International Journal of Interdisciplinary Research Centre (IJIRC) ISSN: 2455-2275(E) Volume II, Issue 1 January 2016 All rights are reserved 1 CORRELATION BETWEEN CALIFORNIA BEARING RATIO AND SHEAR STRENGTH PARAMETERS * Dr. S.K.SUMAN *Assistant Professor, Department of Civil Engineering,(Transportation & Survey Engineering)National Institute of Technology Patna, INDIA Abstract The California bearing ratio (CBR) test is generally used for the design of flexible pavements. The CBR test is relatively expensive and time consuming. A method is proposed for correlating CBR values with the shear strength parameters. Drained direct shear strength test was performed for obtaining cohesion and angle of internal friction. These tests are much more economical and rapid than the CBR test. Soil samples were collected from different proximity locations of Patna in Bihar. Thirty soil samples were identified as cohesive and thirty more were identified as non-cohesive soil. Various correlation models were developed like power and logest function. Goodness of fit statistical analysis was carried out. Developed models were also validated using t-test and F-test. Finally logest function correlation is accepted based on the coefficient of determination along with standard error of estimate and root mean squared error. Validation of model criteria also reveals the same. Keywords: CBR, Direct shear, Power and LOGEST function Introduction Large scale road constructions are taking place over the length and breadth of India due to adoption of highly intensified activities in road construction like Pradhan Mantri Gram Sadak Yojana(PMGSY) and Golden Quadrilateral Project etc. Rural roads have a pride of place in India, as they cover 27.5 lakh km land surface. The subgrade is the foundation layer which eventually supports all the roads, which come on the pavement. The subgrade soil and its properties are important in the design of pavement structure. All the pavement structures rest on subgrade foundation. The main function of subgrade is to give adequate support to the pavement and the subgrade should have as property of sufficient stability under adverse climate and loading condition.
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International Journal of Interdisciplinary Research Centre (IJIRC) ISSN: 2455-2275(E)
Volume II, Issue 1 January 2016
All rights are reserved 1
CORRELATION BETWEEN CALIFORNIA BEARING RATIO AND
SHEAR STRENGTH PARAMETERS
*Dr. S.K.SUMAN
*Assistant Professor, Department of Civil Engineering,(Transportation & Survey
Engineering)National Institute of Technology Patna, INDIA
Abstract
The California bearing ratio (CBR) test is generally used for the design of flexible
pavements. The CBR test is relatively expensive and time consuming. A method is proposed
for correlating CBR values with the shear strength parameters. Drained direct shear strength
test was performed for obtaining cohesion and angle of internal friction. These tests are much
more economical and rapid than the CBR test. Soil samples were collected from different
proximity locations of Patna in Bihar. Thirty soil samples were identified as cohesive and
thirty more were identified as non-cohesive soil. Various correlation models were developed
like power and logest function. Goodness of fit statistical analysis was carried out. Developed
models were also validated using t-test and F-test. Finally logest function correlation is
accepted based on the coefficient of determination along with standard error of estimate and
root mean squared error. Validation of model criteria also reveals the same.
Keywords: CBR, Direct shear, Power and LOGEST function
Introduction
Large scale road constructions are taking place over the length and breadth of India due to
adoption of highly intensified activities in road construction like Pradhan Mantri Gram Sadak
Yojana(PMGSY) and Golden Quadrilateral Project etc. Rural roads have a pride of place in
India, as they cover 27.5 lakh km land surface. The subgrade is the foundation layer which
eventually supports all the roads, which come on the pavement. The subgrade soil and its
properties are important in the design of pavement structure. All the pavement structures rest
on subgrade foundation. The main function of subgrade is to give adequate support to the
pavement and the subgrade should have as property of sufficient stability under adverse
climate and loading condition.
International Journal of Interdisciplinary Research Centre (IJIRC) ISSN: 2455-2275(E)
Volume II, Issue 1 January 2016
All rights are reserved 2
CBR is the basic parameter for design of flexible pavement. This test is relatively expensive
and time consuming. Direct shear test for the soil is the primary test for finding shear strength
parameters like cohesion and angle of internal friction. CBR test value indirectly indicates the
bearing capacity of the soil.It cannot be used for evaluating soil strength properties such as
cohesion and internal friction and the CBR value has no mathematical relationship to soil
strength. In this direction, the aim of this paper is to establish correlation of soaked California
bearing ratio (CBR) with shear strength parameters i.e. cohesion(c) and angle of internal
friction (φ).
Literature Review
Al-Almoudi et al (2002) had made an investigation to assess the efficacy of the Clegg impact
hammer (CIH) for estimating the strength of compacted soils by conducting a comparative
study between CBR & CIH tests. The test was conducted in two phases. In phase-1,
compacted marl samples were prepared in the laboratory under three different comparative
efforts and different moulding moisture contents and then subjected to CBR and CIH tests on
existing soils. The tests result analysed and indicated that the Clegg impact value correlates
relatively well with CBR values.
Garry, H.G and Stephen, A.C (2007) had proposed a method for correlating CBR values
with the undrained shear strength of clayey soils. For correlation purpose only limited
number of soil samples has been taken. The proposed method should be used with good
judgment and engineering experience to provide a quick method of determining subgrade soil
properties for pavement thickness design.
Joseph D.and Vipulanandan C. (2010) studied on laboratory and field compacted soil
samples (CL, CH, SC) that were characterized using the CBR tests and further the soil
parameters were correlated with CBR. The relationship between CBR and undrained shear
strength of soil was found non-linear.
Nugroho S.A. et al (2012) made an attempt to correlate between soaked CBR and unsoaked
CBR with their soil properties. The result showed that there was a linear correlation between
the soaked CBR and unsoaked CBR influenced by the nature of index.
Roy T.K. et al (2009) developed a relationship between compaction characteristics and the
CBR of different groups of soils like CL, CI and CH for prediction and quality control
purposes. The limitation of this correlation was that the evaluated correlation cannot predict
International Journal of Interdisciplinary Research Centre (IJIRC) ISSN: 2455-2275(E)
Volume II, Issue 1 January 2016
All rights are reserved 3
the values of soaked CBR from optimum moisture content and maximum dry density but
helps in checking of evaluated CBR values in different laboratories.
Saklecha P.P. et al (2011) examined the feasibility of simple regression analysis in
correlation the mechanical properties of sub grade soil with strength characteristics CBR. The
correlation of mechanical properties of subgrade soils as atterberg’s limit and compaction
properties could be used for foundation characterization by estimating the characteristics
strength in terms of CBR of foundation soils.
Experimental Programme
Soil samples were collected from different locations of in and around Patna. Thirty soil
samples were identified as cohesive soil and thirty more samples were identified as non-
cohesive soil. Consolidated drained direct shear test was performed on sixty number of soil
samples as per Indian Standard (IS: 2720(Part13):1986) guidelines and soaked CBR was also
performed on same samples as per Indian Standard (IS: 2720(Part16):1987) guidelines as
shown in Table1.
Standard deviation for cohesion, angle of internal friction and soaked CBR are 0.078, 1.756
and 0.560 respectively when cohesive soil is taken into account whereas 0.049, 2.589 and
1.666 respectively when non cohesive soil is taken into account. After combining all the sixty
data it was found that cohesion, angle of internal friction and soaked CBR are 0.179, 8.425
and 3.251 respectively.
Table 1: Experimental data for correlation
No. of
Samples
c value
(kg/m2)
Phi value
(φ)in degree
Soake
d CBR
No. of
Samples
c value
(kg/m2)
Phi value
(φ) in
degree
Soaked
CBR
Cohesive Soils Non Cohesive Soils
1 0.35 8.5 3.4 1 0.04 24 9
2 0.4 7.5 2.3 2 0.05 23 7.3
3 0.325 9 2.95 3 0.04 24 9
4 0.3 10 3.15 4 0.03 26 10
5 0.35 8 2.7 5 0.04 25 9.85
6 0.375 8 2.85 6 0.03 26.5 10
International Journal of Interdisciplinary Research Centre (IJIRC) ISSN: 2455-2275(E)
Volume II, Issue 1 January 2016
All rights are reserved 4
7 0.4 7 2.3 7 0.03 27 11.5
8 0.35 8 2.75 8 0.04 23 8
9 0.3 11 3.45 9 0.05 22 6.8
10 0.275 12.5 3.5 10 0.04 23 8
11 0.35 8 2.5 11 0.06 21 7.3
12 0.3 10.5 3.7 12 0.05 21.5 7.4
13 0.45 7 2.2 13 0.04 24 8
14 0.5 6 2.05 14 0.05 22 8.1
15 0.425 7 2.2 15 0.04 25 7.5
16 0.4 7.5 2.4 16 0.3 26 9.9
17 0.45 7 2.6 17 0.03 28 11
18 0.5 6 2.35 18 0.02 28.5 11
19 0.5 6.5 2.4 19 0.04 25 8.5
20 0.3 9.5 3.8 20 0.03 27 11.2
21 0.5 6.5 2.5 21 0.02 30.5 12
22 0.375 8 2.8 22 0.02 29 11.5
23 0.275 11 3.9 23 0.04 23 7
24 0.5 6 2.35 24 0.05 22 8.1
25 0.4 7.5 2.5 25 0.03 25.5 10.2
26 0.275 11 3.6 26 0.05 22 7.4
27 0.3 10 3.8 27 0.04 22.5 7.3
28 0.325 9 2.97 28 0.04 23.5 7.85
29 0.35 8 2.9 29 0.06 20 6
30 0.5 6 2.35 30 0.04 22 7.5
Correlation Analysis
Correlation analysis between soaked CBR and shear strength parameters was carried out on
soil samples data to know the functional relationship between the two or three. For this, seven
different models such as power and logest, both at different cases are considered to
investigate the appropriate relation between the dependent parameter and independent
parameter.
Model-1 and Model-2 have been established using power and logest function respectively
when cohesion as independent variable was considered.Model-3 and Model-4 have been
International Journal of Interdisciplinary Research Centre (IJIRC) ISSN: 2455-2275(E)
Volume II, Issue 1 January 2016
All rights are reserved 5
established using power and logest function respectively when angle of internal friction was
considered as independent variable.Mode-5 and Model-6 have been correlated separately for
cohesive soil and non-cohesive soil respectively when cohesion and angle of internal friction
both were considered as independent variables.Model-7 has been modelled after combining
cohesive and non-cohesive sixty numbers of soil samples data, considering both cohesion and
angle of internal friction as independent parameters.
Table 2 presents the different models along with function used and their correlations and
goodness of fit values. Three goodness of fit parameters such as coefficient of determination
(R2), Standard error of estimate (SEE) and Root mean squared error (RMSE) were considered
to identify the best fit model for the data.
Table 2: Correlations and goodness of fit parameters
Model Function Correlation R2
SEE RMSE
Model-1
POWER CBRsoaked =1.232 x C
-0.828 0.7693 0.265 0.256
Model-2
LOGEST CBRsoaked =6.198 x 0.122
C 0.727 0.290 0.280
Model-3
POWER CBRsoaked =0.0446 x φ1.6521
0.853 0.626 0.604
Model-4
LOGEST CBRsoaked =1.717x 1.069
φ 0.849 0.647 0.625
Model-5
LOGEST CBRsoaked =1.814x0.597
Cx1.079
φ 0.797 0.271 0.257
Model-6
LOGEST CBRsoaked =1.703x1.10
Cx1.069
φ 0.850 0.656 0.623
Model-7
LOGEST CBRsoaked =1.880 x 0.703
Cx1.066
φ 0.980 0.514 0.501
It is observed that the coefficient of determination value is comparatively higher in the case
of Model-7.The SEE and RMSE values suggest that the Model-1is better than other models
but only single independent variable is involved whereas Model-5 gives little bit higher value
but two independent variable is involved. Ultimately model-7 is finally accepted. Out of the
seven models, selected Model-7 has higher value of R2 and relatively lower SEE and RMSE
values than other models, indicating that these models are the best fit model considered in the
analysis.
International Journal of Interdisciplinary Research Centre (IJIRC) ISSN: 2455-2275(E)
Volume II, Issue 1 January 2016
All rights are reserved 6
Figure 1: Comparison between experimental and predicted CBR for Model-1
The Figure 1 shows the comparison between CBR values obtained from model-1 and
experimental CBR for soak condition. It is observed that results obtained from model-1are
nearer to experimental results. The mean percentage error calculated is -0.43 for model-1.
Figure 2:Comparison between experimental and predicted CBR for Model-2