Statistical Damage Constitutive Model of Quasi-Brittle Materials

Recent studies have shown that statistical damage mechanics is one effective method to study the failure process of quasi-brittle materials. There are two key problems in setting up the statistical damage constitutive model of quasi-brittle materials, namely, determining the microunit strength and the parameters of statistical distribution that the microunit strength obeys. The four-parameter criterion is a failure criterion consisting of four unknown parameters. When the four parameters equal appropriate values, it may become the Drucker-Prager criterion (for rock), Mohr-Coulomb criterion (for rock), and Hsieh-Ting-Chen criterion (for concrete), so the four-parameter criterion may be used to simulate the elastoplastic behavior of rock and concrete quasi-brittle materials. In the paper, microunit strength is determined with the four-parameter criterion, thus the statistical damage constitutive model suits rock and concrete. The deficiencies of existing methods in determining the distribution parameters are investigated, and a new method for determining the distribution parameters is proposed. First, the theoretical relationships between the parameters and the strain and stress at the peak point of material failure curve are derived; second, the approximate relations between the strain and stress at the peak point of material failure curve and confining pressure are established through the curve fitting method; finally, the relations between the parameters and confining pressure are established. The proposed statistical damage softening constitutive model of quasi-brittle materials has universal meaning, the determination of distribution parameters has strict theoretical basis, and the distribution parameters can be conveniently obtained with general triaxial tests. Numerical examples are also presented to validate the model.