A mechanical equation of state for brittle rock part I—The pre-failure behavior of brittle rock

Abstract

The results of a theoretical study of the mechanical behavior of brittle rock up to strength failure are presented. The mechanical behavior of brittle rock up to strength failure is defined in this paper to be pre-failure region. At strength failure the maximum nominal stress the rock can sustain is reached and the slope of the nominal stress-strain curve changes its sign. The nominal stress is defined to be the force acting on the surface of the rock divided by the original cross-sectional area of the surface. It is shown that the constant temperature mechanical behavior (i.e. the constitutive relationships) of brittle rock can be described by three equations which relate the three principal stresses and the three principal nonelastic strains resulting from void growth (i.e. microcracking) occurring within the rock structure. The three rules are shown to form the brittle material counterparts of the three ‘laws’ governing the plastic behavior of ductile materials. The three equations are applied to solve quantitatively the effect of microfractures on the stress distribution in the vicinity of a circular tunnel in a brittle rock which is subject to a uniform hydrostatic stress at a large radial distance from the opening.