Deep coal rocks exhibit strong time-dependent behavior, including significant plastic deformation and large tunnel displacements, which complicate tunnel support in deep underground engineering. A fractional creep model considering strong time-dependence was developed based on the classical Nishihara framework to capture this behavior. Additional time-dependent strains induced by stress-state variations were considered, with long-term rock strength adopted as the damage stress threshold. The stress difference between nominal and post-damage stress, ${\sigma }_D\left(t\right)$, defined as the stress gradient, was applied to a viscoelastic–plastic body containing a fractional Abel dashpot, producing conventional creep strain and strong time-dependent strain. The model was extended from one-dimensional to three-dimensional under triaxial stress conditions. The validity of the model was verified using triaxial creep test data for argillaceous sandstone and coal in deep roadways, and the model parameters were determined. The results demonstrate that the model accurately reproduces the full creep process, particularly the nonlinear accelerated stage influenced by strong time-dependence. Through stress-gradient-induced variations in strong time-dependent strain, the proposed creep model elucidates the progression of deformation in the strong time-dependent stage, offering a theoretical framework for the quantitative assessment of deep rock’s strong time-dependence. Sensitivity analysis identified the stress level, fractional order, and strong time-dependence coefficient $\alpha$ as key factors affecting strong time-dependent creep behavior. These findings indicate that tunnel support structures in deep environments are prone to instability, underscoring the necessity of accounting for strong time-dependence to ensure long-term stability.

Understanding the evolution of pore and fracture structures (PFSs) in coal under mining-induced unloading is essential for the prevention and control of gas disasters in coal mines. In this study, coal specimens from the Dongqu Mine, Taiyuan, Shanxi, were subjected to online triaxial nuclear magnetic resonance (NMR) tests under constant axial compression and stepwise confining pressure unloading conditions. Based on the measured T₂ spectra, the evolution of PFSs, permeability, and pore space complexity during unloading was investigated, and fractal theory was used to quantify the structural complexity of the pore system. The results show that large pores and fractures (LPFs) exhibit the most pronounced volume variation during unloading and are most sensitive to stress change. Small pores (SPs) contribute negligibly to permeability, whereas permeability is controlled primarily by medium pores (MPs) and LPFs. During unloading, neither SPs nor the overall pore system exhibits clear fractal characteristics, whereas MPs and LPFs display distinct fractal behavior. In addition, pore-volume evolution is inconsistent with fractal dimension variation, indicating that pore-volume change alone cannot adequately characterize PFS complexity. The complexity of the pore system is governed mainly by new pore generation, the expansion of existing pores and fractures, and the interaction between competing processes such as compaction and expansion.

Understanding the evolution of coal pore–fracture structures under coupled stress paths and creep deformation is critical for enhancing coalbed methane extraction and preventing coal and gas outbursts. In this study, coal samples from the Ningtiaota Mine were investigated using online Nuclear Magnetic Resonance (NMR) technology combined with triaxial loading–creep coupled experiments. The dynamic evolution of pore–fracture structures (PFSs) under different deviatoric stress levels was characterized and visualized in real time and across multiple scales. The results reveal a pronounced stress-dependent pore evolution during creep. Under low-stress conditions, seepage pores were compressed and gradually transformed into adsorption pores, whereas under high-stress conditions, seepage pores expanded and interconnected, dominating deformation and failure. Fractal theory was employed to quantify pore structure complexity, and repeated experiments demonstrated a significant positive correlation between the fractal dimension and the fractional order. Based on these findings, a fractal-dimension-based fractional creep model was developed by introducing a Riemann–Liouville fractional dashpot. The proposed model accurately captures the nonlinear creep behavior of coal and provides a microstructural interpretation of the fractional order. This study provides theoretical and experimental support for long-term stability assessment of deep coal–rock masses and prediction of coalbed methane migration.

Understanding the dynamic evolution of pore and fracture structure (PFS) in coal under mining disturbance is essential for safe coal extraction. In this study, coal specimens collected from the Dongqu Mine, Taiyuan, Shanxi Province, China, were subjected to stepwise cyclic confining pressure loading–unloading tests using a triaxial in situ nuclear magnetic resonance (NMR) system. Based on T₂ spectrum measurements, the real-time evolution of PFS, stress–strain response, permeability-related behavior, average pore diameter, and fractal characteristics were systematically investigated. The results show that irreversible damage developed in the coal specimens during cyclic confining pressure loading–unloading. With increasing cycle number, the load-bearing capacity gradually decreased, internal damage intensified, and pore expansion and coalescence became more pronounced. Seepage pore porosity showed an overall increasing trend, indicating a gradual enhancement of inferred permeability. Therefore, seepage pore porosity can be used as an effective indicator for evaluating permeability-related evolution in coal. During both loading and unloading stages, the relative volumes of small pores (SP), medium pores (MP), and large pores and fractures (LPF) continued to increase, whereas their average pore diameters fluctuated. This indicates that pore volume growth was controlled not only by the enlargement or shrinkage of pre-existing pores but also by new PFS generation. Fractal analysis showed that the fractal dimensions of MP, LPF, and total pores exhibited clear scale-dependent evolution, whereas the calculated SP fractal dimensions were lower than 2 and were therefore not suitable for pore-surface fractal interpretation. Among the valid pore systems, LPF exhibited the highest fractal dimension, indicating that LPF dominate the structural complexity of coal. These findings provide new insight into the fractal evolution of unloading-induced PFS damage and offer theoretical support for mitigating gas outburst and water inrush hazards during coal mining.

An investigation into spontaneous imbibition in porous media is of paramount scientific significance in various projects. However, a precise understanding of the interaction mechanisms between media structural characteristics and imbibition remains elusive, and quantitative analysis of the interfacial interaction is lacking. Therefore, to mitigate the influence of dispersion, this study first investigates cyclic imbibition experiments of coal samples to explore the interaction mechanism between pore-fracture structure (PFS) and imbibition. Nuclear magnetic resonance is used to visualize water transport during imbibition across all scales. Subsequently, the slake durability index is suggested to clarify the coupling relationship between water–coal interactions and imbibition. Two more comprehensive and accurate imbibition models are established, based on pore size and comprehensive seepage parameters, respectively. The results demonstrate that both new models exhibit superior conformity with experimental data compared to traditional models. The memory factor quantifies interface interaction within these models. Sensitivity analysis reveals that strong interface interaction diminishes the effective imbibition ratio, while the structural characteristics of porous media significantly influence the interaction. Furthermore, the fractal dimension quantitatively characterizes the PFS features of coal samples. An exploration of the relationship between fractal dimension and memory factor indicates the influence of porous media heterogeneity on imbibition.

In deep high-geostress and high-temperature environments, understanding the creep deformation of deep coal is of great significance for effectively controlling coal deformation and improving gas control efficiency. In this paper, the Abel dashpot is defined based on the conformable derivative, and a damage variable is introduced into the conformable derivative order, thereby constructing a damaged Abel dashpot. Combining the Weibull distribution and the Drucker–Prager yield criterion, the thermo-mechanical coupling damage variable is defined, and the coupling damage variable is introduced into the damaged Abel dashpot to establish a thermo-mechanical coupling damaged Abel dashpot. Based on the traditional framework of the Burgers creep model, a three-dimensional fractional creep model of deep coal considering the influence of thermo-mechanical coupling damage is proposed. Experimental data on coal creep under different temperatures and stress conditions are utilized to validate the effectiveness and applicability of the proposed three-dimensional fractional creep model and to determine the model parameters. A comparison between experimental data and model results reveals that the creep model effectively characterizes the time-dependent deformation of coal samples under varying temperature and stress influences. Additionally, an in-depth analysis is carried out on the influence mechanism of key parameters in the creep model, particularly focusing on the effects of stress levels and temperature on creep deformation.