sgr ms thesis - University of Maine

5.1. Brittle Failure of Rock
5.1.1. Basic Principles of Griffith Fracture Theory
Failure occurs when a rock is no longer able to support a stress increase
without fracture; for brittle failure this implies the loss of cohesion along fractured
planes within the rock. Differential stresses are necessary to provide brittle failure
and shape change in a rock, and the value of differential stress achieved at
failure is a measure of the rock’s strength (Goodman, 1980; Grady and Kipp,
1987; Hoek and Brown, 1997; Twiss and Moores, 2007). Fracture development
can be described by the work of A. A. Griffith (1920), whose theory successfully
explained the inequality between material strength as calculated by the strength
of atomic bonds in the material, and the actual observed strength of the
respective material. Griffith’s theory states that all solids contain many
microscopic cracks of random orientation, which greatly reduce the potential
strength of the material. These cracks are meant to represent the imperfections
in crystal lattice planes or grain boundaries, and are typically modeled as
elliptical and penny shaped in three dimensions, with an extremely small radius
of curvature at the crack tip (Figure 5.1a).
Failure of the material at the fracture tip is determined by a critical tensile
stress
defined as
(5.1)
where is Young’s modulus, is the specific surface energy required to break
the atomic bonds of the material (surface tension), and
is the fracture half
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