## 1 Introduction  
Over the past three decades, there has been growing curiosity about multi-field couplings within rock masses, driven by the need to accomplish assessments and optimize designs in radioactive waste disposal, geothermal energy, and deep underground mining. Multi-field coupling refers to the interaction between processes like fluid flow and stress-strain behavior, where one operation influences the commencement and progression of another process [1]. In rock mechanics, these couplings describe the interaction between stress, oozing, and thermal fields, which are integral to rock mass formation and evolution, influenced by both natural forces and human activities. Coupled processes imply that a piece of each process affects and is influenced by the others. Consequently, the behavior of rock masses in scenarios like radioactive waste storage cannot be accurately forecast by isolating these processes. While much research has focused on two-way couplings like TM and HM, understanding and predicting full THM and THMC couplings is essential, especially for repository performance [2; 3; 4; 5; 6; 7; 8]. This remains a significant challenge caused by the differing impermanent and spatial scales of the processes involved and the need for improved constitutive models. Coupled processes are also critical in subsurface engineering fields, including carbon sequestration, geothermal systems, energy storage, and distinctive oil and gas productivity through hydraulic stimulation. Temperature significantly impacts the behavior of geomaterials, which is essential in geotechnical and underground engineering [9]. Various applications, such as high-level nuclear waste disposal [10; 11; 12; 13; 14], heat storage [15], geothermal structures [16; 17], petroleum drilling [18; 19], and zones surrounding high-voltage cables [20], rely on understanding these effects. Recent studies have particularly focused on the TM behavior of geomaterials like Boom Clay [21; 22; 23; 24], Opalinus Clay [25; 26; 27], Callovo-Oxfordian argillite [28], and Aspo Pillar [29; 30], emphasizing the importance of evaluating their mechanical properties under long-term exposure to high temperatures. These temperature-induced changes affect mechanical parameters such as friction angle [31; 32], permeability/porosity [33; 34; 35], elastic modulus [36; 37], shear strength [38; 39; 40], and dilatancy [41] and lead to softening, brittle-to-ductile transitions [42; 43], and creep behavior [27; 28]. [PERSON] et al. conducted Scanning Electron Microscope (SEM) tests on pre-cracked red sandstone prototypes to assess the efficacy of a THMC coupling indicator, which was developed to quantify the impact of THMC coupling fields on the stress field through rock porosity analysis. This indicator, measured in real-time using a novel permeability method for brittle fracture criteria, enables a continuous evaluation of THMC-field effects on rock stability [44]. Under external loads, natural discontinuities like cracks or joints in brittle rock can initiate and propagate rapidly, often leading to unstable fracture progression and eventual failure of the rock mass [45; 46; 47]. These findings are particularly relevant in the context of underground nuclear waste repositories, where elevated temperatures could alter the steadiness and long-term probity of the surrounding rock. The overall understanding of these changes provides insights into optimizing underground storage and other geotechnical applications. As underground spaces continue to be developed and mineral resource extraction deepens, the environmental conditions in which rocks exist have become significantly more complex. Studies indicate that rocks and soils can experience significant changes in mechanical properties when exposed to elevated temperatures over various time frames. Since [PERSON]'s foundational work on non-isothermal plastic deformation modeling [48], numerous constitutive models have emerged, incorporating these thermal impacts within computational inelasticity frameworks [49].