## 1 Introduction  
Under the consensus of coal and gas co-mining, coal mine safety and efficient production represent critical challenges in coal resource extraction [1, 2], with coal and gas outburst prevention and coalbed methane (CBM) development being particularly vital [3], with both intrinsically associated with the migration behavior of methane within coal seams [4, 5]. For CBM development, reservoir permeability serves as the governing parameter, that is, enhancing permeability to optimize methane migration through the coal's pore-crack system constitutes the cornerstone technology for boosting its production [6, 7]. While coal and gas outbursts, catastrophic and instantaneous dynamic disasters, manifest as a specific type of gas emission phenomena encountered during underground coal mining [8], where coal is fragmented and thereto ejected abruptly and violently with massive gas from the working face [9; 10]. Although extensive domestic and international research spanning over a century has yielded significant insights, a definitive consensus on its triggering and developmental mechanism remains absent. However, some foundational insights have been gained, various theoretical hypotheses have been proposed, which commonly attribute the occurrence of coal and gas outburst to a comprehensive result of in situ stress, gas pressure, coal's physico-mechanical properties, geological structure, etc. [11; 12; 13; 14]. Notably, recent studies suggest gas release as a dominant energy contributor in both triggering outburst initiation and maintaining its further chain-type development, where gas migration plays a pivotal role [15; 16]. Gas migration within coal structure involves gas desorption, diffusion, and seepage [4; 16; 17]. The well-developed porous network, comprising interconnected pores, joints, and cracks, serves as sites and pathways for gas migration [16; 18; 19]. Specifically, gas desorption is the physical process in which gas molecules obtain sufficient energy to overcome van der Waals force for escaping from coal matrix surface when adsorption equilibrium is disrupted, predominantly occurring on micropore surfaces (<0.01 \(\upmu\)m) [20]. Gas diffusion is the process in which free gas migrates from micropores to fractures under concentration gradients, driven by the stochastic thermal motion of gas molecules, dominating in micropores and mesopores (<1 \(\upmu\)m), generally subject to [PERSON]'s law and its derivative laws [21]. While gas seepage is the directional gas flow through mesopores and macropores (>1 \(\upmu\)m) under pressure gradient, governed by [PERSON]'s law for porous media [22]. Overall, the gas migration could alter the coal's pore structure and redistribute effective stress within the matrix. Such stress state modifications could influence coal fragmentation and outbursts initiation [23; 24; 25; 26]. Thus, elucidating the influence of gas migration, especially gas seepage, on coal's physico-mechanical properties and coal breaking is of significance for clarifying outbursts mechanism. Thus far, ongoing efforts intended to understand gas seepage regularity have acquired great progress. [PERSON] et al. [27] experimentally demonstrated that the permeability of Russian coking coals perpendicular to butt cleat direction decreases by 6.7 times under an 8-fold increase in confining pressure. Based on site characteristics of coal-gas co-mining in Pingdingshan, China, [PERSON] et al. [28] introduced a mining-enhanced permeability parameter to quantify the permeability evolution of coal and other rocks. Their findings revealed a 0.14% increase in volumetric strain and 7.77% permeability enhancement under mining-induced stresses. Moreover, the impact of different factors on gas seepage regularity in coal was widely investigated. [PERSON] et al. [29; 30] explored true triaxial stress effects on intact and fractured coal, showing that macroscopic fractures elevated permeability by 1-3 orders of magnitude. [PERSON] et al.