Failure Criterion of Rock under Static Loading

Abstract

A new failure criterion of rocks and rock-like materials is hereunder proposed in this paper. The theoretical consideration of the criterion is presented as well as its experimental verification. In this study failure is defined as collapse of the material.
The criterion is based on the assumption that the ultimate strength of the material under a compressive state of stress depends on its shearing strength, while under the tensile stress it may be collapsed by the tensile fracture which is thought to be predictable in the Griffith theory.
It has already been verified that the shearing strength of the material can be utilized as the function of the mean stress instead of being concluded as peculiar to the material itself. Theoretically, however, the shearing strength of the material may be considered in effect as dependent on the quantity of the tensile fractures induced around the crack or discontinuity, and the said quantity of the tensile fractures is, according to the Griffith theory, the function of the minimum stress. Therefore it is proposed as condition for the criterion that the ultimate octahedral shearing stress represents the function of both the mean stress and the minimum principal stress. The proposed failure condition may also be expressed in this way that the maximum elastic strain energy of distortion stored in the material depends upon both the mean stress and the minimum principal stress.
Under an extreamly high compressive stress state, failure may be caused by plastic flow, so that the failure criterion may also be proposed in this way that the maximum octahedral shearing stress is the function only of the mean stress.
As extended application of Coulomb's and Mohr's criteria to the three dimensional stress state will some of particular cases of the criterion be defined.
The experimental results obtained from rock salt, marble, sandstone, and concrete show fairly good agreement with the failure criterion proposed above.