Typical parallel fractures are often observed in the outcrops of inclusions in the field. To reveal the failure mechanism of inclusions embedded in rock matrix, a series of heterogeneous models are established and tested based on the damage mechanics, statistical strength theory, and continuum mechanics. The results show that, with the spacing between two adjacent fractures decreasing, the stress is firstly transferred from negative to positive, then from positive to negative. Stress transition is profound for the fracture spacing. Meanwhile, three types of fractures, i.e., consecutive fracture, non-consecutive fracture, and debonding fracture, are found, which are consistent with the observed modes in the field. Multiple inclusions are often fractured easier than an isolated inclusion due to the stress disturbance between inclusions and newly generated fractures. Either in single or multiple inclusions, tensile stresses inside the inclusions are the main driving force for fracture initiation and propagation. Besides, although the material heterogeneity has a small effect on the stress variation, it has an evident impact on the fracturing mode of inclusions. The stiffness ratio is critical for the stress transition and failure pattern; the interface debonding occurs earlier than the fracture initiation inside the inclusion when the stiffness ratio is relatively high. Additionally, the inclusions content only affects the sequence of fracture initiation rather than the final fracture spacing pattern.

In order to investigate freeze–thawed red sandstone failure processes under cyclic loading and unloading conditions, real-time acoustic emission (AE) and scanning electron microscopy (SEM) techniques were used to reveal the fracture process of the saturated red sandstone after cyclic loading and unloading tests using uniaxial compression. The results show that the stress–strain curves of the freeze–thawed sandstones show signs of hysteresis and exhibit a two-stage evolution of “sparse → dense”. In the cyclic loading and unloading process, the modulus of elasticity in the loading process is always larger than that in the unloading process, while the Poisson’s ratio is the opposite, and the radial irreversible strain and cumulative irreversible strain are larger than those in the axial direction. As the number of freeze–thaw cycles increases, the rock specimens need more cycles of loading and unloading to make the crack volume compressive strain $\Delta {\epsilon }_{cv}^{+}$ reach the maximum value and tend to stabilize, while the crack volume extensional strain $\Delta {\epsilon }_{cv}^{-}$ tends to decrease gradually. This study also shows that the growth phase of the cyclic loading and unloading process has more ringing counts and a shorter duration, while the slow degradation phase has more ringing counts with loading and less with unloading. In addition, the F-T cycle gradually changes the internal microcracks of the red sandstone from shear damage, which is dominated by shear cracks, to tensile damage, which is dominated by tensile cracks. This study’s findings contribute to our knowledge of the mechanical characteristics and sandstone’s degradation process following F-T treatment, and also serve as a guide for engineering stability analyses conducted in the presence of multiphysical field coupling.

The mechanical properties of gas-containing coal and rock mass play important roles in controlling the occurrence and development of coal and gas outbursts. The gradual increase in mining depth will change the failure mechanism of gas-containing coal and rock mass. In order to further study the failure mechanism of gas-containing coal and rock mass, samples were taken from the gas-containing coal seam in the Wuhushan Coal Mine of the Wuhai Mining area of China. The mechanical parameters of coal samples during the failure process under different gas pressure conditions were measured and analyzed with the SAW-2000 rock mechanics testing machine, the gas-containing coal uniaxial compression device and inflation system. Meanwhile, the failure process and mechanical parameters of coal samples under different gas pressure were simulated by RFPA^2D gas plate numerical simulation software. The results show that with increasing gas pressure in the coal there is decrease in Compressive strength, Elastic modulus, Strain, Peak strength and Bearing capacity and increase in Poisson’s ratio. When the failure state appears in the coal, the cracks are longer and wider, more random cracks are genareted, and the damage degree of the coal is greater. The numerical analysis’ results are in good agreement with experimental results. The research results are applicable to the gas bearing coal with the same or similar gas geological conditions. The tests can be carried out repeatedly and reasonable results can be obtained according to the physical and mechanical parameters of the actual coal seam and the occurrence of gas. On this basis, physical experiments and numerical simulations of triaxial compression can also be carried out to further study the mechanical characteristics of deformation and the failure of gas-containing coal under gas pressure and provide technical support for revealing the mechanism of coal and gas outbursts.