Is there Link between the Type of the Volumetric Strain Curve and Elastic Constants, Porosity, Stress and Strain Characteristics ?

The stress [crack damage stress (sigma (cd)) and uniaxial compressive strength (sigma (c))] and strain characteristics [maximum total volumetric strain (epsilon (cd)), axial failure strain (epsilon (af))], porosity (n) and elastic constants [elastic modulus (E) and Poisson's ratio (nu)] 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, sigma (cd) is less than the uniaxial compressive strength (sigma (c)). Type 2 has no reversal point, and the bulk volume of rock decreases until its failure occurs (i.e., sigma (cd) = sigma (c)). It is confirmed that the ratio between the elastic modulus (E) and the parameter lambda = n/epsilon (cd) strongly affects the crack damage stress (sigma (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 sigma (cd)/sigma (c) = 0.54-1 for carbonate rocks is wider than the range (0.71 < sigma (cd)/sigma (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, sigma (cd), nu, E/(1 - 2 nu), M (R) = E/sigma (c) and E/lambda. On the other hand, the type of volumetric strain curve is connected with the values of lambda and the ratio between the axial failure strain (epsilon (af)) and the maximum total volumetric strain (epsilon (cd)). It is argued that in case of small epsilon (af)/epsilon (cd)-small lambda, volumetric strain curve follows the type 2.