International Journal of Science, Engineering and Technology Research (IJSETR)
Volume 1, Issue 1, July 2012
Soil Compression Index Prediction Model for
Clayey Soils
Seinn Moh Moh Dway, Daw Aye Aye Thant

Abstract— This study presents soil compression index
prediction model for clayey soils. As compressibility is the most
significant parameter while evaluating the settlement of soil
under the load of an infrastructure constructed on that soil
mass, compressibility of a soil mass is indicated by soil
characteristics like coefficient of compressibility, compression
index and coefficient of consolidation. Compressibility index is
one of the soil parameters that are required for calculation of
foundation settlements, however , the determination of
compression index is expensive, cumbersome and time
consuming. Therefore, in this study, an attempt has been made
to
estimate compression index as a function of soil index
properties. Soil samples are collected from three locations at 3
feet and 6 feet depths in Mandalay. The soil data used in this
investigation is collected to develop the predictive models for
estimation of compression index. Linear regression analysis is
performed to establish empirical models relating compression
index and index properties. Correlation between compression
index as dependent variable and various index properties based
on test results as independent variables is presented. Coefficient
of determination (R2) is used as evaluation criteria to check for
the empirical correlation that best fits studied soils. The root
mean square error (RMSE) is used as statistical index for
comparison of reliability of the different empirical equations.
Keywords— Soil Compressibility, Index Properties,
Compression Index , Linear Regression Analysis and Coefficient
of determination
I. INTRODUCTION
Soil is one of the most important materials used in
construction. The primary reason that civil engineers study
the properties of soil is foundations of all structures have to be
placed on soil. All structures will be designed depending on
soil results.
Compressibility is a measure of the relative volume of a
fluid or a soil as a response to a pressure. It is the most
significant parameter while evaluating the settlement of soil
under the load of an infrastructure constructed on that soil
mass. Compressibility of a soil mass is its susceptibility to
decrease in volume under pressure and is indicated by soil
characteristics like coefficient of compressibility,
compression index and coefficient of consolidation. Although
coefficient of volume compressibility is the most suitable, and
most popular, of the compressibility coefficients for the direct
calculation of settlement of structures, its variability with
Manuscript received Oct 15, 2011.
Seinn Moh Moh Dway, Department of Civil Engineering, Mandalay
Technological University, (e-mail: seinnmohmohdway@gmail.com).
Mandalay, Myanmar, 09-402534706
Aye Aye Thant, Department of Civil Engineering, Mandalay
Technological University, Mandalay, Myanmar, 09-2010603 (e-mail:
yelinthant 05@gmail.com).
confining pressure makes it less useful when quoting typical
compressibilities or when correlating compressibility with
some other property. For this reason, the compression index
of soils is generally preferred as its value does not change with
the change in confining pressure for normally consolidated
clays. However, the determination of compression index in
the labs is a cumbersome and time consuming process. Hence,
several attempts have been made in the past to predict the
compression index using index properties which are relatively
easier to determine and take lesser time to obtain in the
laboratory. Therefore, this study reveals establishing
empirical correlations in terms of index properties by linear
regression analysis. This correlation can also be useful for
checking of quality control which needs easy and faster ways.
II. LINEAR REGRESSION
Linear regression is a statistical tool for the investigation
of relationships between dependent variable and independent
variables. The methods of linear regression analysis are to
describe the relationship between two variables by identifying
an equation. The constants in the linear relationships were
calculated by utilizing a least-squares approach. The form of
the regression equation is commonly written as
Y = MX + C
(1)
where,
Y
= the dependent variable
X
= the independent variable
M = the slope of the regression line
C
= Y - axis intercept
The strength of the evidence of a linear relationship
between two variables is described by the coefficient of
correlation, r. This measures has no units. The coefficient of
correlation always assumes a value between -1.00 and +1.00.
The sign establishes whether the relationship is direct
(positive correlation) or inverse( negative correlation). The
following table describes for interpreting the strength of
either positive or negative correlation.
TABLE I
STRENGTH OF CORRELATION
Value of r
Interpretation
0.00-0.25
Little or no relationship
0.30-0.45
Fair relationship
0.50-0.75
Moderate to good relationship
0.80-1.00
Strong relationship to perfect
correlation
1
All Rights Reserved © 2012 IJSETR
International Journal of Science, Engineering and Technology Research (IJSETR)
Volume 1, Issue 1, July 2012
The coefficient of determination (r2) represents the
percent of the data that is the closest to the line of the best fit
where the highest amount of r2 shows the best relationship
between parameters.
The root mean square error (RMSE), also called the
standard deviation of the errors, is a measure of the typical
spread of the data around the regression line. The accuracy of
proposed model was also checked by calculating the
statistical parameter root mean square error.
III. PERFORMED TESTS
The capability of soils to bear loading are differ depending
on the soil types. Generally, fine-grained soils have a
relatively smaller capacity in bearing of load than the coarser
grained soil. Hence, fine grained soils therefore have a greater
degree of compressibility. In order to get the correlation
between compression index and index properties, following
tests are performed.
A. Water -Content Determination
Water-content determination is a routine laboratory test to
determine the amount of water present in a quantity of soil in
terms of its dry weight. It can be calculated from the following
equation.
W
ω  w  100%
Ws
(2)
where, Ww = Weight of water
Ws = Weight of dry soil
B. Specific Gravity Test
Specific gravity is defined as the ratio of the unit weight of
a given substance to the unit weight of water.
G t Ws
(3)
G 
s
can be divided into four basis states - solid, semi-solid, plastic
and liquid. The moisture content , in percent, at which the
transition from solid to semi-solid state takes place, is defined
as the shrinkage limit. The moisture content at the point of
transition from semi-solid to plastic state is the plastic limit,
and from plastic to liquid state is liquid limit. The plastic
index is the difference of liquid limit and plastic limit. The
following equation is to find the plasticity index.
PI = LL - PL
(4)
E .Free Swell Test
Ten grams of oven-dried soil specimens passing No.40
sieve (0.425 mm openings) is placed in the graduated
cylinders containing distilled water and kerosene. Sediment
volumes are measured after complete sedimentation of
specimens in respective fluid. It takes about 24 hours to 120
hours in distilled water. Kerosene is used instead of carbon
tetrachloride since it is easily available in Myanmar. Table II
shows classification of clays on the basis of their free swell
ratio.
Calculation;
V
(5)
FSR  w
Vk
where,
FSR = Free Swell Ratio
Vw = Sediment volume of soil in distilled water in cm3
Vk = Sediment volume of soil in kerosene in cm3
TABLE II
CLASSIFICATION OF CLAYS ON THE BASIC OF THEIR FREE
SWELL RATIO
Free Swell Ratio
Clay Type
Soil Expansivity
≤ 1.0
Non- swelling
Negligible
1.0 – 1.5
Mixture of
swelling and
non-swelling
Low
1.5 – 2.0
2.0 – 4.0
> 4.0
Swelling
Swelling
Swelling
Moderate
High
Very High
Ws  W2 - W1
where, Gs = Specific gravity of soil
Gt = Specific gravity of water at t, temperature
Ws = Weight of dry soil
W1 = Weight of bottle plus water plus soil
W2 = Weight of bottle plus water
C. Grain-Size Analysis of Soil
Grain size analysis is the determination of the size range of
particles presented in a soil, and can be expressed as a
percentage of the total dry weight. Two methods are generally
used to find the particle size distribution of soil.
 Sieve Analysis
 Hydrometer Analysis
Sieve analysis is used for particle sizes larger than
0.075mm in diameter and consists of shaking the soil sample
through a set of sieve that has progressively smaller openings.
Hydrometer analysis is used for particles sizes smaller
than 0.075mm in diameter. Hydrometer analysis is based on
the principle of sedimentation of soil grains in water, the
particles settle at different velocities, depending in their
shape, size, weight and viscosity of the water.
D. Atterberg Limit Test
Consistency varies with the water content of the soil. The
consistency of a soil can range from (dry ) solid to semi-solid
to plastic to liquid (wet ). The water contents at which the
consistency changes from one state to the next are called
consistency limits or Atterberg limits. Hence, on an arbitrary
basis depending on the moisture content, the behavior of soil
F. Modified Free Swell Index Test
Sivapullaiah et al. (1987) suggested a new test method of
obtaining a modified free swell index for clays, which appears
to give a better indication for the potential of clayey soils.
This test begins with an oven-dried soil with a mass of about
ten grams. The soil mass is well pulverized and transferred
into a 100 ml graduated jar containing distilled water. After
24 hours, the swollen sediment volume is measured. Table III
shows the soil classification on modified free swell index. The
modified free swell index is then calculated;
Modified free swell index =
V  Vs
Vs
(6)
where,
V
= Soil volume after swelling
Vs
= Volume of soil solid
Ws
Gs
= Weight of oven-dried soil
= Specific gravity of soil solid
= Unit weight of water
γw
=
Ws
Gsγw
2
All Rights Reserved © 2012 IJSETR
International Journal of Science, Engineering and Technology Research (IJSETR)
Volume 1, Issue 1, July 2012
TABLE III
SOIL CLASSIFICATION SCHEME BASED ON MODIFIED FREE
SWELL INDEX
Modified Free Swell Index
< 2.5
2.5 to 10
10 to 20
>20
Swelling Index
Negligible
Moderate
High
Very High
G. Standard Proctor Compaction Test
In the Proctor compaction test, the soil is compacted in a
mold that has a volume of 1/30 ft³. The diameter of the mold
is 4 in. During the laboratory test, the mold is attached to a
base plate at the bottom and to an extension at the top. The
soil is mixed with varying amounts of water and then
compacted in three equal layers. The hammer weighs 5.5 lb
and has a drop of 12 in. For a given soil, the process is
repeated at least five times, the water content of the samples
being increased each time. This test is used for determining
optimum moisture content and maximum dry density.
H. Consolidation Test
Consolidation is the process in which reduction in volume
takes place by expulsion of water under long term static loads.
It occurs when stress is applied to a soil that causes the soil
particles to pack together more tightly, therefore reducing its
bulk volume. When this occurs in a soil that is saturated with
water, water will be squeezed out of the soil. In the Classical
Method, developed by Terzaghi, soils are tested with an
oedometer test to determine their compression index.
I. Compression Index (Cc )
The compression index is useful for the determination of
the settlement in the field. The compression index, Cc, is equal
to the slope of the linear portion of the void ratio(e) versus
log pressure (log p) plot or vertical strain (  v ) versus vertical
applied stress (log p). Thus compression index can be
calculated as follow:
e e
(7)
Cc  2 1
P2
log
P1
But, Δε  Δe1
(8)
1 e
(9)
ε 2  ε1
Cc 
log
P2
P1
 (1  e 0 )
Mandalay. For the performed tests, disturbed samples
collected from three locations at 3 feet and 6 feet depths in
Mandalay are used to know the engineering properties of
studied soil. These locations are denoted as location A, B and
C.
A. Specific Gravity Test
Specific gravity is determined using equation 3 and results
are described in Table IV.
TABLE IV
TEST RESULTS OF SPECIFIC GRAVITY TEST
Location
ɛ
Compression index
Void ratio at mid height = e2 - e1
Void ratio at applied load
Initial void ratio
Effective overburden pressure
Vertical strain (%)
IV. TEST RESULTS FOR THE STUDIED SOIL
All tests were made at Soil, Concrete Laboratory and
Irrigation Technology Centre, Patheingyi Township,
2.68
6
2.69
3
2.73
6
2.73
3
2.54
6
2.73
C
B. Grain Size Analysis
Sieve analysis and hydrometer test are performed for grain
size distribution. Results are shown in Table V. Sieve analysis
gives the intermediate dimensions of a particle; hydrometer
analysis gives the diameter of an equivalent sphere that would
settle at the same rate as the soil particle.
TABLE V
RESULTS FOR GRAIN SIZE ANALYSIS
Sample
Location A
Location B
Location C
3 feet
6 feet
3 feet
6 feet
3 feet
Gravel (%)
0
0
0
0
0
0
Sand (%)
13.6
10
10.3
7.7
22.2
18.2
6 feet
Silt (%)
64.5
54
55.7
61.0
49.8
36.8
Clay (%)
21.9
36
34
31.3
28.0
45.0
F200
89.6
91.2
93.6
93
80.2
85.4
R
2.2
2.4
2
4.6
9.6
7.6
F
89.6
91.2
93.6
93
80.2
85.4
R
2.2
2.4
2
4.6
9.6
7.6
F
100
100
100
100
100
100
R (GF)
0
0
0
0
0
0
2.2
2.4
2
4.6
9.6
7.6
200
200
200
SF=R
=
=
=
=
=
=
3
B
4
Cc
Δe
e
e0
p0
Specific Gravity (Gs)
A
4
where,
Sample Depth (ft)
R
200
-
4
C. Atterberg Limit Test Results
For describing the limit consistency of fine-grained soils
on the basis of moisture content, three basic limits are
determined. These limits are calculated from liquid limit test,
plastic limit test and shrinkage limit test. The plasticity index
indicates the range of consistency within which a soil exhibits
plastic properties. Atterberg limit test results are described in
Table VI.
3
All Rights Reserved © 2012 IJSETR
International Journal of Science, Engineering and Technology Research (IJSETR)
Volume 1, Issue 1, July 2012
TABLE VI
ATTERBERG LIMIT TEST RESULTS
Location
A
B
F .Modified Free Swell Index Test
This method is for obtaining a modified free swell index
for clays, which appears to give a better indication for the
potential of clayey soil. Results are shown in Table IX.
Sample
Depth
(ft)
3
6
3
PL
LL
SL
PI
16.8
21.3
21.5
54.7
70.1
58.2
13.1
17.8
17.4
37.9
48.8
36.8
6
16.0
41.0
-
25.0
3
18.0
43.7
-
25.7
6
17.6
50.0
12.7
32.4
C
Atterberg Limits (%)
D .Classification of Soil According to USCS
The Unified Soil Classification System is based on the
grain size distribution, plasticity index and liquid limit of soil.
The studied soil can be classified as shown in Table VII
according to USCS.
TABLE VII
CLASSIFICATION OF SOIL TYPES FOR DIFFERENT
LOCATIONS
Location
Depth (ft)
3
6
3
6
3
6
A
B
C
Group
Symbol
CH
CH
CH
CL
CL
CH
Group
Name
Fat Clay
Fat Clay
Fat Clay
Lean Clay
Lean Clay
Fat Clay
E. Free Swell Test Results
The free swell test is one of the most commonly used
simple tests in the field of geotechnical engineering for
getting an estimate of soil swelling potential. Results for
location A,B and C are shown in Table VIII.
TABLE VIII
SOIL CLASSIFICATION SCHEME BASE ON FREE SWELL
RATIO
Location
3 feet
Free
Swell
Index
1.16
A
6 feet
3 feet
1.6
1.2
B
6 feet
3 feet
1.1
1.1
C
6 feet
1.2
Clay Type
Mixture of
swelling and
non-swelling
swelling
Mixture of
swelling and
non-swelling
Mixture of
swelling and
non-swelling
Mixture of
swelling and
non-swelling
Mixture of
swelling and
non-swelling
Soil
Expansivity
TABLE IX
SOIL CLASSIFICATION SCHEME BASED ON MODIFIED FREE
SWELL INDEX
Modified Free
Swell Index
Location
Swelling
Potential
3 feet
2.89
Moderate
6 feet
3.37
Moderate
3 feet
3.03
Moderate
6 feet
2.96
Moderate
3 feet
2.55
Moderate
6 feet
2.96
Moderate
A
B
C
G. Compaction Test Results
The Standard Proctor test is used for determining optimum
moisture content and maximum dry density. Table X shows
compaction test results.
TABLE X
COMPACTION TEST RESULTS
Samples
Optimum
Moisture
Content
(%)
Dry Unit
Weight
(lb/ft3)
Location A
3 ft
6 ft
Location B
3 ft
6 ft
Location C
3 ft
6
19.3
20.6
18.5
19.2
18.9
19.5
107.7
105
106.7
109.2
104.1
108.5
ft
H. Consolidation Test Results
Consolidation is the process whereby soil volume
decreases under the application of a load. Consolidation is
caused by loads being applied to soil and the grains of being
packed together more closely as a result. From this test,
compression indices are described in Table XI.
TABLE XI
COMPRESSIBILITY INDICES OF DIFFERENT LOCATIONS
Low
Moderate
Low
Location
Depth (ft)
Cc
Cs
eo
3
0.451
0.088
1.356
6
0.396
0.108
1.365
3
0.298
0.060
1.400
6
0.323
0.036
0.632
3
0.320
0.058
0.565
6
0.296
0.066
0.713
A
Low
B
Low
Low
C
4
All Rights Reserved © 2012 IJSETR
International Journal of Science, Engineering and Technology Research (IJSETR)
Volume 1, Issue 1, July 2012
V. CORRELATION BETWEEN COMPRESSION INDEX AND INDEX
PROPERTIES
It is well-known that compression index is related to
different index properties of the soils. By using linear
regression, analysis and validation for the studied soil are
done and empirical equations for prediction model of
compression index are developed and described in equation
10-14. The correlation between compression index and soil
index properties are evaluated. These indices are liquid limit,
plasticity index, natural water content and initial void ratio.
A linear correlation using liquid limit is done with seven
data sets to get higher correlation.
Cc = 0.0027 LL + 0.1994
(10)
The following proposed models are done with six data
sets obtained from studied soil test results.
Cc =0.0038 PI + 0.22
(11)
Cc = 0.01 ωn +0.027
(12)
Cc =0.196 eo + 0.207
(13)
Cc = 0.52 - 0.03 LL + 0.03 PI
(14)
The statistical indices for the above equations are shown in
Table XII.
TABLE XII
STATISTICAL INDICES
Independent
variables
Correlation
coefficient, r
Coefficient of
determination,r2
LL
PI
0.50
0.550
0.701
0.75
0.923
0.250
0.303
0.491
0.563
0.852
ωn
eo
LL, PI
permission and supervision. The author would like to thank
Daw Khin Thida and her staff members of Soil, Concrete
Laboratory and Irrigation Construction Quality Control,
Chaung Woon, Patheingyi, for their kind help during the
study of this paper. Finally, the author would like to thank to
her parents and family members for their supports and
encouragements.
REFERENCES
[1]
[2]
[3]
[4]
[5]
Slamet Widodo, Abdelazim Ibrahim, Estimation of Compression
Index(Cc) Using Physical Properties of Pontianak Soft Clay, Gustav
Strasse 1,09599 Freiberg (SN), Germany
Nader Abbas, Akbar A Javadi and Reza Bahramloo, Empirical
Prediction of Compression Behaviour of Normally Consolidated
Fine-Grained Soils, Iranian Agricultural Engineering Research
Institute (IAERI), Geotechnical Engineering, School of Engineering,
Computing and Mathematics, University of Exerter, Exerter EX4.40F,
Hamadan Agricultural and Natural Resource Center
Azzous, A.S.,Krizek, R.J, and Corotis,R.B., Regression analysis of
Soil Compressibility, Soils and Foundations,16 (2),19-29,1976
Braja M. Das, : Principal of Geotechnical Engineering, Fourth
Edition.Boston. U.S.A : PWS Publishing Company (1998)
Braja M. Das, : Principal of Geotechnical Engineering,Fifth
Edition.California State University, Sacramento, PWS Publishing
Company (2006)
Root mean
square
error,
RMSE
0.048
0.047
0.084
0.038
0.030
VI. DISCUSSION AND CONCLUSIONS
Compression index and index properties are used to
conduct a statistical study to determine correlations.
Regression analysis is carried out to develop the predictive
models for estimation of compression index (Cc).In this study,
single and multiple variable empirical equations are
developed for estimation of the compression index. Linear
regression analysis is performed using variables that obtained
from the test results, individually to develop single variable
equations. Also, two variable equation is developed utilizing
combinations of a representative parameter, liquid limit and
plasticity index. Equation-14 with the least RMSE and the
largest r2 is a reliable model for prediction of the compression
index. The values of RMSE (0.038) and r 2(0.563) show the
equation-13 that it has good relationship. The other equations
with LL, PI and ωn cannot be used to accurately predict the
compression index in the study area.
ACKNOWLEDGMENT
Firstly, the author would like to thank Dr. Myint Thein,
Rector of Mandalay Technological University for her
motivation, supports and guidance. The author is particularly
grateful to Dr. Kyaw Moe Aung, Associate Professor and
Head of Civil Engineering Department of Mandalay
Technological University, for his motivation, supports and
guidance. The author would like to express her heartfelt
gratitude to her supervisor Daw Aye Aye Thant, Lecturer of
Mandalay Technological University, for her kind advice,
5
All Rights Reserved © 2012 IJSETR