The time-dependent creep behavior of coal is essential for assessing long-term structural stability and operational safety in deep coal mining. Therefore, this work develops a full-stage creep constitutive model. By integrating fractional calculus theory with statistical damage mechanics, a nonlinear fractional-order (FO) damage creep model is constructed through serial connection of elastic, viscous, viscoelastic, and viscoelastic–plastic components. Based on this model, both one-dimensional and three-dimensional (3D) fractional creep damage constitutive equations are acquired. Model parameters are identified using experimental data from deep coal samples in the mining area. The result curves of the improved model coincide with experimental data points, accurately describing the deceleration creep stage (DCS), steady-state creep stage (SCS), and accelerated creep stage (ACS). Furthermore, a sensitivity analysis elucidates the impact of model parameters on coal creep behavior, thereby confirming the model’s robustness and applicability. Consequently, the proposed model offers a solid theoretical basis for evaluating the sustained stability of deep coal mining and has great application potential in deep underground engineering.

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.

As challenges in gas extraction from coal mines increase, precise measurement of permeability becomes crucial. This study proposes a novel pulse transient method based on a fractional derivative model derived on physical fractal space, incorporating operator algebra and the mechanics–electricity analogy to derive a new control equation that more accurately delineates the permeability evolution in coal. To validate the approach, permeability experiments were conducted on coal samples under mining stress conditions. The results showed that the adoption of a physically meaningful fractional-order relaxation equation provides a more accurate description of non-Darcy flow behaviour in rocks than traditional integer-order control equations. Additionally, the method proved effective across different rock types, verifying its broad applicability. By establishing a new theoretical foundation, this approach illustrates how the microscale fractal structure of rocks is fundamentally linked to their macroscale fractional responses, thereby enhancing the understanding of fractional modelling methods in rock mechanics and related domains.

Coal resource extraction and utilization are essential for sustainable development and economic growth. This study integrates a pseudo-triaxial mechanical loading system with low-field nuclear magnetic resonance (NMR) to enable the preliminary visualization of coal’s pore-fracture structure (PFS) under mechanical stress. Pseudo-triaxial and cyclic loading–unloading tests were combined with real-time NMR monitoring to model porosity recovery, pore size evolution, and energy dissipation, while also calculating the fractal dimensions of pores in relation to stress. The results show that during the compaction phase, primary pores are compressed with limited recovery after unloading. In the elastic phase, both adsorption and seepage pores transform significantly, with most recovering post-unloading. After yield stress, new fractures and pores form, and unloading enhances fracture connectivity. Seepage pore porosity shows a negative exponential relationship with axial strain before yielding, and a logarithmic relationship afterward. The fractal dimension of adsorption pores decreases during compaction and increases afterward, while the fractal dimension of seepage pores decreases before yielding and increases post-yielding. These findings provide new insights into the flow patterns of methane in coal seams.

Deep mining is often accompanied by complex geological conditions, which can cause damage to the coal seam roof surrounding rock, thereby reducing its safety and stability. Therefore, analyzing the long-term mechanical behavior of multiscale damaged sandstone under deep mining conditions is of great significance. To describe the long-term deformation and damage evolution of multiscale damaged sandstone under deep mining conditions, this work establishes a fractional-order multiscale damage creep model by incorporating fractional calculus and damage mechanics theory into the Nishihara model. The model parameters were determined by fitting the creep data of damaged sandstone using the least squares method. The results demonstrate that the proposed model can accurately simulate the complete creep process, including the decelerated, steady-state, and accelerated stages. Compared with the classical integer-order multiscale damage creep model, the fractional-order model can better capture the time-dependent behavior of materials and thus shows superior performance in characterizing the nonlinear features of the accelerated creep stage. Furthermore, through sensitivity analysis of the parameters reveals the influence of key parameters on different creep stages, thereby validating the model’s effectiveness and reliability. This model provides a solid theoretical foundation for evaluating the long-term stability of coal mine roof strata in deep mining environments.

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.