Viscoelastoplastic Displacement Solution for Deep Buried Circular Tunnel Based on a Fractional Derivative Creep Model

Time-dependent deformation of surrounding rock is a common phenomenon for tunnels situated in soft rock stratum or hard rock stratum with high geo-stress. To describe this phenomenon, a creep model combining the Abel dashpot and a non-Newton viscous element was adopted, and the analytical solution about the viscoelastoplastic deformation for circular tunnel was obtained based on this creep model. Then, the auxiliary tunnel of Jinping II hydropower station was taken as an example to reveal the influence of creep parameters on the creep deformation. The research shows that (1) the creep model can well describe the whole creep stage of rocks, that is, the decay, constant, and accelerated creep stages, (2) the creep deformation has a positive relation with the value of fractional order of Abel dashpot and the order of the non-Newton viscous element, and (3) the creep curves between test results and analytical solutions are well consistent with each other, which demonstrate the validity of the analytical solution.

A non-linear creep constitutive model for salt rock based on fractional derivatives

The creep property of the salt rock is an important determinant of deep underground repository of energy storage for long-term operatio. Starting from fractional derivative, this paper proposes a new concept of super Abel dashpot based on Abel dashpot. According to the Nishihara model, the non-linear element of super Abel dashpot is introduced, and a new salt rock creep constitutive model is established. The theoretical analytic solution of this model is then deduced. Fitting analysis of the experimental data indicates that the model can well reflect the whole-process creep curve, especially the non-linear accelerated creep stage.

Viscoelastic Parameter Model of Magnetorheological Elastomers Based on Abel Dashpot

In this paper, a parametric constitutive model based on Abel dashpot is established in a simple form and with clear physical meaning to deduce the expression of dynamic mechanical modulus of MREs. Meanwhile, in consideration for the pressure stress on MREs in the experiment of shear mechanical properties or the application to vibration damper, some improvements are made on the particle chain model based on the coupled field. In addition, in order to verify the accuracy of the overall model, five groups of MREs samples based on silicone rubber with different volume fractions are prepared and the MCR51 rheometer is used to conduct the experiment of dynamic mechanical properties based on frequency and magnetic field scanning. Finally, experimental results indicate that the established model fits well with laboratory data; namely, the relationship between the dynamic modulus of MREs and changes in frequency and magnetic field is well described by the model.