Abstract
Compressive strength and Young's modulus are key design parameters in rock engineering, essential for understanding the mechanical behavior of carbonate rocks. Understanding the mechanical behavior of carbonate rocks under varying load conditions is crucial for geotechnical stability analysis. In this paper, empirical relationships are developed to predict the mechanical properties of carbonate rocks. A series of uniaxial and triaxial compression experiments were conducted on carbonate rocks including limestone, dolostone, and granite from Wyoming. In addition, experimental data on different carbonate rocks from the literature are compiled and integrated into this study to evaluate the goodness of fit of our proposed empirical relationships in the prediction of compressive strength and Young's modulus of carbonate rocks. Regression analysis was used to develop predictive models for the uniaxial compressive strength (UCS), Young's modulus (E), and triaxial compressive strength (σ1) incorporating parameters such as the porosity (n) and confining pressure (σ3). The results indicated that the UCS and Young's modulus showed a power relationship with porosity (n), whereas the σ1 showed a linear relationship with n and σ3. Furthermore, an analytical model expanded from the wing crack model was applied to predict the σ1 of limestone based on the coefficient of friction, the initial level of damage, the initial flaw size, and the fracture toughness of the rock. The model showed a good predictability of the σ1 with a mean bias (i.e., the ratio of the measured to the predicted strength) of 1.07, indicating its reliability in accurately predicting the rock strength. This predictability is crucial for making informed engineering decisions, design optimization, and improving safety protocols in practical applications such as structural analysis and manufacturing processes.