Application of the Christensen Failure Criterion to Intact Rock

The Christensen criterion, originally introduced in materials science, has a simple mathematical form and uniaxial tensile and compressive strength as the only parameters, making it an attractive candidate for rock engineering purposes. In this study, the applicability of the criterion to rock materials is examined. Explicit equations for application of the criterion under biaxial, triaxial compression, triaxial extension, and polyaxial states of stresses are derived. A comprehensive strength data set including the results of tests on synthetic rock, chert dyke, Carrara marble and Westerly granite is utilized to examine the accuracy of the Christensen criterion to the failure of rock material. The two surprising findings about the Christensen criterion are the zero values of tensile strength and the very low slopes of the failure envelope obtained from fitting analyses for chert dyke and Westerly granite. It is shown that the two problems are interrelated and the values of tensile strength tend to zero to produce higher slopes. It is then mathematically proven that the maximum initial slope of the Christensen failure envelope is limited to 4 in triaxial compression and 2.5 in triaxial extension which is considerably lower than the slope of experimental data. The accuracy of the Christensen criterion was found to be significantly lower than the well-established Hoek-Brown criterion. The circular pi-plane representations and brittle-to-ductile transition limits from the Christensen criterion are also inconsistent with the observed behavior of rocks.