Abstract
This paper describes a constitutive equation of rock which undergoes strain-softening deformation beyond its strength failure. The equation consists of stress-strain relations in elastic, strain-softening and residual strength regions. The stress-strain relation in strain-softening region was idealized to be linear and expressed in terms of a few parameters that are related to postfailure characteristics and fracture criterion of rock. For an illustrative example was demonstrated an analytical solution of displacement and stress around a circular hole under hydrostatic pressure. The solution shows that three annuli which correspond to elastic, plastic and flow regions, will be formed around it if hydrostatic pressure exceeds a critical value. The plastic zone is decayed with increase of the negative slope in the post-failure region, and ceases to exist as the negative slope gets infinitive. Both the radii of elastic-plastic and plastic-flow boundaries are given by analytical formulae. The formula for elastic-plastic boundary is reduced to one of the elastic-perfectly plastic model when the negative slope gets flat. while it is coincident with one of the elastic-flow model when the negative slope gets infinitive. The formula also suggests that the raidius of elastic-plastic boundary is much greater than that predicted by elastic-perfectly plastic model. This implys that the formula allows us to estimate a rational elastic-plastic boundary for a circular tunnel in rock or a relief boring in coal seam.
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