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

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 7, Issue 1, Jan-Feb 2016, pp. 373-415, Article ID: IJCIET_07_01_030
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ISSN Print: 0976-6308 and ISSN Online: 0976-6316
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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 v20.0.0) 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 every1.5m 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. 373-415.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType=1

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 1964. 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 (PL) rather than a deterministic (yes/no) estimate (Juang et al. 2008) [31]. Probability
of Liquefaction (PL) 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

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 (σv), 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>1.0. Seed and Idriss (1982) [42] considered the soil layer
with FS value between 1.25 and 1.5 as non-liquefiable. Soil layers with FS greater than 1.2 and FS between 1.0 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 2nd
largest city in
north, east and central India after Delhi. It is the world’s 74th
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 25th
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 19 1 ’N to 18 ’N and longitude of about 19 1 ’ to 18 ’ is chosen

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 : www.mapsofindia.com)

Figure 3 Site Location (IIM Road, Lucknow)
OBJECTIVE OF THE STUDY
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. stimated values of Soil friction and cohesion based on uncorrected
SPT blow counts from Karol (1960) [44] are presented in Table 2.
SITE LOCATION

Table 1 Correlations relating SPT blow counts for silts & clays and for Sands & Gravels, from Peck et al. (1953)
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 ‘‘N60’’ 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). N60 is given as
where, N60 is the SPT N-value corrected for field procedures and apparatus, m is the hammer efficiency, CB is the
borehole diameter correction, CS is the sample barrel correction, CR is the rod length correction, and N is the raw
S.No.
Blows/Ft (NSPT)
Sands and
Gravels
Blows/Ft
(NSPT)
Silts and
Clay
1 0-4 Very Loose 0-2
Very
Soft
2 4-10 Loose 2-4 Soft
3 10-30 Medium 4-8 Firm
4 30-50 Dense 8-16 Stiff
5 Over 50 Very Dense 16-32
Very
Stiff
6. _ _ Over 32 Hard
S.No.
Soil Type
SPT Blow
Counts
Undisturbed Soil
Cohesion
(psf)
Friction
Angle (◦)
1.
CohesiveSoil
Very Soft <2 250 0
2. Soft 2-4 250-500 0
3. Firm 4-8 500-1000 0
4. Stiff 8-15 1000-2000 0
5. Very Stiff 15-30 2000-4000 0
6. Hard >30 >4000 0
7.
Cohesi
onless
Soil
Loose <10 0 28
8. Medium 10-30 0 28-30
9. Dense >30 0 32
10.
Interme
diate
Soil
Loose <10 0 28
11. Medium 10-30 0 28-30
12. Dense >30 0 32

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, (N1)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 (N1)60 as :
where, N is the raw SPT blow-count value, CN = (Pa/σ'vo)0.5
(with the restriction that CN ≤ 2) is the correction for
effective overburden stress (Liao and Whitman,1986), Pa is a reference pressure of 100 kPa, σ'vo is the vertical
effective stress, CE = ER/60% is the correction to account for rod energy, ER is the actual energy ratio of the drill
rig used in percent, CB is a correction for borehole diameter, CS is a correction for the sampling method, CR is a
correction for length of the drill rod.
Factors Equipment Variables Term Corrections
Overburden Pressure _ CN (Pa/σ'vo)0.5
(but CN ≤ 2)
Energy Ratio
Donut Hammer
CE
0.5-1.0
Safety Hammer 0.7-1.2
Automatic Hammer 0.8-1.5
Borehole Diameter
65-115mm
CB
1.0
150mm 1.05
200mm 1.15
Rod Length
3-4m
CR
0.75
4-6m 0.85
6-10m 0.95
10-30m 1.0
>30m <1.0
Sampling Method
Standard Sampler
CS
1.0
Sampler without liners 1.1-1.3
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. 161–179 )
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 v20.0.0) 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 every1.5m 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,

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 (FSLiq) along the depths of soil profiles for
peak ground acceleration of 0.30g and earthquake magnitude of 7.5 on Richter scale. The evaluated factor of safety
against liquefaction (FSLiq) (based on Boulanger & Idriss) is compared to the modeled factor of safety against
liquefaction (FSLiqMod) 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; amax is the maximum horizontal acceleration at the ground surface; vo and '
vo are
total vertical overburden stress and effective vertical overburden stress, respectively, at a given depth below the
ground surface; rd is depth-dependent stress reduction factor; MSF is the magnitude scaling factor and Kσ is the
overburden correction factor.
Stress reduction coefficient (rd) is expressed as a function of depth (z) and earthquake magnitude (M):
where, z is depth (in metre); M is the Magnitude of earthquake
The above equations were appropriate for depth, z ≤ 3 m. However, for depth, z > 34m the following expression is
used:
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:
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:
The coefficient C is expressed in terms of (N1)60
where, (N1)60 is the overburden stress corrected blow count

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 (N1)60 to an equivalent clean sand standard penetration resistance value (N1)60cs. Idriss and Boulanger (2006)
[49] determined CRR value for cohesionless soil with any fines content using the following expression:
Subsequent expressions describe the way parameters in the above equation are calculated as:
where,
Δ(N1)60 is the correction for fines content in percent (FC) present in the soil and is expressed as:
(N1)60 is the overburden stress corrected blow count; N60 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 CN is the Overburden Correction Factor for Penetration resistance.
5.3. Determination of Factor of Safety (FSLiq)
The factor of safety against liquefaction (FSLiq) is commonly used to quantify liquefaction potential. The factor of
safety against liquefaction (FSLiq) can be defined by
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 ≤ 1.0, 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.
5.4. SPT N-value Corrections
To calculate liquefaction potential corrected SPT-N values are used. Value correction was adopted as given by IS:
2131-1981 [53].
5.4.1. 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: 2131-1981) [53]. (Fig.4)

Figure 4 Correction due to overburden Pressure
It can also be calculated using the relationship:
σ'z= effective overburden pressure in kN/m2
.
5.4.2. Correction for Dilatancy
The values obtained in overburden pressure (N1) shall be corrected for dilatancy if the stratum consist of fine sand
and silt below water table for values of N1 greater than 15 as under [55]:
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
v20.0.0), 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., 1994-2015) [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 (FSLiqMod) is calculated and its compared to the computed value of factor of safety against
liquefaction (FSLiq) (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

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)
4.100 4.600 4.600 4.750 4.670 4.350 4.100 4.600 4.600 4.750 4.700 4.670
Earthquake
magnitude
(Rector scale)
7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5
Table 5 IS Soil Classification (IS: 1498-1970)
Symbol Soil Description
SP Poorly graded sand
SM Silty sand
ML Very fine sand
CL Silty clay with low plasticity
CI Sandy clay with medium plasticity
CH 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 FSLiq Status
1. 1.00 11 0.084 0.23 2.74 No
2. 2.50 4 0.083 0.13 1.56 No
3. 4.00 1 0.082 0.10 1.22 No
4. 5.50 7 0.096 0.15 1.56 No
5. 7.00 7 0.105 0.14 1.33 No
6. 8.50 8 0.111 0.15 1.35 No
7. 10.00 9 0.115 0.11 0.95 Yes
8. 11.50 11 0.117 0.13 1.10 MLL
9. 13.00 13 0.119 0.19 1.59 No
10. 14.50 15 0.119 0.21 1.76 No
11. 16.00 17 0.118 0.23 1.94 No
12. 17.50 17 0.117 0.22 1.88 No
13. 19.00 19 0.116 0.25 2.15 No
14. 20.50 19 0.114 0.24 2.10 No

Liquefaction Potential for Bore Hole (BH-1)
Depth below Ground Surface (m)
0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Depth below Ground Surface (m) vs FSLiq
Figure 5 Graph of FSLiq vs Depth (z) for Bore Hole (BH-1)
Bore Hole (BH-2)
Table 7 Study about liquefaction potential for water table at 4.600
S.No.
Depth (Z)
m
SPT N
value
CSR CRR FSLiq Status
1. 1.00 11 0.084 0.23 2.74 No
2. 2.50 4 0.083 0.13 1.57 No
3. 4.00 3 0.082 0.11 1.34 No
4. 5.50 9 0.090 0.17 1.88 No
5. 7.00 10 0.101 0.17 1.68 No
6. 8.50 10 0.107 0.17 1.58 No
7. 10.00 11 0.112 0.13 1.16 MLL
8. 11.50 13 0.115 0.14 1.20 MLL
9. 13.00 14 0.116 0.20 1.72 No
10. 14.50 15 0.117 0.21 1.79 No
11. 16.00 16 0.116 0.21 1.81 No
12. 17.50 19 0.116 0.26 2.24 No
13. 19.00 19 0.114 0.25 2.19 No
14. 20.50 20 0.113 0.26 2.30 No

0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
MLL = Marginally Liquefiable Layer
Bore Hole (BH-3)
S.No.
Depth
(Z) m
SPT N
value
1. 1.00 12 0.084 0.22 2.61 No
2. 2.50 10 0.083 0.19 2.28 No
3. 4.00 1 0.082 0.10 1.22 No
4. 5.50 2 0.090 0.10 1.11 MLL
5. 7.00 6 0.099 0.13 1.31 No
6. 8.50 9 0.106 0.15 1.41 No
7. 10.00 11 0.110 0.12 1.09 MLL
8. 11.50 11 0.112 0.12 1.07 MLL
9. 13.00 12 0.114 0.16 1.40 No
10. 14.50 15 0.114 0.18 1.57 No
11. 16.00 16 0.114 0.18 1.57 No
12. 17.50 20 0.113 0.22 1.94 No
13. 19.00 20 0.112 0.21 1.87 No
14. 20.50 18 0.110 0.19 1.72 No

0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Bore Hole (BH-4)
S.No.
Depth (Z)
m
1. 1.00 11 0.084 0.23 2.73 No
2. 2.50 1 0.083 0.10 1.22 No
3. 4.00 3 0.082 0.11 1.34 No
4. 5.50 1 0.088 0.10 1.13 MLL
5. 7.00 7 0.099 0.14 1.41 No
6. 8.50 8 0.105 0.15 1.42 No
7. 10.00 9 0.110 0.11 1.00 Yes
8. 11.50 11 0.113 0.12 1.06 MLL
9. 13.00 11 0.114 0.16 1.40 No
10. 14.50 13 0.115 0.18 1.56 No
11. 16.00 16 0.115 0.21 1.82 No
12. 17.50 15 0.114 0.19 1.66 No
13. 19.00 17 0.113 0.21 1.85 No
14. 20.50 19 0.112 0.24 2.14 No

0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Bore Hole (BH-5)
S.No.
Depth (Z)
m
SPT N
value
1. 1.00 12 0.084 0.25 2.97 No
2. 2.50 10 0.083 0.15 1.81 No
3. 4.00 1 0.082 0.10 1.22 No
4. 5.50 2 0.089 0.10 1.12 MLL
5. 7.00 6
0.099 0.14
1.41 No
6. 8.50 9
0.106 0.16
1.51 No
7. 10.00 11
0.11 0.13
1.18 MLL
8. 11.50 11
0.112 0.12
1.07 MLL
9. 13.00 12
0.114 0.17
1.49 No
10. 14.50 15
0.114 0.20
1.75 No
11. 16.00 16
0.114 0.21
1.84 No
12. 17.50 20
0.113 0.23
2.03 No
13. 19.00 20
0.112 0.24
2.14 No
14. 20.50 18
0.111 0.23
2.07 No

0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Bore Hole (BH-6)
S.No.
Depth
(Z) m
SPT N
value
1. 1.00 11 0.084 0.23 2.73 No
2. 2.50 4 0.083 0.13 1.57 No
3. 4.00 3 0.082 0.11 1.34 No
4. 5.50 9 0.093 0.17 1.82 No
5. 7.00 9 0.103 0.16 1.55 No
6. 8.50 10 0.109 0.17 1.56 No
7. 10.00 11 0.114 0.13 1.14 MLL
8. 11.50 13 0.116 0.14 1.20 MLL
9. 13.00 14 0.117 0.20 1.71 No
10. 14.50 16 0.118 0.22 1.86 No
11. 16.00 17 0.117 0.23 1.96 No
12. 17.50 19 0.116 0.26 2.24 No
13. 19.00 19 0.115 0.25 2.17 No
14. 20.50 20 0.114 0.26 2.28 No

0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Bore Hole (BH-7)
S.No.
Depth
(Z) m
SPT N
value
1. 1.00 5 0.0840 0.1400 1.67 No
2. 2.50 8 0.0830 0.1900 2.28 No
3. 4.00 11 0.0820 0.2000 2.43 No
4. 5.50 13 0.0970 0.2400 2.47 No
5. 7.00 15 0.1070 0.2700 2.52 No
6. 8.50 11 0.1130 0.1900 1.68 No
7. 10.00 12 0.1160 0.1900 1.63 No
8. 11.50 15 0.1180 0.2300 1.94 No
9. 13.00 14 0.1190 0.2000 1.68 No
10. 14.50 17 0.1180 0.2400 2.03 No
11. 16.00 20 0.1180 0.3000 2.54 No
12. 17.50 21 0.1160 0.3200 2.75 No
13. 19.00 23 0.1150 0.2200 1.91 No
14. 20.50 20 0.1130 0.1700 1.50 No
15. 22.00 19 0.1110 0.1600 1.44 No
16. 23.50 21 0.1090 0.1700 1.56 No
17. 25.00 21 0.1070 0.2400 2.24 No
18. 26.50 23 0.1060 0.2700 2.54 No
19. 28.00 22 0.1040 0.2400 2.30 No
20. 29.50 25 0.1030 0.3000 2.91 No

0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Bore Hole (BH-8)
S.No. Depth (Z) m SPT N value CSR CRR FSLiq Status
1. 1.00 5 0.0840 0.1400 1.67 No
2. 2.50 6 0.0830 0.1500 1.80 No
3. 4.00 9 0.0820 0.1700 2.07 No
4. 5.50 10 0.0900 0.1800 2.00 No
5. 7.00 11 0.1000 0.1800 1.80 No
6. 8.50 12 0.1060 0.1900 1.79 No
7. 10.00 13 0.1100 0.1900 1.72 No
8. 11.50 14 0.1130 0.2000 1.77 No
9. 13.00 16 0.1140 0.2200 1.93 No
10. 14.50 16 0.1140 0.2100 1.84 No
11. 16.00 19 0.1140 0.2500 2.19 No
12. 17.50 18 0.1130 0.2200 1.94 No
13. 19.00 22 0.1120 0.2000 1.78 No
14. 20.50 21 0.1100 0.1800 1.63 No
15. 22.00 20 0.1090 0.1600 1.46 No
16. 23.50 22 0.1070 0.1800 1.68 No
17. 25.00 23 0.1050 0.2800 2.67 No
18. 26.50 23 0.1040 0.2700 2.59 No
19. 28.00 23 0.1020 0.2600 2.54 No
20. 29.50 25 0.1010 0.3000 2.97 No

0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Bore Hole (BH-9)
S.No.
Depth (Z)
m
1. 1.00 5 0.0840 0.1400 1.67 No
2. 2.50 6 0.0830 0.1500 1.80 No
3. 4.00 9 0.0820 0.1600 1.95 No
4. 5.50 10 0.0900 0.1800 2.00 No
5. 7.00 11 0.1000 0.1800 1.80 No
6. 8.50 12 0.1070 0.1900 1.77 No
7. 10.00 13 0.1110 0.1900 1.71 No
8. 11.50 14 0.1140 0.2000 1.75 No
9. 13.00 16 0.1150 0.2200 1.91 No
10. 14.50 16 0.1150 0.2100 1.82 No
11. 16.00 19 0.1150 0.2500 2.17 No
12. 17.50 18 0.1140 0.2200 1.93 No
13. 19.00 22 0.1130 0.2100 1.85 No
14. 20.50 21 0.1120 0.1800 1.60 No
15. 22.00 20 0.1100 0.1700 1.54 No
16. 23.50 22 0.1080 0.1800 1.67 No
17. 25.00 23 0.1070 0.2900 2.71 No
18. 26.50 23 0.1050 0.2800 2.67 No
19. 28.00 23 0.1040 0.2700 2.59 No
20. 29.50 25 0.1030 0.3100 3.00 No

0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Fig. 13: Graph of FSLiq vs Depth (z) for Bore Hole (BH-9)
Bore Hole (BH-10)
S.No.
Depth (Z)
m
1. 1.00 5 0.0840 0.1400 1.67 No
2. 2.50 6 0.0830 0.1500 1.80 No
3. 4.00 9 0.0820 0.1600 1.95 No
4. 5.50 10 0.0890 0.1700 1.91 No
5. 7.00 11 0.0990 0.1800 1.81 No
6. 8.50 12 0.1060 0.1900 1.79 No
7. 10.00 13 0.1110 0.1900 1.71 No
8. 11.50 14 0.1140 0.2000 1.75 No
9. 13.00 16 0.1150 0.2200 1.91 No
10. 14.50 16 0.1160 0.2100 1.81 No
11. 16.00 19 0.1150 0.2600 2.26 No
12. 17.50 18 0.1150 0.2300 2.00 No
13. 19.00 22 0.1140 0.3200 2.80 No
14. 20.50 21 0.1120 0.1900 1.69 No
15. 22.00 20 0.1110 0.1700 1.53 No
16. 23.50 22 0.1090 0.1900 1.74 No
17. 25.00 23 0.1080 0.3000 2.77 No
18. 26.50 23 0.1060 0.2800 2.64 No
19. 28.00 23 0.1050 0.2700 2.57 No
20. 29.50 25 0.1040 0.3200 3.07 No

0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Bore Hole (BH-11)
1. 1.00 5 0.0840 0.1400 1.67 No
2. 2.50 6 0.0830 0.1500 1.80 No
3. 4.00 9 0.0820 0.1700 2.07 No
4. 5.50 10 0.0890 0.1800 2.02 No
5. 7.00 11 0.0990 0.1800 1.82 No
6. 8.50 12 0.1060 0.1900 1.79 No
7. 10.00 13 0.1100 0.1900 1.73 No
8. 11.50 14 0.1130 0.2000 1.76 No
9. 13.00 16 0.1140 0.2200 1.93 No
10. 14.50 16 0.1140 0.2200 1.93 No
11. 16.00 19 0.1140 0.2600 2.28 No
12. 17.50 18 0.1130 0.2300 2.03 No
13. 19.00 22 0.1120 0.2100 1.88 No
14. 20.50 21 0.1110 0.1800 1.62 No
15. 22.00 20 0.1090 0.1700 1.56 No
16. 23.50 22 0.1080 0.1800 1.67 No
17. 25.00 23 0.1060 0.2900 2.74 No
18. 26.50 23 0.1050 0.2800 2.67 No
19. 28.00 23 0.1030 0.2600 2.52 No
20. 29.50 25 0.1020 0.3100 3.04 No

0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Bore Hole (BH-12)
1. 1.00 5 0.0840 0.1400 1.67 No
2. 2.50 6 0.0830 0.1500 1.80 No
3. 4.00 9 0.0820 0.1600 1.95 No
4. 5.50 10 0.0890 0.1800 2.02 No
5. 7.00 11 0.0990 0.1800 1.81 No
6. 8.50 12 0.1060 0.1900 1.79 No
7. 10.00 13 0.1100 0.1900 1.73 No
8. 11.50 14 0.1130 0.2000 1.76 No
9. 13.00 16 0.1140 0.2200 1.93 No
10. 14.50 16 0.1140 0.2100 1.84 No
11. 16.00 19 0.1140 0.2500 2.19 No
12. 17.50 18 0.1130 0.2200 1.94 No
13. 19.00 22 0.1120 0.2000 1.78 No
14. 20.50 21 0.1100 0.1800 1.64 No
15. 22.00 20 0.1090 0.1700 1.55 No
16. 23.50 22 0.1070 0.1800 1.68 No
17. 25.00 23 0.1060 0.2900 2.73 No
18. 26.50 23 0.1040 0.2700 2.59 No
19. 28.00 23 0.1030 0.2600 2.52 No
20. 29.50 25 0.1020 0.3000 2.94 No

0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
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 v20.0.0) 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).
7.1.1. MULTI-LINEAR REGRESSION MODEL
Model Summaryb
Model R
R
Square
Adjusted R
Square
Std. Error of
the Estimate
Change Statistics
Durbin-WatsonR Square
Change
F Change df1 df2
Sig. F Change
(p-value)
1 .878a
.771 .628 .0205641536 .771 5.398 5 8 .018 1.490
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 (Ho). Since p-value is less than the level of significance
(α= 0.0 ) for the developed Multi-Linear Regression Model, i.e; (0.018 < 0.05), hence the Null Hypothesis (Ho) is
rejected and Alternate Hypothesis (H1) is accepted resulting the developed model to be strongly accepted. The term
‘R’ is defined as Multiple Coefficient of Correlation. The value of R= 0.878 signifies that 87.8% changes are due to
the factors considerd in Regression Modeling. The Coefficient of Determination (R2
) 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 R2
= 0.771 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)
1
Regression .011 5 .002 5.398 .018b
Residual .003 8 .000
Total .015 13
a. Dependent Variable: Cyclic Resistance Ratio
b. Predictors: (Constant), Cyclic Shear Stress, Fine Content, Depth, Water Content, Bulk Density
CRRModel = - 0.010619 + 0.005028 z + 0.000655 FC – 0.002386 wc + 0.029002 ϒ + 1.085240 CSR

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.
7.1.2. DISCRIMINANT TEST FOR OUTLIERS IN THE MULTI-LINEAR REGRESSION MODEL
a. Summary of Canonical Discriminant Functions
Eigenvalues
Function Eigenvalue % of Variance Cumulative % Canonical
Correlation
1 2.395a
100.0 100.0 .840
a. First 1 canonical discriminant functions were used in the analysis.
Wilks' Lambda
Test of Function(s) Wilks' Lambda Chi-square df Sig.
1 .295 11.612 5 .041
b. Classification Statistics
Classification Processing Summary
Processed 14
Excluded
Missing or out-of-range group
codes
0
At least one missing
discriminating variable
0
Used in Output 14
Classification Function Coefficients
CRR Mod
.00000 1.00000
Depth -9.586 -8.917
Fine Content 20.790 21.470
Water Content -37.584 -37.108
Bulk Density 16734.253 17048.437
Cyclic Shear Stress -38937.170 -40042.473
(Constant) -12886.153 -13375.574
Fisher's linear discriminant functions
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients t-test
Sig. (p-
value)
Collinearity Statistics
B Std. Error Beta Tolerance VIF
1.
(Constant) -.011 .757 -.014 .989
Depth .005 .002 .935 2.465 .039 .199 5.037
Fine Content .001 .001 .445 .866 .412 .109 9.215
Water Content -.002 .005 -.312 -.521 .617 .080 12.530
Bulk Density .029 .494 .058 .059 .955 .029 34.596
Cyclic Shear Stress 1.085 1.407 .433 .772 .463 .091 11.006
a. Dependent Variable: Cyclic Resistance Ratio

7.1.3. CORRELATION TEST FOR PARAMETERS IN THE MULTI-LINEAR REGRESSION MODEL
7.1.4. 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

liquefaction (FSLiq) (based on Boulanger & Idriss) is compared to the modeled factor of safety against liquefaction
(FSLiqMod) 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
0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Depth below Ground Surface (m) vs FSLiqCal
Depth below Ground Surface (m) vs FSLiqMod
S.No
Depth
(Z) m
CRRcal CRRMod FSLiq FSLiqMod
Status
Calculated Modeled
1. 1.00 0.23 0.1671 2.74 1.4040 No No
2. 2.50 0.13 0.1804 1.56 1.5160 No No
3. 4.00 0.10 0.1156 1.22 1.4098 No No
4. 5.50 0.15 0.1221 1.56 1.2718 No No
5. 7.00 0.14 0.1638 1.33 1.3763 No No
6. 8.50 0.15 0.1777 1.35 1.4935 No No
7. 10.00 0.11 0.1332 0.95 1.1583 Yes MLL
8. 11.50 0.13 0.1387 1.10 1.1855 MLL MLL
9. 13.00 0.19 0.1723 1.59 1.4478 No No
10. 14.50 0.21 0.1906 1.76 1.6016 No No
11. 16.00 0.23 0.2220 1.94 1.8657 No No
12. 17.50 0.22 0.2333 1.88 1.9608 No No
13. 19.00 0.25 0.2387 2.15 2.0056 No No
14. 20.50 0.24 0.2454 2.10 2.0619 No No

Bore Hole (BH-2)
0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
S.No
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.23 0.1744 2.74 1.4903 No No
2. 2.50 0.13 0.1850 1.57 1.5816 No No
3. 4.00 0.11 0.1631 1.34 1.3944 No No
4. 5.50 0.17 0.1370 1.88 1.1712 No MLL
5. 7.00 0.17 0.1553 1.68 1.3276 No No
6. 8.50 0.17 0.1712 1.58 1.4634 No No
7. 10.00 0.13 0.1653 1.16 1.4132 MLL No
8. 11.50 0.14 0.1764 1.20 1.5073 MLL No
9. 13.00 0.20 0.2079 1.72 1.7766 No No
10. 14.50 0.21 0.2173 1.79 1.8569 No No
11. 16.00 0.21 0.2188 1.81 1.8704 No No
12. 17.50 0.26 0.2261 2.24 1.9326 No No
13. 19.00 0.25 0.2301 2.19 1.9670 No No
14. 20.50 0.26 0.2361 2.30 2.018 No No

MLL = Marginally Liquefiable Layer
Bore Hole (BH-3)
0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Figure 19 Graph of FSLiq vs Depth(z) for Bore Hole (BH-3)
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.22 0.1826 2.61 1.6016 No No
2. 2.50 0.19 0.1912 2.28 1.6770 No No
3. 4.00 0.10 0.1643 1.22 1.4416 No No
4. 5.50 0.10 0.1044 1.11 1.1600 MLL MLL
5. 7.00 0.13 0.1533 1.31 1.3445 No No
6. 8.50 0.15 0.1712 1.41 1.5016 No No
7. 10.00 0.12 0.1264 1.09 1.1491 MLL MLL
8. 11.50 0.12 0.1339 1.07 1.1955 MLL MLL
9. 13.00 0.16 0.2009 1.40 1.7618 No No
10. 14.50 0.18 0.2076 1.57 1.8208 No No
11. 16.00 0.18 0.2163 1.57 1.8974 No No
12. 17.50 0.22 0.2215 1.94 1.9432 No No
13. 19.00 0.21 0.2272 1.87 1.9928 No No
14. 20.50 0.19 0.2340 1.72 2.0530 No No

Bore Hole (BH-4)
0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.23 0.1692 2.73 1.4712 No No
2. 2.50 0.10 0.1889 1.22 1.6423 No No
3. 4.00 0.11 0.1607 1.34 1.3974 No No
4. 5.50 0.10 0.1027 1.13 1.1670 MLL MLL
5. 7.00 0.14 0.1561 1.41 1.3574 No No
6. 8.50 0.15 0.1680 1.42 1.4610 No No
7. 10.00 0.11 0.1231 1.00 1.1187 Yes MLL
8. 11.50 0.12 0.1361 1.06 1.2044 MLL MLL
9. 13.00 0.16 0.2023 1.40 1.7591 No No
10. 14.50 0.18 0.2130 1.56 1.8525 No No
11. 16.00 0.21 0.2204 1.82 1.9164 No No
12. 17.50 0.19 0.2256 1.66 1.9616 No No
13. 19.00 0.21 0.2306 1.85 2.0056 No No
14. 20.50 0.24 0.2378 2.14 2.0682 No No

Bore Hole (BH-5)
0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.25 0.1762 2.97 1.5456 No No
2. 2.50 0.15 0.1903 1.81 1.6697 No No
3. 4.00 0.10 0.1628 1.22 1.4285 No No
4. 5.50 0.10 0.1053 1.12 1.1831 MLL MLL
5. 7.00 0.14 0.1550 1.41 1.3599 No No
6. 8.50 0.16 0.1701 1.51 1.4925 No No
7. 10.00 0.13 0.1265 1.18 1.1501 MLL MLL
8. 11.50 0.12 0.1349 1.07 1.2045 MLL MLL
9. 13.00 0.17 0.2019 1.49 1.7710 No No
10. 14.50 0.20 0.2101 1.75 1.8429 No No
11. 16.00 0.21 0.2181 1.84 1.9135 No No
12. 17.50 0.23 0.2233 2.03 1.9591 No No
13. 19.00 0.24 0.2287 2.14 2.0062 No No
14. 20.50 0.23 0.2359 2.07 2.0696 No No

Bore Hole (BH-6)
0 5 10 15 20 25
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.23 0.1707 2.73 1.4468 No No
2. 2.50 0.13 0.1830 1.57 1.5512 No No
3. 4.00 0.11 0.1655 1.34 1.4022 No No
4. 5.50 0.17 0.1415 1.82 1.5215 No No
5. 7.00 0.16 0.1595 1.55 1.3521 No No
6. 8.50 0.17 0.1748 1.56 1.4814 No No
7. 10.00 0.13 0.1323 1.14 1.1605 MLL MLL
8. 11.50 0.14 0.1397 1.20 1.2043 MLL MLL
9. 13.00 0.20 0.2074 1.71 1.7574 No No
10. 14.50 0.22 0.2158 1.86 1.8289 No No
11. 16.00 0.23 0.2204 1.96 1.8679 No No
12. 17.50 0.26 0.2295 2.24 1.9451 No No
13. 19.00 0.25 0.2344 2.17 1.9866 No No
14. 20.50 0.26 0.2413 2.28 2.0446 No No

Bore Hole (BH-7)
0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.1400 0.1575 1.67 1.3236 No No
2. 2.50 0.1900 0.1264 2.28 1.5225 No No
3. 4.00 0.2000 0.1365 2.43 1.6641 No No
4. 5.50 0.2400 0.1804 2.47 1.8593 No No
5. 7.00 0.2700 0.1831 2.52 1.5584 No No
6. 8.50 0.1900 0.1910 1.68 1.6049 No No
7. 10.00 0.1900 0.2020 1.63 1.6979 No No
8. 11.50 0.2300 0.2169 1.94 1.8225 No No
9. 13.00 0.2000 0.2271 1.68 1.9084 No No
10. 14.50 0.2400 0.2310 2.03 1.9413 No No
11. 16.00 0.3000 0.2368 2.54 1.9897 No No
12. 17.50 0.3200 0.2351 2.75 1.9752 No No
13. 19.00 0.2200 0.2123 1.91 1.7839 No No
14. 20.50 0.1700 0.2174 1.50 1.8270 No No
15. 22.00 0.1600 0.2235 1.44 1.8781 No No
16. 23.50 0.1700 0.2284 1.56 1.9191 No No
17. 25.00 0.2400 0.2840 2.24 2.3868 No No
18. 26.50 0.2700 0.2911 2.54 2.4462 No No
19. 28.00 0.2400 0.2956 2.30 2.4841 No No
20. 29.50 0.3000 0.3013 2.91 2.5319 No No

Bore Hole (BH-8)
0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.1400 0.1635 1.67 1.4345 No No
2. 2.50 0.1500 0.1703 1.80 1.4940 No No
3. 4.00 0.1700 0.1370 2.07 1.2018 No MLL
4. 5.50 0.1800 0.1498 2.00 1.3137 No No
5. 7.00 0.1800 0.1571 1.80 1.3784 No No
6. 8.50 0.1900 0.1645 1.79 1.4426 No No
7. 10.00 0.1900 0.1784 1.72 1.5648 No No
8. 11.50 0.2000 0.1869 1.77 1.6393 No No
9. 13.00 0.2200 0.1953 1.93 1.7135 No No
10. 14.50 0.2100 0.2051 1.84 1.7990 No No
11. 16.00 0.2500 0.2124 2.19 1.8636 No No
12. 17.50 0.2200 0.2154 1.94 1.8894 No No
13. 19.00 0.2000 0.2137 1.78 1.8749 No No
14. 20.50 0.1800 0.2176 1.63 1.9086 No No
15. 22.00 0.1600 0.2235 1.46 1.9606 No No
16. 23.50 0.1800 0.2325 1.68 2.0397 No No
17. 25.00 0.2800 0.2860 2.67 2.5084 No No
18. 26.50 0.2700 0.2946 2.59 2.5839 No No
19. 28.00 0.2600 0.2996 2.54 2.6284 No No
20. 29.50 0.3000 0.3074 2.97 2.6968 No No

Bore Hole (BH-9):
Table 26: Study about liquefaction potential for water table at 4.600
0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.1400 0.1649 1.67 1.4339 No No
2. 2.50 0.1500 0.1722 1.80 1.4974 No No
3. 4.00 0.1600 0.1340 1.95 1.1649 No MLL
4. 5.50 0.1800 0.1430 2.00 1.2433 No No
5. 7.00 0.1800 0.1618 1.80 1.4071 No No
6. 8.50 0.1900 0.1696 1.77 1.4751 No No
7. 10.00 0.1900 0.1833 1.71 1.5937 No No
8. 11.50 0.2000 0.1932 1.75 1.6804 No No
9. 13.00 0.2200 0.2018 1.91 1.7552 No No
10. 14.50 0.2100 0.2069 1.82 1.7992 No No
11. 16.00 0.2500 0.2168 2.17 1.8849 No No
12. 17.50 0.2200 0.2213 1.93 1.9248 No No
13. 19.00 0.2100 0.2193 1.85 1.9073 No No
14. 20.50 0.1800 0.2244 1.60 1.9516 No No
15. 22.00 0.1700 0.2294 1.54 1.9947 No No
16. 23.50 0.1800 0.2380 1.67 2.0700 No No
17. 25.00 0.2900 0.2916 2.71 2.5353 No No
18. 26.50 0.2800 0.2988 2.67 2.5980 No No
19. 28.00 0.2700 0.3042 2.59 2.6453 No No
20. 29.50 0.3100 0.3133 3.00 2.7247 No No

Bore Hole (BH-10)
0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.1400 0.1628 1.67 1.4033 No No
2. 2.50 0.1500 0.1646 1.80 1.4189 No No
3. 4.00 0.1600 0.1080 1.95 1.3170 No No
4. 5.50 0.1700 0.1219 1.91 1.3697 No No
5. 7.00 0.1800 0.1545 1.81 1.4336 No No
6. 8.50 0.1900 0.1633 1.79 1.4578 No No
7. 10.00 0.1900 0.1769 1.71 1.5252 No No
8. 11.50 0.2000 0.1862 1.75 1.6048 No No
9. 13.00 0.2200 0.1946 1.91 1.6777 No No
10. 14.50 0.2100 0.2054 1.81 1.7709 No No
11. 16.00 0.2600 0.2143 2.26 1.8470 No No
12. 17.50 0.2300 0.2177 2.00 1.8767 No No
13. 19.00 0.3200 0.2284 2.80 1.9691 No No
14. 20.50 0.1900 0.2192 1.69 1.8897 No No
15. 22.00 0.1700 0.2251 1.53 1.9408 No No
16. 23.50 0.1900 0.2341 1.74 2.0177 No No
17. 25.00 0.3000 0.2873 2.77 2.4768 No No
18. 26.50 0.2800 0.2984 2.64 2.5412 No No
19. 28.00 0.2700 0.3009 2.57 2.5942 No No
20. 29.50 0.3200 0.3093 3.07 2.6667 No No

Bore Hole (BH-11)
0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.1400 0.1625 1.67 1.4253 No No
2. 2.50 0.1500 0.1650 1.80 1.4471 No No
3. 4.00 0.1700 0.1143 2.07 1.3947 No No
4. 5.50 0.1800 0.1247 2.02 1.4012 No No
5. 7.00 0.1800 0.1398 1.82 1.4123 No No
6. 8.50 0.1900 0.1665 1.79 1.4602 No No
7. 10.00 0.1900 0.1796 1.73 1.5755 No No
8. 11.50 0.2000 0.1888 1.76 1.6565 No No
9. 13.00 0.2200 0.1980 1.93 1.7369 No No
10. 14.50 0.2200 0.2110 1.93 1.8507 No No
11. 16.00 0.2600 0.2176 2.28 1.9089 No No
12. 17.50 0.2300 0.2194 2.03 1.9247 No No
13. 19.00 0.2100 0.2156 1.88 1.8915 No No
14. 20.50 0.1800 0.2206 1.62 1.9354 No No
15. 22.00 0.1700 0.2255 1.56 1.9784 No No
16. 23.50 0.1800 0.2355 1.67 2.0656 No No
17. 25.00 0.2900 0.2864 2.74 2.5125 No No
18. 26.50 0.2800 0.2942 2.67 2.5810 No No
19. 28.00 0.2600 0.2993 2.52 2.6251 No No
20. 29.50 0.3100 0.3071 3.04 2.6936 No No

Bore Hole (BH-12)
0 5 10 15 20 25 30 35
FSLiq
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
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.
S.No.
Depth (Z)
m
Status
Calculated Modeled
1. 1.00 0.1400 0.1642 1.67 1.4405 No No
2. 2.50 0.1500 0.1712 1.80 1.5021 No No
3. 4.00 0.1600 0.1034 1.95 1.2610 No No
4. 5.50 0.1800 0.1146 2.02 1.2872 No No
5. 7.00 0.1800 0.1587 1.81 1.3921 No No
6. 8.50 0.1900 0.1662 1.79 1.4576 No No
7. 10.00 0.1900 0.1796 1.73 1.5756 No No
8. 11.50 0.2000 0.1907 1.76 1.6725 No No
9. 13.00 0.2200 0.1989 1.93 1.7449 No No
10. 14.50 0.2100 0.2062 1.84 1.8089 No No
11. 16.00 0.2500 0.2139 2.19 1.8759 No No
12. 17.50 0.2200 0.2180 1.94 1.9120 No No
13. 19.00 0.2000 0.2161 1.78 1.8953 No No
14. 20.50 0.1800 0.2179 1.64 1.9116 No No
15. 22.00 0.1700 0.2261 1.55 1.9831 No No
16. 23.50 0.1800 0.2353 1.68 2.0641 No No
17. 25.00 0.2900 0.2880 2.73 2.5261 No No
18. 26.50 0.2700 0.2959 2.59 2.5954 No No
19. 28.00 0.2600 0.3045 2.52 2.6714 No No
20. 29.50 0.3000 0.3111 2.94 2.7290 No No

b) Based on SPSS, the Coefficient of Determination (R2
) 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 0.018.
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 (Ho). Since p-value is less than the level of significance (α= 0.0 ) for the
developed Multi-Linear Regression Model, i.e; (0.018 < 0.05), hence the Null Hypothesis (Ho) is rejected and
Alternate Hypothesis (H1) 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 (Fs)
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 FSLiq<1 is generally classified as liquefiable and with FSLiq>1 is classified as non-liquefiable.
However, some of the studies reveals that liquefaction have also occurred when FSLiq> 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.
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APPENDIX
A. Box-Plot Test for Outliers in the Multi-Linear Regression based CRR Model (CRRMod)
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)

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)

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

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