Study On Statistical Damage Constitutive Model For Rocks Based On Triaxial Compression Tests

The constitutive relationship of rocks is one of the most concerned questions in theengineering field. Combining the statistical strength theory and the continuum damagetheory, a statistical damage constitutive model for rocks is established in this paper. Thedamage variables in the statistical damage evolution equation and the continuumdamage evolution equation are eliminated, so the statistical damage constitutiveequation doesn’t contain the damage variable, which is different from conventionaldamage constitutive equations.During the establishing of the statistical damage evolution equation, the probabilitydistribution of micro-element strength and the expression of micro-element stress levelshould be introduced. For the distribution of micro-element strength, the lognormaldistribution and Weibull distribution are brought in, which are usually used for theresistance. For the expression of micro-element stress level, the compositions of stressin the M-C yield criterion and D-P yield criterion are referred, which work well for therock and soil materials. During the establishing of the continuum damage evolutionequation, Hooke’s Law is introduced in this paper.Based on the triaxial compression tests for rocks, considering that the stress andstrain measured during the tests are not the actual values, it is suggested in this paperthat the actual stress and strain in the statistical damage constitutive equation should berevised, which leads to the statistical damage constitutive equation based on themeasured stress and strain. For the uniaxial compression situation, the statistical damageconstitutive equation is explicit, and for the triaxial compression situation, the statisticaldamage constitutive equation is implicit.The statistical damage constitutive equation includes two statistical parameters,which can be determined through fitting with the uniaxial and triaxial compression testcurves. The linear regression method and peak point method for the determination of thestatistical parameters are mainly introduced in this paper, and the peak point method issuggested after the comparison and analysis.Analyzing the mathematical, physical meanings and feasibility of the statisticaldamage constitutive equation, it is known that the constitutive equation could describe the nonlinear mechanics behavior well, and that it could approach the elasticconstitutive relationship of rocks. For the compaction stage of uniaxial compression testcurves, the estimation method of initial damage of rocks is provided in this paper.Comparing the theoretical curves of the statistical damage constitutive equation basedon different distributions, different yield criterions and uniaxial, triaxial compressiontest curves of rocks, the rationality of the constitutive equation is proved, and themethods for determination of statistical parameters and revision of the constitutiveequation are affirmed. The comparison results indicate that the type of micro-elementstrength distribution does not much affect the statistical damage constitutive equation.For the uniaxial compression and the low confining pressure triaxial compressionsituations, the type of yield criterion also does not much affect the statistical damageconstitutive equation. For the high confining pressure triaxial compression situation,D-P yield criterion works better than M-C yield criterion.