framework for assessment of shear strength parameters of

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308

(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME

189

FRAMEWORK FOR ASSESSMENT OF SHEAR STRENGTH

PARAMETERS OF RESIDUAL TROPICAL SOILS

Nagendra Prasad.K1

, Sivaramulu Naidu.D2

, Harsha Vardhan Reddy. M3, Chandra.B

4

1Professor, Dept. of Civil Engineering, SV University, Tirupati, India,

2Research Scholar, Dept. of Civil Engineering, SV University, Tirupati, India.

3Former under-graduate student, Dept. of Civil Engineering, SV University, Tirupati, India.

4Post-graduate student, Dept. of Civil Engineering, SV University, Tirupati, India.

ABSTRACT

Failure of soil may cause collapse of structures resulting in loss of lives and economic

damage. Most geotechnical instability problems including failure of soil are associated with

shear failure. Shear strength is one of the most important properties for design of engineering

structures and also one of the most difficult to evaluate. In order to determine the shear

strength parameters that govern shear strength, such as angle of internal friction and

cohesion, typical laboratory tests such as the direct shear test and triaxial test are used.

However, these laboratory tests have some shortcomings regarding sample collection such as

lack of in-situ conditions and difficulties for obtaining undisturbed soil samples. In-situ

testing methods are also used to determine the shear strength of soil such as the Vane Shear

Test, the Standard Penetration Test and the Cone Penetration Test. However, these tests

estimate the shear strength of the soil with appropriate empirical correlations that have a wide

margin of error. Traditional testing methods to acquire the shear strength parameters are

expensive, complicated, time consuming, and require extreme care during the process of

collecting, storing, transporting and preserving samples. The objective of this paper is to

develop a phenomenological model that could be used to predict the shear strength

parameters from their index properties (liquid limit) and other engineering properties

(specific gravity, void ratio, maximum dry density), which are relatively easy to determine.

The validity of the method was proven by determining shear strength parameters for various

types of soils and by comparing them with the results taken from a conventional testing

method. This could be used to rapidly estimate cohesion and friction angle in situations

where either the good quality samples or the equipment needed to conduct such tests are not

available.

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND

TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 4, Issue 2, March - April (2013), pp. 189-207

© IAEME: www.iaeme.com/ijciet.asp

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IJCIET

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190

Keywords: shear strength parameters, bulk modulus, normal compression line, triaxial

test, volumetric strain, maximum dry density.

1. INTRODUCTION

The structural strength is primarily a function of shear strength of soil. Soil failure

usually occurs in the form of “shearing” along internal surface within the soil. Shear

strength is soils’ ability to resist sliding along internal surfaces within the soil mass. The

strength of clayey soil is influenced by compaction energy, optimum moisture content,

dry density, percentage of fines, degree of saturation, consistency limits, cohesion and

frictional resistance between the particles. According to Mohr’s theory, a soil mass will

fail when the shearing stress on the failure plane, which is a definite function of the

normal stress acting on that plane, is greater than the shear resistance of the soil i.e. S = f

(σn). The shearing strength of a soil is represented by the following Mohr-Coulomb’s

equation,

S = c + σn tan ф

Where,

S = Shear stress at failure

c = cohesion i.e. the resistance of soil particles to displacement due to intermolecular

attraction and surface tension of the held water

σn = Normal stress

ф = Angle of internal friction.

The angle of internal friction depends upon dry density, particle size distribution,

shape of particles, surface texture, and water content. It is directly proportional to the

applied normal force acting between the particles. In clayey soils, partially saturated soils,

and cemented soils, the individual soil particles are bonded together. This is another

source of the shear strength of soil which is independent from the normal force, called

cohesion. Cohesion depends upon size of clayey particles, type of clay minerals, valence

bond between particles, water content, and proportion of the clay. In geotechnical design

practice, two important considerations that need careful examination are whether

construction will cause deformation of the soil and /or instability due to shear failure. An

engineer has to ensure that the structure is safe against shear failure in the soil that

supports it and does not undergo excessive settlement. Therefore knowledge about the

stress-strain behaviour, deformation and shear strength of the soil is essential. These

considerations are more complicated and challenging when dealing with clayey soil,

which is known to be highly deformable and have low shear strength. It can be

determined either in the field or in the laboratory, or both. The tests employed in the

laboratory may include unconfined compression test, triaxial test, laboratory vane, direct

shear box and direct simple shear test. In situ tests are normally conducted to test the

validity of the laboratory tests and for design purposes. However, these laboratory tests

have some shortcomings regarding sample conditions such as lack of in-situ conditions



191

and difficulties for obtaining undisturbed soil samples apart from difficulties associated

with simulating drainage conditions appropriately. Insitu tests available include field

vane, standard penetration test, cone penetration test, and piezocone and pressure meter.

However, these tests estimate the shear strength of the soil with appropriate empirical

correlations that have a wide margin of error. The present work aims at evaluating the

shear strength parameters of soil at a state of maximum dry density taking into

consideration its liquid limit and Proctors maximum dry density since soil is compacted

to its maximum dry density in almost all earth structures.

2. BACKGROUND INFORMATION

Investigation carried out by Burak (2008) has established correlation between

index properties and shear strength parameters of normally consolidated clays by

statistical and neural approaches. Amin (1997) made studies to predict and determine

undrained shear strength, a very important parameter in design practice, for Klang clay,

Malaysia. Shear strength is determined using field and laboratory vane shear and

recompression method utilizing the direct simple shear apparatus. Analysis of the triaxial

test results of Satija (1978) reveals some nonlinearity in the shear stress versus matric'

suction failure envelope (Fredlund et al. 2000). Fredlund and Vanapalli (2000) in a recent

study have provided comparisons between the measured and predicted values of

unsaturated shear strength using the shear strength functions published in the literature.

Comparisons were provided both for low suction range (i.e., 0 to 1,500 kPa) as well as

large suction range (0 to 10,000 kPa or higher).

Vanapalli et al. (2001) predicted the shear strength of an unsaturated soil with a

semi-empirical shear strength function developed at the University of Saskatchewan both

for low and as well as large suction ranges. Rajeev Jain et al. (2010) presented an

artificial neural network technique to predict the shear strength parameters of medium

compressibility soil, which influenced by basic properties of soil in unconsolidated

undrained conditions. Kamil Kayabali (2011) investigated the shear strengths at plastic

limit and liquid limit by reappraising a large body of shear strength and soil consistency

data. . If the shear strength at plastic limit and liquid limit are set properly, the undrained

shear strength of remolded soils at any water content between Plastic limit and liquid

limit can be determined easily. Erfan Hosseini (2012) studied shear strength parameters

by using grading test, Atterberg limits, compression, direct shear and consolidation.

Soil State

It is widely known that the stress and strain are inseparable for all materials under

loading. The stress the particulate materials experience depends on the associated strain

and vice versa. Accordingly, an attempt has been made to analyse the mobilisation of

shear strength in relation to the volumetric strain, the sample experiences to exhibit

maximum resistance. The volumetric strain is reckoned with reference to the possible

loose state in order to arrive at the current state. It is the current state of soil that

determines the shear strength of soils irrespective of the stress path the soil follows to

reach the current state as demonstrated in the Figure 1. At (a) the soil is under a pressure

of 1 kPa and at (b) the soil is at maximum dry density.



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Figure 1: Depiction of Soil State

Bulk Modulus Bulk modulus (K) of a substance measures the substance's resistance to uniform

compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting

relative decrease of the volume.

The bulk modulus K>0 can be formally defined by the equation,

Where,

P = Pressure

V = Volume

= Derivative of pressure with respect to volume.

3. EXPERIMENTAL INVESTIGATION

3.1 Introduction

The study area lies to the extreme south of Andhra Pradesh state (India)

approximately between 12° 37' - 14° 8' north latitudes and 78° 3' - 79° 55' east longitudes.

The experimental methods of different laboratory investigations are carried out on the

tropical residual soils of Tirupati region.

3.2 Details of the Experimental Investigation The present experimental investigation is carefully planned to understand the behavior

of tropical residual soils. The experimental program involves determination of the following

aspects.

� Basic properties

� Compaction properties

� Undrained triaxial compression test

All the tests were conducted as per the relevant provisions stipulated in Bureau of Indian

Standards.



193

3.3 Soils Tested

The soils considered in the present investigation have been obtained from the

surroundings of Tirupati region. The location of soil samples can be seen from Figures 2 and

3. The details of locations of sampling are shown in Table 1. Laboratory data of the samples

1 to 15 are used to analyze and predict the correlation among c, ф and bulk modulus (K) of

various soil samples. Data of samples A, B and C obtained from the laboratory are examined

to verify the accuracy of prediction in a phenomenological model. These soils are residual in

nature, which are deposited at the place of formation.

Figure 2: Sample locations at Tirupati region in India map

Figure 3: Detailed sample locations at Tirupati region



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Table 1: Soil Sample Locations

S.No Sample Location

1 Beerakuppam (Village)

2 Gongutapalli (Village)

3 RC Kandriga

4 Nagari

5 Avalkonda

6 Renigunta by-pass

7 Tiruchanur

8 Kottramangal(village)

9 Pillaripattu

10 Padmavathipuram

11 Nagari Station

12 Dhodlamitta (village)

13 Kandriga(village)

14 Daminedu

15 Padmavatipuram

A K.T.Road

B Kothapalem layout

C Padipeta

3.4 Collection of Samples Soil samples considered represent wide spectrum of typical soils encountered in

practice, ranging from predominantly clayey sand to clay with low to high compressibility.

Soil samples have been collected by exercising necessary care to see that the natural

constituents are represented and the same were transported to geotechnical engineering

laboratory. The samples were air dried and stored in air tight containers for use in rest of the

investigation.



195

3.5 Properties of Soils Index properties and the compaction properties for all the samples including A, B and C

are presented in Tables 2 and 3. It may be seen that most of the soils represent clayey sand

(SC) and few samples fall under clay with intermediate and high compressibility (CI, CH).

The liquid limit values for the samples considered ranges from 31% to 67% and the plastic

limit varies from 14% to 22%. The fine fraction ranges from 29% to 83% which is typical for

the soils encountered in practice in this region. The cohesion values ranges from 28.70 kPa to

74.80 kPa and angle of internal friction ranges from 14.25o to 23.37

o.

4 ANALYSIS OF TEST RESULTS

The usual object of detailed experimental investigation will be to propose a

mechanistic approach for understanding the behavior of materials tested in a coherent manner

by properly analyzing the observed behavior. Accordingly a detailed analysis of test results

is presented in the following section.

4.1 Triaxial test data Triaxial compression tests have been conducted on samples 1 through 15 and the test

results are depicted from Figures 4 to 21. Mohr’s circles are drawn for soil samples 1 to 8 as

shown in Figures 22 to 29. Similar Mohr circles can be drawn for other soil samples also. The

values of c and ф thus determined from the Mohr’s circle approach are represented in Tables

2 and 3. The stress-strain response of the sample is noticed to be typical with greater

deviatoric stress for greater confining pressures. The shear strains experienced by the samples

seem to be related to the degree of compression to which the samples is subjected.

Figure 4: Deviatoric stress verses strain

for sample 1


for sample 2



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for sample 3


for sample 4


for sample 5

Figure 9: Deviatoric stress verses strain for

sample 6



197


for sample 7 Figure 11: Deviatoric stress verses strain

for sample 8


for sample 9 Figure 13: Deviatoric stress verses strain

for sample 10



198


for sample 12


for sample 11


for sample 13


for sample 14



199


for sample A


for sample 15


for sample B


for sample C



200

Figure 23: Mohrs circle approach to

determine c and ф for sample 2









201











202

Table 2: Soil Properties

Sl.

No: Description

Values

Sample

1

Sample

2

Sample

3

Sample

4

Sample

5

Sample

6

Sample

7

Sample

8

Sample

9

1 Gravel (%) 2 2.4 4.2 3.30 11.2 0.40 3.20 16.87 7.30

2 Sand (%) 26.6 65.2 49.4 28.00 61.4 36.8 53.20 33.18 42.30

3 Silt+Clay (%) 71.4 32.4 46.4 68.70 27.4 62.8 43.6 49.64 50.40

4 0.425 mm Size (%) 83.2 46.4 55.2 29.8 29.8 75.2 63.4 58.21 66.20

5 Liquid Limit, WL (%) 31 32 36 41 44 45 46 49 52

6 Plastic Limit, PL (%) 14 17 18 16.00 19 20 17 22 18

7 Plasticity Index, PI (%) 17 15 18 25 25 25 29 27 34

8 IS Classification CL SC CI CI SC CI SC CI CH

9 Free Swell Index (%) 25 25 20 45.00 45 55 60 80 70

10 Degree of Expansion Low Low Low Low Low Medium Medium Low Mediu

m

13 Optimum moisture content,

(%) 13.75 13.98 14.9 16.05 16.74 16.97 17.43 17.89 18.58

14 Maximum dry density, γd

(kN/m3) 18.54 18.47 18.13 17.71 17.48 17.40 17.24 17.09 16.87

Shear strength parameters

15 Cohesion, C in kPa

28.70 29.70 39.40 49.20 55.90 54.50 47.40 59.00 61.20

16 Angle of internal friction,

Φ in degrees 14.25 15.12 16.09 16.88 17.84 18.24 19.90 19.67 20.93



203

Table 3: Soil Properties

Sl.

No: Description

Values

Sample

10

Sample

11

Sample

12

Sample

13

Sample

14

Sample

15

Sample

A

Sample

B

Sample

C

1 Gravel (%) 7.75 6 3.80 3.2 1.8 3.4 3.9 16.87 10.25

2 Sand (%) 51.50 71.9 12.60 18.8 59.7 26.8 58.1 33.18 59.3

3 Silt+Clay (%) 40.75 22.1 62.6 78 38.5 69.8 38 49.94 30.5

4 0.425 mm Size (%) 50 30.7 41 80 50.1 83.2 52 58.21 48.10

5 Liquid Limit, WL (%) 54 57 59 60 64 67 38 50 63

6 Plastic Limit, PL (%) 19 18 19 20 20 15 16 22 20

7 Plasticity Index, PI (%) 35 39 40 40 44 52 22 28 43

8 IS Classification SC SC CH CH SC CH SC CI SC

9 Free Swell Index (%) 80 60 75 80 105 140 50 80 80

10 Degree of Expansion Medium Medium Medium Medium High High Mediu

m

Mediu

m

Mediu

m

13 Optimum moisture content,

(%) 19.04 19.73 20.19 20.42 21.34 22.03 15.36 18.12 21.11

14 Maximum dry density, γd

(kN/m3) 16.72 16.51 16.37 16.30 16.03 15.80 17.96 17.02 16.10

Shear strength parameters

15 Cohesion, C in kPa 64.00 65.50 64.20 68.70 71.80 74.40 41.50 55.50 74.80

16 Angle of internal friction, Φ

in degrees 21.23 21.86 23.29 22.41 23.37 23.35 16.94 18.42 22.04

4.2 Behaviour with respect to Normal Compression Line (NCL)

An attempt has been made to examine the compression behavior with respect to

Normal Compression Line (NCL) for which the equation given by Nagaraj et.al. (1994) as

reproduced below has been adopted.

(1)

Where,

e = Void ratio at a given pressure of σv’

eL = Void ratio corresponding to liquid limit.

'log276.023.1

v

Le

eσ−=



204

4.3 Determination of Void Ratio Void ratio corresponding to liquid limit will be minimum and can be determined as the

product of specific gravity (G) and liquid limit (WL). When the soil is compacted to its maximum

dry density, void ratio decreases accordingly which can be determined from the equation,

(2)

Where,

= Maximum dry density

G = Specific gravity of soil

= Unit weight of water

e = Void ratio at a given pressure of σv’

σvmax, pressure corresponding to maximum dry density is now determined from equation (1), by

substituting e and eL values. The void ratio (eo) in the loosest state under a pressure of 1kPa is

determined from equation (1) for all the soil samples knowing their liquid limits.

4.4 Volumetric Strain

The volumetric strain (ϵv) can now be determined from the equation,

Where,

eo = void ratio under pressure of 1kPa

e = void ratio at a state of maximum dry density

4.5 Bulk Modulus Bulk modulus (K) can be obtained as the ratio of the infinitesimal pressure increase to

volumetric strain,

dP for all the 15 soil samples (1-15) can be evaluated as the difference of the pressure between

loosest state (corresponding to a normal stress of 1 kPa) and pre-compression stress (σvmax,

referred to a normal compression line of natural state of soil).

4.6 Bulk Modulus versus c and ф A graph of bulk modulus (K) versus c and bulk modulus (K) versus ф is plotted as

depicted in Figures 30 and 31 respectively. Experimental results usually show small deviations

and a best fit straight line from plotted data is normally drawn to establish a definite relation. A

correlation of 97.60% and 96.10% are obtained for bulk modulus (K) versus cohesion (c) and

bulk modulus (K) versus angle of internal friction (ф) respectively.

The equation thus obtained for bulk modulus (K) versus c is as follows:

c = 0.034K - 13.46 (5)

And for bulk modulus (K) versus ф it is:

ф = 0.007K + 4.812 (6)



205

Figure 30: Bulk modulus (K) versus Cohesion (c)

Figure 31: Bulk modulus (K) versus Angle of internal friction (ф)



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5 PREDICTION OF SHEAR STRENGTH PARAMETERS (C & Ф)

The validity of the present investigation can be checked by determining shear strength

parameters of the samples A, B and C. The shear strength parameters c and ф are determined

from the conventional triaxial test to check the accuracy of predicted data. Using liquid limit,

void ratio in loosest state under a pressure of 1 kPa (eo), is determined by equation (1). Void

ratio at maximum dry density (e), for samples A, B and C are determined from equation (2).

Now volumetric strain and bulk modulus are determined from equations (3) and (4)

respectively. From bulk modulus, the cohesion(c) values for each sample A, B and C are

obtained using equation (5). Similarly the angle of internal friction (ф) for these samples is

obtained from equation (6).

5.1 Accuracy in Prediction Data thus predicted is compared with the laboratory data obtained from conventional

triaxial test. It is observed that the accuracy of prediction in the evaluation of both c and ф

accounts to about 96%.

6. CONCLUDING REMARKS

The objective of this study is to suggest a phenomenological model to correlate liquid

limit, maximum dry density with shear strength parameters such as cohesion and angle of

internal friction.

1) The values of cohesion (c) and angle of internal friction (ф) alters with the state of

soil or simply, they represent the state of soil.

2) Void ratio decreases when the soil is compacted from loosest state to its maximum

dry density.

3) Both cohesion (c) and angle of internal friction (ф) increases with increase in bulk

modulus (K).

4) Relation between bulk modulus (K) and cohesion (c) is almost linear.

5) Also, the relation between bulk modulus (K) and angle of internal friction (ф) is

almost linear.

6) Increase in cohesion (c) is more when compared to increase in angle of internal

friction (ф) with increase in bulk modulus.

7) The present state of soil determines its shear strength irrespective of the path

followed.

8) The compacted soil state lies on left hand side of the Normal Compression Line and

hence the state is quite akin to over-consolidated state.

9) The volumetric strain to which the sample undergoes depends on the stress which in

turn depends on the compaction energy imparted.

10) Accuracy of prediction in the evaluation of both cohesion (c) and angle of internal

friction (ф) accounts to about 96%.



207

REFERENCES

[1] Amin (1997), “Prediction and Determination of Undrained Shear Strength of Soft

Clay”, Pertanika J. Sci. & Techno! 5(1): 111-126.

[2] Burak (2008), “Shear strength estimation of plastic clays with statistical and neural

approaches”, Journal of Building and Environment, vol. 43.

[3] Fredlund (1987), “Nonlinearity of strength envelope for unsaturated soils, proceedings

of the 6th international conference on expansive soils”, New Delhi.

[4] Fredlund, D.G. and Vanapalli (2000), “Comparison of different procedures to predict

unsaturated soil shear strength”, ASTM Proceedings, Unsaturated Soils, Geo-Denver

2000.

[5] Erfan Hosseini, Mohammad K. Alizadeh, and Amir Mesbah (2012), “Evaluation of

Shear Strength Parameters of Amended Loess Using Common Admixtures in Gorgan,

Iran”, International Journal of Science, Engineering and Technology.

[6] Kamil Kayabali (2011), “Assessment of Shear Strength at Consistency Limits - A

Reappraisal”, Vol. 16, EJGE Journal.

[7] Nagaraj,T.S. & Srinivasa Murthy B.R. and Vatsala, A. (1994), “Analysis and Prediction

of Soil Behavior”, Wiley Eastern Journal, New Delhi.

[8] Rajeev Jain and Pradeep Kumar Jain (2010), “Computational approach to predict soil

shear strength”, International Journal of Engineering Science and Technology.

[9] Satija B. S. (1978), “Shear behavior of partly saturated soils”, Ph.D. thesis, Indian

Institute of Technology, Delhi, India.

[10] Vanapalli (2001), “Predicting the shear strength of an unsaturated soil”, The Canadian

Geotechnical Society Journal.

[11] Ercan Serif Kaya, Takuro Katayama and Toshitaka Yamao, “Seismic Characteristics Of

The Folded Cantilever Shear Structure”, International Journal of Civil Engineering &

Technology (IJCIET), Volume 4, Issue 2, 2013, pp. 58 - 79, ISSN Print: 0976 – 6308,

ISSN Online: 0976 – 6316.

[11] M. Alhassan and I. L. Boiko, “Effect of Vertical Cross-Sectional Shape of Foundation

and Soil Reinforcement on Settlement and Bearing Capacity of Soils”, International

Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 2, 2013,

pp. 80 - 88, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.