The study focuses on the bearing strength of subgrade soils strengthened with geosynthetic materials, which are used in road construction to improve weak soils through functions including separation, reinforcement, filtration and drainage. CBR is a key measure of subgrade bearing capacity and informs pavement design. Conventional soaked CBR testing can be slow and labor-intensive: specimens remain submerged for 96 hours, while Proctor compaction tests to determine optimum moisture content and maximum dry density can extend the work on an individual sample to five or six days. Heterogeneous site conditions may require testing many samples. The compiled dataset therefore offers a potential route to estimating CBR from properties that can be obtained more readily, although the study does not establish that the models can replace laboratory testing in routine practice.

To build the database, the researchers combined 90 soaked CBR observations from nine previously published studies. The records covered sandy and fine-grained soils classified under the Unified Soil Classification System, with samples representing several combinations of soil properties, geosynthetic materials and reinforcement configurations. Eleven predictors were used: liquid limit, plastic limit, plasticity index, maximum dry unit weight, optimum moisture content, percentage of fines, percentage of sand, geosynthetic tensile strength, number of reinforcement layers, position of the first layer and position of subsequent layers. Soaked CBR was the target variable. Across the dataset, CBR ranged from 1.32% to 88.3%, with a mean of 16.067%. Reinforcement tensile strength ranged from 0.75 to 140, and the number of layers ranged from one to three.

The model comparison used a common 80/20 partition, retaining 72 records for training and holding out 18 for final testing. Input scaling parameters were derived only from the training data and then applied unchanged to the test data, limiting information leakage. The authors evaluated plain and AOA-assisted versions of three learners under the same split: ANN, Ridge regression and XGBoost. AOA is a population-based metaheuristic inspired by the hunting behavior of Aquila eagles. It was used to tune model weights and hyperparameters, with mean squared error serving as the optimization objective for the neural-network training. The AOA configuration used a population of 150 and up to 500 generations, and the ANN had an 11–6–1 architecture: 11 inputs, six hidden neurons and one output neuron.

AOA improved the reported test performance of every base model, although the size of the gain differed. For ANN, R² increased from 0.929 to 0.945, MSE declined from 3.06 to 2.87 and MAE fell from 18.09 to 13.87. Ridge remained the weakest performer despite optimization: AOA-Ridge reached R² = 0.831, MSE = 4.90 and MAE = 42.81, compared with R² = 0.815, MSE = 5.17 and MAE = 47.09 for plain Ridge. The AOA-XGBoost model ranked first under the study’s weighted color-intensity scheme, which assigned weights of 0.5 to R², 0.3 to MSE and 0.2 to MAE. Its advantage was especially visible in MAE, which fell by 57.1% relative to plain XGBoost. For this dataset and modeling setup, AOA-assisted XGBoost was the most accurate of the six evaluated models.

Five-fold cross-validation on the training data was used to test whether the ranking depended on the particular hold-out split. AOA-XGBoost again performed best, with cross-validated R² = 0.8819 ± 0.0765, root mean squared error of 6.4218 ± 3.1846, MAE of 3.5217 ± 1.4826, mean absolute percentage error of 19.6842 ± 4.7315%, and A20 = 0.6427 ± 0.1186. The A20 metric represents the proportion of predictions falling within ±20% of the corresponding measured values. AOA-ANN ranked second, with R² = 0.8347 ± 0.1062, while AOA-Ridge had R² = 0.6487 ± 0.3628. The broadly consistent ordering between the held-out test and cross-validation results supports the reported advantage of the optimized tree-based model, but the cross-validated R² is substantially lower than the 0.980 obtained on the test set, illustrating the sensitivity of performance estimates in a small dataset.

Training behavior for the AOA-ANN was also monitored over 500 generations. Its mean squared error fell from approximately 177 initially to around 95 in the first 20 epochs, then declined in stages to approximately 58 at epoch 40, 50 near epoch 160 and 44 around epoch 190. Improvement slowed after roughly 200 epochs, reaching about 40 by epoch 250 and approximately 38 at the end. The authors interpreted this as convergence toward a near-stable solution, with further optimization offering limited gains. The study also published the final ANN weights and biases and provided a worked calculation for a non-plastic reinforced soil condition, yielding a predicted CBR of 41.35%. That example lies within the observed CBR range and was presented as an implementation demonstration, not as independent validation of the model outside the compiled data.

Two sensitivity methods, the Cosine Amplitude Method (CAM) and Garson’s algorithm, were used to estimate the relative influence of the 11 inputs. Their combined analysis assigned 29.4% of the sensitivity to the number of reinforcement layers and 21.8% to geosynthetic tensile strength. The position of the first reinforcement layer contributed 12.1%, followed by the position of subsequent layers at 9.9% and plastic limit at 7.2%; the other variables together accounted for 19.5%. Thus, the four reinforcement-related variables collectively represented more than 73% of the model’s reported sensitivity. CAM and Garson ranked some secondary variables differently, however, and a separate stability analysis gave dry unit weight the most consistent rank even as the two methods disagreed about the ordering of tensile strength, sand and fines. The percentages are model-based importance measures rather than estimates of causal effects or direct physical contributions to strength.

The most important limitation is the database’s size and composition. Only 90 records were assembled, and differences among source studies could not be eliminated in soil type, material characteristics, specimen preparation or testing conditions. Five-fold validation and the independent hold-out set reduce but do not remove the risk of overfitting, especially for a model with 11 inputs and relatively few observations. The models should therefore be used primarily within the parameter domain represented by the compiled data; predictions outside the reported ranges involve extrapolation. The neural network and XGBoost also retain elements of a black box, and the sensitivity results do not replace direct testing or mechanistic evaluation of soil–reinforcement interaction. The study’s strongest conclusion is therefore bounded but promising: within its experimental dataset and evaluation protocol, AOA-XGBoost was the most accurate and consistently top-ranked model for estimating soaked CBR, and larger independent validation will be needed before its performance can be established beyond the current scope.

Subject of Research: Optimization-assisted machine learning for predicting the California Bearing Ratio of geosynthetic-reinforced subgrade soil

Article Title: New hybrid models integrating the aquila optimizer with machine learning algorithms to predict the strength of geosynthetic-reinforced subgrade soil

Article References: Tiang, J.-J., Ateş, B., Eirgash, M. A., Zhao, Y., Anand, P., Sharma, A., & Lim, W. H. (2026). New hybrid models integrating the aquila optimizer with machine learning algorithms to predict the strength of geosynthetic-reinforced subgrade soil. Frontiers in Built Environment, 12, Article 1947550. https://doi.org/10.3389/fbuil.2026.1947550

Image Credits: AI Generated

DOI: 10.3389/fbuil.2026.1947550

Keywords: geotechnical engineering, machine learning, XGBoost, metaheuristic optimization, California Bearing Ratio, geosynthetics, subgrade soil, sensitivity analysis, pavement design, hybrid models, hybrid, models