1. Introduction
Transportation facilities are potential requirements for national development, which include industrialization, rural/urban development, and social-economic development [
1]. Nowadays, in developing nations, highways and transportation facilities schemes are gaining importance to improve living standards and comforts. In India, from 2014 to 2022, the development of national highways witnessed a phenomenal growth of 55% (from 91,287 km to 141,190 km). In most highways, one of the most challenging tasks is providing quality subgrade soil. In this context, many projects depend on locally available soils or treated soils [
2,
3,
4].
Lateritic soils and expansive clays are most common soils found globally. Most road projects on expansive clays often use strong subbase material and subgrade soil containing a montmorillonite mineral, which offers high swelling and shrinkage and is unsuitable for highway or building projects [
5,
6]. Under wet conditions, they can swell and lose their strength. To counter volume change behavior of black cotton soils, many modification techniques are in practice, such as mechanical stabilization and chemical stabilization [
7,
8,
9]. Moreover, these techniques enhance the index and engineering properties of clays due to the chemical reaction in the clays blended with chemical additives and gradation improvement with the addition of non-cohesive granular materials [
7,
8]. In expansive clay blends with additives such as cement, lime, CaCl
2, fly ash, rice husk ash, and other pozzolanic additives, at certain dosages of these additives possess improvement in grain size and plasticity behavior [
10,
11,
12]. The chemically altered blends exhibit larger particle sizes than the montmorillonite clay, probably conforming to kaolinite and illite sizes. An interesting observation was montmorillonite could behave like kaolinite and illites.
On the other hand, Lateritic soils are created by the in-situ weathering and disintegrating rocks in tropical and subtropical locations with heat and humid climates. Lateritic are extensively weathered and changed residual soils. These soil formations are frequently applied as building materials for civil engineering projects. The characteristics of lateritic residual soils vary from location to location owing to variations in the prevalent geological settings, climatic circumstances, and mineral types. In India, most of the highway projects rely on the lateritic soils even though huge variation in geotechnical characteristics.
In pavements, assessment of soil subgrade, and design of pavements, the California bearing ratio (CBR) test plays a vital role [
13]. However, determining the CBR values in subgrade soil samples is time-consuming, especially for large-scale highway projects [
14]. Moreover, the CBR of subgrades is affected by many factors, such as grain size distribution, compaction effort, moisture content, and plasticity characteristics of the soils [
15,
16,
17]. So, in this context, many others developed a correlation between the CBR values and the gradation distribution and plasticity characteristics [
18,
19,
20]. In the case of chemically altered clays, the volume change of clays is markedly reduced, which can lead to dense phases of the blends and improves the densities [
21,
22]. Densities and moisture content of the blended clays are described as the most important parameters to evaluate the CBR value [
12].
Sharma and Sivapullaiah [
23] carried out an experimental investigation to evaluate the CBR values with varying densities and moisture content to describe the significant relationships between the compaction characteristics and CBR. The CBR values and densities correlations illustrate significant correlation coefficients of 0.879. Vinod et al. [
24] reported that compaction efforts affect the CBR value of soils, and the correlations developed between the CBR value and energy ratio were dependent on the compaction energy and marginally dependent on the soil type. The wetting and drying effect on the soils influence the CBR value; the rate of change of the CBR value on the dry side of optimum (before optimum moisture content (OMC)) is more than 3 to 7 times wet side of optimum [
25,
26].
In recent years, correlations made by traditional approaches such as statistical correlations and regression analysis were surpassed by emerging artificial intelligence (AI) techniques [
27,
28]. The main asset of the AI techniques is the potential learning process of datasets without any assumption or uncertainty to improve the estimation model with accuracy. Nowadays, for predicting the CBR values of soils, a few AI techniques, including both supervised learning and unsupervised learning techniques, are emerging to reduce rigorous testing and time-consuming tests. Notably, researchers have employed artificial neural networks (ANN) to predict the CBR value of soils [
15,
16,
17,
29,
30]. The CBR value of soils was successfully predicted using the ANN, and the sensitivity analysis of the input variable revealed that the dry density values demonstrated the most effective parameters in the prediction model [
15]. Backpropagation neural networks (BP-ANN) are a hybrid tool that efficiently predicts the CBR values of chemically treated soils [
17]. In the case of blended pond ash clays, the curing period of the blended clays is the most effective parameter that influences the CBR value predicted using the ANN [
29]. Meanwhile, the genetic algorithm, support vector machine, and particle swarm optimization (PSO) algorithm have generalization capability and rational structure that can predict non-linear problems with convergent results [
31,
32,
33]. The genetic algorithm successfully indicated the CBR value and amount of additive (fly ash) required to attain a fixed CBR value [
34].
In previous studies, when a CBR was predicted using index properties of soils, different parameters were considered to achieve the CBR value of soils [
32,
33]. The parameters influencing the CBR, and prediction equations are provided in the
Table 1. These parameters include grain size proportions, liquid limit (LL), plastic limit (PL), OMC, and maximum dry density (MDD). The parameters showed to have effect on the penetration resistance of the subgrade soil. The AI tools described above, including genetic programme (GP), PSO, radial basis network (RBN), and ANN demonstrated better performance with R
2 value ranging from 0.842 to 0.918, based on the nature of the dataset. The CBR has been estimated in numerous earlier research works utilizing soil factors such as OMC, MDD, LL, PL, plasticity index (PI), gravel (G), sand (S), coarse sand (CS), fine sand (FS), fines (F), specific gravity, lime sludge content (LS), and lime content (L). The three variables most frequently employed as input for predicting the CBR value of soils are the grain size distribution, plasticity characteristics, and compaction characteristics, as summarized in
Table 1. In this study, the CBR prediction of soils using the ELM considering reliable field dataset includes the information about gradation distribution of soils, plasticity characteristics, and compaction characteristics.
By integrating machine learning and optimization, an enhanced tool can be developed to obtain acceptable prediction results compared with earlier methods. Therefore, an integrated extreme learning machine-cooperation search optimizer (ELM-CSO) model is proposed in this research to predict the CBR value of subgrade soils. This article also explores the efficacy of the current model with the standard ELM. The CSO algorithm is used in the process of the training of the ELM to find its optimal parameters to estimate the CBR from known input variables. This integrated method is adaptable for missing data to predict the CBR whenever it is required. The comparisons with the ELM in terms of R, R2, and RMSE values illustrate the improvements of the proposed scheme for prediction studies. Further, the optimal parameters achieved at a specific training rate, activation function, and other selective parameters of the ELM produce significant improvements in the estimation of the CBR at other choices.
5. Conclusions
CBR is a crucial statistic in highway construction projects for figuring out how thick the pavement layers should be. Typically, subgrade soil samples are tested in laboratories under wet conditions for three days, which is both time intensive and costly. This develops effective AI models for predicting the CBR of lateritic soils based on the experimental dataset in place of the time-consuming task of performing actual laboratory tests. It is important to note that the wet CBR estimation can eliminate the need for costly and time-consuming laboratory testing. To perform this testing, experimental CBR data and fine-grained soils were acquired from an ongoing highway project in India that ran from Kovvuru to Gundugolanu (NH-216 (A)) and utilized to create an effective prediction solution.
The current article used soft computing to predict the CBR indices of the lateritic soils with considerable variability. Individual ELMs and ELM paired with an ELM-CSO were suggested for this purpose. The proposed models’ predictability and performance were evaluated using the minimize MAE, MSE, and RMSE or maximize R and R2 criteria.
The findings indicated that both suggested models could anticipate the CBR of lateritic soils, hence avoiding the need for extensive experimentation and saving time. According to experimental findings, the ELM-CSO model had the best prediction ability, with R2 = 0.996, RMSE = 0.479, and average error (%) = 2.622. These results outperform those from the ELM model by a wide margin; because of this, combining the ELM and CSO can improve the performance of the ELM model and is recommended to be employed.
The current models’ primary benefits significantly reduced computational costs and improved predicted accuracies. The created prediction model is useful for calculating the CBR of lateritic soils under wet conditions. Additionally, choosing or evaluating the lateritic soils’ CBR will be simple for academics and practitioners. Here, it appears to be quite successful in estimating the saturated CBR by utilizing the lateritic soil properties, such as gradation distribution, plasticity characteristics, and compaction characteristics of soils. However, the ELM-CSO model, which is the current model, can be suggested as a viable option for predicting the CBR and is also helpful in assessing suitable lateritic cushion over expansive clays, based on the results.