Relation between normalized axial stress and failure strain in heterogeneous carbonate rocks exhibiting large axial strains

A semi-analytical equation for the modeling of stress-strain relationship for heterogeneous carbonate rocks exhibiting large axial strains (ε _af>1%) is formulated. The equation is derived by modifying the stress-strain model based on Haldane's distribution proposed by Palchik (2006) for carbonate rocks exhibiting ε _af ≤ 1%. The developed exponential model is used to relate normalized axial stress (σ _a/σ _c) over the whole pre-failure strain range to current axial strain (ε _a) and failure strain (ε _af). For carbonate rocks exhibiting ε _af>1%, the value of pre-calculated parameter d involved in the stress-strain model is not constant, but dependent on the failure strain value (ε _af). The normalized stress-strain model can be used to calculate the failure strain in terms of uniaxial compressive strength and stress-strain measurement at one point only. The advantages of the failure strain model and ways of its use in engineering practice are discussed.