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基于非静水应力场中圆形衬砌隧道围岩与衬砌的弹性复变函数表达,利用黏弹性对应原理推导了隧道衬砌与围岩在光滑接触和完全接触情况下的黏弹性通解。推导中围岩符合黏弹性,衬砌为线弹性,且考虑了衬砌支护滞后效应,得到的理论解适用于所有线弹性元件模型。推导的理论解与以往理论解及数值解较一致。根据解答,假定围岩符合广义开尔文(H-K)黏弹性体时,分析表明,衬砌所受的径向、切向应力、衬砌的环向位移以及轴力弯矩均随时间增长而逐渐增大,并收敛于定值;两种接触条件下,围岩的位移、衬砌的应力、位移和内力沿环向分布规律均有较大不同,且随时间增大,二者相差越大。相比已有解析,文中所推导的非静水应力场中衬砌与围岩两种接触下黏弹性解更具普适性,且完全接触下的黏弹性解与深埋圆形衬砌隧道实际情况更为接近。对比两种解析可为实际中衬砌的合理选择和施工提供参考。
Based on the elastic complex function expression of surrounding rock and lining of circular lining tunnel in non-hydrostatic stress field, the viscoelastic general solutions of tunnel lining and surrounding rock under the condition of smooth contact and complete contact are deduced by using the viscoelastic principle. The results show that the surrounding rock complies with the viscoelasticity and the lining is linear elastic, and considering the hysteresis effect of lining support, the theoretical solution obtained is suitable for all linear elastic element models. The deduced theoretical solution is consistent with the previous theoretical solution and numerical solution. According to the solution, when the surrounding rock meets the generalized Kelvin (HK) viscoelastic body, the analysis shows that the radial and tangential stress on the lining, the circumferential displacement of the lining and the axial force and bending moment increase with time, And converges to the fixed value. Under the two contact conditions, the displacement of surrounding rock, the stress and displacement of lining and the distribution of internal force in the circumferential direction are quite different, and the difference between them increases with time. Compared with the previous analysis, the viscoelastic solutions of the lining and the surrounding rock in the non-hydrostatic stress field derived from the paper are more universal, and the viscoelastic solution under complete contact is more in line with the actual situation of the deep-buried circular lining tunnel To be close. Comparing the two kinds of analysis can provide a reference for the reasonable selection and construction of lining in practice.