Implementation and verification of a thermal-hydraulic-mechanical model based on fractional seepage theory in ABAQUS

Fractional seepage theory has been extensively developed in multi-field coupling issues. However, general finite element software still lacks dedicated elements for its numerical applications, especially for the thermal–hydraulic-mechanical (THM) modeling aspect. To this end, a THM-coupled fractional seepage model is first developed and implemented via a user-defined element (UEL) subroutine in ABAQUS, and then its accuracy is verified progressively using a stepwise scheme, starting from the hydraulic model, extending to the hydraulic-mechanical model, and finally to the THM model. Further, the developed subroutine is applied to the simulation of the ATLAS experiment to assess its capability in practical engineering. Numerical predictions could well reproduce the overall trends observed in the experimental results. In addition, the fractional seepage models implemented via the UEL subroutine and the user-defined material with heat transfer (UMATHT) subroutine are also compared in terms of computational accuracy and time, as well as convergence behavior. The obtained results suggest that the UEL subroutine requires fewer iterations and shorter computational time in benchmark tests, and significantly advances the numerical implementation of fractional seepage theory for THM problems.