A modeling approach to creep behavior of salt rock is of great significance for long-term operation of underground facilities in salt rock. A computer-controlled creep setup is employed to investigate creep behavior of salt rock under the condition of triaxial compression. In addition, suppose the evolution of the internal defects correspond to be the Weibull distribution, a new variable-viscosity Abel dashpot is established by means of definition of damage variable. By replacing a Newtonian dashpot in the classical Nishihara model with the variable-viscosity Abel dashpot, a new creep constitutive model is proposed on the basis of damage evolution and fractional derivative. Furthermore, the parameters in the new constitutive model are determined by fitting analysis of experimental data. The comparison of modeling approach with experimental data indicates that the fractional derivative constitutive model can reflects the three stages of creep of salt rock, especially the tertiary one.

1 Introduction

Salt rock has been recognized as an ideal medium for the underground strategic energy storage, permanent repositories ofCO2 and disposal of high-level radioactive wastes (Urai et al. 1986), with its extremely low porosity, low permeability and high solubility in water. However, owing to the time-dependent creep behavior of salt rock, large deformation of effective storage volume may influence the stability of the salt caverns in their long-term service. An increasing studies indicate the time dependent behavior of the salt rock induce a loss of cavern volume. As a result, a research for the creep behavior of salt rock is of great importance for deformation controlling of the salt rock caverns.

Generally the achievements in the creep properties of salt rock include several aspects, i.e., creep experimental studies, creep constitutive relations of salt rock and long-term stability of salt caverns. In last decades, most of the effects have been devoted to modeling of salt rock creep, and three approaches to the creep constitutive models of salt rock have been proposed, namely, empirical models, component models and mechanism-based creep constitutive models (Zhou et al. 2011). In order to describe the accelerated creep stage (the tertiary stage) of creep of rock, the function of creep parameters with the time is usually suggested to be nonlinear. Many efforts have been devoted to application of micro-mechanics theory (Miura et al. 2003) or endochronic theory (Auberin et al. 1991) to creep constitutive models. Hou and Lux proposed a damage variable creep constitutive model of salt rock called Hou/Lux model, which shows the development of dilatancy, damage and healing of salt caverns (Hou et al. 1999, 2003). Wang (2004) proposed a new creep constitutive model based on the theory of damage mechanics and described the creep and damage of salt rock. Adolfsson et al. (2005) proposed a fractional order viscoelastic model based on the concept of internal variables which find out that the corresponding rate equations can be formulated by the fractional order integrals rather than the fractional order derivatives.

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