A Class of Elastic‐Plastic Constitutive Laws for Brittle Rock

Abstract

The inelastic behavior of fissured rock masses is due primarily to microcracking from the tips of preexisting fissures and frictional sliding on fissure surfaces. Consequently, the macroscopic inelastic response is inhibited by an increase of hydrostatic compression and exhibits volume change and strain softening. By generalizing the type of laws often used in metal plasticity, Rudnicki and Rice introduced a class of simple constitutive laws that incorporate these features and is useful for studying the inception of rupture. An important aspect of this generalization is that normality of the inelastic strain increment vector to a yield surface in stress space, as assumed in classical metal plasticity, is not appropriate. More detailed consideration of the preferential activation of sliding on differently oriented fissure surfaces during a program of loading suggests that, although this class of laws will be suitable for describing loading in which stress components increase nearly in proportion to a single parameter, they will be inadequate for describing abrupt changes in the pattern of deformation. An approximate remedy for this inadequacy can be interpreted as deformation (or total strain) theory of plasticity. Mechanical coupling between diffusion of an infiltrating pore fluid, for example, ground water, and deformation can also be included by replacing the hydrostatic stress σ by the effective stress σ−ζp, where p is the pore fluid pressure and ζ satisfies 0<ζ⩽1 for elastic deformation and ζ=1 for inelastic deformation typical of brittle rock. This coupling causes the response to be time dependent even when the response of the matrix material is time independent. Specifically, the response is stiffer for load alterations that are rapid by comparison to the diffusion time of pore fluid than for those that allow time for equilibration of pore fluid pressure among neighboring material elements.