Elastic modulus (E) is a key parameter in predicting the ability of a material to withstand pressure and plays a critical role in the design process of rock-related projects. E has broad applications in the stability of structures in mining, petroleum, geotechnical engineering, etc. Accurate estimation of deformation properties of rocks, such as E, is very important for the design process of any underground rock excavation project. Intelligent indirect techniques for designing and excavating underground structures make use of a limited amount of data for design, saving time and money while ensuring the stability of the structures. This study has economic and even social implications, which are integral elements of sustainability. Moreover, this paper aims to determine the stability of underground mine excavation, which may otherwise result in a disturbed overlying aquifer and earth surface profile, adversely affecting the environment. E provides insight into the magnitude and characteristics of the rock mass deformation due to changes in the stress field. Deformation and behavior of different types of rocks have been examined by different scholars [1,2,3,4]. Usually, there are two common methods, namely, direct (destructive) and indirect (non-destructive), to calculate the strength and deformation of rocks. Based on the principles suggested by ISRM (International Society for Rock Mechanics) and the ASTM (American Society for Testing Materials), direct evaluation of E in the laboratory is a complex, laborious, and costly process. Simultaneously, in the case of fragile, internally broken, thin, and highly foliated rocks, the preparation of a sample is very challenging [5]. Therefore, attention should be given to evaluate E indirectly by the use of rock index tests.

Several authors have developed prediction frameworks to overcome these limitations by using machine learning (ML)-based intelligent approaches such as multiple regression analysis (MRA), artificial neural network (ANN), and other ML methods [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Advances in ML have so far been driven by the development of new learning algorithms and theories, as well as by the continued explosion of online data and inexpensive computing [22]. Similarly, Waqas et al. used linear and nonlinear regression, regularization and ANFIS (using a neuro-fuzzy inference system) to predict the dynamic E of thermally treated sedimentary rocks [23]. Abdi et al. developed ANN and MRA (linear) models, including porosity (%), dry density (γd) (g/cm³), P-wave velocity (Vp) (km/s), and water absorption (Ab) (%) as input features to predict the rock E. According to their results, the ANN model showed high accuracy in predicting E compared to the MRA [10]. Ghasemi et al. evaluated the UCS and E of carbonate rocks by developing a model tree-based approach. According to their findings, the applied method revealed highly accurate results [24]. Shahani et al. developed a first-time XGBoost regression model in combination with MLR and ANN for predicting E of intact sedimentary rock and achieved high accuracy in their results [25]. Ceryan applied the minimax probability machine regression (MPMR), relevance vector machine (RVM), and generalized regression neural network (GRNN) models to predict the E of weathered igneous rocks [26]. Umrao et al. determined strength and E of heterogeneous sedimentary rocks using ANFIS based on porosity, Vp, and density. Thus, the proposed ANFIS models showed superb predictability [27]. Davarpanah et al. established robust correlations between static and dynamic deformation properties of different rock types by proposing linear and nonlinear relationships [28]. Aboutaleb et al. conducted non-destructive experiments with SRA (simple regression analysis), MRA, ANN, and SVR (support vector regression) and found that ANN and SVR models were more accurate in predicting dynamic E [29]. Mahmoud et al. employed an ANN model for predicting sandstone E. In that study, 409 datasets were used for training and 183 datasets were used for model testing. The established ANN model exposed highly accurate results (coefficient of determination (R²) = 0.999) and the lowest mean absolute percentage error ((AAPE) = 0.98) in predicting E [30]. Roy et al. used ANN, ANFIS, and multiple regression (MR) to predict the E of CO₂ saturated coals. Thus, ANN and ANFIS outperformed the MR models [31]. Armaghani et al. predicted E of 45 main range granite samples by applying the ANFIS model in comparison with MRA and ANN. Based on their results, ANFIS proved to be an ideal model against MRA and ANN [32]. Singh et al. proposed an ANFIS framework for predicting E of rocks [33]. Köken predicted the deformation properties of rocks, i.e., tangential E (E_ti) and tangential Poisson’s ratio (v_ti) of coal-bedded sandstones located in the Zonguldak Hard Coal Basin (ZHB), northwestern Turkey, using various statistical and soft computing methods such as different regression and ANN evaluations including the physicomechanical, mineralogical, and textural properties of the rocks. According to this analysis, the remarkable results were that the mineralogical characteristics of the rock have a significant influence on the deformation properties. In addition to comparative analysis, ANN was considered as a more effective tool than regression analysis in predicting E_ti and v_ti of coal-bed sandstones [34]. Yesiloglu-Gultekin et al. used the different ML-based regression models such as NLMR, ANN, and ANFIS, and 137 datasets using unit weight, porosity, and sonic velocity to indirectly determine E of basalt. Based on the results and comparisons of various performance matrices such as R², RMSE, VAF, and a20-index, ANN was successful in predicting E over NLMR and ANFIS [35]. Rashid et al. used non-destructive tests, i.e., MLR and ANN, to estimate the Q-factor and E for intact sandstone samples collected from the Salt Range region of Pakistan. The ANN model predicted Q-factor (R² = 0.86) and E (R² = 0.91) more accurately than MLR regression for Q-factor (R² = 0.30) and E (R² = 0.36) [36]. E was predicted using RF by Matin et al. For comparison, multivariate regression (MVR) and generalized regression neural network (GRNN) were used for the prediction of E. The input V_p-R_n was used for E. According to their results, RF yielded more satisfactory conclusions than MVR and GRNN [37]. Cao et al. used an extreme gradient boosting (XGBoost) integrated with the firefly algorithm (FA) model for predicting E. consequently, the proposed model was appropriate for predicting E [17]. Yang et al. developed the Bayesian model to predict the E of intact granite rocks; thus, the model performed with satisfactory predicted results [38]. Ren et al. developed several ML algorithms, namely, k-nearest neighbors (KNN), naive Bayes, RF, ANN, and SVM, to predict rock compressive strength by ANN and SVM with high accuracy [39]. Ge et al. determined rock joint shear failures using scanning and AI techniques. Thus, the developed SVM and BPNN were considered as sound determination methods [40]. Xu et al. developed several ML algorithms, namely, SVR, nearest neighbor regression (NNR), Bayesian ridge regression (BRR), RF, and gradient tree boosting regression (GTBR), to predict microparameters of rocks by RF with high accuracy [41].

Based on the above literature and the limitations of the conventional predictive methods, a single model has low robustness, cannot achieve ideal solutions for all complex situations, and its performance varies with the input features. Therefore, authors have endeavored to use ML-based intelligent models that integrate multiple models to overcome the drawbacks of individual models and play a key role in determining the accuracy of the corresponding data for tests performed in the laboratory. However, there are few studies in predicting E. In addition, there are no comprehensive studies on the selection and application of such models in E prediction. To address this gap, this study developed six models based on an intelligent prediction approach, namely, light gradient boosting machine (LightGBM), support vector machine (SVM), Catboost, gradient boosted tree regressor (GBRT), random forest (RF), and extreme gradient boosting (XGBoost) to predict E, including wet density (ρ_wet) in gm/cm³, moisture in %, dry density (ρ_d) in gm/cm³, and Brazilian tensile strength (BTS) in MPa as input features under intricate and unsteady engineering situations. Next, 70% of the actual dataset of 106 is used for training and 30% for testing each model. To enhance the performance of the developed models, a repetitive 5-fold cross-validation approach is used. Intelligent prediction of E of sedimentary rocks from Block-IX of Thar coalfield has been applied for the first time. To the best of the author’s knowledge, application of intelligent prediction techniques in this scenario is lacking. Figure 1 depicts a systematic ML-based intelligent approach for predicting E.