Liquefaction resistance evaluation of soils using artificial neural network for Dhaka City, Bangladesh

Soil liquefaction resistance evaluation is an important site investigation for seismically active areas. To minimize the loss of life and property, liquefaction hazard analysis is a prerequisite for seismic risk management. Liquefaction potential index (LPI) is widely used to determine the severity of liquefaction quantitatively and spatially. LPI is estimated from the factor of safety of liquefaction that is the ratio of cyclic resistance ratio (CRR) to cyclic stress ratio calculated applying simplified procedure. Artificial neural network (ANN) algorithm has been used in the present study to predict CRR directly from the normalized standard penetration test blow count (SPT-N) and near-surface shear wave velocity (Vs) data of Dhaka City. It is observed that ANN models have generated accurate CRR data. Three liquefaction hazard zones are identified in Dhaka City on the basis of the cumulative frequency (CF) distribution of the LPI of each geological unit. The liquefaction hazard maps have been prepared for the city using the liquefaction potential index (LPI) and its cumulative frequency (CF) distribution of each liquefaction hazard zone. The CF distribution of the SPT-N based LPI indicates that 15%, 53%, and 69% of areas, whereas the CF distribution of the Vs based LPI indicates that 11%, 48%, and 62% of areas of Zone 1, 2, and 3, respectively, show surface manifestation of liquefaction for an earthquake of moment magnitude, Mw 7.5 with a peak horizontal ground acceleration of 0.15 g.


Introduction
Liquefaction occurs when granular, loosely compacted or cohesionless, saturated or partially saturated sediments lose their shear strength and transform from solid to liquid state at or near the ground surface resulting from cyclic loading or other abrupt alteration of stress conditions (Castro 1969;Castro and Poulos 1977;Castro et al. 1982). The loss of 1 3 strength takes place in cohesionless soil due to reduction in effective stress resulting from increased pore water pressure caused by rapid, usually cyclic loading exerted by strong ground shaking (Marcuson 1978).
During an earthquake, liquefaction can be devastating incurring widespread damage, which was revealed by Niigata Earthquake in 1964, Alaska Earthquake in 1964, Loma Prieta Earthquake in 1989, Chi-Chi Earthquake in 1999, and Sulawesi Earthquake in 2018(Seed and Idriss 1967Ku et al. 2004;Lee et al. 2007;Chao et al. 2010;Sassa and Takagawa 2019;Hossain et al. 2020). Therefore, in a seismic hazard-prone area, liquefaction resistance evaluation is an integral part of site characterization.
Both in situ tests (e.g., SPT, V s , Cone Penetration Test (CPT) data) and soil laboratory tests (e.g., cyclic triaxial test) can be used to evaluate soil liquefaction resistance during seismic loading. Good-quality undisturbed soil samples are essential to assess the soil liquefaction resistance by the laboratory tests. However, collecting such samples from degraded loosely compacted silty or sandy soils are sometimes difficult and expensive. Due to these drawbacks of the laboratory tests, geotechnical engineers widely use in situ tests as it is simple and economical Idriss 1971, 1982;Seed et al. 1983Seed et al. , 1984Seed et al. , 1985Seed and de Alba 1986). Over the last five decades, the Simplified Procedure, developed initially by Seed and Idriss (1971), has been used in liquefaction resistance evaluation of soils. Since its inception in 1971, many researchers have updated, modified, revised, and validated this method (e.g., Juang et al. 2003Juang et al. , 2000Olsen 1997Olsen , 1988Olsen and Koester 1995;Robertson and Wride 1998;Stark and Olson 1995). To assess liquefaction resistance by this procedure, the corrected SPT-N is widely used as input Idriss 1971, 1982;Seed et al. 1983Seed et al. , 1984Seed et al. , 1985Kayen et al. 1992;Juang et al. 2000;Youd et al. 2001;Idriss and Boulanger 2004).
Using field V s measurement, a method of liquefaction resistance estimation was introduced by Andrus et al. (2000) and Andrus and Stokoe (1997). The use of the V s data has more advantages than the SPT-N and CPT data as the V s data can easily be collected from stiff and gravelly soils. The soil profile can be easily obtained and the analytical procedures that analyze the small-scale shear modulus for evaluating soil-structure interaction and dynamic soil response are related to V s value of the soil materials.
In Bangladesh, most of the subsurface lithology is characterized by unconsolidated, sandy and clayey floodplain sediments. In alluvial deposits of Bangladesh, following the Srimangal Earthquake in 1918, Great Indian Earthquake in 1897, and the Bengal Earthquake in 1885, the evidences of widespread liquefaction were documented (Middlemiss 1885;Oldham 1899;Stuart 1920;Hossain et al. 2020). In the north and northeast areas of the country, the evidences of liquefaction were observed during paleoseismic studies, which are considered to be triggered by a series of earthquakes along the Dauki fault (Morino et al. 2011(Morino et al. , 2014a. In addition, the country is sitting close to the tectonically active Himalayan orogenic belt and Arakan megathrust where there are at least five major active fault zones, which have shown evidence of large magnitude earthquakes (Aitchison et al. 2007). Steckler et al. (2016) claimed a locked megathrust exists along the Indo-Burman mountain ranges, which reinforces the notion of the resistance future for major earthquakes. Therefore, it is an absolute necessity for the country to further study the liquefaction resistance evaluation of soils for the major cities. Rahman et al. (2015) and Rahman and Siddiqua (2017a, b) have conducted liquefaction potential studies based on simplified procedure for Dhaka, Chittagong, and Sylhet cites in Bangladesh using limited standard penetration test blow count (SPT-N), cone penetration test (CPT), and shear wave velocity (V s ) data. The studies observed that the Holocene alluvium of these cities is susceptible to liquefaction. In those studies, the empirical equations of Youd et al. (2001) were used to calculate the factor of safety (FS) of liquefaction, cyclic resistance ratio (CRR), cyclic stress ratio (CSR), and magnitude scaling factor (MSF). The equations of Iwasaki et al. (1982) were used to calculate liquefaction potential index (LPI).
However, in the present study, the ANN models were incorporated based on Juang et al. (2002Juang et al. ( , 2000 to predict the CRR where a variant of performance function Idriss 1971, 1982) termed as limit state function (LSF), was considered. This mechanical process of defining LSF has remarkably reduced drawbacks of simplified method, used by Rahman et al. (2015) and Rahman and Siddiqua (2017a, b). Those drawbacks primarily are reliance on engineering judgement in drawing limit state curve and giving limited consideration to all possible interaction among different type of soil and load parameters. Additionally, the ANN models are useful particularly for studying multivariate nonlinear relationships. The scope of this study does not allow for a comprehensive discussion of the ANN methodology. The fundamental architecture of ANN has been extensively discussed in Rumelhart et al. (1986Rumelhart et al. ( , 1988, Lippmann (1987), Eberhart et al. (1990), Hammerstrom (1993a, b), Flood and Kartam (1994), Krogh (2008), etc. The ability to detect complex nonlinear relationships between independent and dependent variables without requiring much formal statistical training, the availability of multiple training algorithms, and the ability of detecting all possible interactions between predictor variables are some of the advantages of ANN models (Hammerstrom 1993a;Flood and Kartam 1994;Tu 1996;Krogh 2008). The effectiveness of ANN methods in classifying field performance cases have been found in many studies (Goh 1994(Goh , 1995(Goh , 1996Agrawal et al. 1997;Ali and Najjar 1998;Juang and Chen 1999;Juang et al. 2000Juang et al. , 2001Juang et al. , 2003. Thus, this study utilizes an improved, robust, and promising method in assessing liquefaction resistance of soils for Dhaka City. The SPT-N and V s data from Dhaka City have been used in the assessment of liquefaction resistance of soils for an earthquake of moment magnitude, M W 7.5 with a peak ground acceleration (PGA) of 0.15 g. According to the proposed Bangladesh Nation Building Code (BNBC), the PGA value for Dhaka City is 0.2 g for the maximum considered earthquake (MCE), which is equivalent to 2% probability of exceedance in 50 years (2475year return period). The PGA of the design basis earthquake (DBE) is equal to the 2/3 (two-third) of the MCE. Therefore, the PGA of DBE in Dhaka City is 0.13 g. It is observed from historical record of earthquakes that more than M w 7.0 earthquakes occurred beyond 50 km radius from city center of Dhaka (Middlemiss 1885;Oldham 1899;Stuart 1920). Therefore, the magnitude of earthquake is considered as M w 7.5 with PGA of 0.15 g in this study.
Firstly, a liquefaction indicator function was formulated for predicting the occurrence of liquefaction, then points at the limit state surface (Juang et al. , 2002 were generated to determine the CRR through simulation of borehole data of the city in neural network models that were trained using the derived points at the limit state surface. The CSR was estimated on the basis of simplified procedure (Seed and Idriss 1971). The factor of safety (FS) of liquefaction was calculated at selected locations of Dhaka City using estimated CSR and CRR values. Even though the FS may provide an idea of the resistance of soils, it is not enough to represent the state of the liquefaction severity of any location (Sonmez and Gokceoglu 2005). Therefore, the FS values up to the depth of liquefiable layers, which is considered as 20 m depth, were used to determine the LPI of all selected locations of Dhaka City for both datasets (SPT-N and V s ) based on the developed method of Iwasaki et al. (1982) to prepare liquefaction hazard maps for calculating LPI values of the areas where SPT-N and V s data were not available. For each georgical unit, the liquefaction hazard is also predicted from the cumulative frequency (CF) distribution of the LPI according to Holzer et al. (2006).

Surface geology of Dhaka City
Dhaka City, the capital of Bangladesh, located is on the bank of the Buriganga River, is now one of the world's megacities. The city is encircled by the rivers of Buriganga, Balu, Turag, and Tongi Khal. It occupies an area of about 321 square kilometers with a population of about 14 million. Dhaka City has an average elevation of 6.5 m ranging between 2 and 14 m (above the mean sea level) with many depressions (Rahman et al. 2015). Dhaka is situated in the central part of Bangladesh bounded by the Shillong Massif in the north, Precambrian Indian Shield in the west, the Indo-Burman Folded Belt in the east and it is open to the Bay of Bengal in south. Bangladesh covers most part of the Bengal Basin with the maximum sedimentary thickness of 22 km (Alam 1989;Reimann 1993). Dhaka City is developed partly on the Madhupur Terrace of the Pleistocene age and partly on the low-lying floodplains of the Holocene age. The sediment of the Pleistocene terrace has been deposited on the older floodplains, whereas the Holocene alluvium has been deposited on the recent floodplains of the Ganges-Brahmaputra River Systems (Morgan and McIntire, 1959).
The Pleistocene terrace deposits exposed in the central part of the city are primarily comprised of a 6-8 m thick layer of reddish to yellowish-brown, medium stiff to stiff silty clay that is underlain by a layer of medium dense to very dense silty sand and sand down to the depth of investigation of 20 m. The Holocene alluvium deposits composed of very loose to loose sand, silt, and very soft to soft silty clay that are present down to the depth of investigation in northwestern, southeastern, and eastern parts of the city (Rahman et al. 2021). Gray sand, silty sand, and clayey silt make up the artificial fills that are emplaced to the west and east portions of the city. For the emplacement of the artificial fills, both hydraulic dragging from the river and trucks from the land were used, but the ground was not compacted properly during filling, which creates the area prone to liquefaction (Rahman et al. 2015).

Seismotectonics of the region
The Bengal Basin is in the northeastern part of the Indian plate and bordering the Indian-Eurasian convergent plate boundary where the Himalayan ranges in the north and Indo-Burman ranges in east have been created due to the collision between these plates (Curray et al. 1982;Aitchison et al. 2007). Besides Bangladesh, the Bengal Basin also contains portions of Assam, Tripura, and West Bengal.
Dhaka is seismically vulnerable due to its proximity to the Eurasian and Indian convergent plate boundary (Rahman et al. , 2021. Bangladesh, Myanmar, Nepal, and northeastern India experienced several historical earthquakes (Table 1) that occurred along this plate boundary and associated faults. The Himalayan and the Arakan subduction-collision systems (Fig. 2) also generated many devastating earthquakes in these regions (Fig. 3).
The Dauki Fault (DF) and the Himalayan Frontal Thrust (HFT) are the main seismotectonic elements of the Himalayan system, while the Arakan subduction-collision system manifests itself through the Indo-Burman Folded Belt along with the megathrust beneath (Steckler et al. 2008;Wang et al. 2014). Bilham and Hough (2006) anticipated that a large earthquake with a magnitude ranging from M w 7.5 to 8.5 may occur in the Himalayan system because of the movement of the Indian   (Goda et al. 2015). It has been revealed by recent paleoseismological investigations that the Dauki fault was activated three times during last thousand years (Yeats et al. 1997;Morino et al. 2011Morino et al. , 2014a The convergence of the tectonic plates and increasing frequency of earthquakes with large magnitude are, therefore, the indication of active seismic activities in these regions (Rahman and Siddiqua 2017a).

Database establishment
The SPT-N and V s data from sixty-five (65) boreholes including relevant geotechnical properties of soils were used to assess soil liquefaction resistance of Dhaka City in terms of the FS, which was estimated using ANN incorporated (Juang et al. , 2002 Simplified Procedure of Seed and Idriss (1971). Fifty (50) borehole profiles were obtained from the Comprehensive Disaster Management Programme (CDMP) while the most of the authors were present during data collection, and the remaining fifteen (15) borehole data were collected by all the authors. Typical borehole profiles of SPT-N and V S are shown in Fig. 2. Then, the LPI of each borehole profile was estimated using all FS values of each borehole that were estimated at every 1.5 m interval to a depth of 20 m below the ground surface according to the method introduced by Iwasaki et al. (1978). The borehole sites were selected considering the variation of the geological units in the city ( Table 2). The surface geological map ( Fig. 1) shows the borehole locations. For training purpose, artificial neural network (ANN) requires the SPT-N and V s data of the sites where the historical data of liquefaction and non-liquefaction cases are available to find liquefaction indicator (LI) function and points of the limit state function (LSF).

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The SPT-N data of the historical cases for liquefaction and non-liquefaction were primarily collected by Fear and McRoberts (1995) and later summarized by Idriss and Boulanger (2010). The V s data were compiled by Andrus et al. (1999). After screening as per the ANN model applicability criteria of used parameters as described in Juang et al. (2000), total 225 SPT cases (127 cases liquefied) and 225 V s cases (97 cases liquefied) from 26 earthquakes over 70 sites identified by Andrus et al. (1999) were used for the analysis of the present study.

Factor of safety of liquefaction (FS)
In this study, an updated simplified procedure proposed by Youd et al. (2001)is used in calculating the factor of safety (FS) of liquefaction that is the ratio of the cyclic resistance ratio (CRR) to the cyclic stress ratio (CSR).

Calculation of CSR
The CSR defines the cyclic loading characteristic of soils, by which the seismic demand of the soil layer is determined on a level ground condition. It is the ratio of the cyclic loadinginduced average cyclic shear stress to the initial vertical effective stress on the soil particles (Robertson and Campanella 1985). The following equation of Seed and Idriss (1971) that was slightly adjusted by Juang et al. (2003) has been used to estimate the CSR at z depth from the ground surface due to earthquake loading: where CSR 7.5 = CSR adjusted to an earthquake magnitude of M w 7.5 using a magnitude scaling factor (MSF); av = average cyclic shear stress exerted by an earthquake, v = total vertical stress, ′ v = effective vertical stress at a depth of question (z); g = gravitational acceleration; a max = peak horizontal ground acceleration (PGA); R p = overburden pressure ratio v ∕ � v ; S L = seismic loading parameter (a max /g)/MSF; r d = stress reduction coefficient represents soil flexibility that depends on z. The calculation formula of r d according to Youd et al. (2001) is as follows: (1) The MSF is the magnitude scaling factor used in liquefaction resistance adjustment to the M W 7.5 reference magnitude earthquake (Youd et al. 2001).
where M w = moment magnitude.

Calculation of CRR using ANN
The ability of soil to resist cyclic stress is denoted by the CRR. In the present study, Juang et al. (2000Juang et al. ( , 2002 recommended procedures were used for calculating CRR from LSFs derived using the SPT-N and V s . Initially, the LI function was produced by training with the cases of actual field performance using neural network. The LI function is a trained neural network capable of predicting liquefaction or no liquefaction occurrences with high precision. In general, the LI function (Eq. 4) is a multi-dimensional and highly nonlinear function. It can be developed using a neural network model of three layers: where B o refers to the output layer bias (consisting of one neuron only); W k is the connection weight between kth neuron in the hidden layer and the only one neuron of output layer; B Hk refers to the bias at neuron k (k = 1, n) of the hidden layer; W ik is the connection weight between input variable i (i = 1, m) and the neuron k of the hidden layer.
Secondly, a search mechanism is established using the LI function for searching points at the surface of the limit state. Thirdly, the LSF is specified collectively by the generated points. Finally, neural network models were trained for both datasets (SPT-N and V s ) to determine the CRR for the selected locations of Dhaka City using these generated data points. Conceptually, the LI function of the SPT-N and V s data may take the following ANN model forms, respectively, as suggested by Juang et al. (2002Juang et al. ( , 2000: In this analysis, critical CSR = CRR = f (indices of soil properties) defines the limit state. The LSF, conceptually illustrated in Fig. 4, is defined based on a robust but simple system that was introduced by Juang et al. (2000). For each case in training data, either by increasing normalized soil strength (path B showed in Fig. 4) or by lowering seismic load (path A shown in Fig. 4), the limit state could be reached when liquefaction has been observed. Using path A, as an example, by lowering seismic load while keeping soil resistance unchanged, a new data pattern is created. With a new input pattern, the LI function would generate a new output. Initially, it is expected that the output would remain the same with a slight lowering of the seismic load. Nonetheless, if this cycle continues to decrease seismic load, ultimately no-liquefaction will be implied by the output. In the given soil condition, the critical load determining (2) r d = 1.000 − 0.4113z 0.5 + 0.04052z + 0.0017532z 1.5 1.000 − 0.4177z 0.5 + 0.05729z − 0.00625z 1.5 + 0.001210z 2 FCI,CSR 7.5 the limit state (also called critical CSR), is the upgraded seismic load resulting in a shift in the LI function. Likewise, when any case shows no liquefaction, critical CRR values of the LSF can be generated either by raising the seismic load (path C showed in Fig. 4) or by lowering the value of normalized soil strength parameters (path D showed in Fig. 4). Note that, in some cases, critical CSR searches might not be effective. It occurs when the upper limit of a normal load range is exceeded by seismic load using Path C in Fig. 4 for example. As a result, the liquefaction output of the LI function remains the same.
From each search that would be successful, a data point on the surface of the limit state, which is multidimensional is produced. Since CRR = CSR 7.5 or critical CRR defines the limit state boundary surface by its definition, an LSF is defined through CRR = f (indices of soil properties) once enough data points were obtained. Figure 4 illustrates the described searching mechanism.
After generating the boundary surface points based on the algorithm mentioned above, by training those points with a feed-forward, three-layer neural network, connection weights and biases can be produced, that would then be used in CRR estimation: This equation is the same as Eq. 4. Conceptually, the LSF from the SPT-N and V s data may take the following ANN model forms, respectively, as suggested by Juang et al. (2002Juang et al. ( , 2000: Tables 3 and 4 show all specifications of the ANN model for training that were implemented using the neural network toolbox of MATLAB for LI and LSFs, respectively. FCI   Fig. 4 Conceptual model of the mechanism to search limit state boundary (after Chen and Juang, (2000)) MATLAB offers an immersive computational platform with numerous built-in algorithms, along with a programming language. It provides a network neural toolbox containing source code for all such algorithms for training neural networks including the LM algorithm (Levenberg-Marquardt) that could be adjusted according to the circumstances provided (Beale et al. 2017).

Calculation of FS
The FS was calculated using Eq. 10 from the CSR, CRR, and MSF for earthquake magnitude other than M w 7.5. The CSR was calculated for all data points of two datasets (SPT-N and V s ) using Eq. 1 and the CRR was predicted from the simulating normalized data (SPT-N and V s ) of Dhaka City using the developed ANN models of LSF.
If FS ≤ 1 it is considered that liquefaction occurs; and if FS > 1 liquefaction is not likely to occur.

LPI Calculation
The calculation of the LPI uses the FS derived from the CRR and CSR. Iwasaki et al. (1978) suggested the LPI, which can be estimated using the FS values calculated from the SPT-N, V s, and CPT over the top 20 m, as follows: where W(z) = 10 − 0.5z; z < 20 m 0; z > 20 m ; z = Depth in meters and F(z) = 1 − Fs; Fs < 1.0 0; Fs ≥ 1.0 Iwasaki et al. (1982) mentioned that, if the LPI of a site is greater than 15, it is highly prone to severe liquefaction and if the LPI of any site is lower than 5, the liquefaction is not expected to show surface manifestation.

Results
Based on the approach discussed above, initially using 225 field performance cases (85% for training and 15% for testing) for the SPT-N and V s were used separately to train the LI function for each data set. One of the most effective ways to assess the ANN (10) F s = CRR 7.5 CSR MSF model efficiency is by observing the coefficient of determination (R) value. In the case of the ANN model for the LI function, the R-value for the SPT-N data training was 0.886 and testing 0.92, and the R values for the V s data training and testing were 0.89. Next, points were generated in the limit state boundary with the help of the respective LI functions for different datasets using the searching mechanism shown in Fig. 5. From the searching, total of 143 and 236 points have been generated for the SPT-N and V s datasets, respectively, on the limit state surface. Then, to approximate the LSF for the respective datasets (Eqs. 8 and 9), these data points were then used in training neural networks. The trained neural networks approximate the unknown but real functional relation between the output (CRR) and the inputs (indices of soil properties). Plotting the output values from training against the actual field performance value (or targeted value) also shows the performance of an ANN model. Figures 6 and 7 show such plots for the training and testing according to Eqs. 8 and 9 of generated data points at limit state surface from the SPT-N and V s data. Tables 6 and 7 are showing the weights and biases of connections obtained the trained ANN models for SPT-N and V s data, respectively.
The FS values were calculated from the CSR and CRR values that were derived from simulating trained ANN models for the LSF using normalized parameters (as in Eqs. 8 and 9) of each location. The LPI values were calculated using Eq. 11 from the FS of the SPT-N and V s datasets are shown in Table 8.
The surface geological units of Dhaka City is divided into three liquefaction hazard zones based on the LPI values (Table 9). For each zone, the cumulative frequency (CF) distributions of the LPI values of the SPT-N and V s data are shown in Figs. 8 and 9, respectively.
The LPI values of sixty-five (65) borehole profiles along with the contour of LPI values (0, 5, 10, 15, and 20) are shown on the maps to visualize the spatial distribution of liquefaction severity in the city (Figs. 10 and 11). The contours of the LPI values have been drawn using inverse distance weighting (IDW) interpolation technique in ArcGIS software considering the surface geological units and depth of the Pleistocene deposit below the Holocene deposits and artificial fillings. Therefore, biases of dense boreholes and sparse boreholes in some geological units have been removed justifying the liquefaction potential based on geological units, e.g., Holocene deposits and artificial fillings are likely to be liquefy during a strong ground motion that is reflected in the liquefaction hazard maps. One the basis of the LPI values, the liquefaction hazard of different areas of Dhaka City is classified according Iwasaki et al. (1982) (Table 10).
Liquefaction hazard of each surface geological unit was also classified by the cumulative frequency (CF) distribution at the LPI value of 5, which can be used to define the threshold for observing liquefaction surface effects (Holzer et al. 2006). The map of the SPT-N data shows that 15%, 53%, and 69% areas, whereas the map of the V s data shows that 11%, 48%, and 62% of areas of Zone 1, Zone 2, and Zone 3, respectively, will exhibit liquefaction surface effects.

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A comparison between the LPI values derived from the SPT-N and V s is illustrated in Fig. 12. In most of the cases, the LPI values of the SPT-N data are higher than that of the V s data.

Discussion
The liquefaction hazard map offers an opportunity to quantitatively estimate the liquefaction susceptibility of Dhaka City. The spatial liquefaction potential was determined by calculating the LPI values from the liquefaction FS estimated from both SPT-N and Vs at each 1.5 m interval of a borehole down to a depth of 20 m. The contour lines of equal LPI values were drawn to represent the LPI values of the locations where there was no borehole. Three liquefaction hazard zones were identified in the city based on the CF distribution of LPI of each geological unit to determine the percentage of the area of these zones that are likely to liquefy in a defined earthquake. Rahman and Siddiqua (2017a, b) have conducted liquefaction potential study for Dhaka, Chittagong, and Sylhet cites in Bangladesh using limited SPT-N, cone penetration test (CPT), and Vs data. Only seven (7) SPT-N and V S profiles and three (3) CPT profiles in Dhaka city were used in that study. Though this study effectively showed a comparison among LPI derived from three (3) different in-situ tests and give an idea of liquefaction of the Dhaka City, but number of SPT-N, V S and CPT data were not sufficient enough to illustrate the heterogeneity of the subsurface of the city. Rahman et al. (2015) also studied liquefaction potential of Dhaka City using SPT-N values of fifty-three (53) borehole profiles. In this study, more SPT and V S profiles have been used to characterize the subsurface heterogeneity with more accuracy. A statistical comparison between the current study and Rahman et al. (2015) is shown in Table 11.
It has been observed from the resultant LPI that there are some differences in the outputs derived from SPT-N and V S data ( Fig. 12 and Table 11). From the observed differences, in many cases LPI calculated from SPT-N has been found to higher than LPI from V S (e.g., 11,12) and the opposite was also observed (e.g., BH-3, 4). Such differences have also been found in other studies (Ateş et al. 2014;Siddiqua 2016, 2017a, b). These differences could occur due to inherent uncertainties in data retrieval procedure of SPT-N and V S . Due to the varied energy efficiency of various components of the standard penetration test (SPT) equipment, there is uncertainty in estimating SPT-N (Mayne et al. 2009). And the uncertainties in estimating V S include the expertise knowledge and skill of the personnel doing the test, the type of casing used in the borehole, the type of instrument  10 Liquefaction hazard map for Dhaka City using the LPI values of the SPT-N data for an earthquake of M w 7.5 with a peak horizontal ground acceleration (PGA) of 0.15 g. According to Iwasaki et al. (1982), liquefaction hazard for LPI > 15 is very high, for 5 < LPI ≤ 15 is high, for 0 < LPI ≤ 5 is low; and for LPI = 0 is very low. According to Holzer et al. (2006), the cumulative frequency (CF) distributions of the LPI of three zones indicate that 15%, 53%, and 69% of areas of Zone 1, 2, and 3, respectively, exhibit surface manifestation of liquefaction and V S in the same location and then compare the findings for an accurate evaluation of liquefaction resistance.

Fig. 11
Liquefaction hazard map for Dhaka City using the LPI values of the Vs data for an earthquake of M w 7.5 with a peak horizontal ground acceleration (PGA) of 0.15 g. According to Iwasaki et al. (1982), liquefaction hazard for LPI > 15 is very high, for 5 < LPI ≤ 15 is high, for 0 < LPI ≤ 5 is low; and for LPI = 0 is very low. According to Holzer et al. (2006), the cumulative frequency (CF) distributions of the LPI of three zones indicate that 15%, 53%, and 69% of areas of Zone 1, 2, and 3, respectively, exhibit surface manifestation of liquefaction In Zone 1, up to 6-8 m depth is formed of stiff to hard, reddish-to yellowish-brown Pleistocene clayey soils that is underlain by the medium to very dense, yellowish-brown Plio-Pleistocene sandy soils up to the depth of investigation of 20 m. In the case of the SPT-N data, the liquefaction potential in Zone 1 ranges from low to very low with the LPI values from 0 to 4.46, except boreholes BH-22 and BH-25 with the LPI values of 9.10 and 6.39, respectively. The cumulative frequency (CF) distribution of the SPT-N based LPI values of Zone 1 suggests that fifteen percent (15%) of the area of this zone would have liquefaction surface effects (Fig. 10). For the V s data, the liquefaction potential in Zone 1 is also from very low to low with the LPI values from 0 to 4.77, except boreholesBH-37 with the LPI value of 6.12. The CF distribution of the V s based LPI values of Zone 1 suggests that eleven percent (11%) of the area of this zone would have liquefaction surface effects (Fig. 11). In case of outliers, the SPT-N based LPI values of boreholes BH-22 and BH-25 are 9.10 and 6.39, respectively, but the V s based LPI values are 0 for both boreholes, which seems more accurate as these two boreholes are in the Pleistocene terrace (Madhupur terrace) that is not likely to liquefy. On the other hand, at borehole BH-37, the V s based LPI value is 6.12 while SPT-N based LPI is 3.84 and it is also in the Pleistocene terrace, therefore, the LPI value of 3.84 from the SPT-N data seems more accurate.
Zone 2 includes the Holocene terrace deposits and alluvial valley fill where the terrace deposits are formed of sandy and silty gray soils which include point and channel bars and natural levees of the existing rivers. The valley-fill deposits that have been deposited in the depressions and valleys of the Pleistocene terrace, are comprised of gray sandy soils and gray to dark gray clayey soils. In Zone 2, the SPT-N based LPI values range from 0 to 23.08, which imply a range of no potential to very high potential of liquefaction. The surface effects of liquefaction will be exhibited in fifty-three percent (53%) area of Zone 2. The V s based LPI values are from 0 to 18.98, which also imply a range of no potential to very high potential of liquefaction in Zone 2. The surface effects of liquefaction will be exhibited in forty-eight percent (48%) area of this zone. At boreholesBH-11 and BH-49 of this zone, the SPT based LPI values are 12.76 and 14.19, respectively, whereas the V s based LPI values are 0 at these boreholes. BH-11 is located on point bar and BH-49 is on the natural levee and both are usually more prone to liquefaction. Therefore, the SPT-N provides a more accurate result in this case.
Zone 3 contains artificial fills and Holocene alluvium that are comprised of gray sandy and clayey soils. The SPT-N based LPI values of this zone vary from 0 to 20.70, which indicate a range of no potential to very high potential of liquefaction. The CF distribution of the SPT-N based LPI values suggest that the surface effects of liquefaction will be exhibited in sixty-nine percent (69%) area of this zone. The V s based LPI values of this zone range from 0 and 21.13, which also indicate a range of no potential to very high potential of liquefaction. The CF distribution of the V s based LPI values suggest that the surface effects of liquefaction would be exhibited in sixty-two percent (62%) area of this zone. In case of Zone 3, the SPT-N based LPI values of boreholesBH-8, 6.66,11.96,and  Borehole BH-34 is in a floodplain, which is more likely to have an LPI value of more than 5, therefore, the SPT-N based LPI value (11.96) appears more reliable than the V s based LPI (3.23) value. Borehole BH-19 and BH-41 are in the floodplain and back swamp, respectively, and in both cases for both datasets their LPI values are greater than 5, but it cannot be reliably said either of these will be greater than 15 or not as the output differs. From the historical earthquake records of Bangladesh, it was observed that liquefaction occurred in silty and sandy alluvium of the Holocene floodplains during the 1885 Bengal earthquake (M w 6.87), 1897 Great Assam earthquake (M w 8.03), and 1918 Srimangal earthquake (M w 7.2) (Middlemiss 1885;Oldham 1899;Stuart 1920). The results of the present study also suggest that severe liquefaction may occur in the silty and sandy alluvium of the Holocene floodplains and the Pleistocene terrace deposits are not likely to liquefy during an earthquake of M w 7.5 having a PGA of 0.15 g. It can also be mentioned that during the 1995 Kobe earthquake in Japan, severe liquefaction occurred in loose fills (Hamada et al. 1995). Holzer et al. (2006) have also identified that the Pleistocene deposits have low liquefaction potential and the artificial fills and alluvium have high liquefaction potential.

Conclusions
In this study, both SPT-N and V s data have been used to calculate the LPI for the preparation of liquefaction hazard maps of Dhaka City using simplified procedure considering an earthquake of M W 7.5 with a PGA of 0.15 g. In the present study, ANN model has been used to predict the CRR from the SPT-N and V s data, as it provides more realistic and reliable results using sufficient actual field performance cases. From the results, it is noted that the SPT-N based LPI value is higher than the V s based LPI value at most of the boreholes. Three liquefaction hazard zones are identified in the city based on the CF distribution of the LPI of each geological unit and the LPI contour lines 0, 5, 10, 15, and 20 have been drawn to demonstrate spatial distribution of liquefaction hazard in the city. The map of the SPT-N based LPI values indicates that 15%, 53%, and 69% areas, whereas the map of the V s based LPI values indicates that 11%, 48%, and 62% areas of Zone 1, 2, and 3 exhibit surface manifestation of liquefaction for an earthquake of M w 7.5 with a PGA of 0.15 g. Therefore, it can be concluded that the CF distribution of the LPI of both SPT-N and V s data show almost similar severity of liquefaction in Zone 1, 2, and 3.
The uncertainties associated with the calculation of the LPI can be reduced by using more SPT-N, V s data, variation in groundwater level, accurate surface geological unit boundary delineation, and appropriate ground motion. Finally, this liquefaction hazard map of Dhaka City can be used as a guide for future urban development and planning to reduce the liquefaction associated damages and loss.