考虑分形效应的煤岩损伤模型及渗透率模型

Research on coal damage model and permeability model considering fractal effect

为探索煤岩失稳破坏过程中损伤演化和渗透率演化规律,用分形维数表征损伤演化,研究煤岩损伤破坏过程中渗透特性。基于孔裂隙的体积分形维数与应力关系,推导出分形维数表征的Weibull分布参数,利用煤岩孔裂隙的分形维数和孔隙率的关系,求解煤岩裂隙随有效应力的变化量γ;根据Mohr-Coulomb准则和Poiseuille定律,分别构建考虑分形效应的煤岩损伤本构模型和煤岩渗透率模型,分析损伤和渗透率的联动关系。结果表明:峰值应力前,孔裂隙体积分形维数与轴向应力和应变均成线性关系;随着有效应力的增大,煤岩孔隙率增大,煤岩渗透率先平缓增大后急剧增大;同一应力点下的渗透率随ln(1/r)的增大而增大;所建立的煤岩损伤本构模型和渗透率模型,与试验结果均有较高的吻合度。

In order to investigate the law of damage evolution and permeability evolution of coal during unstable failure process,relationships between volume fractal dimension of pore-fracture networks and stress and strain were introduced respectively.According to the relationship between volume fractal dimension of pore-fracture and stress,Weibull distribution parameters characterized by fractal dimension characteristics were derived.According to the relationship between the fractal dimension and porosity of pore-fracture of coal,variation(γ)of coal fractures with effective stress was solved.Based on Mohr-Coulomb criterion and Poiseuille law,a coal damage constitutive model and a permeability model considering the fractal effect were built.Then the relationship between damage and permeability was analyzed.The results show that before peak stress,the volume fractal dimension of pore-fracture is linear with axial stress and strain,that porosity of coal increases with the increases of effective stress,and the permeability increases first slowly and then sharply,that the permeability increases with the increase of ln(1/r)at the same stress point,and that solutions of both the damage constitutive model and the permeability model of coal conform closely with the experimental data.