Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

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.

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

There are many methods to construct true triaxial strength criteria for rocks.Jaiswal and Shrivastva(2012)proposed a strength criterion,named J–S criterion,in the deviatoric plane,which provides nearly the same misfts for true triaxial test data as the exponential criterion.It is diffcult to calculate the strength at given2and3using the J–S criterion,and the multiple solutions to the nonlinear equation may induce confusion and mistake.Strength envelopes in deviatoric planes are not geometric similar;therefore,true triaxial test data cannot be grouped in the mean stress to check strength criteria in the deviatoric plane.