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Vipulanandan failure models to predict the tensile strength, compressive modulus, fracture toughness and ultimate shear strength of calcium rocks

Abstract In this study, over 1000 data from the literature were used to characterize and compare the density, strengths, modulus, fracture toughness, porosity and the ultimate shear strengths of the calcium rocks. The ranges of the densities for gypsum rock (CaSO4 2H2O) and limestone rock (CaCO3) were 2.10 to 2.83 and 1.70 to 2.75 gm/cm3, respectively. The compressive and tensile strengths of the gypsum and limestone rocks varied from 2 to 250 MPa and 1.8 to 25 MPa, respectively. The compressive modulus and Mode-1 fracture toughness of the gypsum and limestone rocks varied from 0.7 to 70 GPa, and from 0.03 to 2 MPa.m0.5, respectively. Vipulanandan correlation model was effective in relating the modulus of elasticity, fracture toughness with the relevant strengths of the rocks. A new non-linear Vipulanandan failure criterion was developed to not only better quantify the tensile strength, pure shear (cohesion) strength and to predict the maximum shear strength limit with applied normal stress on the gypsum and limestone rocks. The prediction of the failure models for the two rock types was also compared to the Mohr–Coulomb failure model. The Vipulanandan failure model predicts the maximum shear strength limit was, as the Mohr–Coulomb failure model does not have a limit on the maximum shear strength. With the Vipulanandan failure model based on the available data, the maximum shear strengths predicted for the gypsum and limestone rocks were 64 and 114 MPa, respectively.