Thermodynamically Consistent Computation of J-Integral in 3D Thermo–Hydro–Mechanical Fracture

  • Saeedmonir, Saeed (Imperial College London)
  • Paluszny, Adriana (Imperial College London)
  • W.Zimmerman, Robert (Imperial College London)

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Fracture propagation in thermo–hydro–mechanically (THM) coupled porous media is of great importance in many subsurface energy and geoengineering applications, including geothermal systems, hydraulic stimulation, and underground energy storage. Despite significant progress in multi-physics modelling, a robust and rigorous evaluation of crack driving forces and stress intensity factors (SIFs) seems to be as yet unavailable, due to challenges involving coupled and transient THM processes. This work presents a three-dimensional finite element framework for THM fracture analysis, with consistent procedures for computing the energy release rate and fracture parameters. A thermodynamically consistent configurational J-integral is formulated and implemented in localized domain form, incorporating mechanical, hydraulic, and thermal contributions including both diffusive and advective heat transfer regimes through the underlying THM coupling. Compared to the classical formulation, the proposed J-integral consistently incorporates additional configurational contributions arising from pore pressure, thermal coupling, while preserving its interpretation as an energetic crack driving force. The formulation further includes explicit crack-face work terms, enabling consistent energy accounting in three-dimensional finite element models with explicitly represented crack surfaces. The proposed J-integral retains path-independence as the energetic driving measure under coupled THM conditions and is applicable to both transient and steady-state analyses without reliance on auxiliary fracture parameters. Numerical examples, including fully coupled THM simulations, are presented to demonstrate the robustness, accuracy and numerical stability of the proposed approach. The results confirm the stability of the formulation for evaluating crack driving forces in complex multi-physics environments. The proposed framework provides a consistent and extensible basis for 3D fracture assessment in coupled THM simulations and offers a rigorous foundation for future developments in multi-physics fracture mechanics.