Study on time-dependent behavior and stability assessment of deep-buried tunnels based on internal state variable theory

•The creep damage model based on internal state variables is developed.•The central-difference form of the creep damage model has been presented.•The developed model in FLAC3D, TMVP, is applied in the tunnel stability analysis.•The long-term stability criterion is presented based on energy dissipation rate.

The creep model based on thermodynamics with internal state variables theory can simulate complex time-dependent deformation of rock mass, describe process of energy dissipation of material system, and can be used to evaluate the long-term stability of underground structures quantitatively. In this paper, the creep model proposed by author is improved further and recast to be central difference equation. The redevelopment interface of FLAC3D is used to develop a new calculation program, which is based on thermodynamics for vsico-plasticity (PTV-P). Program validation has been conducted by comparing the results from FLAC3D and Matlab software under uniaxial compression condition. Then the developed program has been applied to analyze the time-dependent behavior of deep-buried double tunnels. The integral values of energy dissipation rate and its time derivative in domain can be calculated and are used to evaluate the long-term stability of tunnels quantitatively, and the evaluation criterion is also proposed. Moreover, the contour map of energy dissipation rate is used to exhibits the local non-equilibrium region clearly.