Young’s modulus (E) is essential for predicting the behavior of materials under stress and plays an important role in the stability of surface and subsurface structures. E has a wide range of applications in mining, geology, civil engineering, etc.; for example, coal and metal mines, tunnels, foundations, slopes, bridges, buildings, drilling, etc. This study developed a novel machine learning regression model, namely an extreme gradient boosting (XGBoost) to predict the influences of four inputs such as uniaxial compressive strength in MPa; density in g/cm³; p-wave velocity (Vp) in m/s; and s-wave velocity in m/s on two outputs, namely static Young’s modulus (E_s) in GPa; and dynamic Young’s modulus (E_d) in GPa. Using a series of basic statistical analysis tools, the accompanying strengths of each input and each output were systematically examined to classify the most prevailing and significant input parameters. Then, two other models i.e., multiple linear regression (MLR) and artificial neural network (ANN) were employed to predict E_s and E_d. Next, multiple linear regression and ANN were compared with XGBoost. The original dataset was allocated as 70% for the training stage and 30% for the testing stage for each model. To improve the performance of the developed models, an iterative 10-fold cross-validation method was used. Therefore, based on the results XGBoost model has revealed the best performance with high accuracy (E_s: correlation coefficient (R²) = 0.998; E_d: R² = 0.999 in the training stage; E_s: R² = 0.997; E_d: R² = 0.999 in the testing stage), root mean square error (RMSE) (E_s: RMSE = 0.0652; E_d: RMSE = 0.0062 in the training stage; E_s: RMSE = 0.071; E_d: RMSE = 0.027 in the testing stage), RMSE-standard deviation ratio (RSR) index value (E_s: RSR = 0.00238; E_d: RSR = 0.00023 in the training stage; E_s: RSR = 0.00304; E_d: RSR = 0.001 in the testing stage) and variance accounts for (VAF) (E_s: VAF = 99.71; E_d: VAF = 99.99 in the training stage; E_s: VAF = 99.83; E_d: VAF = 99.94 in the testing stage) compared to the other developed models in this study. Using a novel machine learning approach, this study was able to deliver substitute elucidations for predicting E_s and E_d parameters with suitable accuracy and runtime.

The uniaxial compressive strength (UCS) of rock is one of the essential data in engineering planning and design. Correctly testing UCS of rock to ensure its accuracy and authenticity is a prerequisite for assuring the design of any rock engineering project. UCS of rock has a broad range of applications in mining, geotechnical, petroleum, geomechanics, and other fields of engineering. The application of the gradient boosting machine learning algorithms has been rarely used, especially for UCS prediction, and has performed well, based on the relevant literature of the study. In this study, four gradient boosting machine learning algorithms, namely, gradient boosted regression (GBR), Catboost, light gradient boosting machine (LightGBM), and extreme gradient boosting (XGBoost), were developed to predict the UCS in MPa of soft sedimentary rocks of the Block‐IX at Thar Coalfield, Pakistan, using four input variables such as wet density (ρ_w) in g/cm³; moisture in %; dry density (ρ_d) in g/cm³; and Brazilian tensile strength (BTS) in MPa. Then, 106‐point dataset was allocated identically for each algorithm into 70% for the training phase and 30% for the testing phase. According to the results, the XGBoost algorithm outperformed the GBR, Catboost, and LightGBM with coefficient of correlation (R²) = 0.99, mean absolute error (MAE) = 0.00062, mean square error (MSE) = 0.0000006, and root mean square error (RMSE) = 0.00079 in the training phase and R² = 0.99, MAE = 0.00054, MSE = 0.0000005, and RMSE = 0.00069 in the testing phase. The sensitivity analysis showed that BTS and ρ_w are positively correlated, and the moisture and ρ_d are negatively correlated with the UCS. Therefore, in this study, the XGBoost algorithm was shown to be the most accurate algorithm among all the investigated four algorithms for UCS prediction of soft sedimentary rocks of the Block‐IX at Thar Coalfield, Pakistan.

Drilling rate index (DRI) is a fundamental parameter in the investigation of rock drillability, as drillability is considered one of the main problems in rock engineering. Several researchers have continuously tried to analyze and correlate rock DRI, but the problem remains unchanged. This study elucidates the machine learning approaches, namely long short term memory (LSTM), simple recurrent neural network (RNN) and random forest algorithm (RFA) to predict DRI of rocks using multivariate inputs, that is, uniaxial compressive strength in MPa; Brazilian tensile strength (BTS) in MPa; brittleness value (S₂₀); Sievers’ J value (S_j); modulus ratio (MR); shore hardness (SH), porosity (n) in %; shimazeks F abrasitivity in N/mm; and equivalent quartz content in %. For all proposed methods, the original dataset was divided into 70% for training and the remaining 30% for testing. Next, the performance indices, such as correlation coefficient (R²), root mean square error (RMSE), variance accounts for (VAF) and a-20 index of each proposed method were determined to examine the accuracy of the predicted data. In this study, according to the results of LSTM, simple RNN and RFA methods, the LSTM revealed the best prediction output for DRI with the strongest R², the lowest RMSE, the largest VAF and an appropriate a-20 index values as 0.999, 0.13416, 0.997, and 0.999 in the training stage and 0.998, 0.19479, 0.996, and 0.997 in the testing stage, respectively. Therefore, LSTM is an applicable machine learning approach that can be applied to accurately predict the DRI.

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 of rock engineering projects. E has broad applications in the stability of structures in mining, petroleum, geotechnical engineering, etc. E can be determined directly by conducting laboratory tests, which are time consuming, and require high-quality core samples and costly modern instruments. Thus, devising an indirect estimation method of E has promising prospects. In this study, six novel machine learning (ML)-based intelligent regression models, namely, light gradient boosting machine (LightGBM), support vector machine (SVM), Catboost, gradient boosted tree regressor (GBRT), random forest (RF), and extreme gradient boosting (XGBoost), were developed to predict the impacts of four input parameters, namely, wet density (ρ_wet) in gm/cm³, moisture (%), dry density (ρ_d) in gm/cm³, and Brazilian tensile strength (BTS) in MPa on output E (GPa). The associated strengths of every input and output were systematically measured employing a series of fundamental statistical investigation tools to categorize the most dominant and important input parameters. The actual dataset of E was split as 70% for the training and 30% for the testing for each model. In order to enhance the performance of each developed model, an iterative 5-fold cross-validation method was used. Therefore, based on the results of the study, the XGBoost model outperformed the other developed models with a higher accuracy, coefficient of determination (R² = 0.999), mean absolute error (MAE = 0.0015), mean square error (MSE = 0.0008), root mean square error (RMSE = 0.0089), and a20-index = 0.996 of the test data. In addition, GBRT and RF have also shown high accuracy in predicting E with R² values of 0.988 and 0.989, respectively, but they can be used conditionally. Based on sensitivity analysis, all parameters were positively correlated, while BTS was the most influential parameter in predicting E. Using an ML-based intelligent approach, this study was able to provide alternative elucidations for predicting E with appropriate accuracy and run time at Thar coalfield, Pakistan.

The safe and sustainable design of rock slopes, open-pit mines, tunnels, foundations, and underground excavations requires appropriate and reliable estimation of rock strength and deformation characteristics. Cohesion (𝑐) and angle of internal friction (𝜑) are the two key parameters widely used to characterize the shear strength of materials. Thus, the prediction of these parameters is essential to evaluate the deformation and stability of any rock formation. In this study, four advanced machine learning (ML)-based intelligent prediction models, namely Lasso regression (LR), ridge regression (RR), decision tree (DT), and support vector machine (SVM), were developed to predict 𝑐 in (MPa) and 𝜑 in (°), with P-wave velocity in (m/s), density in (gm/cc), UCS in (MPa), and tensile strength in (MPa) as input parameters. The actual dataset having 199 data points with no missing data was allocated identically for each model with 70% for training and 30% for testing purposes. To enhance the performance of the developed models, an iterative 5-fold cross-validation method was used. The coefficient of determination (R²), mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and a10-index were used as performance metrics to evaluate the optimal prediction model. The results revealed the SVM to be a more efficient model in predicting 𝑐 (R² = 0.977) and 𝜑 (R² = 0.916) than LR (𝑐: R² = 0.928 and 𝜑: R² = 0.606), RR (𝑐: R² = 0.961 and 𝜑: R² = 0.822), and DT (𝑐: R² = 0.934 and 𝜑: R² = 0.607) on the testing data. Furthermore, to check the level of accuracy of the SVM model, a sensitivity analysis was performed on the testing data. The results showed that UCS and tensile strength were the most influential parameters in predicting 𝑐 and 𝜑. The findings of this study contribute to long-term stability and deformation evaluation of rock masses in surface and subsurface rock excavations.

Sedimentary rocks provide information on previous environments on the surface of the Earth. As a result, they are the principal narrators of the former climate, life, and important events on the surface of the Earth. The complexity and cost of direct destructive laboratory tests adversely affect the data scarcity problem, making the development of intelligent indirect methods an integral step in attempts to address the problem faced by rock engineering projects. This study established an artificial neural network (ANN) approach to predict the uniaxial compressive strength (UCS) in MPa of sedimentary rocks using different input parameters; i.e., dry density (ρ_d) in g/cm³, Brazilian tensile strength (BTS) in MPa, and wet density (ρ_wet) in g/cm³. The developed ANN models, M1, M2, and M3, were divided as follows: the overall dataset, 70% training dataset and 30% testing dataset, and 60% training dataset and 40% testing dataset, respectively. In addition, multiple linear regression (MLR) was performed for comparison to the proposed ANN models to verify the accuracy of the predicted values. The performance indices were also calculated by estimating the established models. The predictive performance of the M2 ANN model in terms of the coefficient of determination (R²), root mean squared error (RMSE), variance accounts for (VAF), and a20-index was 0.831, 0.27672, 0.92, and 0.80, respectively, in the testing dataset, revealing ideal results, thus it was proposed as the best-fit prediction model for UCS of sedimentary rocks at the Thar coalfield, Pakistan, among the models developed in this study. Moreover, by performing a sensitivity analysis, it was determined that BTS was the most influential parameter in predicting UCS.