The California Bearing Ratio (CBR) is a critical parameter utilized to assess the strength of subgrade or subbase materials in pavement design. It serves as a means to estimate the necessary thickness of subgrade layers. CBR is defined as the ratio of the resistance to penetration of a piston into a compacted soil sample, prepared at its optimum moisture content (OMC) with a penetration rate of 1.27 mm/min, compared to the resistance of a standard crushed rock sample at the same penetration depth.
CBR tests are typically conducted in both laboratory and field settings, under both soaked and unsoaked conditions. It is important to note that laboratory tests may have certain limitations, including potential inaccuracies resulting from disturbances during sample preparation. Consequently, the application of predictive models presents a more efficient and cost-effective approach to estimate CBR values by considering relevant soil parameters.
Recent studies have employed various techniques for predicting California Bearing Ratio (CBR), including linear models and multiple linear regression; however, it has been noted that the proposed regression equations did not achieve an acceptable level of correlation. Furthermore, these formulas have historically lacked generalized solutions and demonstrated limited accuracy in their predictions. This shortcoming may stem from the complex relationships between soil parameters and the application of inappropriate calculation methods.
With advancements in computational techniques, researchers have turned to a range of machine learning methodologies, such as artificial neural networks (ANN), genetic expression programming (GEP), support vector machines (SVM), multiple linear regression (MLR), and local polynomial regression (LPR) for CBR predictions. The results indicate that these machine learning algorithms demonstrate a significant improvement in accurately predicting the CBR of soil.
A study conducted by Lanh Si Ho and Van Quan Tran from the University of Transport Technology in Thanh Xuan district, Hanoi, Vietnam, focused on predicting the California Bearing Ratio (CBR) of stabilized soil containing industrial waste. The authors developed twelve distinct machine learning models, including artificial neural networks (ANN), gradient boosting (GB), extreme gradient boosting (XGB), random forest (RF), support vector machine (SVM), and K-nearest neighbors (KNN). Additionally, six hybrid models were created by combining these individual models with random restart hill-climbing optimization (RRHC), resulting in the following configurations: ANN-RRHC, GB-RRHC, XGB-RRHC, RF-RRHC, SVM-RRHC, and KNN-RRHC.
The study employed a dataset comprising 290 samples, characterized by eleven input parameters, including Liquid Limit (LL), Plasticity Index (PI), optimum moisture content (OMC), maximum dry density (MDD), coal ash, bagasse ash, groundnut shell ash, sawdust ash, quarry dust and cement. The dataset was strategically divided, allocating 70% for training purposes and 30% for testing. To assess model performance and prediction accuracy, K-Fold cross-validation was utilized, which is a well-established method aimed at minimizing bias within sampling processes. This cross-validation was conducted exclusively on the training set. Throughout the procedure, ten iterations were executed, with one subset designated for testing and nine subsets utilized for training in each iteration. The optimal model was identified by determining the configuration with the lowest error across these iterations.
The optimal hyperparameters utilized by all algorithms are as:
For ANN,
Activation = Relu; Hidden_layer_sizes_1 = 7; max_iter = 15000; solver = lbfgs.
For GB,
Number of estimators = 14; Learning rate = 0.3150; Max depth = 7; Max features = 8; Min samples split = 0.092; Min samples leaf = 0.052.
For RF,
Numberof estimators = 941; Max depth = 8; Max features = 4; Min samples split = 0.011; Min samples leaf = 0.001.
For XGB,
Number of estimators = 260; Learning rate = 0.606; Max depth = 8; min_split_loss = 6.
For KNN,
Number of neighbor = 33; algorithm = ball_tree; Leaf size = 2; P = 3.
For SVM,
C = 996; kernel = rbf; epsilon = 1.253.
The models were assessed according to the specified hyperparameter settings, with evaluations conducted based on R-squared, RMSE, and MAE to determine mean performance values. The Random Forest (RF) model achieved the highest prediction accuracy, with R² = 0.9614, RMSE = 3.4264%, and MAE = 1.7552%. This was closely followed by the RF-RRHC model, which recorded R² = 0.9602, RMSE = 3.4804%, and MAE = 1.8041%. The XGB-RRHC model achieved R² = 0.9582, RMSE = 3.5661%, and MAE = 1.8856%. Conversely, the Support Vector Machine (SVM) model yielded the lowest prediction accuracy among the evaluated models.
The evaluation of feature importance regarding input variables affecting the California Bearing Ratio (CBR) of stabilized soil was conducted using SHAP (SHapley Additive exPlanation) values. The SHAP value represents the mean marginal contribution of each input variable across all possible combinations. Input variables are ranked according to their SHAP values, with higher values indicating greater importance.
The analysis identified cement as the most significant input variable, positively influencing CBR due to its role in densifying soil and facilitating binding through hydration reactions. The Plasticity Index (PI) emerged as the second most important variable in the majority of models, with its influential effect on CBR being corroborated by previous studies. Sawdust ash ranked third in importance in specific models, though its ranking exhibited variability across different assessments. Optimum Moisture Content (OMC) and Maximum Dry Density (MDD) demonstrated moderate importance, but their rankings were inconsistent among the models. Other variables displayed varying levels of significance, lacking a clear consensus on their contributions to CBR performance. Overall, this analysis underscores the differing degrees of influence that these factors have on models predicting the CBR of stabilized
soil.
The concept of Individual Conditional Expectation (ICE) serves to enhance partial dependence plots (PDP) by offering a more nuanced analysis of the relationship between specific input variables and the output of machine learning models. In the context of predicting the California Bearing Ratio (CBR) of stabilized soil, the following observations have been made:
– The cement content plays a significant role in influencing the CBR, particularly up to approximately 2%, after which the impact begins to diminish.
– The relationship between CBR and the plasticity index (PI) exhibits a linear decrease up to a PI of 20%. Beyond this threshold, CBR appears to be largely independent of PI.
– Additional factors such as plastic limit, maximum dry density, sawdust ash, optimum moisture content, liquid limit, and quarry dust exhibit negligible effects on CBR.
– There is a slight increase in CBR with the addition of coal ash, groundnut shell ash, and bagasse ash, observed between 2% to 8% content, after which the CBR levels off.
The interrelationship among input variables has a considerable effect on the California Bearing Ratio (CBR) of stabilized soil. A partial dependence plot was employed to examine the interaction between the plasticity index (PI) and additional parameters, including cement content and dust. The analysis revealed that CBR is significantly influenced by both cement content and PI when these factors are at lower levels. In particular, as the cement content increases from 0% to 2%, there is a corresponding rise in CBR, particularly at lower PI values. However, once the cement content surpasses 2%, the CBR becomes largely independent of cement levels across all PI values. Additionally, the impact of dust and ashes on CBR was found to be minimal, while the dependence on PI remained significant for values below 15%. These findings underscore the importance of PI as a key variable that substantially affects CBR in stabilized soil, particularly at lower PI levels.
In conclusion, this study offers a comprehensive evaluation of the California Bearing Ratio (CBR) predictions for stabilized soil. The findings provide valuable practical insights into the CBR of stabilized soil.
Reference
Ho, L. S., & Tran, V. Q. (2022). Machine learning approach for predicting and evaluating California bearing ratio of stabilized soil containing industrial waste. Journal of Cleaner Production, 370, 133587.