The objective of this study is the determination of the various stages of deformation of brecciated marbles, under uniaxial compression, and the application of regression techniques, to investigate the relations of these stages, with physical, dynamical, and mechanical properties. Therefore, a total number of fifteen specimens, prepared from samples obtained from various locations from the southern part of the East Attica Prefecture, Greece. The laboratory program involved the determination of the uniaxial compressive strength (UCS), the crack initiation (Cci) and crack damage stress (Ccd) levels, the static elastic modulus (Es), as well as the basic physical and dynamical properties, such as the dry density (γd), the effective porosity (neff) and the ultrasonic velocities of both primary (VP) and secondary (VS) waves. Results obtained from the mechanical tests reveal that the onset of stable (Cci) and unstable (Ccd) crack growth varies between 0.19–0.38 and 0.66–0.92 of the UCS values, respectively. Applying simple nonlinear regression models, it was found that crack initiation and crack damage stresses, decrease exponentially with the increase of effective porosity, while increase exponentially with the increase of static elastic modulus, dynamic elastic modulus (Ed), and the primary wave velocity.
It is generally accepted that the experimental stress-strain curves of uniaxial compression tests up to the ultimate strength (UCS) can be distinguished into four sections corresponding to different stages of rock deformation [1, 2, 3]. The initial section (stage I) is related to pre-existing microcracks closure. When the majority of these microcracks are closed the rock can be roughly considered to behave as an elastic material (stage II). The onset of dilatancy delimits the beginning of the stable cataclastic phase (stage III). The tensile microcracks, which initiate at this stage, propagate mainly parallel to the applied axial stress direction. The stress level associated with the beginning of this stage is defined as the crack initiation stress (Cci). With the increase of the applied load, new microcracks initiate and propagate while at the same time new and old microcracks coalesce and interact at oblique angles to the applied loading direction (stage IV). The stress level where unstable crack growth begins is defined as crack damage stress (Ccd).