CORRELATION BETWEEN CALIFORNIA BEARING RATIO …ijirc.com/upload/55081a9b5b6238ca64ea5d376408bb48.pdf · CORRELATION BETWEEN CALIFORNIA BEARING RATIO AND ... for correlating CBR values

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.




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




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




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




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.




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

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Soak

ed

CB

R (

%)

Number of samples

ExperimentalCBR

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Soak

ed

CB

R(

%)

Number of samples

Experimental CBR

Predicted CBR





experimental CBR for soak condition. It is observed that results obtained from model-2 are







0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Soak

ed

CB

R(

%)

Number of samples

Experimental CBR

Predicted CBR

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

So

ake

d C

BR

(%

)

Number of samples

Experimental CBR

Predicted CBR











0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Soak

ed

CB

R(%

)

Number of samples

Eperimental CBR

Predicted CBR








Figure 7: Comparison between experimental and predicted CBR for Model-7




Developed models from one to six are based on thirty numbers of experimental data but

model seven is based on sixty numbers of experimental data. Figure 7 shows that initial thirty

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Soak

ed

CB

R(

%)

Number of samples

Experimental CBR

Predicted CBR

0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

Soak

ed

CB

R (

%)

Number of samples

Experimental CBR

Predicted CBR




numbers of soil samples have the low CBR value between two to four. This may be due to

the influence of cohesion in soil. Afterwards thirty number of soil samples have higher value

of CBR between six to fourteen. This may be due to the influence of angle of internal

friction.

Validation of Models

The best fit individual model is validated in this section. The validation result is summarised

in Table 3.Mainly these models are validated by considering Student’s t-test for significance

difference between the means of observed Soaked CBR and estimated CBR values. F-test is

considered for validating the significance difference in variance of observed and estimated

CBR values. The method of estimation of these two statistical tests is discussed below.t-

Statistic value is estimated using Eqn 1 to assess the statistical validity of mean between the

observed and estimated CBR value.

√

Eqn 1

Where xa and xm are the mean values of observed and modelled CBR values, sa and sm are the

variance observed and modelled and Na and Nm are the sample size of observed and predicted

values. Similarly F-test value has been estimated using Eqn 2 to assess the statistical validity

of variance between observed and estimated values.

Eqn 2

Where and

are the standard deviations of observed and estimated CBR values.

Table 3: Statistical summary of Validation Result

Model

Observed Estimated Validation of Models

Average

CBR Variance Average Variance

F-

Value Fcritical t-value tcritical

Model-

1 2.840 0.314 2.828 0.220 1.424 1.860 0.092 1.672,2.00

Model-

3 8.806 2.776 8.780 2.430 1.142 1.860 0.064 1.672,2.00

Model-

7 5.824 10.568 5.811 10.451 1.011 1.539 0.021 1.657,1.980

It can be observed from Table 3 that t-value obtained from Eqn.1 is less than t-critical value

which is obtained from standard t-table. This emphasises that the estimated CBR values have

no significant difference with observed values. It can be observed from Table 3 that F-values




obtained by Eqn 2 are less than F-critical value which is obtained from standard F-table. This

means that the two sets of data is statistically significant. This explains that the aggregate

model is better than the individual models is significant to estimate CBR values than the

individual models.

Comparison between Predicted and Experimental data

Developed models are validated using experimental data apart from the Table-1 as shown in

Table-4.Predicted soaked CBR value by using models 1,3 and 7are compared with

experimental soaked CBR. Compared data are represented through a plot as shown in Figure-

8, 9 and 10. It is observed that the relations for all the three models are linear and their

coefficients of correlation are0.673, 0.757 and 0.832 respectively. Out of these three models,

model-7 reveals the significant result.

Table 4:Soil Properties for comparison purpose

Sl.

No.

IS

Classification

LL

(%)

PL

(%)

PI

(%)

OMC

(%)

MDD

(g/cm3)

Soaked

CBR

(%)

c

(kg/cm2)

Ø

(degree)

1 SM Non

plastic

Non

plastic

Non

plastic 10 1.692 20.464 0.032 38

2 SM 31.838 27.47 4.368 17 1.61 11.89 0.056 30

3 SM 28.988 25 3.998 10 1.79 10.31 0.1 26

4 SC 20.8376 14.264 6.5736 14 1.69 5.464 0.096 18

5 CL 23.0762 8.6753 14.4009 6 1.74 9.013 0.08 26

6 CL-ML 21.6828 16.878 4.8048 14.5 1.83 5 0.13 21

7 CL 28.0552 19.514 8.5414 10 1.86 4.585 0.28 20

8 CL-ML 27.9834 20.267 7.7164 11 1.81 3.65 0.23 18

9 ML 32.943 25.1733 7.7697 16 1.69 10.585 0.16 30

10 CL-ML 23.9124 18.5583 5.3541 10 1.84 11.01 0.16 32

11 CL 30.4214 21.284 9.136 13 1.772 4 0.16 28

12 ML 27.211 23.418 3.793 18 1.71 10.16 0.1 33

13 ML 28.169 25.779 2.39 15 1.73 4.1 0.23 22

14 SP 29.261 25.126 4.135 16 1.71 12.31 0.12 33

15 ML 27.4904 22.917 4.5736 14 1.76 5.16 0.16 26




Figure 8: Experimental v/s Predicted soaked CBR for Model-1



y = 0.8068x + 0.995 R² = 0.6793

0

5

10

15

20

25

0 5 10 15 20 25

Pre

dic

ted

so

ake

d C

BR

(%)u

sin

g M

od

el-

1

Experimental soaked CBR(%)

y = 0.7194x + 4.2985 R² = 0.7574

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25

Pre

dic

ted

so

ake

d C

BR

(%)u

sin

g M

od

el-

3


y = 0.846x + 3.4987 R² = 0.8319

0

5

10

15

20

25

0 5 10 15 20 25

Pre

dic

ted

so

ake

d C

BR

(%)u

sin

g M

od

el-

7





Conclusion Based on the above study following conclusions have been drawn. Sixty numbers of soil data

were investigated and found that the thirty number of soil samples are cohesive in nature and

another thirty are non-cohesive in nature. Seven different forms of correlations are attempted

between soaked CBR and shear strength parameter. Goodness of fit statistics and validation

of models were carried out to achieve the best model. Finally Model-7 namely LOGEST

function model is found to be satisfactory and that can be used to predict the soaked CBR

based on cohesion value and angle of internal friction.

References

1. Al-Almoudi, BaghabraO.S., Asi ,I.M,Wahhab Hamad I. Al- Abdul and Khan

Ziauddin A. (2002) Clegg Hammer – California Bearing Ratio Correlations, Journal

of Materials In Civil Engineering, Vol.14,No.6,pages 512-523,Saudi Arabia

2. Garry, H.G and Stephen, A.C (2007) Correlation Between CBR and Shear Strength

Parameters, Journal of Transportation Research Board, No.-1989,Vol-1,page 148-153,

USA

3. Joseph, D and Vipulanandan, C. (2010) Correlation Between CBR and Soil

Parameters, Centre of Innovative Grouting Material and Technology, USA

4. Kadyali, L.R.(2007) Principle And Practice of Highway Engineering, Khanna

Publishers, page 258,India

5. Nugroho, S.A., and Hendri, Andy and Ningsih, S.R. (2012) Correlation Between

Index Properties And California Bearing Ratio Test of Pekanbaru Soils with and

without soaked, Canadian Journal on Environmental, Construction And Civil Engg.,

Vol.3,No.1,page 7-17,Canada

6. Roy, T.K. and Chattopadhay, B.C. and S.K.(2009) Prediction of CBR From

Compaction Characteristics Of Cohesive Soils, Highway Research Journals, page 77-

87,India

7. Saklecha, P.P. and Katpatal, Y.B and Rathore S.S, & Agarwal D.K.(2011) Spatial

Correlation of Mechanical Properties of Sub Grade Soil For Foundation

Characterization, International Journal Of Computer Application, Vol.36, No.11,page

109-115,USA

8. IS:2720-1987(Part 16), Laboratory Determination of CBR, Bureau of Indian

Standards, New Delhi

9. IS:2720-1986(Part 13), Direct Shear Test, Bureau of Indian Standards, New Delhi

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CORRELATION BETWEEN CALIFORNIA BEARING RATIO …ijirc.com/upload/55081a9b5b6238ca64ea5d376408bb48.pdf · CORRELATION BETWEEN CALIFORNIA BEARING RATIO AND ... for correlating CBR values