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| Analytical solution of deep buried rectangular tunnel under the action of far field shear wave |
| ZHANG Zhiguo1，2，3，YANG Feng1，ZHAO Qihua3 |
(1. School of Environment and Architecture，University of Shanghai for Science and Technology，Shanghai 200093，China；
2. Key Laboratory of Geohazard Prevention of Hilly Mountains，Ministry of Land and Resources，Fuzhou，Fujian 350002，China；
3. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection，Chengdu University of Technology，
Chengdu，Sichuan 610059，China) |
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Abstract The existed solutions on the interaction between the seismic responses of soil and structure have focused on the tunnels of circular cross section. The dynamic analysis for the rectangular tunnel tends to increase in complexity of calculation. An analytical solution of the seismic response of deep buried rectangular tunnel under the action of far field shear waves is derived based on the pseudo static method by using the complex analysis and conformal transformation. The shear and normal stresses in the interaction between soil and tunnel are considered in the solution of the complex function. The accuracy of calculating the conformal transformation function for rectangular tunnel is improved by introducing a correction factor. The accuracy of the analytical method is verified with the numerical model. The parameters influencing the normalized displacement ratio and the variation of the soil stress field for the rectangular tunnel are analyzed as well. The study shows that the accuracy of the analytical solution is improved by introducing the correcting coefficient，which is more close to the numerical solution. The normalized displacement ratio of the rectangular tunnel decreases with the increase of the relative stiffness ratio of tunnel to soil. The normalized displacement ratio increases as the increasing of the ratio of the cross section size. When the cross section size ratio of the rectangular tunnel and the relative stiffness ratio are unchanged，the normalized displacement ratio of the rectangular tunnel increases with the decrease of the Poisson's ratio of the soil. When the cross section size ratio is 1 (Square tunnel)，the change of Poisson?s ratio of soil has little influence on the normalized displacement ratio of the tunnel. The soil stress field around the rectangular tunnel increases with the increase of the Poisson?s ratio of soil. The soil stress field decreases with the increase of the elastic modulus of soil. The soil stress field decreases with the increase of the shear modulus of the liner.
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2017, Vol. 36 
