In this paper, using the continuum-discontinuum element method (CDEM), the fragmentation and outburst process of coal specimen are simulated, and the main factors affecting coal breaking and outburst are explored. The results show that after the coal seam is uncovered, coal generates obvious failure and outburst trend. Near coal-free surface, the fracture coal blocks generate significant displacement, resulting in larger opening widths of coal cracks. Coal deep generates the cracks without an obvious opening width. The crack density of coal with pore gas is larger than those of coal without gas, and it is larger than those of coal without pores. However, in the early stage of coal failure, the obvious separation and outburst ranges of coal with gas are smaller than those of coal without gas, and are smaller than those of coal without pores. The numbers of fracture coal blocks show an increase with the growth of in situ stress, pore ratio and gas pressure. The effect of in situ stress on fracture coal block number (517–10,203) is larger than the effect (7589–15,170) of pore ratio and is larger than the effect (5803–6836) of gas pressure. The effect of in situ stress on a maximum size (0.0387–0.138 m) of fracture blocks is larger than the effect (0.0342–0.0733 m) of pore ratio and is larger than the effect (0.0454–0.0578 m) of gas pressure. The coal outburst velocity and range show an increase with the growth of gas pressure and in situ stress (3.77–5.65 m/s); however, the coal outburst shows a slow decrease with a growth of pore ratio. The effect of gas pressure on the coal outburst velocity (11.51–21.9 m/s) is larger than the effect (3.77–5.65 m/s) of in situ stress and is larger than the effect (4.52–5.23 m/s) of pore ratio. This investigation is beneficial to understand the mechanisms of coal–gas outburst in coal mining and roadway excavation.

The permeability of low-permeability cores is generally measured using a pulse decay method. The core of low-permeability rocks, such as shale, often has a layered structure. The applicability of pulse decay testing for layered cores is not clear. In this study, the performance of the pulse decay method on layered cores was comprehensively investigated. Numerical simulations were conducted to investigate the influence of the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers on the pulse decay pressure and pressure derivative curves, as well as the permeability obtained from pulse decay testing. The results revealed that the pressure curves of layered cores exhibit distinct differences from those of homogeneous cores if the upstream permeability is larger than the downstream one. The pressure derivative curve shows more inclined or horizontal straight-line segments than in the homogeneous case. The shapes of the pressure and pressure derivative curves are affected by the upstream and downstream positions of the core, but the tested permeability is not affected. The tested permeability differs from the equivalent model permeability, with an error of up to 22%. If the number of layers is not less than 10, the permeability obtained from the pulse decay test is consistent with that of the equivalent model. These differences are influenced by the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers. To improve the accuracy of permeability analysis in pulse decay testing for layered cores, curve fitting using the characteristics of the pressure derivative curve can be employed.

Hydraulic fracturing is the primary technology for extracting unconventional oil and gas resources. Rock apparent fracture toughness is the most critical parameter in hydraulic fracturing processes. Rock apparent fracture toughness exhibits characteristics distinct from those of metallic materials, particularly as field-estimated values of rock apparent fracture toughness in hydraulic fracturing exceed laboratory-measured values by 1–2 orders of magnitude. Existing interpretation models assume a constant stress distribution in the fracture process zone (FPZ), which contradicts the softening behavior of rock. To address this gap, and based on the assumption of a power-law softening stress distribution in the FPZ of quasi-brittle rock, we develop a mode I apparent fracture toughness model for rock under far-field tensile and compressive stress configurations. This model considers both the softening characteristics of rock and the fluid lag effect. A comparative analysis was conducted on the differences in rock apparent fracture toughness between far-field compressive stress and tensile stress configurations. The results reveal that the difference in configuration between far-field compressive stress and tensile stress constitutes the fundamental reason for the order-of-magnitude discrepancy between the rock apparent fracture toughness estimated from hydraulic fracturing field tests and that measured in laboratory experiments. The influence of the ratio of in situ stress to tensile strength, the ratio of FPZ length to fracture length, the ratio of fluid lag zone length to fracture length, and stress distribution within the FPZ on rock apparent fracture toughness was analyzed, and these factors are found to have decisive effects on the rock apparent fracture toughness. Additionally, the size effect on rock apparent fracture toughness was discussed. This research contributes to more precise hydraulic fracturing parameter design.