Determination of a New Failure Criterion for Rock Mass and Concrete

The present investigation is based on a new quadratic equation that links the principal stresses σ₁ and σ₃ at the moment of failure, which allows to obtain the strength in rocks and brittle materials such as concrete. Through this new empirical two-dimensional failure criterion, the normal stress acting on the fracture plane is determined in the first calculation phase by solving the first order linear differential equation, and subsequently the shear streng‘th envelope. To facilitate the calculations, the expression that relates the major and minor principal stresses σ₁ and σ₃ at failure are defined for a parabolic equation and presented in normalized form. Thus, the algebraic curve is expressed as a function of (σ₃/σ_c) and the parameter ξ. Where, σ_crepresents the uniaxial compressive strength of intact rock (rock matrix) or concrete at 28 days, \(f_{c}^{{^{\prime}}}\), and on the other hand, ξ = (σ_t/σ_c) is a dimensionless parameter whose quotient is obtained by dividing the tensile strength σ_t by σ_c. Through the procedure described on this research (Focus Procedure) the parameters k₁ and k₂ that relate the principal stresses are determined with a good approximation grade through the relation ξ = (σ_t/σ_c), both in the intact rock condition as a function of rock mass quality index. All of this, with the additional advantage, that it is not required to know the interval of the principal failure stress (σ₃, σ₁) through the experimental tests.