Rock mechanical properties reflect its geological history. The geometry of its crack and fissure network as well as its evolution under a stress or thermal load tends to follow fractal like patterns in space and time. This characterization is also related to the percolation like fluid transport and fracture development in the rock mass under applied pressure or stress load.
Les proprietes mecaniques des rochas met tent en evidence leur histoire geologique. La geometrie du reseau de fractures et de fissures autant que leur evolution sous tension ou charge thermique sont souvent du type fractal dans l'espace et dans le temps. Cette caracterisation se rapporte aussi à la percolation du type transport des fluides et developpement de fractures dans les masses rocheuses sous compression ou tension.
Die mechanische Eigenschafte von Gesteine zeigen ihre geologische Geschicht. Die Geometrie der Bruche und Risse Netzwerk ebenso wie ihre Entwicklung durch Spannungen und thermische Schutllast neigen zu zersteilende Vorbilder in Platz und Zeit. Diese Charakteristik steht auchin Beziehung mit Einsickern und Entwicklung der Bruche in Gesteinemass durch anlegende Spannungen und Schuttlast.
Rock mechanical and transport properties reflect its geological history. A microscrack network develops in a crystalline rock after solidification as a result of the interplay of stress and thermal loads imposed by the boundary conditions to which the rock is submitted along its geological history. This process is a very complex one. We try to understand and modellize it by invoking the pertinent physical laws. This equation comprises the elastic strain of the material but excludes the slower creep processes.
Cohesive forces acting near a microcrack edge represent an internal load that deforms the crack lips and lead to a stress intensity factor which balances the one due to the external loading; the stress field remains thus finite at the crack edge; in the whole cohesive zone the normal stress equals the yield stress. In a slit shaped microcavity, the energy of adhesion W, the maximum stress between the two surfaces σth and the equilibrium spacing are inter-related and can be quantified from first principles (Maugis, 1992).
Microcrackes develop as inter-grain cavitation and as intra and trans-grain microfracture. Fast fracture results from the intensification of the average stress field in the neighbourhood of the edge of a pre-exhisting microcrack. On the other hand, another length is required to characterize the profile, namely the "topothesy", which adds a real measurable scale to the profile and is reflected in the magnitude of the structure function. Poon et al, (1992) studied four types of sedimentary rock and found in all cases a fractal dimension of 1.2 for the crack profiles, which means 2.2 for the crack surface. At the extreme limit of the microcrack network development, one has the rock fragmentation. Barbery (1987), discussed the fragmentation process in connection with the comminution and liberation of minerals and showed how it can be modellized by random geometrical sets of Poisson polyheadra and lead to power-law frequency-size distributions, over a broad size range, in agreement to earlier empirical data and statistical models. Turcotte (1992), interpreted the fractal character of fragment size frequency distributions invoking either renormalization or comminution models and collected experimental evidence of such fractal behaviour in a number of geological instances. In the case of granitic rock, examples give fractal dimensions in the interval 2.2 through 2.5. Wong and collaborators have studied the fractallity of porous media, namely sedimentary rocks.
