 0.19 0.87 27.72 0.75 20.76 25.41 1.00 0.30 0.30 1.56 

15.00 20.11 82.40 38 301.66 193.75 0.761 0.18 0.87 32.92 0.72 23.65 28.88 0.82 0.40 0.33 1.80 
 

 

 

Fig. 2.  Variation of the factor of safety with depth in seismic zone IV. 

 

 

 

Fig. 3.  Variation of the factor of safety with depth in seismic zone V. 

 



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TABLE IV.  LIQUEFACTION ANALYSIS OF ZONE IV (PGA: 0.36, MSF: 1, KA: 1) 

District 
Depth 

(m) 

ϒ 

(kN/m
3
) 

FC N-value 
σv 

(kPa) 

σ´v 

(kPa) 
rd CSR C60 N60 CN (N1)60 (N1)60CS Kσ CRR7.5 CRR FOS 

Madhubani 
GWT: 0.85m 

1.50 17.96 23.20 3 26.95 20.57 0.990 0.30 0.65 1.95 1.70 3.31 7.73 1.00 0.09 0.09 0.31 

3.00 17.95 17.20 6 53.85 32.76 0.979 0.38 0.69 4.16 1.70 7.07 10.56 1.00 0.12 0.12 0.31 

4.50 18.04 93.68 9 81.20 45.40 0.969 0.41 0.74 6.63 1.48 9.84 12.30 1.00 0.13 0.13 0.33 

6.00 18.07 21.08 10 108.39 57.87 0.958 0.42 0.82 8.23 1.31 10.82 15.55 1.00 0.17 0.17 0.39 

7.50 18.05 13.30 12 135.35 70.11 0.943 0.43 0.82 9.88 1.19 11.79 14.23 1.00 0.15 0.15 0.36 

9.00 18.06 7.35 28 162.55 82.59 0.923 0.43 0.82 23.04 1.10 25.35 25.78 1.00 0.31 0.31 0.72 

10.50 18.29 6.73 32 192.07 97.40 0.894 0.41 0.87 27.72 1.01 28.09 28.38 1.00 0.38 0.38 0.93 

12.00 18.35 37.70 12 220.26 110.88 0.857 0.40 0.87 10.40 0.95 9.87 12.35 1.00 0.13 0.13 0.34 

13.50 18.43 41.34 15 248.77 124.68 0.811 0.38 0.87 12.99 0.90 11.64 14.46 1.00 0.15 0.15 0.41 

15.00 18.45 4.25 28 276.73 137.92 0.761 0.36 0.87 24.26 0.85 20.65 20.65 0.91 0.22 0.20 0.57 

Darbhanga 
GWT: 2.30m 

1.50 18.04 94.80 5 27.07 27.07 0.990 0.23 0.65 3.25 1.70 5.52 7.13 1.00 0.09 0.09 0.38 

3.00 18.57 93.10 7 55.70 48.83 0.979 0.26 0.69 4.85 1.43 6.94 8.83 1.00 0.10 0.10 0.39 

4.50 18.26 86.46 9 82.18 60.60 0.969 0.31 0.74 6.63 1.28 8.51 10.72 1.00 0.12 0.12 0.39 

6.00 18.22 16.75 15 109.31 73.02 0.958 0.34 0.82 12.34 1.17 14.45 18.24 1.00 0.19 0.19 0.58 

7.50 18.68 15.50 10 140.08 89.07 0.943 0.35 0.82 8.23 1.06 8.72 11.80 1.00 0.13 0.13 0.37 

9.00 18.61 16.70 11 167.47 101.75 0.923 0.36 0.82 9.05 0.99 8.97 12.44 1.00 0.14 0.14 0.38 

10.00 18.25 16.75 13 182.51 106.97 0.905 0.36 0.87 11.26 0.97 10.89 14.48 1.00 0.15 0.15 0.43 

Supaul 
GWT: 1.00m 

3.00 19.33 71.00 8 57.98 38.36 0.979 0.35 0.69 5.54 1.61 8.95 11.24 1.00 0.12 0.12 0.36 

4.50 19.33 7.00 13 86.97 52.63 0.969 0.37 0.74 9.57 1.38 13.19 13.43 1.00 0.14 0.14 0.39 

7.50 19.33 9.00 17 144.94 81.18 0.943 0.39 0.82 13.99 1.11 15.53 16.35 1.00 0.17 0.17 0.44 

9.00 19.33 8.00 18 173.93 95.45 0.923 0.39 0.82 14.81 1.02 15.16 15.65 1.00 0.17 0.17 0.42 

10.50 19.33 8.00 19 202.92 109.72 0.894 0.39 0.87 16.46 0.95 15.71 16.21 1.00 0.17 0.17 0.45 

12.00 19.33 8.00 22 231.91 124.00 0.857 0.37 0.87 19.06 0.90 17.11 17.63 1.00 0.19 0.19 0.50 

13.50 19.33 5.00 25 260.90 138.27 0.811 0.36 0.87 21.66 0.85 18.42 18.42 1.00 0.20 0.20 0.55 

15.00 19.33 6.00 28 289.89 152.55 0.761 0.34 0.87 24.26 0.81 19.64 19.76 0.88 0.21 0.19 0.55 

18.00 19.33 7.00 35 347.86 181.09 0.667 0.30 0.87 30.32 0.74 22.53 22.84 0.84 0.25 0.21 0.71 

21.00 19.33 8.00 44 405.84 209.64 0.598 0.27 0.87 38.12 0.69 26.32 26.96 0.80 0.34 0.27 1.00 

 

In seismic zone IV, Begusarai has the highest resistance 
towards liquefaction as the district is liquefiable only up to 
3.5m depth below NGL. Saran is liquefiable up to 10.5m depth 
below NGL which shows that this district is the most 
susceptible to liquefaction in seismic zone IV. All the districts 
of zone V have a factor of safety almost below the FOS-0.5 
line which means that they are most susceptible to liquefaction. 
Madhubani has a sudden increase in factor of safety at 9m to 
10.5m depth below NGL due to a slight decrease in fines 
content and drastically increase in SPT N-value.  

IV. DISCUSSION 

From the above data set, it is found that among the districts 
of seismic zone III, Buxar and Bhojpur have higher fines 
content than Nawada, whereas the SPT N-value of Nawada is 
comparatively high. Begusarai districts have comparatively 
lower fines content than the districts of seismic zone IV. 
Darbhanga district has a sudden decrease in fines content from 
4.5m to 6m depth, whereas Madhubani shows two local peaks 
at 4.5m and 13.5m. Authors in [4] found that more than 10% of 
fines content values of soils are less liquefiable, but in the 
present study, it has been found that the fines content and SPT 
N- values are both critical factors for the liquefaction potential 
of the soil. Liquefaction may occur at higher or lower fines 
content values if the SPT-values are lower and higher 
respectively. 

V. CONCLUSION 

Based on the analysis results and the graphs of the FOS 
versus fines content and SPT N-value, the following 

conclusions have been made relative to the different seismic 
zones of Bihar: 

In seismic zone III, the soil shows comparatively more 
resistance to liquefaction in most cases. The FOS value is more 
than 1 in all cases. Bhojpur shows comparatively more 
resistance to liquefaction, whereas Nawada shows the lowest 
resistance in the mentioned zone. The soil of seismic zone IV is 
relatively more prone to liquefaction. The soil of Begusarai 
district is liquefiable up to 3.5m depth below NGL. Saran 
district is more vulnerable to liquefaction up to 10.5m depth 
below NGL. The other districts in this zone show a similar 
trend of liquefaction up to certain depths. All the districts in 
seismic zone V are most liquefiable as their FOS is much lesser 
than 1. Madhubani shows the peak at 10.5m depth due to a 
slight decrease in fines content and a sudden increase in SPT 
N-value. The soil of Darbhanga district has quite a lower SPT 
N–value and decreasing fines content with the increase in depth 
below NGL. 

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