Abstract: The deformation characteristics of rock under dynamic loading is a common problem in geotechnical engineering. In this article, a Fractional order Burgers Model (FBM) which reflects the deformation characteristics of rock under low dynamic stress is established by replacing constant Maxwell dashpot of Burgers model with fractional order dashpot based on fractional calculus. The dynamic loading is decomposed into a static loading and a cyclic loading with an zero average stress by stress decomposition method. According to rheological mechanics theory, the rheology constitutive equation for rock based on FBM is given under the static loading; and meanwhile according to viscoelastic mechanics theory, the dynamic response constitutive equation of rock based on FBM is deduced under the cyclic loading in consideration of the influence of rock damage, fracture and plastic deformation on energy storage and energy dissipation compliance. Furthermore, a new constitutive equation for rock is obtained by superimposing the constitutive equations under the two stress conditions. Compared with existing test results of rock under dynamic loading, the FBM could better describe the deformation characteristics of rock under low dynamic stress in deceleration stage and constant velocity stage; moreover the FBM parameters can be obtained conveniently by numerical methods.

Key words: rock dynamic mechanics, low dynamic stress, fractional order dashpot, Fractional order Burgers Model (FBM), rheological mechanics