深部立井井筒三维力学模型及解析解
首发时间:2019-12-09
摘要:针对深部立井井筒在围岩作用下的应力分布,基于弹性力学轴对称空间问题,采用勒夫位移函数解法得出了井筒围岩中的应力分布解析解。首先,将立井井筒在均匀分布的随井筒深度线性增加的水平地应力作用下的应力分布分解为两部分:不考虑重力的半无限长厚壁圆筒受均匀分布的沿筒的轴向线性增加的水平应力、仅受重力作用的半无限长厚壁圆筒。然后,采用位移解法,引入勒夫位移函数并通过量纲分析法对位移函数进行假设,结合边界条件得出第一部分的解析解;基于胡克定律得出第二部分的解析解。最后,利用叠加原理,将两部分解析解叠加,得出总的应力分布,并且与平面应变假设下的解析解进行对比,研究结果可以为深立井的理论分析及支护设计提供一定的参考。
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Solution of three dimensional mechanical model of vertical shaft in deep
Abstract:For deep shaft lining under the effect of surrounding rock stress distribution, based on the axisymmetric elastic mechanics problem of space, the wellbore is obtained using low displacement function method analytical solutions of stress distribution of surrounding rock. First of all, the shaft lining in uniform distribution of linear increase with the increase of wellbore depth horizontal in-situ stress under the action of the stress distribution is decomposed into two parts: regardless of the gravity of semi-infinite long thick wall cylinder are evenly distributed along the tube axial linear increase of the horizontal stress, only by the gravity of semi-infinite long thick wall cylinder. Then, the displacement function is introduced, and the displacement function is assumed by the dimensional analysis method, and the analytic solution of the first part is obtained by combining the boundary conditions. The analytic solution of the second part is obtained based on Hooke's law. Finally, using the superposition principle, the analytical solution superposition of two part, it is concluded that the total stress distribution, and compared with analytical solution under the plane strain assumption, the research results can provide deep vertical shaft of theoretical analysis and design of support some reference.
Keywords: deep coal bump roadway constant resistance and large deformation cables laboratory impacting experiment in-situ test
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