Hydro-Thermo-Mechanical Transient Response for a Cylindrical Unlined Tunnel in Poroelastic Medium Based on Non-singular Fractional Derivatives

Background The dynamic coupled hydro-thermo-mechanical behavior of the unlined structure in saturated porous structure under extreme geotechnical and geology engineering (e.g., underground explosion, laser thermal rock breaking) have aroused extensive research interests on the constitutive modeling and transient dynamic responses prediction. Although the current fractional-order hydro-thermo-mechanical models have been historically proposed, the theoretical formulations still adopt the classical fractional derivatives with singular kernels, and the inherent strain relaxation effect and the associated memory dependency remains not considered yet in such complex condition. Purpose To compensate for such deficiencies, the current work aims to establish the new hydro-thermo-mechanical model by introducing the Atangana-Baleanu (AB) and Tempered-Caputo (TC) fractional derivatives with non-singular kernels. Methods The proposed model is applied to investigate transient structural dynamic hydro-thermo-mechanical response of a cylindrical unlined tunnel in poroelastic medium by applying Laplace transformation approach. Results The influences of the AB and TC fractional derivatives on the wave propagations as well as the dimensionless responses of the temperature, displacement, stress, and pore-water pressure are evaluated and discussed. Conclusion The non-singular AB and TC fractional derivatives slower the thermal wave propagation. In addition, the dimensionless pore water pressure dissipation is maximally reduced. The increase of strain relaxation time parameter reduces the mechanical dynamic response regions and eliminates the sharp jumps of mechanical response at the elastic wave front, which are consistent with continuity of displacement in real engineering situations.