Probabilistic and deterministic-based approach for liquefaction potential assessment of layered soil

In the present study, deterministic and probabilistic approaches have been used for the assessment of liquefaction potential of ground during an earthquake. The deterministic approach was used to analyze and assess the liquefaction of loose saturated river bed deposit with emphasis on two benchmark locations. A wide range of earthquake data in the form of peak ground acceleration (PGA) values of 0.18 g, 0.37 g, 0.6 g and 0.75 g was used as input motions. The dynamic properties of soil were evaluated using standard penetration test (SPT) data obtained from the bore logs. The shear stress induced within soil deposit due to the seismic excitation was calculated in the form of cyclic stress ratio (CSR) and cyclic resistance ratio (CRR) in order to calculate the factor of safety (FOS) against liquefaction. In addition, liquefaction potential index (LPI) and probability of liquefaction (PL) were also calculated using input motion. It was observed, based on the probability analysis and liquefaction indices, that the shallow layer soil profile is safe against liquefaction, whereas deep layer soil profile is unsafe.


Introduction
Occurrence of liquefaction during an earthquake in saturated sand deposit may cause serious damage to infrastructure and lifelines due to quick sand, lateral movements and ground failure and excessive foundation settlements among other devastating effects (Idriss and Boulanger 2008;Zhang et al. 2004,Yu andYu 2013). Saturated loose sand undergoes transfer of normal stress onto the pore water under cyclic loading imposed by earthquake. If the soil is unable to drain water during shaking, it causes reduction in confining pressure within the soil mass, resulting in the loss of strength and stiffness and thereby leading to deformation of soil deposit (Idriss and Boulanger 2008).

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Numerous major earthquakes occurred in the past have reported serious losses to infrastructure and life due to liquefaction, necessitating the need for evaluation of LPI for earthquake prone areas. Major devastating earthquakes include Niigata earthquake (1964); Kobe earthquakes (1995); Fukushima earthquake (2011); Chi-Chi earthquake (1999); Bhuj earthquake (2001); Nepal earthquake (2015); and Northridge earthquake (1994) among many. The attention of researchers was particularly drawn toward liquefaction phenomenon after Niigata earthquake in 1964. Various researchers all over the world have worked on this complex phenomenon, but still several aspects related to liquefaction are not well explained. Simplified methods based on standard penetration tests (SPTs), cone penetration tests (CPTs) and the measurement of shear velocities (V s ) are extensively used to obtain the values of LPI.
SPT-based method is extensively used for the assessment of LPI due to its less computational effort. The SPT-based method for assessing the liquefaction potential was initially established in Indian Seismic Code in the year 2016 as IS 1893 Part-1 (2016). The IS method is based on the studies performed by Seed and Idriss (1971). Seed et al. (1985) handled field test examination for perceptivity of liquefaction during seismic tremor is utilized to layout rules for assessing liquefaction capability of sand for a quake of extent M w 7.5. The results obtained from above studies were used for several earthquakes. Effect of silt content on liquefaction was also studied (Ishihara 1993), whereas liquefaction curves for sands with fines having various SPT-N values were suggested (Seed et al. 1985). A few researchers (Ishihara 1993;Fear and McRoberts 1995) fostered the SPT-based techniques for liquefaction investigation of soil. The impact of fines content as well as the impact of nature of fines was introduced in the studies (Ishihara (1993).
In the present work, Ayodhya (26.7922° N, 82.1998° E), one of the holiest cities of India and situated on the banks of River Saryu (Ghaghara) in the northern state of Uttar Pradesh, was selected for liquefaction potential study. Ayodhya, being an old traditional city, most of the major structures have been designed and constructed without much regard to the earthquakes. As per Indian Standards Code BIS 1893, Ayodhya lies in the high seismic risk zone IV and is very close to the Ayodhya (Faizabad)-Pyuthan Lineament ( Fig. 1). Ayodhya has significant tectonic features and liquefaction potential due to the extension of Lucknow fault up to Faizabad ridge or a fault along the Saryu River near the junction of Faizabad ridge and adjoining alluvium, maximum magnitude of earthquake has been assessed as 6 making this area near seismic zone IV instead of zone III according to the Bureau of Indian Standards. In addition, a great earthquake (Mw 8) originating in the Himalayan thrust may generate secondary meizoseismal area near Ayodhya with a possibility of liquefaction (Srivastava and Bhattacharya 2020) (Fig. 1). A range of possible scenarios exist with respect to the significant earthquakes in the recent past, including Bihar-Nepal earthquake (1934) and Nepal earthquake (2015) (Fig. 1). In the last 50 years or so, liquefaction of sandy soil deposit associated with earthquake shaking has caused major damages to the soil structure, reduced useful life of buildings and civil amenities and facilities. Liquefaction makes the structures more vulnerable in the cities, which are located on or near the banks of rivers, coastal areas and/or in backfilled soils.
In the present work, studies have been carried out for assessing the liquefaction capability of soil layers close to Saryu River. The purpose of the study is to bridge existing gap in information and knowledge by conducting field and laboratory tests. To this end, boreholes were advanced on either banks of Saryu River to conduct SPTs and collect the soil samples for laboratory testing. Results were then compared with the similar studies conducted by other researchers in the past ( Fig. 2 and Table 1).

Methodology and formulation
The methodology of analysis includes following steps:

Field/subsurface geotechnical investigation
SPT tests were performed as per IS 2131-2002 (2002), and soil samples were collected up to 30 m of depth from two boreholes situated at 5 m from the river edges on either banks.

Standard penetration test
SPTs were performed at every 1.5 m intervals or wherever the change of stratum was encountered. At each SPT location, the first 15 cm penetration, treated as seating drive, was discarded. The number of blows required for next 15 + 15 (= 30) cm penetrations was recorded and assigned as SPT-N value. Undisturbed soil samples were collected by thinwalled sampling tubes having 100-mm internal diameter and 450 mm length. The sampling tubes were properly sealed on both ends by wax to preserve for laboratory testing.

Laboratory test
Physical characteristics of subsoil were determined by conducting natural water content, bulk and dry densities, grain size distribution analysis and specific gravity tests in laboratory.
1. Water content determination: Oven drying method was used for calculating the water content of the soil samples as per IS 2720-Part II (1973)(Reaffirmed 2006). 2. Dry and bulk density: Dry and bulk densities of soil samples were obtained as per IS 2720-Part III (1980)-1983(Reaffirmed 2006 and were calculated by using the following formula: Ms = mass of mold, base and soil in grams, M 1 = mass of mold and base in grams, V = volume of cylindrical mold in cm 3

Evaluation of liquefaction potential index
MATLAB programming was used to evaluate: (i) shear stress developed due to the occurrence of earthquake by using IS 1893 Part-1 (2016) methods as well as by considering PGA values of previous earthquake events including, Nepal earthquake; Chi-Chi earthquake; Northridge earthquake and Bhuj earthquake; (ii) shear stress causing liquefaction in terms of cyclic stress ratio (CSR) and cyclic resistance ratio (CRR) was calculated; and finally (iii) liquefaction potential at every depth of the borehole was calculated.

Liquefaction potential index
Earthquake-induced loading characterized as cyclic stress ratio (CSR) is opposed by liquefaction resistance offered by the soil mass and is termed as cyclic resistance ratio (CRR). In liquefaction potential studies, CSR and CRR are compared to find factor of safety against the occurrence of liquefaction. Several methods have been proposed for the evaluation of liquefaction potential index by investigators, including Youd et al. (2001), Cetin et al. (2004), Idriss and Boulanger (2008) and Seed-Idriss (1971). In the present study, IS code method was used for the evaluation of CSR and CRR. Seed-Idriss (1971) assumed soil mass as a column having rigid body and derived equation for maximum shear stress as: where (τ max ) r is maximum stress in rigid body, σ vo = total vertical overburden stresses and a max = maximum acceleration at the ground surface.g = acceleration due to gravity However, according to the investigators, soil behaves as a deformable body, hence shear stress gets reduced with depth. Therefore, a reduction factor called stress reduction coefficient is applied to obtain shear stress within the deformable boundary. It measures the attenuation of peak shear stress with depth due to nonelastic behavior of soil.
The average shear stress is evaluated using standard method as per IS 1893-2016 where rd = stress reduction coefficient. where z = depth beneath ground surface in meters.
CSR depends on maximum acceleration occurring due to earthquake. In the present study, maximum PGA (a max /g) is taken from IS 1893 Part-1 (2016) as a max = 0.25 g. The values of PGA (a max /g) for earthquakes being considered for the comparison purpose were taken from the literature and are given in Table 2.
The time history of these earthquakes is shown in Fig. 4. The duration of the actual time history varies for each earthquake, and the peak data were used for the analysis.
SPT-N values are obtained at the selected sites and corrected for overburden pressure.  Seed and Idriss (1971)  Nepal earthquake 0.6 g 4 Bhuj earthquake 0.37 g N 60 , SPT blow count, represents 60 percent efficiency of hammer, whereas N is actual SPT-N number, and C 60 is correction, which depends on various factors such as hammer weight or height of fall, nonstandard sampler set up, borehole diameter and rod length.
The computed N 60 is normalized to effective overburden pressure of approximately 100 kPa using overburden correction factor C N (Fear and McRoberts 4). σ vo ′ is effective stress at the depth of consideration. Value of C N diminishes with increase in overburden pressure (Youd et al. 2001). Seed et al. (1985) proposed a curve to evaluate CRR on the basis of corrected N value and fine contents, respectively, of 5%, 15% and 35%. Youd et al. (2001) suggested some adjustments to the curve, and the same was adopted by IS 1893 (Part-1) (2016) (Fig. 5).
CRR value in the present analysis is calculated using some empirical equation also suggested by IS code. where For an earthquake with magnitude higher than 7.5, overburden pressure is more (depth > 15 m) then CRR 7.5 is multiplied by MSF (magnitude scaling factor) (Seed and Idriss 1982) and high overburden correction factor. Factor of safety against liquefaction is the ratio of resistance offered by soil during shaking (CRR) to the stress generated to the soil (CSR).
On the off chance that FOS is under 1, it is expected that there is more possibility of liquefaction, while assuming it is more than 1 possibilities of event of liquefaction are less.
Factor of safety does not give any idea about liquefaction potential intensity and probability of the occurrence of liquefaction. Iwasaki et al. (1982) proposed a mathematical equation (Eq. 16) correlating LPI and liquefaction potential susceptibility. It was later modified by Sonmez (2003) (Eq. 17) by using differential equation along with various severity classes. Tables 3 and 4, respectively, describe these equations. Juang et al. (2000) proposed an equation to identify probability of liquefaction (P L ) and characterized the chances of occurrence of an earthquake on the basis of various classes of liquefaction as shown in Table 5.
(15) FOS = CRR CSR   where z is depth in meters. F (z) is a function of FOS which depends on limiting equilibrium whereas W (z) is a weighing factor calculated as

Results and discussion
Soil properties and SPT-N values from both the boreholes (shown in Fig. 2) are quite similar; hence, average representative corrected SPT-N or (N 1 ) 60 values at different depths of the bore holes are presented through Tables 6 and 7. Empirical equation given by Ohta and Goto (1978) was used in the calculation of 2-D shear wave velocity from the borehole data. The shear wave velocity was observed between 150 and 175 m/s up to a depth of 8 m indicating loose strata. The shear wave velocity showed increasing trend below 8 m depth and reached up to 250-270 m/s showing presence of medium to dense strata mostly comprising of sand (Fig. 6). Natural frequency of soil is evaluated using free vibration analysis at every depth (Fig. 6). Grains' size distribution for the lower depths of borehole indicating that soil mostly comprises of sand with little fines (Fig. 7).
(18) W z = 10 − 0.5 * z for z < 20 m   Fig. 7 Grain size distribution at selected depths MATLAB programming was used with equations given in IS 1893 (Part-1) (2016) for the calculation of stress reduction factor (r d ), shear stress, CSR, CRR and factor of safety (FOS) against liquefaction at the different depths. Stress reduction factor was also evaluated using equation given by Youd et al. (2001) as IS 1893 Part-1 (2016) method was applicable only up to the depth of 24 m. The results obtained from T.F Blake method (Youd et al. 2001) (Fig. 8a) and IS 1893 Part-1 (2016) (Fig. 8b) are plotted, and variation in the pattern of r d values was observed to be identical and hence both the methods can be employed for calculation of stress reduction factors.
In both the methods, stress reduction factor was observed to be maximal at the surface, i.e., 1, and it decreased with decrease in depth, i.e., 0.3 at 30 m.
Shear stress for the present study was evaluated by considering peak ground acceleration (PGA) value at 0.25 g given in IS 1893 Part-1 (2016) for earthquake zone IV as town of Ayodhya also lies in the same zone. The values of shear stresses obtained were compared with the shear stresses obtained for Chi-Chi earthquake, Northridge earthquake, Nepal earthquake and Bhuj earthquake by using PGA values, respectively, of  (Fig. 9).
Shear stress causing liquefaction is termed as CSR and is dependent on maximum acceleration caused by an earthquake, magnitude of an earthquake and effective stress of soil. CSR values were calculated using Eq. 8 and a relationship between CSR values with depths (Fig. 10). It was observed that increase in the value of PGA due to earthquake leads to increase in shear stress causing liquefaction in soil. Drastic increase in the CSR values was observed at 6 m depth mainly due to the presence of water table.
Resistance offered by soil to resist liquefaction is termed as CRR. It depends on the soil properties, fineness modulus, SPT-N values, presence of water table and procedure adopted for the calculation of CRR value. In the present study, fine soil was found substantially in the upper (up to 9 m) strata resulting in better resistance existing in the top layers, whereas below 9 m content of fine particles goes on reducing, resulting in less resistance offered by soil. This pattern is depicted for CRR in Fig. 11. Both the boreholes show nonplastic soil deposit below 9 m with some fines is reported in Table 7. It was observed that as much as 35 percent increase in silt content leads to increase in the liquefaction resistance as silt begins to influence the soil behavior (Fig. 12).
FOS against liquefaction was computed at different depths as reported in Table 8 and plotted in Fig. 13. FOS of borehole was found to be greater than 1 for Chi-Chi earthquake and less than 1 for other sources of event (Table 8). The results obtained compared well with the works of Rolando P Orense (2005), Jie Zhang et al. (2021), Sana and Nath (2016). Inference can be drawn from results that the threat of liquefaction exists for the particular region of Ayodhya in the close vicinity of Saryu River. Therefore, the present study shows that the evaluation of FOS against liquefaction in Ayodhya is very important as at all depth of selected site.
Liquefaction probability (P L ) and liquefaction potential index (LPI) were calculated at each layer of the borehole soil using Eq. 16 and presented in the Table 8 as shown in Figs. 14 and 15. The summation of LPI calculated at each depth gives an idea about combined LPI of borehole. Based on different set of PGA values as shown in Table 8, only Chi-Chi earthquake with PGA 0.18 g was observed to have low liquefaction potential and therefore less probability of occurrence, whereas very high liquefaction potentials were observed for the other earthquake events.

Comparison with past studies
Liquefaction potential index of several metropolitan cities was evaluated by the researchers but no such study for an important holy city like Ayodhya situated on a river bank and in the close vicinity of a prominent fault line has as yet been taken up. Satyanarayana  and Harika (2023) studied the liquefaction evaluation of coastal area in Visakhapatnam based on SPT-N value and fines content using IS 1893 (Part-1) (2016) and Idriss and Boulanger (2008) methods. Silahtar et al. (2023) accessed the liquefaction potential of Arifiye (Sakarya) region based on SPT-N value of bore logs and seismic measurements considering the Izmit (M w : 7.4) and Mudurnu (M w : 7.0) earthquake scenarios. Subedi and Acharya (2022) undergo liquefaction hazard assessment and probability of the occurrence of ground failure by using methods proposed by Idriss and Baulanger (2008) and Iwasaki et al. (1982) for bore log data including SPT-N value of various locations in Kathmandu Valley. Jie Zhang et al. (2021) had used Chinese code and evaluated the liquefaction potential index based on standard penetration test, further evaluation of stress induced in soil by using PGA value obtained from the case history of CEA 2018 database. Thoithoi.et. al (2016) evaluated the liquefaction potential of Delhi region by using SPT data of subsurface soil up to the depth of 20 m. Using SPT data, Sana and Nath (2016) assessed the liquefaction potential of the Kashmir Valley. Using field and laboratory tests, Muley et al. (2015) assessed the Roorkee region's liquefaction potential. The SPT test was used for the geophysical investigation in this study, and the MASW test was used to evaluate the dynamic properties of soil. Dixit et al. (2012) conducted an assessment of the susceptibility of soil liquefaction in Mumbai city using a simplified empirical procedure that relied on SPT (standard penetration test) data. The researchers evaluated the potential for liquefaction in Mumbai by analyzing the factors of safety against liquefaction at different depths within soil profiles, for earthquakes with a 2% probability of exceedance in 50 years. To determine the liquefaction potential index for Mumbai city, the factors of safety were integrated along the depth, and the results were presented in the form of contour maps. Neupane and Suzuki (2011)) used SPT-N values to determine the liquefaction potential of the Kathmandu Valley and examined the impact of fine content on this potential. Hazarika and Boominathan (2009) reported the liquefaction caused due to Bhuj earthquake (2001). Satyam and Rao (2007) evaluated the liquefaction potential of Delhi region using SPT data for seismic microzonation. Results of the present study compare well with the previous studies.

Summary and conclusions
Soil properties and the other geotechnical data were obtained from boreholes driven up to 30 m at predetermined locations and standard penetration tests (SPTs) were conducted at different depths. Using a simplified method, the FOS, LPI and P L against liquefaction were evaluated using PGA values of 0.18 g, 0.25 g, 0.37 g, 0.6 g and 0.75 g. Based on the experimental work and theoretical analysis, the study is summarized as follows: 1. The SPT (N) values of soil strata at various depths were determined through geotechnical investigation, and it was seen that the N values increased with the depth. Shear wave velocity was found in the range of 150-175 m/s up to the depth of 8 m showing the presence of loose soil, whereas its value was observed in the range of 250-275 m/s beyond 8 m depth indicating the presence of medium-dense sand with little fines. 2. It was also found through laboratory test results that strata up to a depth of 9 m consists mainly of low plastic silt and silty clay, whereas strata beyond 9 m comprises of medium-dense silt and silty sand. 3. Through analysis, it was found that average shear stress in soil will increase with depth due to an earthquake. Similar pattern was deduced for all PGA values.
4. After 6 m, the soil was completely saturated. Increase in pore pressure will lead to higher shear stresses (transient). Its effective weight will be reduced below water table and it becomes more susceptible for boiling due to upward acceleration. 5. Silt content was found greater than 35 percent up to the depth of 9 m, it shows that more resistance toward liquefaction, whereas deeper extent silt content is in the range of 5 to 16 percent reports more susceptible toward liquefaction. 6. Using the provisions of the IS code and taking into account a wide range of PGA values, the FOS against liquefaction was evaluated at the selected location, which is close to the fault line. The soil profile was established to be safe from liquefaction with a PGA value of 0.18 g. 7. The results of LPI show that the selected site has low liquefaction potential for PGA value of 0.18 g, whereas for the higher PGA range, it has very high liquefaction potential, signifying that the site is unsafe to the depth explored. 8. P L was evaluated, and it was inferred that of a PGA range; 0.18 g to 0.25 g, probability of liquefaction was in the range of 35%-65%, representing the fact that occurrences of liquefaction are equally likely and unlikely (Class 3), whereas for the PGA range of 0.6 g to 0.75 g, probability of liquefaction was in range of 65-85% liquefaction is the most likely (Class 4).