Abstract: After excavation, the disturbed natural rock mass tends to be in non-equilibrium evolution state and affects the safety and stability of engineering structure. The time-dependent deformation and damage evolution are the cores of the non-equilibrium evolution process of rock mass structure. In this paper, the effective stress principle of non-equilibrium evolution is proposed within thermodynamics with internal state variables. The effective stress, which can really derive non-equilibrium evolution process, is only a portion of total stress. The rate of inelastic strain and energy dissipation rate can be expressed in form of effective stress, and concept of inelastic complementary energy is proposed. A creep constitutive equation with damage is derived through giving specific complementary energy density function and evolution function of internal state variables. Parameters identification of degraded one-dimension equation is conducted under one dimensional scene through uniaxial creep test of analogue material by load and unload method. Viscoplastic strain rate, rate of energy dissipation and inelastic complementary energy can be calculated, and the comparative discussion is illustrated. The results indicate that the difference between rates of inelastic strain is minor in primary and secondary creep stages but is major in tertiary stage because of theoretical error. The integral value of rate of energy dissipation in domain and inelastic complementary energy can characterize the non-equilibrium process of structure in actual effect and driving potential perspective respectively, and the latter is a more applicable one to assess the long-term stability of structure. At last, a case about deep buried tunnels is shown and its long-term stability is studied.