关键词: 岩石, 分数阶, 蠕变, 时效损伤, 本构模型

Abstract: To accurately describe the whole process of creep deformation and failure of rock, a comprehensive and concise creep constitutive model is established by introducing continuous damage and fractional calculus theory. First of all, damage variable is defined according to the energy damage mode, and the elastic body in consideration of aging damage is constructed based on the attenuation law of elastic modulus with time, and the feasibility of the damage evolution mode is verified. The fractional order software components with nonlinear characteristics are constructe based on the Riemann-Liouville type fractional calculus operator theory, and the viscoelastic strain of rock is described with the aforementioned software components as a fractional viscous body. On such basis, the fractional order viscoplastic body in consideration of aging damage is obtained via damage evolution. Hence, a new fractional creep constitutive model in consideration of aging damage is established. The parameter analysis method is given, and the rationality and superiority of the model are verified by the creep data of argillaceous slate. Moreover, the damage development process is analyzed to determine the sensitivity of the model parameters, and the applicability of the model is verified by creep test data of red sandstone and phyllite. The research results offer reference for identifying the whole creep process and the long-term stability of rock mass.

Key words: rock, fractional order, creep, aging damage, constitutive model