framework for assessment of shear strength parameters of
TRANSCRIPT
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME
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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)
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ISSN 0976 – 6316(Online)
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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
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
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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.
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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.
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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
Figure 5: Deviatoric stress verses strain
for sample 2
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Figure 6: Deviatoric stress verses strain
for sample 3
Figure 7: Deviatoric stress verses strain
for sample 4
Figure 8: Deviatoric stress verses strain
for sample 5
Figure 9: Deviatoric stress verses strain for
sample 6
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Figure 10: Deviatoric stress verses strain
for sample 7 Figure 11: Deviatoric stress verses strain
for sample 8
Figure 12: Deviatoric stress verses strain
for sample 9 Figure 13: Deviatoric stress verses strain
for sample 10
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Figure 15: Deviatoric stress verses strain
for sample 12
Figure 14: Deviatoric stress verses strain
for sample 11
Figure 16: Deviatoric stress verses strain
for sample 13
Figure 17: Deviatoric stress verses strain
for sample 14
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Figure 19: Deviatoric stress verses strain
for sample A
Figure 18: Deviatoric stress verses strain
for sample 15
Figure 20: Deviatoric stress verses strain
for sample B
Figure 21: Deviatoric stress verses strain
for sample C
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Figure 23: Mohrs circle approach to
determine c and ф for sample 2
Figure 22: Mohrs circle approach to
determine c and ф for sample 1
Figure 24: Mohrs circle approach to
determine c and ф for sample 3
Figure 25: Mohrs circle approach to
determine c and ф for sample 4
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Figure 26: Mohrs circle approach to
determine c and ф for sample 5
Figure 27: Mohrs circle approach to
determine c and ф for sample 6
Figure 28: Mohrs circle approach to
determine c and ф for sample 7
Figure 29: Mohrs circle approach to
determine c and ф for sample 8
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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
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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−=
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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)
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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%.
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