A Progressive Failure Model of Rocks in Uniaxial Compression

Abstract

As a probability model of rock failure, the weakest link model has been usually used in pure tension. In compression, however, recent laboratory investigations show that most rock specimens can have the load bearing capability if subjected further displacement after the peak load has been reached. In order to explain the complete stress-strain characteristics of rock in compression, the weakest link model is not adequate to be applied.In this paper, a new model is proposed for compression of rocks on the assumption that the strain in compression consists of the permanent strain (ep) and the elastic strain (ee), the ratio of permanent strain to the total strain being increased according to the Weibull's cumulative distribution function and that the bearing stress of a rock specimen at any deformation is proportional to the amount of elastic strain being survived.By these hypotheses, the following equation can be derived to express the complete stress-strain relation for uniaxial compression of rock.σ=E(1-F(e))ewhere, E=Young's modulus, F(e)=ep/e=1-exp(-em/α)The results computed for various values of inhomogenity parameter p(=m=α) are shown Fig. 3 (a) and (b).By expanding the idea to the dilatancy of rock in uniaxial compression. an equation to represent to volumetric strain (eV) over the whole range of pre-and post-failure regions can be derived. The equation is as follows.eV={(1-2ν0)(1-F(e))-CF(e)}ewhere, ν0=intrinsic poisson's ratioC=dilatancy coefficientThe effects of dilatancy coefficient C and the parameter p on the complete stress-volumetric strain curve are shown in Figs. 5, 6 and 7.According to the present analysis, the apparent secant modules and the apparent poisson's ratio are found to beE*=E(1-F(e))ν*=1/2(2ν0+(1-2ν0+C)F(e))They are shown in Figs. 8, 9, 10 and 11.