Co-Relationship between California Bearing Ratio and Index Properties of Jamshoro Soil

Subgrade is a most important part of a pavement structure, which should have a reasonable stiffness modulus and shear strength. CBR (California Bearing Ratio) test is performed to evaluate stiffness modulus and shear strength of subgrade soils. However, CBR test is laborious and time consuming, particularly when soil is highly plastic like Jamshoro soil. In order to overcome this limitation, it may be appropriate to correlate CBR value of soil with its index properties like grain size analysis, Atterberg limits, and compaction characteristics such as MDD (Maximum Dry Density) and OMC (Optimum Moisture Content). This paper expresses the correlations between CBR value of Jamshoro soil and its index properties. SLRA (Single Linear Regression Analysis) and MLRA(Multiple Linear Regression) based Models were utilized. It is seen that MLRA gave better correlations up to R of about 0.984. It is observed that the Soaked CBR value can be predicted with confidence from LL (Liquid Limit), PI (Plasticity Index) and percent finer while the un-soaked CBR value can be obtained from LL, plasticity index and MDD.


INTRODUCTION
P avement design is considered to be the most important parameter in the construction of a road network. Generally, pavement, a relatively stable crust, is constructed over the natural soil in order to support the wheel and traffic loads as well as to provide a hard, durable and abrasion resistant surface [1]. A flexible pavement consist of a number of layers including sub-base, base course, surfacing etc. which ultimately lies on subgrade. Basically, subgrade is not the physical part of the pavement but it is considered as the functional pavement [3][4]. If the subgrade has higher CBR value, this means that it has more strength and will be able to bear more traffic load coming over it and ultimately the thickness of pavement layers will be small and vice versa [5]. The soaked CBR value of the subgrade soil is of great importance, which is required to be determined as it helps in assessing the swelling potential and almost the actual strength of subgrade soil over the entire road length.
Though this conventional method helps in evaluating the strength of the subgrade soil by obtaining its soaked CBR value, but it is quite time consuming and laborious method and also its reproducibility is low [1]. Moreover, this test is costly as it involves a high level technical supervision and quality control assessment. Therefore, more samples are required to be tested in order to achieve better accuracy and to obtain proper idea about the soaked CBR value of subgrade materials over the entire length of the road which is quite difficult because it is difficult to take large number of samples. This would result in serious delay in the progress of the project, since in most situations the materials for earthwork construction come from highly variable sources. Any delay in construction inevitably leads to rise of project cost [1,[4][5][6].
In Pakistan, most of the roads are designed as flexible pavements. Nowadays, infrastructure development in the country, particularly in Sindh province is quite fast.
Development of road networks, particularly the highway is at its peak in order to connect the rural and urban areas, production and market places, and other basic infrastructures like hospitals, public buildings, public health and sanitation sector which includes proper water supply and sewage treatment systems, irrigation sector [4] etc. Due to the increasing development of road networks, it has become quite imperative to speed up the construction works and this CBR test may cause delay in the progress of the project. This research paper is written on Jamshoro Soil. Jamshoro is the capital of Jamshorodistrict, which includes the cities namely Kotri, Nooriabad, ThanoBula Khan and Jamshoro itself. It is located on the right bank of Indus River, approximately 18 km Northwest of Hyderabad and 150 km Northeast from Karachi, the Capital of Sindh Province.
The soil is dark yellow brown in color and mostly contains clay, silt and shale particles along with limestone mixed in it. Out of these, the major soil element encountered in this Jamshoro soil is shale. Shale is a fine-grained sedimentary rock that forms from the compaction of silt and clay-size mineral particles. This type of rock is very much fissile and laminated [7][8][9].
The Jamshoro soil has been observed to create many problems in highway works such as rutting due to the shale content in it. It is also found that this soil is very much problematic in the construction of roads and buildings because of its low bearing capacity as well as large changes in the volume due to its expansive nature.
The swelling potential of this soil is very much high and variable. The soil becomes stiff with an irregular increase in its plasticity and sticks to the rammer with the increase in moisture content due to which it is quite difficult to transfer the proctor compaction energy to the samples [7][8][9]. Similar problems are observed during the CBR testing of this soil. While determining the soaked CBR value, this soil shows varying swelling potential when The major benefit from this research outcome is that the developed correlations will be utilized for directly obtaining strength of Jamshoro soil instead of performing tests on this highly plastic soil, thus avoiding unnecessary consumption of time and delay in project construction. Moreover, this will provide an advantage to the designers and constructors as they will be knowing already that which important properties are required to be determined for knowing the accurate strength of soil and thus, they will only perform those tests which will determine those important properties instead of performing all tests.

Single Linear Regression Analysis
A SLRA provides an attempt to develop a correlation between two variables only in which one is the response (dependent) variable and other is the explanatory (independent) variable. In this research work, CBR is the dependent variable and each individual IP of soil is independent variable. Graph is plotted between CBR and IP and a suitable trend line is drawn through the plotted points for obtaining the value of coefficient of determination (R 2 ). The value of R 2 provides a measure of how well the future outcomes are likely to be predicted by the model [10]. Generally speaking, any correlation greater than 0.88 is usually considered as a best fit.

Multiple Linear Regression Analysis
A MLRA provides an attempt to develop a correlation between more than two variables. One is the response (dependent variable) and others are explanatory (independent) variables. In this research work, CBR is the dependent variable and all other IP are independent variables. In the equation, CBR value is the function of all other index properties. Mathematically: The equation will be created as follows: Whereb o , b 1 , b 2 , b 3 , b 4 , b n are constants, Y is CBR and, x 1 ,

EXPERIMENTAL PROGRAM
The samples for this research work have been collected from various places within the closed proximity of MUET  [11][12][13][14].
The soil classifications of these samples have been done according to AASHTO method. The results are given in Table 1 along with % finer passing from #200 sieve (%F) for each sample.

RESULTS AND DISCUSSION
Whereas, the Cu is the ratio of square of D30 by product of D60 and D10 and is given by Equation (4): If Cu is greater than 4-6 and Cc lies between 1 and 3, the soil is well graded otherwise it is poorly graded.

CORRELATIONS/MODELS
The

Correlations By Single Linear Regression Analysis
The correlations by SLRA were developed and are described in Model 1-11 ( Fig. 6-16) indicating linear relationship between the variables. Some models gave very low values of reliability R 2 . However, in this paper, all models are shown:

Model-1:Correlation of Unsoaked California Bearing
Ratio (CBR U ) With Liquid Limit: Fig. 6 represents a graph, which shows a correlation between unsoaked CBR and LL for all soil samples. The mathematical relation between the two parameters is shown in Equation (5)

Model-2: Correlation of Unsoaked California Bearing
Ratio with Plasticity Index: Fig. 7 represents a graph, which shows a correlation between unsoaked CBR and PI for all soil samples. The mathematical relation between the two parameters is shown in Equation (6)

Model-3: Correlation of Unsoaked California Bearing
Ratio with Optimum Moisture Content: Fig. 8 represents a graph, which shows a correlation between unsoaked CBR and OMC for all soil samples. The mathematical relation between the two parameters is shown in Equation (7). It can be seen that the reliability factor R 2 obtained from this equation is 0.3812, which is still not significant.

Model-4: Correlation of Unsoaked California Bearing
Ratio with Maximum Dry Density: Fig. 9 represents a graph, which shows a correlation between unsoaked CBR and MDD for all soil samples. The mathematical relation between the two parameters is shown in Equation (8). It can be seen that the reliability factor R 2 obtained from this equation is 0.4413, which is still not significant.

Model-5: Correlation of Unsoaked California Bearing
Ratio with %Finer Passing From #200 Sieve (%F): Fig. 10 represents a graph which shows a correlation between unsoaked CBR and % finer passing from #200 sieve for all soil samples. The mathematical relation between the two parameters is shown in Equation (9)

Model-7: Correlation of Soaked California Bearing Ratio
with Plasticity Index: Fig. 12 represents a graph, which shows a correlation between soaked CBR and PI for all soil samples. The mathematical relation between the two parameters is shown in Equation (11) Fig. 16 represents a graph, which shows a correlation between soaked CBR and unsoaked CBR for all soil samples [15]. The mathematical relation between the two parameters is shown in Equation (15)  On the other hand, the correlation between soaked and unsoaked CBR has been found to be a bettercorrelation with a value of R 2 = 0.5153.

Correlations By Multiple Linear Regression Analysis
This analysis has been performed by taking CBR as function of more than one independent variables [Equation (1)

VALIDATION ANALYSIS
From section 4, it is observed that high reliability for CBR prediction is observed from MLRA instead of SLRA. So now, equations of MLRA are utilized for obtaining relation between predicted and actual CBR (Table 6) Now, the graph between predicted and actual CBR (Soaked) along with line of equality is presented in Fig,   17. The trend line in Fig. 17 shows that the ratio of predicted to actual CBR value is 1 i.e. P/A =1. Points above this line of equality indicate those samples whose predicted CBR value is higher than their actual CBR value  The difference between experimental/actual and predicted CBR values is graphically shown below: Fig. 18 represents difference in values of predicted and actual CBR value in soaked condition for each soil sample in a graphical format. It can be seen that predicted CBR values of Samples 2, 5 and 6 under estimate their actual CBR values, but for Sample 1 and 7, predicted CBR values over estimate their actual CBR values. Fig. 18 depicts the results of Soaked CBR value obtained from laboratory results as well as model.  Now, the graph between predicted and actual CBR (Unsoaked) along with line of equality is presented in Fig. 19. It is observed that predicted CBR values of Sample 1, 5 and 7 slightly deviate from the line of equality while the remaining samples predicted CBR values scatters near the line of equality. Moreover, the predicted CBR values of Sample 1, 2 and 6 are higher than their actual CBR values while the predicted CBR values of Sample 5 and 7 are lower than their actual CBR values (