A generalized three-dimensional failure criterion for rock masses

The smooth convex generalized failure function, which represents 1/6 part of envelope in tile deviatoric plane, is proposed. The proposed function relies on four shape parameters （L, a, b and c）, in which two parameters （a and b） are dependent on the others. The parameter Ls is called extension ratio. The proposed failure function could be incorporated with any two-dimensional （2D） failure criteria to make it a three-dimensional （3D） version. In this paper, a mathematical formulation for incorporation of Hoek-Brown failure criterion with the proposed function is presented. The Hoek-Brown failure criterion is the most suited 2D failure criterion tbr geomaterials. Two types of analyses for best-fitting solution of published true tri-axial test data were made by considering （1） constant extension ratio and （2） variable extension ratio. The shape and strength parameters for different types of rocks have been determined by best-fitting the published true tri-axial test data for both the analyses. It is observed from the best-fitting solution by considering uniform extension ratio （L~） that shape constants have a correlation with Hoek-Brown strength parameters. Thus, only two parameters （c~. and m） are needed for representing the 3D failure criterion for intact rock. The statistical expression between shape and Hoek-Brown strength parameters is given. In the second analysis, when considering varying extension ratio, another parameterfis introduced. The modified extension ratio is related tofand extension ratio. The results at minimum mean misfit for all the nine rocks indicate that the range off varies from 0.7 to 1.0. It is found that mean misfit by considering varying extension ratio is lower than that in the first analysis. But it requires three parameters. A statistical expression betweenfand Hoek-Brown strength parameters has been established. Though coefficient of correlation is not reasonable, we may eliminate it as an extra parameter. At the end of the paper, a methodology has also been given for its application to isotropic jointed rock mass, so that it can be implemented in a numerical code for stability analysis of jointed rock mass structures.

Reply to Discussion on “A generalized three-dimensional failure criterion for rock masses”

General:Jaiswal and Shrivastva(2012)proposed the mathematical formulations,i.e.the J–S criterion for converting generalized H-B failure criterion into 3D smooth convex failure criterion at deviatoric plane.The J–S strength criterion is in two versions:uniform and variable extension ratio.It has been observed from the analysis that at uniform extension ratio,the required strength parameters are only UCS and m(other parameters such as Ls,a,b and c are related with m).In the case of variable extension ratio,extra parameter f is required along with UCS and m.Thus,it has minimal strength parameters compared to You strength criterion.Furthermore,You strength criterion does not obey the smooth convex condition at deviatoric plane.