Multivariate regression model for indirect estimation of uniaxial compressive strength of limestone

Abstract

The strength of rock under uniaxial compression, commonly known as Uniaxial Compressive Strength (UCS), plays a crucial role in various Geomechanical applications such as designing foundations, mining projects, slopes in rocks, tunnel construction, and rock characterization. However, sampling and preparation can become challenging in some rocks, making it difficult to determine the UCS of the rocks directly. Therefore, indirect approaches are widely used for estimating UCS. This study presents a multivariate Regression Model implemented in Matlab to calculate the UCS of Limestone rocks. To validate the proposed model’s effectiveness, a comprehensive dataset of 22 limestone rock samples is collected from the old city center of Annaba, Algeria. The dataset included measurements of Ultrasonic Pulse Velocity (UPV), Schmidt rebound number (SRN), and actual UCS values from laboratory tests. Three regression metrics, including Coefficient of Regression (R²), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE), were used to evaluate and compare the performance of the models. The results indicate a high predictive capability of the developed model, with an R² value of 0.848, an RMSE of 3.562 MPa, and an MAE of 2.962 MPa. To place these findings in the frame of the international state of the art, our model was compared with other established models from previous studies. Our model demonstrates significant practical applicability by effectively predicting UCS with a minimal number of parameters, showcasing a lower RMSE compared to many existing models.