Abstract A simplified analytical solution is developed for estimating the thrusts and bending moments of the circular tunnel in half space under the obliquely incident SV wave. The seismic waves impinging on the tunnel is obtained according to the elastic wave motion theory in half space firstly, which is the superposition of the incident and reflected SV waves and reflected P wave. Then, by considering the tunnel lining as a thick-wall cylinder, analytical solutions for internal forces of circular tunnel due to the incident and reflected SV waves and the reflected P wave are deduced, which enables more precise forecasts than previous analytical solutions by the thin shell model. The total tunnel internal forces are obtained finally through the superposition of the above solutions under three kinds of waves. The accuracy of the proposed analytical solution is verified by comparing with the dynamic numerical results. Moreover, the discussion about the effect of critical factors on the accuracy of the proposed analytical solutions is conducted, including the tunnel structure inertia, the seismic wavelength, the lining thickness and the tunnel depth. These results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnel under obliquely incident SV wave in seismic design.

中文翻译：

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斜入射SV波作用下圆形隧道的简化解析解

摘要 针对斜入射SV波作用下半空间圆形隧道推力和弯矩的估计，提出了一种简化的解析解。冲击隧道的地震波首先根据半空间的弹性波运动理论得到，它是入射、反射SV波和反射P波的叠加。然后，通过将隧道衬砌视为厚壁圆柱体，推导出了由于入射和反射 SV 波和反射 P 波引起的圆形隧道内力的解析解，这使得比以前的薄壁解析解更精确的预测。壳模型。在三种波浪作用下，通过上述解的叠加，最终得到隧道总内力。通过与动态数值结果的比较，验证了所提出的解析解的准确性。此外，还讨论了隧道结构惯性、地震波长、衬砌厚度和隧道深度等关键因素对解析解精度的影响。这些结果表明，所提出的解析解表现良好，可用于预测抗震设计中斜入射SV波下圆形隧道的内力。