圆形坑道的精确弹性解

EXACT ELASTIC SOLUTION FOR CIRCULAR TUNNELS

本文按弹性理论和应力释放法概念,用一个简单的应力函数求出了圆形坑道的精确弹性解,舍弃了近似解中以坑道中心初始应力替代周边初始应力的假定,使计算结果更接近实际。本文推导的公式可用以检算弹性介质中圆形坑道的稳定性,并可作为检验数值分析精度的依据。

Based on the theory of elasticity and the concept of stress relieving,an exact elastic solution forcircular tunnels is fucnpresented in this paper by means of a simple airy stress tion,not considering theapproximate solution assumption of substituting the values of in situ initial stresses around the tunnelperiphery by those at the center,so that the calculated values of stresses and displacments caused byexcavating a tunnel can better approach the actual conditions. The proposed formulas may be used toanalyze the stability of the circular tunnel in the surrounding elastic medium and also as a basis forchecking the accuracy of the numerical analysis.