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Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics

Exadaktylos Georgios, Vardoulákīs, Iōánnīs

Πλήρης Εγγραφή

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Περίληψη

An account on the role of higher order strain gradients in the mechanical behavior of elastic-perfectly brittle materials, such as rocks, is given that is based on a special grade-2 elasticity theory with surface energy as this was originated by Casal and Mindlin and further elaborated by the authors. The fundamental idea behind the theory is that the effect of the granular and polycrystalline nature of geomaterials (i.e. their microstructural features) on their macroscopic response may be modeled through the concept of volume cohesion forces, as well as surface forces rather than through intractable statistical mechanics concepts of the Boltzmann type. It is shown that the important phenomena of the localization of deformation in macroscopically homogeneous rocks under uniform tractions and of dependence of rock behavior on the specimen's dimensions, commonly known as size or scale effect, can be interpreted by using this ‘non-local’, higher order theory. These effects are demonstrated for the cases of the unidirectional tension test, and for the small circular hole under uniform internal pressure commonly known as the inflation test. The latter configuration can be taken as a first order approximation of the indentation test that is frequently used for the laboratory or in situ characterization of geomaterials. In addition, it is shown that the solution of the three basic crack deformation modes leads to cusping of the crack tips that is caused by the action of ‘cohesive’ double forces behind and very close to the tips, that tend to bring the two opposite crack lips in close contact, and further, it is demonstrated that the fracture toughness depends on the size of the crack, and thus it is not a fundamental property of the material. This latter outcome agrees with experimental results which indicate that materials with smaller cracks are more resistant to fracture than those with larger cracks.

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