A New Approach to the Modeling of the Pressure Dependency of the Strength of Rocks

Based on the hypothesis that shearing stresses and normal tensile stresses both play a decisive role in fracturing and brittle failure of rock material, a novel strength criterion was developed in one of the earlier works of the author. In the criterion, a certain parameter ν′ occurs which depends on the structure of the material. Originally, the parameter was treated as a constant, which resulted in a linear form of the strength function ^F σ ₁ = f(σ ₃), where σ ₃ = σ ₂. Although the linear strength criterion is sometimes found to be applicable to various particular rock materials, it is not, in general, of a universal character. Analysis of the triaxial test results for 75 different sandstones revealed that parameter ν′ usually increases in an exponential or linear manner as confining pressure increases, and only in isolated cases does it seem to be independent of the confining pressure. For these three types of function ν′ = f(p) appropriate strength criteria ^F σ ₁ = f(σ ₃) are given in the present paper. These criteria were used to fit all of the collected empirical data sets. In general, a very good fit to the data was obtained.