Introduction

Whenever a major earthquake occurs, it is observed that it causes serious damage to the foundation, structure, and underground structure constructed on the extensive areas of reclaimed land due to soil liquefaction and displacement of ground in the horizontal direction [1]. It has been shown that the determination of liquefaction potential of any region must be taken into account for ground improvement before the construction of any structure [2]. When a high-intensity earthquake hits a sandy soil deposit which is in loose, saturated, and undrained cohesionless condition, then the rapid decrease in the shear strength of the soil takes place such that the shear strength of the soil eventually becomes zero. This phenomenon is termed as liquefaction. As the pore water pressure increases, soil particles lose their contact with each other and move in unidentified directions resulting in sinking of heavyweight structures and floating of low-weight structures. The occurrence of soil liquefaction depends on various factors like the type of soil, thickness of the soil strata, soil grain size, relative density, water table depth, fines content, etc. [2]. Correspondingly, severity of liquefaction is influenced by the reduction of effective stress, shear modulus degradation, and intensity and magnitude of the earthquake, duration of the ground motion, distance from the source of the earthquake, ground acceleration, etc. [2,3,4]. Ground failure is influenced by the liquefied and non-liquefied thickness of the soil layers induced by liquefaction.

After the Alaska and the Niigata earthquakes, the liquefaction analysis became a major issue in the geotechnical earthquake engineering. Seed and Idriss [5] presented the evaluation of liquefaction potential work for the first time and it was further carried gradually by [4, 6,7,8,9,10,11,12,13,14,15]. Some of these cited works are based on field methods such as the standard penetration test (SPT) and the cone penetration test (CPT). The SPT is extensively used by the researchers worldwide to evaluate the liquefaction potential of the soil. Many researchers in India too have determined liquefaction susceptibility for different sites using the SPT test data. Some examples are [16] for Bangalore City; [17] for Guwahati City; [18] and [19] for Mumbai; [20] for Lucknow City; [21,22,23,24] for Kanpur City; [25] for Kolkata region and [26,27,28] for Roorkee region.

The FoS indicates the liquefaction potential of a soil layer at a specific depth but it does not indicate the level of severity against liquefaction potential of a site on the whole. To overcome this drawback of the FoS, [29] suggested the liquefaction potential index (LPI) to evaluate the liquefaction susceptibility. The value of LPI includes depth, thickness, and factor of safety for liquefaction of soil layers and predicts the capability of liquefaction to cause damage at the ground level at selected sites. The LPI is repetitively used by experts to evaluate the level of liquefaction severity for different locations of soils. The LPI is a single value factor evaluated for the liquefaction hazard map of the selected location as an alternative for many factors at different layers of the soil [18, 30,31,32]. The LPI has been calibrated using the SPT test data to characterize the liquefaction potential of sites [18, 28, 30, 33].

In the present study, the liquefaction potential of the sites within the All India Institute of Medical Sciences (AIIMS) Kalyani, Kolkata Campus, is assessed based on the SPT data. The present analysis is done for the six borehole locations in the AIIMS Kolkata Campus. Liquefaction susceptibility of the six sites is evaluated in terms of the FoS against liquefaction for three different magnitudes of earthquakes (Mw) covering moderate to high-magnitude earthquake scenarios with Mw = 6.5, 7.0, and 7.5, corresponding to peak ground acceleration (PGA) values of 0.143g, 0.170g, and 0.202g, respectively [21]. The water table is considered at the ground surface for all the scenarios. Further, the level of liquefaction severity is also evaluated in terms of the LPI for the selected sites and a liquefaction hazard map for the AIIMS Kolkata Campus is prepared. This liquefaction hazard map could be of use to design engineers in the preliminary and detailed design of any construction/infrastructure development within and outside of the Kalyani Campus region.

Study Area

Kolkata, the capital city of West Bengal state in India, is located on the east bank of the Hooghly River, approximately 75 km west of the border with Bangladesh. Kolkata is one of the most populous cities in India [34]. The AIIMS Kalyani region comes under the Nadia District of West Bengal and it is located around 50 km from Kolkata. The Indian Seismic Code (IS 1893:2016) divides the country into four seismic zones (zone II to V). The scale used to measure the susceptibility to earthquakes ranges from II to V in an increasing order. Kolkata lies in seismic zone III.

Damages to the Civil Engineering structures have been reported in Kolkata due to both the far and the near source earthquakes in the past [35]. Based on the available past records of the last 350 years, it can be said that Kolkata and its surrounding region underwent some thirty strongly felt earthquakes. The epicentres of majority of these earthquakes were from ‘far sources’ and only a few of them were from the ‘near sources’. Epicentres for all the moderate to large earthquakes were located south of Kolkata near the Ganges delta mouth.

Details of the study area, site locations are mentioned in Table 1. The table gives the depth of the borehole, latitude, and longitude of the borehole, water table—actual, and water table—assumed along with the number of SPT samples. Due to small variation in the water table, water is assumed at the ground surface for all the sites. The location map is presented in Fig. 1 to visualize the precise area of the AIIMS Kalyani Campus. The 6 boreholes data considered for the liquefaction analysis is widely distributed throughout the considered area of the study as shown in Fig. 1c.

Table 1 Detail location of boreholes in AIIMS Kalyani, Campus, Kolkata
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Fig. 1
figure 1

Location of sites: a map of India, b map of West Bengal (W. B.), c map of Kalyani District (W.B.), and d location of the site in Kalyani

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Methodology

Liquefaction potential is entirely dependent on the earthquake intensity and the resistance of the soil against liquefaction. The susceptibility towards liquefaction in this research work is evaluated using the simplified method based on [5] and [4]. The evaluation procedure of liquefaction potential consists of the following three steps.

  1. 1.

    Evaluation of the cyclic stress ratio (CSR)

  2. 2.

    Evaluation of the cyclic resistance ratio (CRR)

  3. 3.

    Evaluation of the factor of safety (FoS)

Evaluation of the Cyclic Stress Ratio

The cyclic stress ratio/shear stress due to earthquake is calculated using a simplified procedure given by [5]. Fraction of this evaluated shear stress with effective stress gives the value of the Cyclic Stress Ratio (CSR).

$$CSR = 0.65 \times \left( {\frac{{a_{\max } }}{g}} \right)\left( {\frac{{\sigma_{vo} }}{{\sigma_{vo}^{^{\prime}} }}} \right) \times r_{d}$$
(1)

where \({\sigma }_{vo}^{^{\prime}}\) is the effective stress; amax is peak horizontal acceleration at the ground surface; \({\sigma }_{vo}\) is the total stress; g is the acceleration due to gravity and rd is the stress reduction coefficient evaluated using [4].

Evaluation of the Cyclic Resistance Ratio

The cyclic resistance ratio (CRR) gives the resistance of soil against liquefaction. The simplified method developed by [5] and later elaborated by [4] is used to calculate the values of the CRR (Eq. 2).

$$CRR_{7.5} = \left( {\frac{1}{{34 - (N_{1} )_{60cs} }} + \frac{{(N_{1} )_{60cs} }}{135} + \frac{50}{{\left[ {10(N_{1} )_{60cs} + 45} \right]^{2} }} - \frac{1}{200}} \right)$$
(2)
$$(N_{1} )_{60cs} = \alpha + \beta (N_{1} )_{60}$$
(3)

where (N1)60CS = Corrected N values with fines evaluated using Eq. 3, α and β = coefficients factors.

Recorded SPT N values are corrected for fines contents using Eq. 3, denoted as (N1)60CS, for the evaluation of CRR7.5. (N1)60CS in Eq. 3 consists of constants α and β whose values depend on the fine content of soil and in the present study, they are evaluated based on [4].

For evaluation of the CRR from the SPT data, first the measured SPT N value is corrected by applying the following corrections (Eq. 4) leading to (N1)60 value.

$${\left({N}_{1}\right)}_{60}=N\times {C}_{N}{C}_{E}{C}_{B}{C}_{R}{C}_{S}$$
(4)

where (N1)60 = the normalized corrected SPT blow count with hammer efficiency of 60%; N = the measured SPT blow count in situ. In Eq. 4, CN = Overburden pressure Correction; CE = energy ratio correction; CB = borehole diameter correction; CR = Rod correction and CS = sampling method corrections. The values of these corrections are given in Table 2 [4]. Accordingly, values of CN correction are determined using Eq. 5. The value of CN should not exceed 1.7 and it decreases with depth [4].

$$C_{N} = \left( {\frac{{P_{a} }}{{\sigma_{VO}^{^{\prime}} }}} \right)^{0.5} .$$
(5)
Table 2 Characteristics of the soil of AIIMS Kalyani Campus [BH-01 to BH-06]
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Equation 2 is used to evaluate the CRR for the earthquake magnitude of 7.5. For different magnitudes of earthquakes, the CRR is calculated by applying the magnitude scaling factor (MSF) as given in Eq. 6 [4].

$$CRR = CRR_{7.5} \times MSF$$
(6)

The MSF is evaluated from Eq. 7 as suggested by [4].

$$MSF = \frac{{10^{2.24} }}{{M_{w}^{2.56} }}.$$
(7)

Evaluation of the Factor of Safety

The liquefaction potential of sites is assessed in the terms of the Factor of Safety (FoS) against liquefaction. The FoS, calculated using Eq. 8, is defined as the ratio of shear stress causing liquefaction (CRR) to shear stress due to earthquake loading (CSR).

$$FoS = \frac{CRR}{{CSR}}.$$
(8)

For a given site, if the FoS is found to be less than 1.0, then it is susceptible to liquefaction whereas if the FoS is found to be 1.0 or greater than 1.0, it is not susceptible to liquefaction.

Determination of Liquefaction Potential Index

The liquefaction potential index (LPI) is a single-valued factor for the evaluation of the level of the liquefaction severity at a particular site. In this study, the LPI was evaluated by the expression (Eq. 9) given by [36],

$$LPI = \int\limits_{0}^{20} {F\left( z \right).} w\left( z \right)dz$$
(9)

where z is the midpoint depth of the soil layer and dz is a differential increment of depth.

$$\begin{gathered} F(z) = 1{-}FoS\;{\text{for}}\;FoS < 1.0; \hfill \\ F(z) = 0\;{\text{for}}\;FoS \ge 1.0; \hfill \\ w(z) = 10{-}0.5z\;{\text{for}}\;z < 20\;{\text{m}}; \hfill \\ w(z) = 0\;{\text{for}}\;z > 20\;{\text{m}}. \hfill \\ \end{gathered}$$

F(z) and w(z) are the severity factor and the weighting factor, respectively.

The LPI is evaluated using Eq. 10 given by [37] which is valid for the soil depths less than or equal to 20.0 m.

$$LPI = \sum\limits_{i = 1}^{n} {w_{i} } F_{i} H_{i}$$
(10)

where

$$\begin{gathered} F_{i} = 1{-}FoS_{i} \;{\text{when}}\;FoS_{i} < 1.0 \hfill \\ F_{i} = 0\;{\text{when}}\;FoS_{i} \ge 1.0 \hfill \\ \end{gathered}$$

Hi is the thickness of the soil layers; n is layer number; Fi is severity for liquefaction of the ith layer;

$$w_{i} = 10 - 5z_{i}$$
(11)

where wi is the weighting factor and zi is the depth of ith layer (m).

Geotechnical Characteristics of Study Area

Soil profile and soil parameters are essential to evaluate the liquefaction potential of any region/site. Parameters such as water table depth, SPT N values, dry density, specific gravity, and fine contents were collected from the in situ test. Geotechnical investigation, using one of the most traditional and reliable tests, i.e. SPT, was conducted by the [38].

Deposited soil consists of two layers. Soft to medium clay was found to exist up to a depth of 4.0 m to 5.0 m and after that, a layer of silty fine sand be found [21]. The soil of Kolkata region generally consists of normal deposits, river channel deposits, and reclaimed land. Normal deposits contain silty clay/clayey silt layers with traces of silt and fine sand. The top layer of river channel deposits and reclaimed land consists of fine sand with silty soil up to few metres [21]. Mondal et al. [23] observed that the soil of Kalyani District is classified as Gangetic alluvium. Kalyani region soil is a mixture of silt and sand so its moisture-retaining capacity is very low. For shallow depth, the soil consists of soft compressible silty clay/clayey silt and after that clay deposits which are very stiff with intermediate sand were found for a large depth of 40 to 50 m [23].

In Table 2(a, b), the soil profile for all the 6 site locations in the study region is given. The soil profile consists of the characteristics of soil samples, i.e. unit weight (γ), description about soil type, SPT N values, and corrected SPT N values, (N1)60, from the overburden correction and hammer efficiency correction of 60%, which is required for the evaluation of the liquefaction resistance.

From Table 2(a, b), it can be concluded that the top surface of the AIIMS Kalyani Campus is filled with clay, grassroots, and other wastes. From the depth of 1.5 m to 5.0 m, a layer of medium brownish-grey clayey silt with traces of sand and kankar was found followed by medium light grey silty fine sand with traces of mica for the depth up to 12.0 m. The last layer consisted of dense to very dense light grey sand having a size of fine to medium with traces of silt. From the above study, it can be concluded that the soil profile of the AIIMS Kalyani Campus generally consists of clay and sand with traces of mica and silt.

From Table 2(a, b), it can be observed that the minimum corrected value of (N1)60 is 5, obtained at 3.0 m of depth at BH-06. The value of (N1)60 is greater than the corresponding N value up to the depth of 10.0 m. Beyond the depth of 10.0 m, (N1)60 values are less than the corresponding SPT N values, which can be attributed to the overburden (CN) and rods correction (CR). In Table 2(a, b), different symbols (A B C & D) are used to classify different types of soil investigated at various depths of borehole locations. There is a marginal difference in bulk density values (varying from 18.0 kN/m3 to 18.8 kN/m3) for all the sites in the study region.

Liquefaction Potential of Sites

In this study, the liquefaction potential of all the five sites in the AIIMS Kalyani, Kolkata Campus, is evaluated using the SPT data for different earthquake scenarios, i.e. Mw = 6.5, 7.0, and 7.5, corresponding to PGA = 0.143g, 0.170g, and 0.202g, respectively, and considering water table at the ground level.

Liquefaction potential for M w = 7.5, PGA = 0.202g

In Fig. 2, the variation of the CSR, the CRR, and the FoS against liquefaction with depth is given for BH-01. It can be observed from Fig. 2a that up to 6.0 m depth, the CRR is less than the CSR; therefore, the FoS against liquefaction is less than one. This means that the site is susceptible to liquefaction up to the shallow depth of 6.0 m (Fig. 2b). The higher values of the CRR as compared to the CSR can be attributed to the presence of fines and higher N values.

Fig. 2
figure 2

CSR, CRR and FoS with the depth for BH-01 (Mw = 7.5, PGA = 0.202g)

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The variation of the FoS against liquefaction with depth is given for BH-02 to BH-06 in Fig. 3. The FoS values increase with the depth for all the sites in AIIMS Kalyani Campus. It can be observed from Fig. 3, that the values of the FoS against liquefaction are less than unity at shallow depths for all the sites. Figure 3 indicates the zone of liquefaction up to 6.0 m depth for BH-02 to BH-04 and up to 3.0 m for BH-05 & 06.

Fig. 3
figure 3

FoS against liquefaction with the depth of BH-02 to BH-06 for Mw = 7.5, PGA = 0.202g

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Table 3 gives the detailed calculations of the FoS against the liquefaction for BH-02. From Table 3, it can be noted that the sample of the location (BH-02) is taken up to the depth of 15.5 m and fines content varies from 12 to 21%. The values of total and the effective stress of the soil increase with depth. For BH-02, the SPT N values lie from 7 to 30. The corrected N values after overburden correction (N1)60 and correction for fine content (N1)60cs with depth are given in Table 3. It can be observed from Table 3 that the (N1)60 and (N1)60cs values increase with the depth. This trend can be attributed to the overburden correction (CN) and presence of fines contents. The values of the CRR increase with the depth and vary from 0.15 to 0.43 up to the 15.5 m depth. From the values of the FoS reported in Table 3, it is clear that there is a chance for liquefaction up to the shallow depth (up to 9.0 m) in this region, in case of strong earthquake, i.e. Mw = 7.5 and PGA = 0.202g.

Table 3 Detailed calculation of FoS against liquefaction required for liquefaction for BH-02 (Mw = 7.5 and PGA = 0.202g)
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Liquefaction potential for M w = 7.0, PGA = 0.170g

The decrease in the magnitude of the earthquake decreases the severity towards liquefaction. Figures 4 and 5 depict in detail, the variation of the CSR, the CRR, and the FoS against liquefaction for all the 6 sites (BH-01 to BH-06) of AIIMS Kalyani Kolkata Campus. It can be observed from Fig. 4a and b that in the case of BH-01 and BH-02, the values of the CRR are less than the CSR values up to the depth of 5.0 m and after that the CRR values are greater than the CSR values. This means that the FoS is less than one (Fig. 5a, b) and the sites will liquefy up to the depth of 5.0 m. Further, for BH-03 and BH-04, similar trends were observed but the depth of liquefaction is reduced (i.e. 4.0 m depth). Also, the remaining sites performed well and remained safe from liquefaction in the considered earthquake scenario.

Fig. 4
figure 4

CSR and CRR with the depth (Mw = 7.0, amax = 0.170g)

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Fig. 5
figure 5

FoS with the depth (Mw = 7.0, amax = 0.170g)

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Liquefaction potential for M w = 6.5, PGA = 0.143g

For this particular case, the severity of liquefaction decreases and a very minor effect is found. The FoS against liquefaction with respect to depth is presented in Fig. 6. It is observed from Fig. 6a that only for BH-01, the FoS is less than one for depths less than 4.0 m. Thus, it can be said that except for some pockets in BH-01, all the sites are safe from liquefaction susceptibility.

Fig. 6
figure 6

FoS against liquefaction with the depth (Mw = 6.5, amax = 0.143g)

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Liquefaction Potential Index: Kalyani Region

Liquefaction potential index (LPI) has also been evaluated in this study to illustrate the liquefaction susceptibility at the AIIMS Kalyani, Kolkata Campus. The LPI values are determined by Iwasaki et al. (1982) method in the present study. Different parameters are set by various researchers to classify the level of severity against liquefaction based on the LPI values. The classification suggested by [36] has been considered in this study. Different levels of severity in decreasing order are very high (LPI value greater than 15), high (LPI value between 5 and 15), low (LPI value between 0 and 5), and very low (LPI value zero) (Iwasaki et al., 1982). During their post-earthquake investigation for Monterey bay region, California, [33] suggested that the probability of liquefaction exposure on the surface is 93% for the LPI value greater than 15, it is 58% to 93% for the LPI value between 5 and 15 and it is below 58% for the LPI value less than 5.

The computed value of the LPI for BH-02 is presented in Tables 4, 5, and 6 for the earthquake magnitudes Mw = 7.5, 7.0, and 6.5, for the corresponding PGA = 0.202g, 0.170g, and 0.143g, respectively. Further, Table 7 summarizes the LPI values of all the 6 sites for all the earthquake scenarios considered in the present study. It is evident from Tables 4, 5, and 6 that when the earthquake magnitude increases, the values of the LPI will also increase. For Mw = 7.5 and PGA = 0.202g, the LPI values for BH-02 is 22.66 which means that the probability of liquefaction exposure on the surface is 93%. Further for other earthquake scenarios, the LPI value reduced from 9.35 for Mw = 7.0 to 0.0 for Mw = 6.5. Based on the LPI values, it can be said that the level of severity against liquefaction lies in high and low level for earthquake magnitude of 7.0 and 6.5, respectively.

Table 4 Computation of liquefaction potential index for BH-02 with Mw = 7.5 & PGA = 0.202g
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Table 5 Computation of liquefaction potential index for BH-02 with Mw = 7.0 & PGA = 0.170
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Table 6 Computation of liquefaction potential index for BH-02 with Mw = 6.5 & PGA = 0.143
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Table 7 Summarized LPI values of all the six sites for the different earthquake magnitudes
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The LPI values of all the 6 boreholes for all the earthquake scenarios considered in the present study are represented in the graphical form in Fig. 7. From Table 7 and Fig. 7, it can be observed that for Mw = 7.5, all the five locations are having LPI values greater than 15 (except BH-05), which means that the probability of liquefaction is very high for all the sites and the chances for liquefaction exposure on the surface is 93% probability [33].

Fig. 7
figure 7

Graph between LPI values and the site name

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Similarly, for other earthquake scenarios, the level of liquefaction severity lies from high severity (Mw = 7.0) to low severity (Mw = 6.5). In case of Mw = 7.0 and PGA = 0.170g, the LPI values vary from 05 to 15 at all the locations except BH-05 (LPI = 0). Therefore, the LPI values indicate that the chance of liquefaction is high (liquefaction exposure on the surface is 58% to 93%) except for BH-05. From Table 7, it is observed that liquefaction severity was found to be low for Mw = of 6.5 and PGA = 0.143g. When Mw exceeds from 7.0 to 7.5, the liquefaction severity jumps from high to very high. Further, Fig. 7 shows that the LPI values at all the sites show different levels of liquefaction severity depending on the different earthquake scenarios considered in this study.

The LPI interpolation maps against liquefaction severity for AIIMS Kalyani Kolkata Campus are shown in Fig. 8 for different magnitudes of earthquakes. From Fig. 8, it is clear that the major part of the campus is at low to high risk of susceptibility for liquefaction. For an earthquake of low magnitude, all the sites in study region may not liquefy. However, there is chance for liquefaction in this region, in case of strong earthquake.

Fig. 8
figure 8

LPI map of AIIMS Kalyani Campus, Kolkata, for the different earthquake magnitude

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Summary and Conclusions

In the present study, liquefaction potential of sites has been evaluated using the ‘Simplified method’ given by Seed and Idriss’s method for the AIIMS Kalyani, Kolkata Campus. The liquefaction potential was evaluated for moderate to high-magnitude earthquake scenarios (Mw values of 6.5, 7.0, and 7.5, corresponding to PGA values of 0.143g, 0.170g, and 0.202g, respectively). The water table is considered at the ground level for all the 6 sites. Further, the liquefaction hazards map has been prepared on the based on the liquefaction potential index (LPI) values. The following conclusions can be drawn from the present study:

  1. 1.

    For the earthquake magnitude (Mw) of 7.5 and PGA of 0.202g, all the 6 sites were observed to be susceptible to liquefaction, with the average depth of susceptibility being 7.0 m for BH-01 to BH-04 whereas for the rest of the sites (i.e. BH-05 & 06) the susceptibility to liquefaction is up to the shallow depth of 3 m only.

  2. 2.

    The FoS against liquefaction for PGA = 0.170g and Mw = 7.0 is relatively greater. However, it is still less than one for shallow depths at most of the sites except BH-05 & BH-06; thus indicating that most of the sites are susceptible to liquefaction. The depth of liquefaction though reduces for Mw = 7.0 as compared to that for Mw = 7.5. The minimum difference in the FoS obtained for a 7.0 magnitude earthquake is found to be 40% greater than that for Mw = 7.5 due to the difference in MSF and PGA.

  3. 3.

    For Mw = 6.5 and PGA = 0.143g, all the 6 sites in AIIMS Kalyani region may not liquefy. The values of the FoS against liquefaction for this particular case are observed to be two times of the FoS values for Mw = 7.5 and PGA = 0.202g.

  4. 4.

    From the LPI values, it is observed that the liquefaction severity is found to be very high (LPI > 15; expose to liquefaction about 93%) for all the sites except BH-05 (LPI < 5) for the magnitude of earthquake Mw = 7.5 and PGA = 0.202g. When Mw = 7.0 and PGA = 0.170g, liquefaction severity was found to be high (i.e. LPI < 5; chance of liquefaction is in between 58 and 93%) except for BH-05. Further, for Mw = 6.5 and PGA = 0.143g liquefaction severity was found to be low vulnerable/exposure to liquefaction is below 58% based on the LPI values (LPI = 0 to 5).

The findings of the present study are helpful to identify liquefaction-prone zones in the study region. The conclusions drawn are of very much practical significance and liquefaction hazard maps may be employed by design engineers in the preliminary and detailed design of any construction/infrastructure, i.e. design of structures, underground structures, and foundations design. The conclusions of this study are limited to the AIIMS Kalyani, Kolkata Campus area.