Thermal fracturing in orthotropic rocks with superposition-based coupling of PD and FEM

Thermally induced deformation and fracturing in rocks are ubiquitously encountered in underground geotechnical engineering and they are highly influenced by the material anisotropy. In the present manuscript, a superposition-based PD and FEM coupling approach is proposed for simulating thermal fracturing in orthotropic rocks. In this approach, the critical regions with possibility of cracks are encompassed by the non-ordinary state-based peridynamics (NOSBPD) model, while the entire problem domain is discretized by a fixed underlying finite element (FE) mesh. The thermal balance equation is fully approximated by the underlying finite elements without any contribution from the NOSBPD model. The NOSBPD model and FE model are coupled based on the superposition theory. The mechanical anisotropy, thermal anisotropy as well as the hindering effect of the insulated crack on the thermal diffusion are considered in this coupled model. A staggered solution scheme is employed to solve the coupled system. The performance of the coupled method for thermomechanical problems with and without damage is evaluated by two numerical examples. After validation, thermal fracturing in an orthotropic rock specimen under high surrounding temperature is systematically studied. The parametric study shows that the inclination angle of the cracks and the major axes of the elliptical shape of the isotherms are generally consistent with the principal material first axis. Both the mechanical and thermal anisotropy highly affect the thermal fracturing in orthotropic rocks.