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The precondition of rock stress and deformation analysis is a reasonable rock constitutive model. Most of the previous studies have described the heterogeneous microdamage by Weibull distribution or normal distribution. However, both of them have limitations. Therefore, this paper intends to use the lognormal distribution as the probability distribution model of rock microunit strength. Based on the tensile failure of the single-fractured rock under the hydrodynamic force, the maximum tensile strain failure criterion is used as the distribution parameter of rock microunit strength. And, considering the multiphase properties of the filling fractured rock, the equivalent elastic modulus parameter is adopted in the model. We design a triaxial seepage test for the filled single-fractured rock and analyze the applicability and rationality of the modified lognormal statistical damage model for characterizing the fractured rock by using the test data. According to the comparison of the experimental stress-strain curve and the model stress-strain curve and the analysis of the damage value test curve and the model curve, the rationality of the established statistical damage constitutive model is verified, and the advantages and limitations of the model are proposed.

Lognormal Distribution Function for Describing Seepage Damage Process of Single-Cracked Rock