**1. Introduction**

Coal and gas outburst, as a major cause of gas hazards in coal mines, results from a very complex dynamic instability process at underground mine sites [1,2]. When such a hazard occurs, the gas adsorption/desorption and seam stress-strain at the outburst site undergo tremendous change. The gas also affects the deformed coal body, causing it to change further [3–5]. Currently, the mechanisms underlying coal and gas outburst remain unsolved. Wider investigation into the mechanical properties and seepage behavior of gas-bearing coal under stress-seepage coupling is of great importance.

As field testing is impractical, given the high risk factor of seams prone to coal and gas outburst, experimental study of coal-gas coupling mechanisms forms the fundamental means of understanding coal permeability evolution and damage mechanisms [6,7]. Xu et al. [8,9] experimentally characterized coal deformation and permeability under loading/unloading conditions and revealed that coal permeability variation is closely related to coal deformation and damage. Yin et al. [10] evaluated the effect of loading/unloading conditions on the mechanical properties of gas-bearing coal and established a whole process seepage speed–axial pressure equation. Wang et al. [11] studied the dynamic behaviors in coal seams under different mining layouts. Zhao et al. and Wang et al. [12,13] analyzed the relationship between coal permeability, stress difference and strain during loading/unloading through whole-process stress-strain permeability tests. Li et al. [14] observed the deformation and permeability behaviors of outburst coal samples under cyclic loads and found that permeability variation is closely related to coal damage and deformation. Cao et al. [15] analyzed how confining pressure and axial pressure affect coal gas seepage under constant gas pressure. Xue et al. [16] performed uniaxial tension and compression, conventional triaxial and dynamics tests, and obtained the mechanical characteristic parameters and deformation failure behaviors of coal samples under different load paths and load rates.

**Citation:** Sun, H.; Zhang, B.; Song, Z.; Shen, B.; Song, H. Mechanics-Seepage Experimental and Simulation Study of Gas-Bearing Coal under Different Load Paths. *Processes* **2022**, *10*, 2255. https://doi.org/10.3390/pr10112255

Academic Editors: Feng Du, Aitao Zhou and Bo Li

Received: 9 October 2022 Accepted: 31 October 2022 Published: 2 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

<sup>1</sup> School of Safety Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China

The discrete element method (DEM) is an important numerical method of solving coal mechanical problems due to its ability to assess coal mechanics and crack mechanisms from a mesoscopic perspective [17–19]. Indraratna et al. [20] made cyclic biaxial simulation tests at different frequencies with DEM software. They also analyzed the evolution of meso-mechanical parameters such as contact force and bond force formed during cyclic loading and explained the mechanism of particle fracture. Wang et al. [21] simulated crack propagation with a PFC-based particle flow model and observed how coal stress affects crack propagation. Jiang et al. [22] simulated a series of biaxial compression tests with DEM and observed the mechanical behavior of deep-sea methane-hydrate-bearing soils. Ismail et al. [23] built a DEM model for visualizing damage evolution and predicting failure envelopes of composite laminae under biaxial loads. Yang et al. [24] numerically simulated the failure behavior around a circular opening under biaxial compression. Sagong et al. [25] made experimental and numerical analyses of the sliding of fissures and joints in fissurebearing rock under biaxial compression. Raisianzadeh et al. [26] used DEM to simulate the interaction between particles under biaxial load, and studied the crack propagation path and failure strength of rock containing prefabricated cracks Xu et al. [27] studied the influence of the angle between two cracks on the strength and crack propagation of the specimen.

From the literature review above, both physical experiments and numerical simulations help to understand the mechanisms behind coal and gas outburst. However, few attempts have been made to combine physical experiments with numerical simulation. In this paper, the deformation failure and gas-seepage behavior of briquette specimens under different stress paths are tested. The test results are then verified through particle flow code (PFC) numerical simulation. Specimen-crack evolution under different paths is also characterized. Our method offers a new approach to understanding the mechanisms behind coal and gas outburst.

#### **2. Experimental Section**

#### *2.1. Specimen Procurement and Preparation*

The structural complexity of raw coal can give rise to substantial discreteness of test results. Previous studies have demonstrated that briquette, in one way or another, possesses the physical–mechanical and adsorption properties of raw coal. It is also easy to transport and handle. For this reason, briquette is often used in laboratory studies as a substitute for raw coal [28].

The coal sample came from Jixi Mining Group's Xinfa coal mine, which is a high-gas mine. The sample has an ash content of 61.28%, a volatile content of 22.9%, and a solidity factor of 0.5866. After the sample was recovered from the mine face, it was sealed and delivered to the laboratory where it was crushed. When preparing specimens, 30 g river sand, 30 g cement, 210 g crushed coal, and 30 g water were mixed together and kept under 200 kN moulding pressure for 12 h before the specimens were demoulded and placed in a curing box for further use. Figure 1 shows the ready-made briquette specimens.

#### *2.2. Experimental Apparatus*

A triaxial servo-controlled seepage apparatus for thermofluid–solid coupling of gasbearing coal shown in Figure 2 was used for the test, featuring φ50 mm × 100 mm standard specimens [9].

**Figure 1.** Briquette specimens.

**Figure 2.** The triaxial servo-controlled seepage equipment for thermofluid–solid coupling of coal containing methane.

### *2.3. Experimental Methods*

The real load state of mining-disturbed coal at deep levels was simplified into three load paths: axial pressure loading in Test 1, confining pressure unloading in Test 2, and composite loading/unloading in Test 3, as shown in Figure 3, where *σ*<sup>1</sup> represents axial pressure and *σ*<sup>3</sup> represents confining pressure, and the flow chart for the experiment is shown in Figure 4. The exact test plan is described below:

**Figure 3.** Schematic diagram of experimental loading path. (**a**) Test 1, (**b**) Test 2, (**c**) Test 3.

**Figure 4.** Flow chart for the experiment.

Test 1: Load *σ*<sup>1</sup> and σ<sup>3</sup> to 6 MPa, then feed 1 MPa gas. After adsorption for 24 h, load *σ*<sup>1</sup> at the rate of 5 kN/s until the specimen fails. Conduct gas seepage test at the same time.

Test 2: Load *σ*<sup>1</sup> and *σ*<sup>3</sup> to 6 MPa, then feed 1 MPa gas. After adsorption for 24 h, load *σ*<sup>1</sup> to *σ*<sup>U</sup> (which is 60% of the peak axial stress in Test 1) at the rate of 5 kN/s, keep *σ*<sup>1</sup> unchanged and unload *σ*<sup>3</sup> at the rate of 0.01 mm/min until the specimen fails. Conduct gas seepage test at the same time.

Test 3: Load *σ*<sup>U</sup> in the same steps as Test 2, then keep the loading rate of *σ*<sup>1</sup> unchanged and unload *σ*<sup>3</sup> at the rate of 0.01 mm/min until the specimen fails. Conduct gas seepage test at the same time.
