渗流作用下岩溶陷落柱侧壁突水的临界水压解析解

Analytical Solution of Critical Water Pressure of Water Inrush from Karstic Collapse Column′s Side Wall under Seepage Action

在陷落柱侧壁突水研究中引入厚壁筒力学模型,将陷落柱侧壁煤柱视为多孔介质,考虑地下水的渗流体积力,应用摩尔库伦强度理论和弹塑性力学模型,推导出煤柱弹塑性状态应力解析式,以及煤柱内塑性区半径与水压力的关系表达式,同时编程试算出陷落柱侧壁突水的临界水压力。在此基础上,分析了煤柱孔隙率、煤柱抗剪强度参数以及煤柱宽度等因素对陷落柱侧壁突水的临界水压力的影响规律。研究结果表明:1煤柱能够承受的临界水压随着煤柱孔隙率的增加而降低,故当煤柱裂隙发育时,不考虑渗流力的结果将偏于安全;2煤柱宽度越大、抗剪强度越高,则临界水压越大,陷落柱侧壁突水的危险性越低;3可通过注入水泥浆液减小煤柱孔隙率和提高煤柱强度来防止陷落柱侧壁突水,同时可减少煤柱的留设宽度,对减少煤炭损失有着重要意义。

The mechanical model of thick wall cylinder was introduced to study on water inrush from karstic collapse column＇s side wail. Coal pillar of collapse column＇s side wall was regarded as porous medium. Mohr Coulomb strength theory and elastoplastic mechanical model were used to deduce the analytic expression of the coal pillar elastoplastic stress state, and the relational ex- pression between the radius of plastic zone and the water pressure, while the critical water pres- sure of water inrush of subsided column side wall was calculated by the trial and error of pro- gramme. Based on this, the influence of coal pillar＇s porosity, coal pillar^s shear strength param- eters, and coal pillarr s width on critical water pressure were analyzed. The results show that. （1） the values of the critical water pressure decreases with increase of the values of coal pillar＇s porosity. So the result irrespective of seepage action is on the side of safety when the coal pillar fracture development~ （2） The bigger of coal pillar＇s width, the higher of coal pillar＇s shear strength parameters, the lower possibility of water inrush from collapse columnr s side wall will occur. The coal pillar can be injected into the cement slurry to reduce its porosity and improve its strength based on the above results. This approach can effectively prevent water inrush from col- lapse column＇s side wall, and also can reduce the coal pillar＇s width. Therefore, it has important significance to reduce the coal loss.