In this study, we have built a dual porosity/permeability model through accurately expressing the volumetric strain of matrix and fracture from a three-dimensional method which aims to reveal the reservoir permeability evolution during the process of CO₂-enhanced coalbed methane (CO₂-ECBM) recovery. This model has accommodated the key competing processes of mechanical deformation and adsorption/desorption induced swelling/shrinkage, and it also considered the effect of fracture aperture and effective stress difference between each medium (fracture and matrix). We then numerically solve the permeability model using a group of multi-field coupling equations with the finite element method (FEM) to understand how permeability evolves temporally and spatially. We further conduct multifaceted analyses to reveal that permeability evolution near the wells is the most dramatic. This study shows that the farther away from the well, the gentler the evolution of permeability. The evolution of reservoir permeability near the injection well (IW) and the production well (PW) are very different, due to the combined effects of effective stress changes and gas adsorption and desorption. Furthermore, adsorption is the main controlling factor for the change of permeability for regions near the IW, while the change in effective stress is the main cause for the change in permeability near the PW. Increasing the injection pressure of CO₂ will cause the reservoir permeability to evolve more quickly and dynamically.

Under the effect of initial stress and excavation disturbance, there exists interaction between rock mass and rockbolt in deeply buried tunnels. In order to fully explore the mechanism of rock mass supported with rockbolts, this article studied the time-dependent behavior of the rock mass supported with discretely mechanically or frictionally coupled (DMFC) rockbolts. The interaction model elastic solutions under distributed force model were analyzed, then the viscoelastic analytical solutions were conducted to describe the rheological properties of the coupling model, and the solutions were acquired by setting the constitutive models of the rockbolt and rock mass in terms of a one-dimensional Kelvin model and a three-dimensional Burgers model based on material properties and dimension. Several examples were performed and the influence of initial stress σ₀, the viscosity parameters η₁ and η₂ of the three-dimensional Burgers model as well as the pre-tension T₀ on reinforcement effect were analyzed. According to the proposed model, the smaller η₂ is or the larger the pre-tension T₀ is, the more effective the support effect. However, when the pre-tension is too large, the support effect is no longer significantly enhanced. In addition, the early reinforcement effect is controlled by the first creep stage in the Burgers model while the ultimate support effect is mainly influenced by the viscosity coefficient of the second creep stage in the Burgers model. This research can provide an important theoretical reference to guide the parameter design of rockbolt reinforcement engineering in a circular symmetrical tunnel.

In this paper, we present the viscoelastic solutions for rockmass supported with discretely mechanically or frictionally coupled (DMFC) rockbolts to reveal the coupling rheological mechanisms. The analytical solutions are first acquired by applying the Laplace inverse transforms. The effect of different viscosity coefficients and supporting parameters on the coupling model rheological behavior are then investigated. It is concluded that the variation of the rockbolt axial force or rock mass stress and displacement have a close relationship with rheological parameters and support parameters. In addition, the variations of mechanical states of rockbolts and rock mass are closely related to the rheological model.