ASSESSMENT OF LIQUEFACTION POTENTIAL OF SOIL USING MULTI-LINEAR REGRESSION MODELING

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 1, Jan-Feb 2016, pp , Article ID: IJCIET_07_01_030 Available online at Journal Impact Factor (2016): (Calculated by GISI) ISSN Print: and ISSN Online: IAEME Publication ASSESSMENT OF LIQUEFACTION POTENTIAL OF SOIL USING MULTI-LINEAR REGRESSION MODELING Abdullah Anwar and Yusuf Jamal Assistant Prof., Civil Engineering Department, Integral University, Lucknow, Uttar Pradesh (226022), India Sabih Ahmad Associate Professor, Civil Engineering Department, Integral University, Lucknow, Uttar Pradesh (226022), India, M.Z. Khan Professor and Head, Civil Engineering Department, I.E.T. Sitapur Road, Lucknow, Uttar Pradesh (226022), India ABSTRACT The Standard Penetration Test (SPT) is the most widely used in-situ test throughout the world for subsurface geotechnical investigation and this procedure have evolved over a period of 100 years. Estimation of the liquefaction potential of soils is often based on SPT test. Liquefaction is one of the critical problems in the field of Geotechnical engineering. It is the phenomena when there is loss of shear strength in saturated and cohesion-less soils because of increased pore water pressures and hence reduced effective stresses due to dynamic loading. In the present study, SPT based data were analysed to find out a suitable numerical procedure for establishing a Multi- Linear Regression Model using IBM-Statistical Package for the Social Sciences (IBM SPSS Statistics v) and MATLAB(R2010a) in analysis of soil liquefaction for a particular location at a site in Lucknow City. A Multi- Storeyed Residential Building Project site was considered for this study to collect 12 borehole datasets along 10 km stretch of IIM road, Lucknow, Uttar Pradesh (India). The 12 borehole datasets includes 06 borehole data up to 22m depth and other 06 borehole data up to 30m depth to further analyse the behavior of different soil properties and validity of the established Multi-Linear Regression Model. Disturbed soil sample were collected upto 22m and 30m depth in everym interval to determine various soil parameters. In recent years, various researchers have expressed the need for location based specific study of seismic soil properties and analysis of Liquefaction in Soils. Keywords: Liquefaction, Multi-Linear Regression Modeling, MATLAB, SPSS, SPT, CSR, CRR. Cite this Article: Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan, Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling, International Journal of Civil Engineering and Technology, 7(1), 2016, pp editor@iaeme.com

2 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan 1. INTRODUCTION Liquefaction had been studied extensively by researchers all around the world right after two main significant earthquakes in Since than a number of terminologies, conceptual understanding, procedures and liquefaction analysis methods have been proposed. A well-known example is the 1964 Niigata (Japan) and 1964 Great Alaskan Earthquake in which large scale soil liquefaction occurred, causing wide spread damage to building structures and underground facilities [1]. Development of liquefaction evaluation started when Seed and Idriss (1971) [2] published a methodology based on empirical work termed as simplified procedure. It is a globally recognized standard which has been modified and improved through Seed (1979) [3], Seed and Idriss (1982) [4], Seed et al. (1985)[5],National Research Council (1985) [6], Youd and Idriss(1997) [7], Youd et al. (2001) [8]; Idriss and Boulanger(2006) [9]. Liquefaction of loose, cohesionless, saturated soil deposit is a subject of intensive research in the field of Geo-technical engineering over the past 40 years. The evaluation of soil liquefaction phenomena and related ground failures associated with earthquake are one of the important aspects in geotechnical engineering practice. It will not only cause the failure on superstructure, but also the substructure instability and both lead to catastrophic impact and severe casualties. For urban cities with alarmingly high population, it becomes necessary to develop infrastructural facilities with several high rise constructions. It is one of the primary challenge for Civil Engineers to provide safe and economical design for structures, particularly in earthquake prone areas. The in situ data are used to estimate the potential for triggering or initiation of seismically induced liquefaction. In the context of the analyses of in situ data, the assessment of liquefaction potential are broadly classified as: 1. Deterministic (Seed and Idriss 1971; Iwasaki et al. 1978; Seed et al. 1983; Robertson and Campanella 1985; Seed and De Alba 1986; Shibata and Teparaksa 1988; Goh 1994; Stark and Olson 1995; Robertson and Wride 1998; Juang et al. 2000, 2003; Idriss and Boulanger 2006) [10-21] 2. Probabilistic (Liao et al. 1988; Toprak et al. 1999; Juang et al. 2002; Goh 2002; Cetin et al. 2002, 2004; Lee et al. 2003; Sonmez 2003; Lai et al. 2004; Sonmez and Gokceoglu 2005) [22-30] The deterministic method provides a yes/no response to the question of whether or not a soil layer at a specific location will liquefy. However, performance-based earthquake engineering (PBEE) requires an estimate of the probability of liquefaction (P L ) rather than a deterministic (yes/no) estimate (Juang et al. 2008) [31]. Probability of Liquefaction (P L ) is a quantitative and continuous measure of the severity of liquefaction. Probabilistic methods were first introduced to liquefaction modeling in the late 1980s by Liao et al. (1988) [22]. In recent years, innovative computing techniques such as artificial intelligence and machine learning have gained popularity in geotechnical engineering. For example, Goh (1994) [16] and Goh (2002) [25] introduced the artificial neural networks for liquefaction potential, Cetin et al. (2004) [27] and Moss et al. (2006) [32] applied the Bayesian updating method for probabilistic assessment of liquefaction, and Hashash (2007)[33] used the genetic algorithms for geomechanics. An important advantage of artificial intelligence techniques is that the nonlinear behavior of multivariate dynamic systems is computed efficiently with no a priori assumptions regarding the distribution of the data. Various researchers, like Raghukanth and Iyengar [34], Rao and Satyam [35], Sitharam and Anbazhagan [36], Hanumanthrao and Ramana [37], Maheswari et al. [38], Shukla and Choudhury [39] and few others showed the need for location based study for seismic soil properties and analysis of Liquefaction in Soils. In view of the above, for the present study, a site of Lucknow city is chosen for assessment of liquefaction in soil. As per Indian Seismic Design Code (CRITERIA FOR EARTHQUAKE RESISTANT DESIGN OF STRUCTURES) IS 1893 (Part 1): 2002 [40], Lucknow city is located in Seismic Zone III, and a moderate intensity (5.5 to 6.5) Earthquake may occur which may lead to liquefaction of some typical soil sites. Liquefaction occurs due to rapid loading during seismic events where there is not sufficient time for dissipation of excess pore-water pressures by natural drainage. Rapid loading situation increases pore-water pressures resulting in cyclic softening in fine-grained materials. The increased pore water pressure transforms granular materials from a solid to a liquefied state thus shear strength and stiffness of the soil deposit are reduced. Liquefaction is observed in loose, saturated, and clean to silty sands. The soil liquefaction depends on the magnitude of earthquake, peak ground acceleration, intensity and duration of ground motion, the distance from the source of the earthquake, type of soil and thickness of the soil deposit, relative density, grain size distribution, fines content, plasticity of fines, degree of saturation, confining pressure, hydraulic conductivity of soil layer, position and fluctuations of the groundwater table, reduction of effective stress, and shear modulus degradation [41]. Liquefaction-induced ground failure is influenced by the thickness of non-liquefied and liquefied soil layers. Measures to mitigate the damages caused by liquefaction require accurate evaluation of liquefaction potential of soils. The potential for liquefaction to occur at certain depth at a site is quantified in terms of the factors of safety against liquefaction (FS). Seed and Idriss (1971) [10] proposed a simplified procedure to evaluate the liquefaction resistance of soils in terms of factors of safety (FS) by taking the ratio of capacity of a soil editor@iaeme.com

3 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling element to resist liquefaction to the seismic demand imposed on it. Capacity to resist liquefaction is computed as the cyclic resistance ratio (CRR), and seismic demand is computed as the cyclic stress ratio (CSR). FS of a soil layer can be calculated with the help of several in-situ tests such as standard penetration test (SPT), cone penetration test (CPT), shear wave velocity (Vs) test etc. SPT-based simplified empirical procedure is widely used for evaluating liquefaction resistance of soils. Factors of safety (FS) along the depth of soil profile are generally evaluated using the surface level peak ground acceleration (PGA), earthquake magnitude (Mw), and SPT data, namely SPT blow counts (N), overburden pressure (σ v ), fines content (FC), clay content, liquid limits and grain size distribution. A soil layerwith FS<1 is generally classified as liquefiable and with FS>1 is classified as nonliquefiable [10]. A layer may liquefy during an earthquake, even for FS>. Seed and Idriss (1982) [42] considered the soil layer with FS value between 1.25 and as non-liquefiable. Soil layers with FS greater than 1.2 and FS between and 1.2 are defined as non-liquefiable and marginally liquefiable layers (MLL), respectively. 2. STUDY AREA and NEED FOR STUDY Lucknow (26.8 N 80.9 E) is the capital city of the state of Uttar Pradesh, India. It is the 2 nd largest city in north, east and central India after Delhi. It is the world s 74 th fastest growing city and also the largest city in Uttar Pradesh. It continues to be an important centre of government, education, commerce, aerospace, finance, pharmaceuticals, technology, design, culture, tourism, music and poetry. The city stands at an elevation of approximately 123 metres (404 ft) above sea level and covers an area of 2,528 square kilometers (976 sq mi). The climate of Lucknow district is predominantly subtropical in nature. Hot atmosphere during the months of May and June and heavy rainfalls during the months of June, July and August are the typical characteristics of Lucknow. Real estate is one of the many booming sectors of the Lucknow s economy. Lucknow is one of the fastest growing city in construction industry. As per Seismic Zonation Map of India[40], Lucknow city comes under seismic zone III, where an earthquake of magnitude between 5.5 and 6.5 can be expected as shown in fig.1. Recently, on 25 th April 2015, Lucknow experienced an earthquake whose recorded intensity was approximately of 5 intensity as reported by Geological Survey of India in Lucknow. Though Lucknow has not yet experienced any disastrous earthquake for a long time, the possibility of one cannot be ruled out. The Lucknow city falls in Zone III on the seismological ratings and lies on the Faizabad faultline, which has a seismic gap of about 350 years. Experts say that Faizabad fault, which has been under stress for long now, could spell a major disaster in future, when an earthquake does occur. As the Indian plate continues to move north towards the Eurasian plate, the Indian subcontinent is bound to experience more earthquakes. The movement of the Indian plate had been restricted by the Eurasian plate, and now the former is slowly going under the Eurasian plate. The movement results in earthquakes as the rocks cannot sustain the stress for too long. The Indian plate is likely to slip by 5.25 metre when an earthquake does occur along the Faizabad fault. Experts believe that such a slip equates to an earthquake of 8.0 on Richter Scale. Gomati basin and the Ganga basin have soft, alluvial soil, and an earthquake could prove even more damaging for this area. There is a greater chance of liquefaction of soil resulting in buildings sinking into the ground. On the other hand, this alluvial cushion has also protected the region, as slight tremors and shocks are absorbed by it. In a Disaster Risk Management Programme chalked out by the Ministry of Home Affairs in association with United Nations Development Programme, 38 Indian cities have been identified in Zone III and above. Six cities of Uttar Pradesh (UP) also feature on this list that includes Lucknow, Kanpur, Agra, Varanasi, Bareilly, Meerut. For the present study, the area of IIM Road, in Lucknow city bounded between latitude of about N to N and longitude of about E to E is chosen editor@iaeme.com

4 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Figure 1 Uttar Pradesh State Disaster Management Plan for Earthquake (Source: Uttar Pradesh State Disaster Management Plan For Earthquake, March 2010 ) Figure 2 Seismic Zonation Map of India (Source : editor@iaeme.com

5 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling SITE LOCATION OBJECTIVE OF THE STUDY Figure 3 Site Location (IIM Road, Lucknow) Site investigation and estimation of physical soil characteristics are essential parts of a geotechnical design process. Evaluation of soil properties beneath and adjacent to the structures at a specific region is of importance in terms of geotechnical considerations since behavior of structures is strongly influenced by the response of soils due to loading. Due to difficulty in obtaining high quality undisturbed soil samples and cost & time involved their in, the software based modeling may probably help in assessing the factor of safety relevant to location based assessment of soil liquefaction which is being proposed herewith. The main objectives of the study were: a) Assessment of Liquefaction Potential of Soil using the SPT bore hole data for a particular site in Lucknow. b) To develop a reliability based Multi-Linear Regression Model to evaluate the liquefaction potential of soil at a particular alignment of a site in Lucknow. c) To validate the Multi-Linear Regression Model on comparing the modeled factor of safety to the actual site factor of safety in the assessment of soil liquefaction for a particular site in Lucknow 3. IN-SITU TEST 3.1 STANDARD PENETRATION TEST (SPT) In this study, we use the data obtained by Standard Penetration Test. Estimation of the liquefaction potential of saturated granular soils for earthquake design is often based on SPT tests. The test consists of driving a standard 50mm outside diameter thick walled sampler into soil at the bottom of a borehole, using repeated blows of a 63.5kg hammer falling through 760 mm. The SPT N value is the number of blows required to achieve a penetration of 300 mm, after an initial seating drive of 150 mm. Correlations relating SPT blow counts for silts & clays and for Sands & Gravels, from Peck et al. (1953) [43] is depicted in Table 1. The SPT procedure and its simple correlations quickly became soil classification standards. Estimated values of Soil friction and cohesion based on uncorrected SPT blow counts from Karol (1960) [44] are presented in Table editor@iaeme.com

6 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan S. No. Blows/Ft (N SPT ) Sands and Gravels Blows/Ft (N SPT ) Silts and Clay Very Loose 0-2 Table 1 Correlations relating SPT blow counts for silts & clays and for Sands & Gravels, from Peck et al. (1953) Very Soft Loose 2-4 Soft Medium 4-8 Firm Dense 8-16 Stiff 5 Over 50 Very Dense Very Stiff 6. Over 32 Hard Soil Type SPT Blow Undisturbed Soil Counts Cohesion Friction (psf) Angle ( ) 1. Very Soft < Soft Firm Stiff Very Stiff Hard >30 > S. No. 7. Cohesive Soil Cohesi onless Soil Loose < Medium Dense > Loose < Interme diate Soil 11. Medium Dense > Table 2 Estimated values of Soil friction and cohesion based on uncorrected SPT blow counts, from Karol (1960) 3.2 STANDARDIZED SPT CORRECTIONS In Skempton (1986) [45], the procedures for determining a standardized blow count were presented, allowing hammers of varying efficiency to be accounted for. This corrected blow count is referred to as N 60 because the original SPT hammer had about 60 percent efficiency, being comprised of a donut hammer, a smooth cathead, and worn hawser rope, and this is the standard to which other blow-count values are compared. Trip release hammers and safety hammers typically exhibit greater energy ratios (ER) than 60 percent (Skempton, 1986). N 60 is given as =. where, N 60 is the SPT N-value corrected for field procedures and apparatus, E m is the hammer efficiency, C B is the borehole diameter correction, C S is the sample barrel correction, C R is the rod length correction, and N is the raw editor@iaeme.com

7 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling SPT N-value recorded in the field. Robertson and Wride (1997) [46] have modified Skempton s chart and added additional correction factors to those proposed by Liao and Whitman (1986) [47]. This chart is reproduced in Table 3. The overburden stress corrected blow count, (N 1 ) 60, provides a consistent reference value for penetration resistance. This has become the industry standard in assessments of liquefaction susceptibility (Youd and Idriss, 1997) [48]. Robertson and Wride (1997) defined (N 1 ) 60 as : ( ) = where, N is the raw SPT blow-count value, C N = (P a /σ' vo ) (with the restriction that C N 2) is the correction for effective overburden stress (Liao and Whitman,1986), P a is a reference pressure of 100 kpa, σ' vo is the vertical effective stress, C E = ER/60% is the correction to account for rod energy, ER is the actual energy ratio of the drill rig used in percent, C B is a correction for borehole diameter, C S is a correction for the sampling method, C R is a correction for length of the drill rod. Factors Equipment Variables Term Corrections Overburden Pressure _ C N (P a /σ' vo ) (but C N 2) Energy Ratio Borehole Diameter Rod Length Sampling Method Donut Hammer - Safety Hammer C E Automatic Hammer mm 150mm C B 5 200mm m m m C R m >30m < Standard Sampler C S Sampler without liners Table 3 Recommended Corrections for Standard Penetration Test (SPT) blow count values, taken from Robertson and Wride (1997), as modified from Skempton (1986) (Source: Subsurface Exploration Using the Standard Penetration Test and the Cone Penetrometer Test by J. DAVID ROGERS, Environmental & Engineering Geoscience, Vol. XII, No. 2, May 2006, pp ) 4. METHODOLOGY In the present research, SPT based datasets on different soil parameters were analysed to find out suitable numerical procedure for establishing a Multi-Linear Regression Model using MATLAB(R2010a) and IBM- Statistical Package for the Social Sciences (IBM SPSS Statistics v) in analysis of soil liquefaction at a particular location of a site in Lucknow City. A Multi-Storeyed Residential Building Project site was considered for this study to collect 12 borehole datasets along 10 km stretch of IIM road, Lucknow, Uttar Pradesh (India). The 12 borehole datasets includes 06 borehole data up to 22m depth and other 06 borehole data up to 30m depth to further analyse the behavior of different soil properties and validity of the established Multi-Linear Regression Model. Disturbed soil sample were collected up to 22m and 30m depth in everym interval to determine various soil parameters. The different soil parameters includes particle size analysis, grain size distribution, water content, Atterberg s limit, bulk density, dry density, specific gravity, void ratio, shear strength parameters and uniformity coefficient etc. Excel Spreadsheets (v 2007) was used to input of over 200 data for the above said different soil parameters including the SPT-N values and Ground Water Table at different locations on the site. The soil at the site were found to be alluvial deposits. By using all these data- a Multi Linear Regression Model in terms of Cyclic Resistance Ratio (CRR) was developed in SPSS, a predictive statistical analysis software (to make smarter decisions, solve problems and improve the outcomes). After developing the CRR model, it was tested on the available site data and the results were examined in MATLAB (v R2010a), a high-level language and interactive environment for numerical computation, editor@iaeme.com

8 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan visualization, and programming. The results obtained from modeled CRR is then compared and analysed with the calculated value of CRR (based on Boulanger & Idriss) of the soil at varying depth. Seismic soil liquefaction was evaluated for this site in terms of the factors of safety against liquefaction (FS Liq ) along the depths of soil profiles for peak ground acceleration of 0.16g and earthquake magnitude of 7.5 on Richter scale. The evaluated factor of safety against liquefaction (FS Liq ) (based on Boulanger & Idriss) is compared to the modeled factor of safety against liquefaction (FS LiqMod ) to observe its reliability in the assessment of liquefaction potential of soil. 5. ASSESSMENT OF LIQUEFACTION POTENTIAL OF SOIL (USING SPT) 5.1. Calculation of Cyclic Shear Stress Ratio (CSR) The expression for CSR induced by earthquake ground motions formulated by Idriss and Boulanger (2006) [49] is as follows : (). =.!." # $ % & 0.65 is a weighing factor to calculate the equivalent uniform stress cycles required to generate same pore water pressure during an earthquake; a max is the maximum horizontal acceleration at the ground surface; σ vo and σ ' vo are total vertical overburden stress and effective vertical overburden stress, respectively, at a given depth below the ground surface; r d is depth-dependent stress reduction factor; MSF is the magnitude scaling factor and K σ is the overburden correction factor. Stress reduction coefficient (r d ) is expressed as a function of depth (z) and earthquake magnitude (M): () ($ % )= *(+)+ -(+) ' + *(+)=././ (+)= /6 +.7/5 where, z is depth (in metre); M is the Magnitude of earthquake The above equations were appropriate for depth, z 34m. However, for depth, z > 34m the following expression is used: $ % =./89:(.// ) The magnitude scaling factor, MSF, is used to adjust the induced CSR during earthquake magnitude M to an equivalent CSR for an earthquake magnitude, M = 7.5 &= < ;. Idriss (1999) [50] re-evaluated the MSF relation which is given by: &=.=89: #.6 7 where; M is the Magnitude of the earthquake. The MSF should be less than equal to 1.8, i.e. MSF 1.8 Boulanger and Idriss (2004) [51] found that overburden stress effects on the Cyclic Resistance Ratio (CRR). The recommended K curves are expressed as follows: ' = >2? The coefficient C σ is expressed in terms of (N 1 ) 60 =.4 6.=;/. C( ) where, (N 1 ) 60 is the overburden stress corrected blow count editor@iaeme.com

9 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling 5.2. Calculation of Cyclic Resistance Ratio (CRR) Determination of cyclic resistance ratio (CRR) requires fines content (FC) of the soil to correct updated SPT blow count (N 1 ) 60 to an equivalent clean sand standard penetration resistance value (N 1 ) 60cs. Idriss and Boulanger (2006) [49] determined CRR value for cohesionless soil with any fines content using the following expression: =89:D ( / ) EF 7. +?( ) EF / A? ( 4 ) EF /4. A +? ( 7 ) EF /.7 A /.6G Subsequent expressions describe the way parameters in the above equation are calculated as: where, ( ) EF =( ) + ( ) Δ(N 1 ) 60 is the correction for fines content in percent (FC) present in the soil and is expressed as: ( ) =I!J?.4+ =. / &. & # A ( ) = () (N 1 ) 60 is the overburden stress corrected blow count; N 60 is the SPT N value after correction to an equivalent 60% hammer efficiency (because the original SPT (Mohr) hammer has about 60% efficiency, and this is the standard to which other blowcount values are compared) and C N is the Overburden Correction Factor for Penetration resistance Determination of Factor of Safety (FS Liq ) The factor of safety against liquefaction (FS Liq ) is commonly used to quantify liquefaction potential. The factor of safety against liquefaction (FS Liq ) can be defined by & (KL = If the Cyclic Stress Ratio (CSR) caused by an earthquake is greater than the Cyclic Resistance Ratio (CRR) of the in-situ soil, then liquefaction could occur during the earthquake and vice-versa. Liquefaction is predicted to occur when FS, and liquefaction predicted not to occur when FS > 1. The higher the factor of safety, the more resistant against liquefaction [52]. Both CSR and CRR vary with depth, and therefore the liquefaction potential is evaluated at corresponding depths within the soil profile SPT N-value Corrections To calculate liquefaction potential corrected SPT-N values are used. Value correction was adopted as given by IS: [53] Correction for Overburden Pressure N-value obtained from SPT test is corrected as per following equation: ( ) = () C N - Correction factor obtained directly from the graph given in Indian Standard Code (IS: ) [53]. (Fig.4) editor@iaeme.com

10 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan It can also be calculated using the relationship: σ' z = effective overburden pressure in kn/m 2. Figure 4 Correction due to overburden Pressure =. M" = Correction for Dilatancy The values obtained in overburden pressure (N 1 ) shall be corrected for dilatancy if the stratum consist of fine sand and silt below water table for values of N 1 greater than 15 as under [55]: E,.. 6. STATISTICAL PACKAGE FOR THE SOCIAL SCIENCES (IBM SPSS STATISTICS) MODELING The study was conducted to produce a Multi Linear Regression Model in terms of Cyclic Resistance Ratio (CRR) for soil profile using SPSS. SPSS abbreviated as Statistical Package for the Social Sciences (IBM SPSS Statistics v), a predictive statistical analysis software is used for this purpose at a particular location of a site in Lucknow City. The parameters involved in CRR model for soil profile along its depth (z) are fine content (FC), water content (w), bulk density (ϒ) and Cyclic Stress Ratio (CSR). 7. MATLAB ANALYSIS The present study was aimed to examine the reliability of CRR model, developed in SPSS environment, by computing, visualizing and comparing its results to the calculated value of CRR(based on Boulanger & Idriss) of the soil at varying depth. MATLAB is a high-level language and interactive environment for numerical computation, visualization, and pro-gramming. MATLAB is used to analyze data, develop algorithms, and create models and applications. The language, tools and built-in math functions enable to explore multiple approaches and reach a solution faster than with traditional programming languages, such as C/C++ or Java. (Anon., ) [56]. MATLAB was used to provide with a convenient environment for performing many types of calculations and implementation of numerical methods. The results obtained from modeled CRR (computed in MATLAB) is then compared and analysed with the calculated value of CRR (based on Boulanger & Idriss). Further, modeled factor of safety against liquefaction (FS LiqMod ) is calculated and its compared to the computed value of factor of safety against liquefaction (FS Liq ) (based on Boulanger & Idriss) to study the reliability of model in the assessment of soil liquefaction. 8. RESULTS AND DISCUSSION This study refers to the prediction of liquefaction potential of soil by conducting Standard Penetration Test (SPT), to develop a Multi Linear Regression Model in terms of Cyclic Resistance Ratio (CRR) and to examine its reliability in the assessment of liquefaction potential of soil at a particular site in Lucknow. To meet the objectives twelve boreholes sets (BH-1, BH-2, BH-3, BH-4, BH-5, BH-6, BH-7, BH-8, BH-9, BH-10, BH-11 and BH-12) were analyzed, field and laboratory tests were conducted for the prediction of liquefaction potential. The water table at editor@iaeme.com

11 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling varying depth and earthquake magnitude of (M= 7.5) value were considered. In the assessment of Liquefaction Potential YES represents the Liquefiable Layer whereas NO represents the Non-Liquefiable Layer. Table 4 Water Table and Earthquake Magnitude Parameter BH-1 BH-2 BH-3 BH-4 BH-5 BH-6 BH-7 BH-8 BH-9 BH-10 BH-11 BH-12 Depth of water table (m) Earthquake magnitude (Rector scale) Table 5 IS Soil Classification (IS: ) Symbol SP SM ML CL CI CH Soil Description Poorly graded sand Silty sand Very fine sand Silty clay with low plasticity Sandy clay with medium plasticity Silty clay with high plasticity 7.1. ASSESSMENT OF LIQUEFACTION ASSESSMENT USING SPT Bore Hole (BH-1) Table 6: Study about liquefaction potential for Water Table at 4.100m S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No No No No Yes MLL No No No No No No editor@iaeme.com

12 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Liquefaction Potential for Bore Hole (BH-1) FS Liq vs FS Liq Figure 5 Graph of FS Liq vs Depth (z) for Bore Hole (BH-1) Bore Hole (BH-2) Table 7 Study about liquefaction potential for water table at S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No No No No MLL MLL No No No No No No editor@iaeme.com

13 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Liquefaction Potential for Bore Hole (BH-2) FS Liq vs FS Liq MLL = Marginally Liquefiable Layer Bore Hole (BH-3) Figure 6 Graph of FS Liq vs Depth (z) for Bore Hole (BH-2) Table 8 Study about liquefaction potential for water table at S.No. Depth SPT N (Z) m value CSR CRR FS Liq Status No No No MLL No No MLL MLL No No No No No No editor@iaeme.com

14 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Liquefaction Potential for Bore Hole (BH-3) FS Liq vs FS Liq Figure 7 Graph of FS Liq vs Depth (z) for Bore Hole (BH-3) Bore Hole (BH-4) Table 9 Study about liquefaction potential for water table at S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No MLL No No Yes MLL No No No No No No editor@iaeme.com

15 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Liquefaction Potential for Bore Hole (BH-4) FSLiq vs FS Liq Figure 8 Graph of FS Liq vs Depth (z) for Bore Hole (BH-4) Bore Hole (BH-5) Table 10 Study about liquefaction potential for water table at Depth (Z) SPT N S.No. CSR CRR FS m value Liq Status No No No MLL No 1 No 1.18 MLL 7 MLL 1.49 No 1.75 No 1.84 No 3 No 2.14 No 7 No editor@iaeme.com

16 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Liquefaction Potential for Bore Hole (BH-5) 3.5 FS Liq vs FS Liq Figure 9 Graph of FS Liq vs Depth (z) for Bore Hole (BH-5) Bore Hole (BH-6) Table 11 Study about liquefaction potential for water table at S.No. Depth SPT N (Z) m value CSR CRR FS Liq Status No No No No No No MLL MLL No No No No No No editor@iaeme.com

17 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Liquefaction Potential for Bore Hole (BH-6) FS Liq vs FS Liq Bore Hole (BH-7) Figure 10 Graph of FS Liq vs Depth (z) for Bore Hole (BH-6) Table 12 Study about liquefaction potential for water table at S.No. Depth SPT N (Z) m value CSR CRR FS Liq Status No No No No No No No No No No No No No No No No No No No No editor@iaeme.com

18 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Liquefaction Potential for Bore Hole (BH-7) 3.5 FS Liq vs FS Liq Figure 11 Graph of FS Liq vs Depth (z) for Bore Hole (BH-7) Bore Hole (BH-8) Table 13 Study about liquefaction potential for water table at S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No No No No No No No No No No No No No No No No No No editor@iaeme.com

19 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Liquefaction Potential for Bore Hole (BH-8) 3.5 FS Liq Bore Hole (BH-9) vs FS Liq Figure 12 Graph of FS Liq vs Depth (z) for Bore Hole (BH-8) Table 14 Study about liquefaction potential for water table at S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No No No No No No No No No No No No No No No No No No editor@iaeme.com

20 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Liquefaction Potential for Bore Hole (BH-9) 3.5 FS Liq Bore Hole (BH-10) vs FS Liq Fig. 13: Graph of FS Liq vs Depth (z) for Bore Hole (BH-9) Table 15 Study about liquefaction potential for water table at S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No No No No No No No No No No No No No No No No No No editor@iaeme.com

21 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Liquefaction Potential for Bore Hole (BH-10) 3.5 FS Liq vs FS Liq Figure 14 Graph of FS Liq vs Depth (z) for Bore Hole (BH-10) Bore Hole (BH-11) Table 16 Study about liquefaction potential for water table at S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No No No No No No No No No No No No No No No No No No editor@iaeme.com

22 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Liquefaction Potential for Bore Hole (BH-11) 3.5 FSLiq vs FS Liq Figure 15 Graph of FS Liq vs Depth (z) for Bore Hole (BH-11) Bore Hole (BH-12) Table 17 Study about liquefaction potential for water table at S.No. Depth (Z) m SPT N value CSR CRR FS Liq Status No No No No No No No No No No No No No No No No No No No No editor@iaeme.com

23 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Liquefaction Potential for Bore Hole (BH-12) 3.5 FS Liq Model vs FS Liq Figure 16 Graph of FS Liq vs Depth (z) for Bore Hole (BH-12) 7.1. ASSESSMENT OF LIQUEFACTION POTENTIAL USING MULTI-LINEAR REGRESSION MODELING Multi Linear Regression Model in terms of Cyclic Resistance Ratio (CRR) for soil profile was developed using SPSS (IBM SPSS Statistics v) at a particular location of a site on IIM road in Lucknow, Uttar Pradesh (India). The parameters involved in CRR model for soil profile along its depth (z) are fine content (FC), water content (wc), bulk density (ϒ) and cyclic stress ratio (CSR) MULTI-LINEAR REGRESSION MODEL R R Square Adjusted R Square Std. Error of the Estimate Model Summary b R Square Change Change Statistics F Change df1 df2 Sig. F Change (p-value) Durbin-Watson a a. Predictors: (Constant), Cyclic Shear Stress, Fine Content, Depth, Water Content, Bulk Density b. Dependent Variable: Cyclic Resistance Ratio The p-value defined as the probability value is computed using the test statistic, that measure the support (or lack of support) provided by the sample for the Null Hypothesis (H o ). Since p-value is less than the level of significance (α= 5) for the developed Multi-Linear Regression Model, i.e; (18 < 5), hence the Null Hypothesis (H o ) is rejected and Alternate Hypothesis (H 1 ) is accepted resulting the developed model to be strongly accepted. The term R is defined as Multiple Coefficient of Correlation. The value of R= signifies that 87.8% changes are due to the factors considerd in Regression Modeling. The Coefficient of Determination (R 2 ) is used to identify the strength of relationship. The Coefficient of Determination is defined as the ratio of Explained Variation to Total Variation. The value of R 2 = signifies that the strength of relationship for the developed model is 77%. ANALYSIS OF VARIANCE (ANOVA) a Model Sum of Squares df Mean Square F Sig. (p-value) Regression b 1 CRR Model = z FC wc ϒ CSR Residual Total a. Dependent Variable: Cyclic Resistance Ratio b. Predictors: (Constant), Cyclic Shear Stress, Fine Content, Depth, Water Content, Bulk Density editor@iaeme.com

24 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Model 1. Coefficients a Standardized Unstandardized Coefficients Coefficients Sig. (pvalue) Collinearity Statistics t-test B Std. Error Beta Tolerance VIF (Constant) Depth Fine Content Water Content Bulk Density Cyclic Shear Stress a. Dependent Variable: Cyclic Resistance Ratio The t-test shows the test of difference between the predicted value and the observed value. Smaller difference shows the fall in the t-test values resulting in rise of p-value thus improving the fitness of parameters in the developed model DISCRIMINANT TEST FOR OUTLIERS IN THE MULTI-LINEAR REGRESSION MODEL a. Summary of Canonical Discriminant Functions Eigenvalues Function Eigenvalue % of Variance Cumulative % Canonical Correlation a a. First 1 canonical discriminant functions were used in the analysis. Wilks' Lambda Test of Function(s) Wilks' Lambda Chi-square df Sig b. Classification Statistics Classification Processing Summary Processed 14 Missing or out-of-range group 0 codes Excluded At least one missing 0 discriminating variable Used in Output 14 Classification Function Coefficients CRR Mod Depth Fine Content Water Content Bulk Density Cyclic Shear Stress (Constant) Fisher's linear discriminant functions editor@iaeme.com

25 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling CORRELATION TEST FOR PARAMETERS IN THE MULTI-LINEAR REGRESSION MODEL ASSESSMENT OF LIQUEFACTION POTENTIAL After developing the CRR model, it was tested on the available bore hole data and the results were examined in MATLAB (v R2010a). The results obtained from modeled CRR is then compared and analysed with the calculated value of CRR (based on Boulanger & Idriss) of the soil at varying depth. The assessed factor of safety against

26 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan liquefaction (FS Liq ) (based on Boulanger & Idriss) is compared to the modeled factor of safety against liquefaction (FS LiqMod ) to observe the reliability of CRR model in evaluation of liquefaction potential for a particular location and to validate the outcomes. Bore Hole (BH-1 Table 18 Study about liquefaction potential for Water Table at 4.100m S.No Depth Status CRR (Z) m cal CRR Mod FS Liq FS LiqMod Calculated Modeled No No No No No No No No No No No No Yes MLL MLL MLL No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-1) FS Liq vs FS LiqCal vs FS LiqMod Figure 17 Graph of FS Liq vs Depth (z) for Bore Hole (BH-1) editor@iaeme.com

27 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Bore Hole (BH-2) S.No Table 19 Study about liquefaction potential for water table at Depth (Z) m CRR cal CRR Mod FS Liq FS LiqMod Calculated Status Modeled No No No No No No No MLL No No No No MLL No MLL No No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-2) FS Liq vs FS LiqCal vs FS LiqMod Figure 18 Graph of FS Liq vs Depth (z) for Bore Hole (BH-2) editor@iaeme.com

28 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan MLL = Marginally Liquefiable Layer Bore Hole (BH-3) Table 20 Study about liquefaction potential for water table at Depth (Z) Status S.No. CRR m cal CRR Mod FS Liq FS LiqMod Calculated Modeled No No No No No No MLL MLL No No No No MLL MLL MLL MLL No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-3) FSLiq vs FS LiqCal vs FS LiqMod Figure 19 Graph of FS Liq vs Depth(z) for Bore Hole (BH-3) editor@iaeme.com

29 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Bore Hole (BH-4) Table 21 Study about liquefaction potential for water table at Depth (Z) Status S.No. CRR m cal CRR Mod FS Liq FS LiqMod Calculated Modeled No No No No No No MLL MLL No No No No Yes MLL MLL MLL No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-4) FSLiq vs FS LiqCal vs FS LiqMod Figure 20 Graph of FS Liq vs Depth(z) for Bore Hole (BH-4) editor@iaeme.com

30 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Bore Hole (BH-5) S.No. Depth (Z) m Table 22 Study about liquefaction potential for water table at CRR cal CRR Mod FS Liq FS LiqMod Calculated Status Modeled No No No No No No MLL MLL No No No No MLL MLL MLL MLL No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-5) 3.5 FSLiq vs FS LiqCal vs FS LiqMod Figure 21 Graph of FS Liq vs Depth (z) for Bore Hole (BH-5) editor@iaeme.com

31 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Bore Hole (BH-6) S.No. Table 23 Study about liquefaction potential for water table at Depth (Z) m CRR cal CRR Mod FS Liq FS LiqMod Calculated Status No No No No No No No No No No Modeled No No MLL MLL MLL MLL No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-6) FSLiq vs FS LiqCal vs FS LiqMod Figure 22 Graph of FS Liq vs Depth (z) for Bore Hole (BH-6) editor@iaeme.com

32 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Bore Hole (BH-7) S.No. Depth (Z) m Table 24 Study about liquefaction potential for water table at CRR cal CRR Mod FS Liq FS LiqMod Liquefaction Potential for Bore Hole (BH-7) Calculated Status No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No Modeled No No 3.5 FSLiq vs FS LiqCal vs FS LiqMod Figure 23 Graph of FS Liq vs Depth(z) for Bore Hole (BH-7) editor@iaeme.com

33 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Bore Hole (BH-8) Table 25 Study about liquefaction potential for water table at Depth (Z) Status S.No. CRR m cal CRR Mod FS Liq FS LiqMod Calculated Modeled No No No No No MLL No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-8) 3.5 FSLiq vs FS LiqCal vs FS LiqMod Figure 24 Graph of FS Liq vs Depth (z) for Bore Hole (BH-8) editor@iaeme.com

34 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Bore Hole (BH-9): Table 26: Study about liquefaction potential for water table at S.No. Depth (Z) Status CRR m cal CRR Mod FS Liq FS LiqMod Calculated Modeled No No No No No MLL No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-9) 3.5 FSLiq vs FS LiqCal vs FS LiqMod Figure 25 Graph of FS Liq vs Depth (z) for Bore Hole (BH-9) editor@iaeme.com

35 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Bore Hole (BH-10) S.No. Table 27 Study about liquefaction potential for water table at Depth (Z) m CRR cal CRR Mod FS Liq FS LiqMod Liquefaction Potential for Bore Hole (BH-10) Calculated Status Modeled No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No 3.5 FS Liq vs FS LiqCal vs FS LiqMod Figure 26 Graph of FS Liq vs Depth (z) for Bore Hole (BH-10) editor@iaeme.com

36 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan Bore Hole (BH-11) Table 28 Study about liquefaction potential for water table at S.No. Depth (Z) Status CRR m cal CRR Mod FS Liq FS LiqMod Calculated Modeled No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No Liquefaction Potential for Bore Hole (BH-11) 3.5 FSLiq vs FS LiqCal vs FS LiqMod Figure 27 Graph of FS Liq vs Depth (z) for Bore Hole (BH-11) editor@iaeme.com

37 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling Bore Hole (BH-12) S.No. Table 29 Study about liquefaction potential for water table at Depth (Z) m CRR cal CRR Mod FS Liq FS LiqMod Liquefaction Potential for Bore Hole (BH-12) Calculated Status Modeled No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No 3.5 FSLiq vs FS LiqCal vs FS LiqMod Figure 28 Graph of FS Liq vs Depth (z) for Bore Hole (BH-12) CONCLUSION In the present research study, the following conclusions are drawn based on the results and discussion of location based liquefaction potential evaluation : a) The developed Multi-Linear Regression based CRR Model is presented and it can be used to assess site specific liquefaction potential of soil editor@iaeme.com

38 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan b) Based on SPSS, the Coefficient of Determination (R 2 ) of the developed Multi-Linear Regression Model is 77%. As Coefficient of Determination signifies the strength of relationship in the model, hence the proposed model is a tool for assessment of liquefaction potential of a particular site in Lucknow. c) Based on SPSS, the probability value (p-value) of the developed Multi-Linear Regression Model is 18. The p-value is computed using the test statistic, that measure the support (or lack of support) provided by the sample for the Null Hypothesis (H o ). Since p-value is less than the level of significance (α= 5) for the developed Multi-Linear Regression Model, i.e; (18 < 5), hence the Null Hypothesis (H o ) is rejected and Alternate Hypothesis (H 1 ) is accepted resulting the developed model to be strongly accepted. d) The overall success rate of prediction of liquefaction and non-liquefaction cases by the proposed method for all 204 cases in the present database is found to be 97.54% on the basis of calculated Factor of Safety (F s ) e) The proposed Multi-Linear Regression Model could also be used for any such location, where the evaluation of parameters are similar to that obtained and considerd in the development of this model. f) A soil layer with FS Liq <1 is generally classified as liquefiable and with FS Liq >1 is classified as non-liquefiable. However, some of the studies reveals that liquefaction have also occurred when FS Liq > 1 [18], uncertainties exist due to different soil conditions, validity of case history data and calculation method chosen. g) Out of the total evaluated 204 cases in the present study i.e.; from Bore Hole 1 to Bore Hole 12, the model shows insignificant results in Bore Hole 2, Bore Hole 8 and Bore Hole 9. Therefore, further studies is still required to determine the limitations of the developed Multi-Linear Regression based CRR Model for assessment of liquefaction potential of soil. REFERENCES [1] H. Kowasumi (Ed.), Tokyo Electrical Engineering College Press, Tokyo, Japan, [2] H. B. Seed, and I. M. Idriss, Simplified Procedure for Evaluating Soil Liquefaction Potential. Journal of Geotechnical Engineering, 97(9), 1971, [3] H. B. Seed, Soil liquefaction and cyclic mobility evaluation for level ground during earthquakes, Journal of Geotechnical Engineering, 105(2), 1979, [4] H. B. Seed, and I. M. Idriss, Ground motions and soil liquefaction during earthquakes. Earthquake Engineering Research Institute Monograph, Oakland, Califonia, [5] H. B. Seed, K. Tokimatsu, L. F. Harder, and R. M. Chung, The Influence of SPT Procedures in Soil Liquefaction Resistance Evaluations. Journal of Geotechnical Engineering, 111(12), 1985, [6] National Research Council (NRC), Liquefaction of soils during earthquakes, National Academy Press, Washington, D.C, [7] T. L Youd, and I. M Idriss, Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Nat. Ctr. for Earthquake Engrg. Res., State Univ. of New York at Buffalo, [8] T.L. Youd, I.M. Idriss, R.D. Andrus, I. Arango, G. Castro, J.T. Christian, R. Dobry, W.D.L. Finn, L.F. Harder, M.E. Hynes, K. Ishihara, J.P. Koester, S.S.C. Liao, W.F, Marcuson, G.R. Martin, J.K. Mitchell, Y. Moriwaki, R.B. Seed, and K.H. Stokoe, Liquefaction Resistance of Soil: Summary report from The 1996 NCEER and 1998 NCEER NSF Workshops on Evaluation of Liquefaction Resistance of Soils, Journal of Geotechnical and Geoenvironment Engineering, 127(10), 2001, [9] I. M Idriss, and R. W. Boulanger, Semi-Empirical Procedures for Evaluating Liquefaction Potential during Earthquake. Soil Dynamics and Earthquake Engineering 26, 2006, [10] Seed, H. B., and Idriss, I. M. (1971). "Simplified procedure for evaluating soil liquefaction potential." J. Soil Mechanics and Foundations Div., ASCE 97(SM9), [11] Iwasaki, T., Tatsuoka, F., Tokida, K. I., and Yasuda, S. (1978). A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan. Proc., 2nd Int. Conf. on Microzonation for Safer Construction Research and Application, Vol. II, [12] Seed, H. B., Idriss, I. M., and Arango, I. (1983) Evaluation of liquefaction potential using field performance data. J. Geotech. Engrg.,109(3), editor@iaeme.com

39 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling [13] Robertson, P. K., and Campanella, R. G. (1985). Liquefaction potential of sands using the CPT. J. Geotech. Engrg.,111(3), [14] Seed, H. B., and De Alba, P. (1986) Use of SPT and CPT tests for evaluating the liquefaction resistance of sands, Blacksburg, Va., [15] Shibata, T., and Teparaksa, W. (1988) Evaluation of liquefaction potentials of soils using cone penetration tests. Soils Found.,28(2), [16] Goh, A. T. C. (1994) Seismic liquefaction potential assessed by neural networks. J. Geotech. Engrg., 120(9), [17] Stark, T. D., and Olson, S. M. (1995). Liquefaction resistance using CPT and field case-histories. J.Geotech. Engrg., 121(12), [18] Robertson, P. K., and Wride, C. E. (1998) Evaluating cyclic liquefaction potential using the cone penetration test. Can. Geotech. J.,35(3), [19] Juang, C. H., Chen, C. J., Tang, W. H., and Rosowsky, D. V. (2000) CPT-based liquefaction analysis. Part1: Determination of limit state function. Geotechnique,50(5), [20] Juang, C. H., Yuan, H. M., Lee, D. H., and Lin, P. S. (2003). Simplified cone penetration test-based method for evaluating liquefaction resistance of soils. J. Geotech. Geoenviron. Eng., 129(1), [21] Idriss, I. M., and Boulanger, R. W. (2006) Semi-empirical procedures for evaluating liquefaction potential during earthquakes. Soil Dyn. Earthquake Eng., 26, [22] Liao, S. S. C., Veneziano, D., and Whitman, R. V. (1988) Regressionmodels for evaluating liquefaction probability. J. Geotech. Engrg, 114(4), [23] Toprak, S., Holzer, T. L., Bennett, M. J., and Tinsley, J. C. I. (1999) CPT and SPT-based probabilistic assessment of liquefaction. Proc.,7th U.S.-Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures against Liquefaction, MCEER, Seattle, [24] Juang, C. H., Jiang, T., and Andrus, R. D. (2002) Assessing probability based methods for liquefaction potential evaluation. J. Geotech. Geoenviron. Eng., 128(7), [25] Goh, A. T. C. (2002) Probabilistic neural network for evaluating seismic liquefaction potential. Can. Geotech. J.,39(1), [26] Cetin, K. O., Kiureghian, A. D., and Seed, R. B. (2002) Probabilistic models for the initiation of seismic soil liquefaction. Struct. Safety, 24(1), [27] Cetin, K. O., et al. (2004) Standard penetration test-based probabilistic and deterministic assessment of seismic soil liquefaction potential. J.Geotech. Geoenviron. Eng., 130(12), [28] Lee, D.-H., Ku, C.-S., and Yuan, H. (2003) A study of the liquefaction risk potential at Yuanlin, Taiwan. Eng. Geol. (Amsterdam),71(1 2), [29] Sonmez, H. (2003). Modification of the liquefaction potential index and liquefaction susceptibility mapping for a liquefaction-prone area (Inegol, Turkey) Environ. Geol.,44(7), [30] Sonmez, H., and Gokceoglu, C. (2005) A liquefaction severity index suggested for engineering practice. Environ. Geol.,48(1), [31] Juang, C. H., Li, D. K., Fang, S. Y., Liu, Z., and Khor, E. H. (2008) Simplified procedure for developing joint distribution of a max and M W for probabilistic liquefaction hazard analysis. J. Geotech. Geoenviron. Eng., 134(8), [32] Moss, R. E. S., Seed, R. B., Kayen, R. E., Stewart, J. P., Kiureghian, A. D., and Cetin, K. O. (2006) CPT-based probabilistic and deterministic assessment of in situ seismic soil liquefaction potential. J. Geotech. Geoenviron. Eng., 132(8), [33] Hashash, Y. M. A. (2007) Special issue on biologically inspired and other novel computing techniques in geomechanics. Comput. Geotech.,34(5), [34] Raghukanth STG, Iyengar RN (2006) Seismic hazard estimation for Mumbai city. Curr Sci 91(11): editor@iaeme.com

40 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan [35] Rao KS, Satyam ND (2007) Liquefaction studies for seismic microzonation of Delhi region. Curr Sci 92(5) [36] Sitharam TG, Anbazhagan P (2007) Seismic hazard analysis for the Bangalore region. Nat Hazards 40(2): [37] Hanumanthrao C, Ramana GV (2008) Dynamic Soil properties for microzonation of Delhi, India. J Earth Syst Sci 117(S2): [38] Maheswari UR, Boominathan A, Dodagoudar GR (2010) Use of surface waves in statistical correlations of shear wave velocity and penetration resistance of Chennai soils. Geotech Geol Eng 28: [39] Shukla J, Chaoudhury D(2012) Estimation of seismic ground motion using deterministic approach for major cities of Gujarat. Nat Hazards Earth Sys Sci 12: [40] IS 1893-Part 1 (2002) Criteria for Earthquake Resistant Design of Structure. Bureau of Indian Standards, New Delhi, India. [41] Youd, T. L. and Perkins, D. M.: Mapping liquefaction-induced ground failure potential, J. Geotech. Eng. Division, 104, , [42] Seed, H. B., and Idriss, I. M. (1982) Ground Motions and Soil Liquefaction During Earthquakes, Earthquake Engineering Research Institute, Oakland, CA, 134 pp. [43] PECK, R. B.; HANSON, W. E.; AND THORNBURN, T. H., 1953, Foundation Engineering: John Wiley & Sons, New York, 410 p. [44] KAROL, R. H., 1960, Soils and Soil Engineering: Prentice Hall, Englewood Cliffs, NJ, 194 p. [45] SKEMPTON, A. W., 1986, Standard penetration test procedures and the effects in sands of overburden pressure, relative density, particle size, aging and overconsolidation: Geotechnique, Vol. 36, No. 3, pp [46] ROBERTSON,P.K.AND WRIDE, C. E., 1997, Cyclic liquefaction and its evaluation based on the SPT and CPT. In Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils: Technical Report NCEER : National Center for Earthquake Engineering Research, Buffalo, NY, pp [47] LIAO,S.S.C.AND WHITMAN, R. V., 1986, Overburden correction factors for SPT in sand: Journal Geotechnical Engineering, Vol.112, No. 3, pp [48] YOUD,T.L.AND IDRISS, I. M. (Editors), 1997, Summary Report, Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City: Technical Report NCEER : National Center for Earthquake Engineering Research, Buffalo, NY, 40 p. [49] Boulanger, R. W., & Idriss, R. W. (2006). Liquefaction Susceptibility Criteria for Silts and Clays. J. of Geotech. and Geoenviron. Eng., 132:11, [50] Idriss, I.M., (1999), An update to the Seed-Idriss simplified procedure for evaluating liquefaction potential, Proc., TRB Workshop on New Approaches to Liquefaction, January, Publication No.FHWA-RD , Federal Highway Administration, [51] Boulanger, R.W., Idriss, I.M. (2004), State normalization of penetration resistances and the effect of overburden stress on liquefaction resistance, Proc., 11th International Conference on Soil Dynamics and Earthquake Engineering, and 3 rd International Conference on Earthquake Geotechnical Engineering, D. Doolin et al., eds., Stallion Press, Vol. 2, [52] Youd et al., Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops oevaluation of liquefaction resistance of soils, 2001, J. Geotech. Engg. Div. ASCE, 127(10) (2001) pp [53] IS , Methods for Standard Penetration Test For Soil [54] Sabih A, Khan M. Z,, Abdullah A, Ashraf S.M., (2015), Determination of Liquefaction Potential by sub surface exploration using Standard Penetration Test, International Journal of Innovative Science, Engineering & Technology (IJISET), Vol.2, Issue 10, October 2015, pp editor@iaeme.com

41 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling [55] Varghese, P.C. Foundation Engineering, prentice hall of India private limited, New Delhi , 2007 [56] Wikipedia, MATLAB Product Description - MATLAB & Simulink. [Online] Available at: APPENDIX A. Box-Plot Test for Outliers in the Multi-Linear Regression based CRR Model (CRR Mod ) Figure 1 Box Plot Test for Fine Content Figure 2 Box Plot Test for Water Content Figure 3 Box Plot Test for Bulk Density Figure 4 Box Plot Test or Cyclic Shear Stress Figure 5 Box Plot Test or Cyclic Resistance Ratio (CRR) editor@iaeme.com

42 Abdullah Anwar, Sabih Ahmad, Yusuf Jamal and M.Z. Khan B. Curve Estimation: Cyclic Resistance Ratio Calculated (Observed) and Modeled (Linear) Figure 6 Curve Estimation between Cyclic Resistance Ratio Calculated and Modeled (CRRCal and CRRMod) C. Bore Log Chart (Bore Hole 1 to Bore Hole 12) CIET/index.asp 414 editor@iaeme.com

43 Assessment of Liquefaction Potential of Soil Using Multi-Linear Regression Modeling