隧洞边界超欠挖的摄动法解析分析

钻爆法施工常造成隧道边界不平整,隧道分析模型一般将开挖界面光滑处理,忽略了边界不平整对围岩应力的扰动作用。将隧道超欠挖值当作中心偏量小参数,利用摄动法得到了静水压力下圆形隧道的弹性应力解。计算分析表明:超欠挖改变了隧道洞壁附近围岩的应力状态,围岩应力随超欠开挖曲线呈波浪状变化,应力变化量与超欠挖曲线幅值及曲线斜率有关;环向应力变化最大值在洞壁处,其应力集中系数分别在超挖及欠挖顶点达到局部极大与极小值,径向应力变化最大值靠近洞壁表面,切应力变化最大值位于超挖与欠挖表面相交处;扰动应力在径向衰减较快,影响范围约为1~2倍的隧道半径。

An analytical solution to tunnels with over-under-excavated surface based on perturbation method

The tunnels excavated using drilling and blasting often results in a very irregular and rough excavation surface,its influences on the stress of surrounding rock were neglected for adopting a regular and smooth excava-tion surface in tunnel analysis model.Considering the over-under-excavated values as little parameter,an elastic stress solution of circular tunnel under hydrostatic pressure is reached based on perturbation method.Conclusions made from the solution as follows: the stresses of surrounding rocks near opening surface vary with over-under-excavated values,the variation of stress relates to the amplitude and slope of the curve of over-under-excavated;the point of the maximum circumferential stress variation locate in the opening surface,stress concentration coefficient reach local maximum and minimum values at the peak of over-excavated and under-excavated part in the sur-rounding rock respectively,the point of the maximum radial stress variation is near the opening surface,at the in-tersection point of over-excavated and under-excavated surface,the shear stress variation reach its maximum values.the stresses induced by irregular and rough surface decrease rapidly in the radial direction,the disturbed areas is about 1~2 times the radium of tunnels.