Deformation of rock: A pressure-sensitive, dilatant material

Abstract

Permanent (plastic) deformation of rock materials in the brittle regime (cataclastic flow) is modelled here in terms of Mohr-Coulomb behaviour in which all three of the parameters cohesion, friction angle and dilation angle follow hardening (or softening) evolution laws with both plastic straining and increases in confining pressure. The physical basis for such behaviour is provided by a sequence of uniaxial shortening experiments performed byEdmond andPaterson (1972) at confining pressures up to 800 MPa on a variety of materials including Gosford sandstone and Carrara marble. These triaxial compression experiments are important for the large range of confining pressures covered, and for the careful recording of data during deformation, particularly volume change of the specimens. Both materials are pressure-sensitive and dilatant. It is therefore possible to derive from these experiments a set of material parameters which allow a preliminary description of the deformation behaviour in terms of a non-associated, Mohr-Coulomb constitutive model, thus providing the first constitutive modelling of geological materials in the brittle-ductile regime. These parameters are used as input to a finite difference, numerical code (FLAC) with the aim of investigating how closely this numerical model simulates real material behaviour upon breakdown of homogeneous deformation. The mechanical and macrostructural behaviour exhibited by the numerical model is in close agreement with the physical results in that the stress-strain curves are duplicated together with localization behaviour. The results of the modelling illustrate how the strength of the upper-crust may be described by two different but still pressure-dependent models: the linear shear stress/normal stress relationship of Amontons (that is, Byerlee's Law), and a non-linear, Mohr-Coulomb constitutive model. Both include parameters of friction and both describe brittle deformation behaviour. Consideration of the non-linear bulk material model allows investigation of the geologic regimes which favour localization of the deformation over a continuing homogeneous deformation. More complex models are required to describe the deformation of rock with increasing depth and temperature as the behaviour becomes increasingly temperature-sensitive and rate-dependent.