基于弹性理论的煤帮极限平衡区宽度确定方法探讨

回采巷道开挖后，其围岩应力重新分布，两侧煤体在上方集中应力的作用下产生变形后形成极限平衡区，其理论宽度是合理确定巷道煤帮支护方案及其参数的重要依据,目前，计算煤帮极限平衡区的主要方法有:利用松散介质平衡理论建立煤帮应力平衡微分方程来求解极限平衡区宽度;或考虑工程扰动程度和煤体地质强度，运用非线性摩尔-库伦准则建立极限平衡区宽度方程。本文在总结现有研究成果的基础上，建立了回采巷道煤帮在高支承压力作用下体的力学计算模型，运用弹性力学理论分析了帮部任一点煤体的应力应变分量。基于弹塑性界面煤体在峰值支承压力发生片帮的柱条模型，确定该界面上发生最大水平拉应变的单元煤体位于距离底板0.65倍巷道高度处，进而提出了该单元煤体极限拉应变与煤帮极限平衡区及其破裂区宽度的理论计算公式。分析表明,煤帮极限平衡区宽度不仅取决于煤体的极限拉应变、泊松比及弹性模量，而且与原岩应力大小及巷道开挖后发生重分布的最大支承压力及煤帮弹性区宽度密切相关。具体表现为煤帮极限平衡区宽度随巷道埋深增大而不断增加，但随煤体弹性模量及其极限拉应变的增加却快速减小。在此基础上，利用所提出的理论公式计算了百良矿14501工作面运输巷350～400 m区段的煤帮极限平衡区和破裂区宽度，进而优化了巷道帮部锚杆支护参数，取得了良好的支护效果。结果表明，上述研究成果能够较好地进行深埋煤层巷道煤帮极限平衡区的预测分析。

Discussion on determination method of the limit equilibrium zone width based on the deformation analysis of coal wall

The redistribution of the stress in surrounding rock will generally occur after the excavation of the mining roadway.The coal mass deforms under the action of upper concentrated stress and the limit equilibrium zone within the coal-side,whose theoretical width is an important basis for reasonably determining the support scheme and parameters.At present,the width of the limit equilibrium zone is solved according to the stress equilibrium differential equation of the coal-wall based on the stress medium equilibrium theory of loosed material or the width equation about the limit equilibrium zone by the nonlinear Mohr-Coulomb criterion considering the engineering disturbance level and geological strength of coal body.Summarizing the existing research methods on the limit equilibrium zone,this paper established the mechanical calculation model of the coal-side under high bearing pressure,and the stress-strain components of the coal body within the coal-side were analyzed using the theory of elasticity mechanics.The unit coal body with the maximum horizontal tension strain under the action of peak bearing pressure was located at the 0.65 times height of roadway,which was determined by the vertical slice model of the coal body at elastic-plastic interface.Then the theoretical formula connecting the ultimate tensile strain of the coal body with the limit equilibrium zone width was put forward.The analysis shows that the width of the limit equilibrium zone of the coal-wall is dependent on the parameters of the coal mass such as ultimate tensile strain,Poisson’s ratio,elastic modulus,primary rock stress,the maximum bearing pressure as well as the elastic zone width of the coal-wall.Specifically,the width of the limit equilibrium zone of coal-wall increases with the buried depth addition of the roadway,but decreases rapidly with the increase of the elastic modulus of the coal as well as its ultimate tensile strain.On this basis,the limit equilibrium zone and the width of the failure zone of the coal-wall in the 350-400 m section of the transport roadway in 14501 mining face of Bailiang Coal Mine were calculated by the proposed theoretical formulas,and the bolt support parameters of the coal-wall were optimized,and some good supporting effects were obtained.The above research can be used to predict and analyze the limit equilibrium zone of the coal-wall in deep buried seam roadway.