This document discusses a study on the influence of particle size gradation on shear parameters for cohesionless soil. Laboratory direct shear tests were performed on sand samples with different particle size gradations (coarse, medium, fine mixes) and relative densities (30-90%). The results showed that the angle of internal friction increased with increasing particle size and relative density. Specifically, samples with coarser grains had internal friction angles ranging from 36-42 degrees, while finer grained samples ranged from 28-34 degrees. The shear strength parameters were thus found to depend on both the particle size gradation and relative density of the cohesionless soil samples.

1. Influence of Particle Size Gradation On Shear
Parameters for Cohesionless Soil
Akshay Gandhi
M.E. Civil Geotechnical student
L. D. College of Engineering
Ahmedabad, India
akshaygandhi242@gmail.com
Prof. P.J.Mehta
Associate Prof. in Applied Mechanics Dept.
L. D. College of Engineering
Ahmedabad, India
mehta.priti67@gmail.com
Abstract-The wide range of particle shapes and size
distribution of sand, by virtue of its sedimentological process
of formation, plays a significant role in engineering
behavior when used as fill material or foundation material.
The relative density of a granular cohesionless soil indicates
its degree of compaction. Shear strength parameters increase
as we go from lower to higher relative density. The objective
of the research work is to study and analyze the factors that
affect the strength-deformation parameters i.e. Internal
Friction Angle (φ). The research work includes a series of
direct shear tests for UU condition, performed on granular
soils consisting of sand with different particle size gradations
(i.e. C-M,C-M-F,M-F) and different relative densities (i.e.
30%, 45%, 60%, 75%, 90%) reconstituted in the laboratory.
Direct shear testing was performed on all gradations for
different relative density to determine the angle of internal
friction under normal stresses of 50kN/m2
, 100kN/m2
,
150kN/m2
, and 200kN/m2
. The direct shear testing showed
that as the particle size of the sample increased, the angle of
internal friction also increased.
Index Terms—sand, relative density, mixed grading, particle
size gradation, DST.
I. INTRODUCTION
Sand is the most typical cohesionless granular material.
Cohesionless materials include different soils & artificial
substance that do not have the tendency of sticking together
among the individual grains of the material. The particle shape
and size & density of sand are considered to be one of the
most important factors that influence the behavior of the soil
when it is used for various purposes. These two are the
important factors that mainly influence the strength parameter.
All stability analysis in soil mechanics involves a basic
knowledge of shearing properties & shearing resistance of the
soil. From the number of studies done, there has not been any
proper literature found regarding the correlation between
relative density and strength deformation parameters with the
different sand gradation, i.e. coarse, medium and fine sand.
Hence, an attempt through means of experimental study is
being made to find the effect of these parameters. Several lab
experiments are being performed for determining the different
relative density with different proportions & particle size of
sand grades.
Shear strength of soil is defined as the resistance to
deformation by continuous shear displacement of soil particles
upon the action of a shear stress. Shear strength of soil is
mainly due to the cohesion of particles and the internal friction
angle. The shear strength of sand first introduced by Columb.
By theory shear strength is only by the friction between the
particle of sand. Columb simply assumed that frictional
resistance increases with increase in normal pressure.
As per the literature study “Mohammad A. sadek, Ying
Chen” said that laboratory direct shear tests of the sandy soil
showed that the soft and loose soils had similar yield forces
which were lower than those of the Firm soil, and the compact
soil had the highest yield forces Shear strength of cohesionless
soil can be determined by direct shear test. Constant strain
condition is satisfied throughout the test. The friction angle of
sand is determined graphically using the plot of normal stress
and shear stress. The effects of relative density on the bearing
capacity of the soil had been a topic of research. Many studies
have been done establishing a relationship between the
relative density and SPT value (N), the SPT value and the
bearing capacity, etc. This study focuses on particle size
gradation, relative density, and shear strength for sand.
II. MATERIAL AND PROCEDURE
For the present work, the experimental methodology
includes sample procurement followed by preliminary
laboratory testing and detailed laboratory testing
methodologies. Procured Soil sample is graded by sieve
analysis in three different sand as follows.
coarse sand =4.75mm to 2.00mm
medium sand =2.00mm to 0.425mm
fine sand=0.425mm to 0.075mm
There are different samples grade is prepared from above sand
in mixing with a percentage(%) by weight. All laboratory test
performed on Four sample grade prepared as a different
percentage as shown in table 1.

2. Table 1- Percentage grade mix
Coarse Medium Fine
SG-1 50 50
SG-2 50 25 25
SG-3 25 25 50
SG-4 50 50
In preliminary laboratory testing, Sieve analysis has been
carried. On the basis of that samples were classified in the
different gradation i.e. well graded sample and uniformly
graded. In detailed laboratory testing, Vibratory table has been
performed for calculating the minimum and maximum density
of sample in its loosest and densest state. On the basis of
vibratory table test, different relative density values were
taken and the dry density of soil sample has been calculated at
that relative density. Direct shear test has been performed on
each density which is find from relative density. Total 60
number of direct shear test is done to full fill the need of
study. DST is done to get Angle of friction (Φ) at various
grade.
III. LABORATORY INVESTIGATION
Sand sample is procumented from the chandola river
dholka. Four sample is prepared by grading the sand as shown
in the chart. Further work done as per requirement.
Chart 1 – Bar chart for sample grade
1) Particle Size Gradation
Sieve analysis is done on each sample grade to get a
primary idea of sand, the value of the coefficient of
curvature(Cc) and coefficient of uniformity(Cu) get from
the chart as given in table-2. Sand graded is poorly graded
sand.
Graph 1- particle size gradation
Table 2-Particle size gradtion
Sample D60 D30 D10 Coefficient of
Uniformity(Cu)
Coefficient of
curvature(Cc)
SG-1 1.62 0.54 0.42 3.85 0.428
SG-2 2.4 .65 0.42 5.71 0.42
SG-3 0.67 0.40 0.31 2.16 0.77
SG-4 0.87 0.34 0.24 3.63 0.55
2)Relative Density
As per the IS code 2720, part 14 relative density test
was done on the vibrotary table test device. From that
maximum dry density and minimum dry density of sand can
be getting as per shown in the table.
Table 3-Vibrotary table test data
Sample Type ρmin ρmax
SG-1
1.509 1.771
SG-2
1.5535 1.8229
SG-3
1.509 1.7147
SG-4
1.411 1.681
Assuming five relative density value & From the Relative
Density formula, we have all the value except ρd. Find the
density of sample grade at five different relative density as per
loose to the dense state of SG.
Dr-Relative density
ρd – Dry density of sand
ρmax -Maximum density of sand
ρmin –Minimum density of sand
3)DST
Each sample has been tested for five relative density
at 30%,45%,60%,75% and 90%. Direct shear test apparatus is
strain control device. That is a conventional type of direct
shear test apparatus. Box size 60mm x 60mm x 50mm is used.
All test is done at a constant strain rate of 1.25mm/min. in that
plain strain condition is satisfy. The test is done for the
unconsolidated undrained test condition. Test is done under
four normal stress as 50kN/m2
,100kN/m2
,150kN/m2
and
200kN/m2
. The angle of internal friction is found as per
Mohr’s coulomb theory. IS 2720 part 13 for each sample
grade at each relative density.

3. Fig. 1. Direct shear test apparatus: (a) test setup;
(b) shear box
IV. RESULT AND DISCUSSIONS
The direct shear test is performed on the graded sand
sample as per specification. To get the value of the angle of
internal friction graph between normal stress and shear stress
is drawn, shear stress is finding at four normal load. In table 4
average of three value of shear stress are shown with respect
to normal stress. Angle of internal friction for sample
grade1(C:M=50:50) is found by plotting the graph between
Normal stress and Shear stress as shown in Graph-2
Table 4- Stress value for Sample Grade 1
NORMAL
STRESS(kN/m2
)
SHEAR STRESS AT
VARIOUS R.D.(kN/m2)
30 45 60 75 90
50 46.8 50.4 50.4 54 61.2
100 86.4 97.2 100.8 111.6 93.6
150 115.2 115.2 129.6 136.8 129.6
200 165.6 176.4 194.4 194.4 208.8
Graph 2-Angle of internal friction for SG-1
For all 4 Sample Grade that graph is plotted and the angle of
internal friction for all prepared 20 sample of 4 grade and 5
relative density value. Values of the angle of internal friction
obtained through experimental work are as shown below. In
graph 3 shown the Angle of internal friction vary with relative
density for each sample grade.
Table 4-Angle of internal friction of all sample grade
SAMPLE
GRADE
ANGLE OF INTERNAL FRICTION(ϕ)
30 45 60 75 90
SG-1 36 37 40 41.5 44
SG-2 34 35.5 38 40.5 43
SG-3 31 32 35.5 37.5 39
SG-4 29 30 31.5 34 36
Graph 3-Angle of internal friction at relative density for
various sample grade
As per the obtained result, the chart is drawn between
the horizontal displacement and shear stress for a constant
normal load at various relative density. Chart for samle grade
1 shown below for each normal load(i.e.
50kN/m2
,100kN/m2
,150kN/m2
,200kN/m2
).

4. Graph 4-for normal load at 50 kN/m2
Graph 5-for normal load at 100 kN/m2
Graph 6-for normal load at 150 kN/m2
Graph 7-for normal load at 200 kN/m2
V. CONCLUSION
Series of Undrained Direct shear test on various graded
sand have been carried out on river sand is mixed in four
different proportion of C M & F and tested to investigated the
effect of the relative density on the undrained shear
characteristics. This experiment studied have yielded
following major finding.
 The angle of internal friction obtains from laboratory
test increase directly with the increase in particle size
and relative density.
 For a particular density, shear stress reaches at peak
between 1.5mm to 3mm horizontal displacement of
the sample at 1.25mm/min constants strain rate.
 For the SG - Course grain size variation of the angle
of internal friction ranges from 36̊-42̊. while for the
SG- finer grain size angle of internal friction ranges
from 28̊-34̊.
ACKNOLEGEMENT
Authors are highly thankful to Prof. Dr. G.P.
Vadodariya, Dean L.D. college of Engineering and Prof.
A.R.Gandhi, Head of Applied Mechanics Department, L.D.
College of Engineering, Ahmedabad, India for providing all
necessary research facilities.
REFERENCES
[1] Mohammad A. sadek, Ying Chen “Simulating shear
behavior of a sandy soil under different soil conditions”
Journal of Terramechanics 48 (2011) 451-458.
[2] Apurv Kumar siya “Analysis of sand gradation effect on
relative density “Department of civil engineering National
Institute of Technology Rourkela May 2014
[3] Esma Mostefa Kara, Mourad Meghachou,Nabil Aboubekr
“Contribution of particles size Range to sand Friction”
Djillali Liabes University Algeria ESTAR- Engineering
Technology & Applied science research Vol. 3, NO.4,
2013 497-501.
[4] Soonkie Nam, Matre Gutierrez “Determination of the
shear strength of unsaturated soil using the multistage
direct shear test” Engineering Geology 122 (2011) 272-
280.
[5] IS 2720 (Part 4)-1985 “Grain size analysis”.
[6] IS 2720 (part 13)-1986 “Direct Shear Test”
[7] IS 2720 (part 14)-1983 “Determination of Density Index
(RELATIVE DENSITY) of cohesionless soil.
[8] B.M.Das “Principles of Geotechnical Engineering”
Cenage Learning,2006.