Is there link between the type of the volumetric strain curve and elastic constants, porosity, stress and strain characteristics?

The stress [crack damage stress (σ _cd) and uniaxial compressive strength (σ _c)] and strain characteristics [maximum total volumetric strain (ε _cd), axial failure strain (ε _af)], porosity (n) and elastic constants [elastic modulus (E) and Poisson's ratio (ν)] and their ratios were coordinated with the existence of two different types (type 1 and type 2) of volumetric strain curve. Type 1 volumetric strain curve has a reversal point and, therefore, σ _cd is less than the uniaxial compressive strength (σ _c). Type 2 has no reversal point, and the bulk volume of rock decreases until its failure occurs (i.e., σ _cd = σ _c). It is confirmed that the ratio between the elastic modulus (E) and the parameter λ = n/ε _cd strongly affects the crack damage stress (σ _cd) for both type 1 and type 2 volumetric strain curves. It is revealed that heterogeneous carbonate rock samples exhibit different types of the volumetric strain curve even within the same rock formation, and the range of σ _cd/σ _c = 0.54-1 for carbonate rocks is wider than the range (0.71 < σ _cd/σ _c < 0.84) obtained by other researchers for granites, sandstones and quartzite. It is established that there is no connection between the type of the volumetric strain curve and values of n, E, σ _cd, ν, E/(1 - 2ν), M _R = E/σ _c and E/λ. On the other hand, the type of volumetric strain curve is connected with the values of λ and the ratio between the axial failure strain (ε _af) and the maximum total volumetric strain (ε _cd). It is argued that in case of small ε _af/ε _cd-small λ, volumetric strain curve follows the type 2.