一种基于弹性理论的大采高区段煤柱合理尺寸计算方法

A calculation method of reasonable size of coal pillar in large mining height section based on elastic theory

不同工况下区段煤柱两侧支承压力分布及岩体变形存在显著差异,考虑煤柱两侧不同支承压力对煤柱整体稳定性的影响,基于大采高区段煤柱的弹性力学计算模型,分析了支承压力下煤柱任一单元岩体的应力应变分量。通过建立大采高煤柱弹塑性界面上岩体的柱条模型,确定在0.65倍煤柱高度处单元岩体将首先发生水平拉伸破坏,利用虎克定律提出了该单元岩体极限拉应变与煤柱极限平衡区宽度的关系式。依据煤柱破裂区岩体的受力特征,运用摩尔库伦准则推导了煤柱破裂区宽度的计算公式。结果表明:①煤柱极限平衡区宽度与岩体极限拉应变和弹性模量反相关,与煤柱埋深和煤柱高度正相关;②煤柱高度及其与顶底板的界面摩擦角是影响破裂区宽度的关键性因素;③煤柱两侧不同工况下,煤柱岩体极限拉应变与其所受侧压呈正变关系,区段煤柱采空区侧所受侧压较巷道侧偏大,采空区侧岩体的极限拉应变也相应较大,表现为采空侧极限平衡区宽度较巷道侧偏小。最后,将上述理论公式应用于陕北某矿30109工作面大采高区段煤柱极限平衡区和破裂区宽度的分析计算,给出了该工作面两侧区段煤柱的合理宽度及其支护方案。工程应用表明,30109工作面区段巷道围岩变形控制效果良好,满足现场生产需求。

There are significant differences in abutment pressure distribution and rock mass deformation on both sides of section coal pillar under different working conditions,the influence of different abutment pressures on the overall stability of coal pillar is considered,based on the elastic mechanics calculation model of coal pillar in large mining height section,the stress-strain components of any unit rock mass of coal pillar under abutment pressure are analyzed.Through the establishment of large mining height pillar elastic-plastic interface on the rock column model,it is determined that unit rock mass will first undergo horizontal tensile failure at 0.65 times the height of coal pillar,based on Hooke's law,the relationship between the ultimate stretching strain of rock mass and the width of limit equilibrium zone of coal pillar is proposed.According to the mechanical characteristics of the rock mass in the coal pillar fracture zone,the calculation formula of the width of the coal pillar fracture zone is derived by using the Mohr-Coulomb criterion.The results show that:①The width of limit equilibrium zone of coal pillar is inversely related to ultimate tensile strain and elastic modulus of rock mass and positively related to buried depth and height of coal pillar;②The height of coal pillar and the interface friction angle between coal pillar and roof and floor are the key factors affecting the width of fracture zone;③Under different working conditions on both sides of coal pillar,due to the positive relationship between the ultimate tensile strain of coal pillar rock mass and its lateral pressure,the lateral pressure on the gob side of the section coal pillar is larger than that on the roadway side,and the ultimate tensile strain of the rock mass on the gob side is correspondingly larger,which shows that the width of the limit equilibrium area on the gob side is smaller than that on the side of the gateway.Finally,the above theoretical formula is applied to the analysis and calculation of the width of limit equilibrium zone and fracture zone of coal pillar in large mining height section of 30109 working face in a mine in Northern Shaanxi,and the reasonable width of coal pillar and its supporting scheme under different working conditions on both sides of the working face are given.The engineering application shows that the deformation control effect of surrounding rock along the working face is good,which can meet the demand of field production.