Correlations between CBR index, using the modified optimum proctor characteristics and lateritic soils identification parameters

The selection of soils for construction of engineering structures is done on the basic of set number of criteria. In road construction, the criteria used are the value of the CBR index at 4 days imbibition. For earth dams and road embankments where materials should be compacted at their maximum dry density, we will adopt the criterion: the compaction characteristics at its optimum modified proctor. The determination of these criteria are very time consuming and can generate several delays which is inconsistent with the strategies of productivity of Publics Works companies. To reduce these delays, relations permitting us to predict their values from soil identification parameters should be developed. In this context, 1500 laboratory test results obtained from samples collected throughout the Cameroon territory were studied. Correlations which obtained were tested on around thirty results gave a prediction with error lower than 6.02%.


Introduction
Road infrastructure is an essential part of a country's economy: transportation of goods, displacement of users and evacuation or delivery of aid to the populations in distress.The mechanical properties of soils that support these infrastructures have a strong influence on their behavior, longevity and this is why they are used in the road design.The most commonly used parameter is the CBR (California Bearing Ratio) index at 4 days of imbibition, which is an indicator of the resistance of the soil used in road construction.A high value of this indicator means the soil used has a very good characteristic which implies the longevity of the road infrastructure.For earth dams or road embankments, the soils in the site should be compacted up to the maximum dry density.The parameters commonly used in measuring the compaction level of soils are: the characteristics at the optimum modified proctor   Practically, the CBR index (or the characteristics at the optimum Modified Proctor) of the subgrade of any road infrastructure must be determined at regular intervals following the longitudinal or transversal profiles of the road (or embankment).This requires to do several laboratories tests.On the other hand, if the subgrade or the embankment has poor characteristics, it may be necessary to do a mixture of different soils collected from several quarries, in order to obtain the desired soil characteristics.This reconstituted soil will be used as material for embankment.The tests that will be carried out on the soils from different quarries as well as the reconstituted soil is time consuming and this might cause several months of delay in a road construction project.Moreover, to obtain the CBR index of a soil at 4 days imbibition ( 4 j CBR ), it is necessary to carry out the following test: sedimentation, grain size analysis, plasticity, modified proctor, immediate CBR and the CBR at 4 days of imbibition.This globally requires delay time of about 250 hours.This delay time is very long and inconsistent with the criteria of productivity of Public Work Companies.
Considering the fact that a delay in a construction project of transport infrastructures will inevitably increase its cost, we will propose in this article two prediction models: one to estimate the CBR index at 4 days imbibition and the other to give the value of   at the optimum modified proctor when the soil identification parameters are known.
The evaluation of the CBR is one of the important tasks in the design of the road.In the absence of the appropriate infrastructures, many researchers had worked on the determination of this mechanical parameter in tropical countries.Several correlations had been proposed between the CBR and the local soils properties in Cameroon.The characteristics at the optimum modified proctor, represented by the optimum moisture content and the maximum dry density were determined in order to obtain a representative CBR value.The knowledge of these parameters had permitted to find some correlations between CBR (4 days of imbibition), characteristics at the optimum modified proctor and local soil index properties.
To perform these correlations, we also propose to determine the CBR index at 4 days imbibition and the value of at the optimum modified proctor when the soil identification parameters are known.
In this work, we describe the parameters of the developed correlations with the statistical analysis.Their significance is tested with local data using SAS software version 9.2 and the results are illustrated by the nonlinear multiple regression models to predict the measured local data when the soil identification parameters are known.We conclude our study with a summary and a short discussion.

Previous correlations
The prediction of the properties of a soil from some identification parameters is not something new.From past history, we observe that many empirical correlations have been developed between: the angle of friction by Mamba et al. (2013), the resistance at rupture by Goktepe, et al. (2008), the swelling index and the compressibility on one hand, the granular characteristics and the state parameters of soils on the other hand.We retain the following result:  The correlation of the characteristics of a soil at its optimum Proctor, have been given by the authors: Ugbe The common characteristics of these correlations, whether simple or multiple, results from the fact that: they are given in a linear regression form where R² is the coefficient of correlation (Table 1).
The advantage with these proposed models is that: they are simple and don't take into consideration all the grain size analysis parameters.Furthermore, they assume that the effect of all the predictors on the predicted values ( ) is linear.The reproach we have on these previous models is that: the soils of different classes can have the same CBR index (or same characteristics at the optimum modified proctor) and the nonlinearity between some parameters is not taken into consideration (nonlinearity between the percentage of fine particles, the plasticity index and the liquid limit).

Description of soils parameters
Soils can be described by three parameters:  Granular parameters;  Plasticity parameters;  State parameters.

Granular Parameters
The granularity of a soil in our model will be described by: maximum diameter of the particles max D , the percentage of gravel G, the percentage of sand S, the percentage of lemon L, the percentage of fine In this approach, we take into account a set of variables used for the classification of soils (the granular characteristics and plasticity parameters) and the state variables (for the prediction of the CBR4j).
The granularity of soils is represented by seven variables denoted by:

Proposed model
We are trying to predict the CBR index at 4 days imbibition ( Where Where ( 1 9) j j to m  are real.The used data, which were obtained from tests carried out on the Cameroon's lateritic soils, came from laboratories: of Geotechnics and Materials of the Yaounde National Advanced School of Engineering and from Labogenie.This data were obtained from standard tests realized on soil samples collected from the national territory.The results from each sample were exploited to enable their identification to be done using the twelve following variables:


In this work, we obtained a sample of 1500 individuals, identified by the data from the twelve described variables given by relation (4).The maximum, the minimums and averages values of described variables are summarized by Table 2 and three histograms as it is shown in Figures 1, 2 and 3.The outcome of this study is the entries data of the present approach using the SAS software version 9.2 (2009) in order to predict the CBR at 4 days of imbibition and the characteristics at the optimum modified proctor.
We used as criteria (SAS,2009), the values of the following parameters for the selection of the correlation:  The multiple coefficients of correlation R 2 .The correlation becomes more significant as the coefficient approaches 1.  Mallow's coefficient Cp.Good models are ones with small Cp values and/or values of Cp closer to the number of predictor variables. For the construction of the correlation matrix, we used Pearson product moment-correlation coefficient, RXY (where X and Y are variables) and the associated probability when we admit that the two variables (X and Y) are independent is such that rXY.This correlation matrix brings out the relations between the different variables of the model.X and Y are variables used for soil identification (4).
 The described variables that have an insignificant effect on the correlation are automatically neglected.

Proposed linear regression models
To evaluate the relationships between all described parameters, we obtain the following correlation matrix (Table 3): Table 3 Correlation matrix (the number: in the first line represent Pearson correlation coefficient rXYPearson and in the second line the associated probability when we admit that the two variables are independents)  The correlation between: optimum moisture content (Wopm) and variables Dmax, G, S, Cu, P80, L, A, Ip and WL as given by relation (7).In Figure 6, we show the trend between measured and estimated values of opm W .

Applications of the correlations on local data
In the previous section, the correlations as the function of several described variables have been constructed to predict the CBR at 4 days of imbibition and the characteristics at the optimum modified proctor.These correlations are applied on lateritic soils samples coming from: Dschang, Lom Pangar, Kumba, Yaoundé, Bakebe and Fontem which are the Cameroonians towns.These correlations predict the values of CBR4j,(Figure 7) γdopm ,(Figure 8) and Wopm ,(Figure 9) with an error lower than 6.02%, 1.68% et 4.70% respectively.
In order to calculate the error

Conclusion
Definitely, these proposed correlations can be used for the rapid selection of pits of laterite soils destined for road construction or as an indicator for the fabrication of reconstituted soils.Once the pits or the reconstituted soil have been selected, laboratories tests for the determination of the characteristics of the optimum modified proctor and CBR index have to be realized to enable the validity of the choices.

Compliance with ethical standards
level of deformation and a high mechanical resistance of the soils.

d
80 m P  (corresponding to the percentage of particles passing through the 80 m sieve), the percentage of clay A and the coefficient of uniformity is the diameter corresponding to n% of particles passing through).3.1.2.Plasticity ParametersThe parameters used to describe the plasticity of soils are [Mamba et al. (2013)]: liquid limit L W and the plasticity index P I .3.1.3.The state parametersFrom the state parameters describe by [Mamba M et al. (2013)], we shall retain here the ones which characterize the compaction of a soil at its optimum modified proctor.These parameters are: the maximum dry density the maximum diameter of the particles;  G , the percentage of gravel;  S , the percentage of sand;  L , the percentage of lemon;  A , the percentage of clay;  80 m P  , the percentage of particles passing through the 80μm sieve;  u C , the coefficient of uniformity;  The parameters of the plasticity of soils are denoted by;  LL , the Liquid Limit;  PI , the Plasticity Index;  The state parameters that characterize the compaction of soils at its optimum modified proctor are denoted by;  opm d  , the maximum dry density;  opm W , the optimum moisture contents.

Figure 1 Figure 2 Figure 3
Figure 1 Histogram of measured CBR at 4 days of imbibition

Figure 4 Figure 5
Figure 4 The trend of CBR4j index at 4 days of imbibition

Figure 6
Figure 6The trend of the optimum moisture content

Figure 7 Figure 8 Figure 9
Figure 7 Comparison between laboratory CBR and predicted CBR obtained from equation (5) at 4 days of imbibition

Table 2
Maximums, averages, minimums, variance inflation of the parameters of the studied samples (5)given by relation(5).In Figure4, we show the trend between measured and estimated values of CBR4j .