A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily overconsolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as the critical distance. This fracture criterion is known as the Point Method, and is part of the Theory of Critical Distances, which is utilized in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, ó0, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, óc and ót. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (óc/ót=3-50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low confining stresses.The work presented was initiated during a research project on “Structural integrity assessments of notch-type defects", for the Spanish Ministry of Science and Innovation (Ref.: MAT2010-15721)

Continuous and discontinuous stability analysis of the bell-shaped caverns at Bet Guvrin, Israel

The stability of two systems of bell-shaped caverns excavated some 1000 years ago at Bet Guvrin National Park is investigated. The caverns were excavated in a weak, anisotropic, and moderately discontinuous chalk. The cavern stability is considered based on two separate and independent methods: a continuum model framework—FLAC, used for stress analysis, and a discontinuous approach—block theory, used for critical key block analysis. The numerical stress analysis reveals that in the case of very large span openings, tensile fracture of intact rock may be responsible for instabilities, which may lead to global failure. Evidence of tensile rupture at margins of failed caverns is abundant at the Park. The discontinuous block theory analysis reveals that the moderate joint set spacing at Bet Guvrin, up to 45% of the roof area may be comprised of removable blocks. The removable keyblocks in the roof remain in place due to arching stresses, which develop through the roof material. The chalk at the roof can sustain the maximum loads in existing caverns, as predicted by the numerical stress analysis. However, local failures due to exceedingly high compressive stresses at the abutments or by tensile fracture at the roof, may lead to relaxation of arching stresses followed by keyblock displacement. Such a “mixed failure mode” process could eventually lead, over time, to global collapse. Indications that “mixed failure mode” processes are presently active in the studied caverns are substantiated by in-situ measurement of keyblock displacements. It is suggested that in weak and discontinuous rock environments where “mixed failure mode” processes may be active, long term stability evaluation should be based on both continuous and discontinuous stability analyses