Dongjie Xue

The safety evaluation of seepage in interlayer rock beneath the underground water reservoir of coal mines is crucial for the secure extraction of lower coal seams. Accurate calculation of the permeability of interlayer rock serves as a fundamental basis for this seepage safety assessment. The transient testing method is frequently employed to measure permeability in low-permeability rocks, relying on a precise description of the decay curve of the seepage pressure difference. However, the spatial distribution of this seepage pressure difference is often overlooked, leading to permeability calculations being influenced by linear Darcy's laws. Using the interlayer rock of the underground reservoir in the Daliuta coal mine as a prototype, we designed complex disturbance stress paths associated with lower coal seam mining in three stages: in-situ stress, mining stress, and cyclic stress. Multiple seepage tests were conducted at characteristic points throughout the entire process on coal, mudstone, and sandstone under varying hydraulic-mechanical coupling conditions using the transient method. These tests revealed the phenomenon of rebound expansion during the mining stress stage of the interlayer rock. Furthermore, we describe the nonlinearity of the relaxation process of the seepage pressure difference decay curve based on the Forchheimer equation and the Mittag-Leffler function, validating the applicability of the Mittag-Leffler function in characterizing the differential pressure decay process of non-Darcy seepage in rocks. Subsequently, a spatiotemporal theoretical model for the decay process of the seepage pressure difference in interlayer rock under hydraulic-mechanical coupling was established, demonstrating that this decay can be represented by the fluid diffusion equation. An accurate description of the spatiotemporal evolution of seepage pressure difference in rock is achieved through fractional-order theory. We also emphasize that the principle underlying the transient method for measuring permeability is to satisfy Darcy’s law spatially, indicating that transients conform to steady-state tests in space, while seepage exhibits non-Darcy characteristics over time. Finally, based on the hysteresis principle, we derive the discrete format of the one-dimensional fractional-order diffusion equation and complete the discretization of spatiotemporal fractional-order equations for the decay of seepage pressure difference in interlayer rock under hydraulic-mechanical coupling. Utilizing the finite-difference method, we solve and visualize the spatiotemporal distribution surfaces of seepage pressure difference in the interlayer rock, providing a foundation for theoretical solutions regarding the spatial distributions of permeability.

Dynamic failure of surrounding rock often causes many casualties and financial losses. Predicting the precursory characteristics of rock failure is of great significance in preventing and controlling the dynamic failure of surrounding rock. In this paper, a triaxial test of granite is carried out, and the acoustic emission events are monitored during the test. The fractal characteristics of acoustic emission events’ energy distribution and time sequence are analyzed. The correlation dimension and the b value are used to study the size distribution and sequential characteristics. Furthermore, a rock failure prediction method is proposed. The correlation dimension is chosen as the main index and the b value is chosen as a secondary index for the precursor of granite failure. The study shows that: (1) The failure process can be divided into an initial stage, active stage, quiet stage, and failure stage. (2) The b value and correlation dimension both can describe the process of rock failure. There is a continuous decline before failure. Because of the complexity of the field, it is difficult to accurately estimate the stability of surrounding rock using a single index. (3) The combination of the b value and correlation dimension to establish a new method, which can accurately represent the stability of the surrounding rock. When the correlation dimension is increasing, the surrounding rock is stable with stress adjusting. When the correlation dimension is decreasing and the b value remains unchanged after briefly rising, the surrounding rock is stable, and stress is finished adjusting. When the correlation dimension and b value are both decreasing, the surrounding rock will be destroyed.

Permeability in porous media has an important role in many engineering applications, which depends mainly on the pore size, distribution, and connectivity of porous media. As the pore structure distribution of coal has a multi-scale fractal dimension characteristic, this study aimed to propose a multi-scale fractal dimension characteristics units model (MFU) to describe the pore structure distribution by analyzing the multi-scale fractal dimension characteristics of coal pore media. Then, a multi-scale fractal permeability model was established based on MFU. The pore structure distribution was obtained by mercury injection porosimetry (MIP) and nuclear magnetic resonance (NMR) experiments. Based on MIP and NMR experimental data, the permeability contribution of different pore diameters were calculated. The results show that the permeability contribution of the micropore was minimal and can be ignored. The permeability contribution of mesopores was about 1–5%, and the permeability contribution of macropores was about 95–99%, which plays a decisive role in the seepage process. The calculated results, based on multi-scale fractal permeability model and the experimental permeability data, are in the same order of magnitude. The permeability prediction based on proposed model is better than classical single fractal permeability model.