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 δ 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.