Statistical Variations and New Correlation Models to Predict the Mechanical Behavior and Ultimate Shear Strength of Gypsum Rock

Abstract

In this study, over 1000 data from the several research studies was used to characterize and compare the density, strengths, modulus, flexural strength, porosity and the ultimate shear strengths of the calcium rocks. The gypsum rock data were statistically analyzed, quantified and compared with the limestone rock data. The ranges of the densities for gypsum rock (CaSO4·2H2O) and limestone rock (CaCO3) were 2.10 to 2.83 gm/cm3 and 1.70 to 2.75 gm/cm3, respectively. The compressive and tensile strengths of the gypsum and limestone rocks varied from 2 MPa to 250 MPa and 1.8 MPa to 25 MPa, respectively. Vipulanandan correlation model was effective in relating the modulus of elasticity, flexural strength, with the relevant strengths of the rocks. A new nonlinear Vipulanandan failure criterion was developed to better quantify the tensile strength, pure shear (cohesion) strength and 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 predicted 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 MPa and 114 MPa, respectively.

Keywords

• calcium rocks
• strength
• flexural strength
• failure model
• statistical analysis
• modeling