ASSESSMENT OF LIQUEFACTION POTENTIAL OF …...Keywords: Liquefaction, Multi-Linear Regression Modeling, MATLAB, SPSS, SPT, CSR, CRR. Cite this Article: Abdullah Anwar, Sabih Ahmad,

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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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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 ̊ 15’N to 18 ̊54’N and longitude of about 19 ̊ 15’E to 18 ̊ 54’E 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. Estimated 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, Em 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.

Coh

esi

ve

Soil

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.

Coh

esi

on

less

Soil

Loose <10 0 28

8. Medium 10-30 0 28-30

9. Dense >30 0 32

10.

Inte

rme

dia

te

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 0.16g 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; σvo and σ'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):

() ($%) = *(+) + -(+)�

*(+) = −�. ��/ − �. �/ 012 3 +��. �4 + �. �445

-(+) = �. �� + �. ��6 012 3 +��. /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: �−�7 # − �. ��6

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 ?�′��@ A ≤ �. �

The coefficient Cσ is expressed in terms of (N1)60 �� = ��6.=;/.�� C(��) � ≤ �. 4

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:

�� = 89: D(��) �EF �7. � + ?(��) �EF �/ A/ − ?(��) �EF /4. A4 + ?(��) �EF /�. 7 A7 − /. 6G

Subsequent expressions describe the way parameters in the above equation are calculated as:

(��) �EF = (��) � + ∆(��) �

where,

Δ(N1)60 is the correction for fines content in percent (FC) present in the soil and is expressed as:

∆(��) � = I!J ?�. 4 + =. �&� − ��. �&� #/A

(��) � = ��(�) � (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

&�(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 ≤ 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:

�� = �. ��M�"�� = ��+

′

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]:

�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

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

FS

Liq

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

FS

Liq

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


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0




Bore Hole (BH-4)


S.No. Depth (Z)


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

FS

Liq

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


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

FS

Liq

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


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0



Figure 10 Graph of FSLiq vs Depth (z) for Bore Hole (BH-6) Bore Hole (BH-7)


S.No. Depth

(Z) m

SPT N


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

FS

Liq

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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




Bore Hole (BH-9)


S.No. Depth (Z)


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

FS

Liq

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)


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

FS

Liq

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

FS

Liq

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

FS

Liq

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-Watson R 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= 0.05) 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

FS

Liq

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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0




S.No Depth (Z)

m CRRcal CRRMod FSLiq FSLiqMod

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

FS

Liq

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)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0




S.No. Depth (Z)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




S.No. Depth (Z)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0




S.No. Depth (Z)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




S.No. Depth (Z)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




S.No. Depth (Z)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




S.No. Depth (Z)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




S.No. Depth (Z)


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

FS

Liq

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5




S.No. Depth (Z)


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

FS

Liq

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)


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= 0.05) 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)


http://www.iaeme.com/IJCI

B. Curve Estimation: Cyclic Resistance Ratio Calculated (Observed) and Modeled (Linear)

Figure 6 Curve Estimation between Cyclic Resistance Ratio

C. Bore Log


CIET/index.asp 414 [email protected]

Curve Estimation: Cyclic Resistance Ratio Calculated (Observed) and Modeled (Linear)

Curve Estimation between Cyclic Resistance Ratio Calculated and Modeled

Bore Log Chart (Bore Hole 1 to Bore Hole 12)


[email protected]

Curve Estimation: Cyclic Resistance Ratio Calculated (Observed) and Modeled (Linear)

Calculated and Modeled (CRRCal and CRRMod)



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ASSESSMENT OF LIQUEFACTION POTENTIAL OF …...Keywords: Liquefaction, Multi-Linear Regression Modeling, MATLAB, SPSS, SPT, CSR, CRR. Cite this Article: Abdullah Anwar, Sabih Ahmad,