# An Analytical Solution of Shield Tunnel based on Force Method Xiaomin You Zixin Zhang Yongsheng Li Dept. of Geotechnical Engineering Tongji University.

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An Analytical Solution of Shield Tunnel based on Force Method Xiaomin You Zixin Zhang Yongsheng Li Dept. of Geotechnical Engineering Tongji University 3nd Sino-Japan Joint Seminar for the Graduate Students

ITA （ 2000 ） Guidelines for the Design of Shield Tunnel Lining

Tunnel projects constructed in Shanghai in recent years ProjectD cal * (m)Thickness (m) Shanghai Subway Tunnels5.850.35 East Yanan Rd. Tunnel10.450.55 Dalian Rd. Tunnel10.520.48 East Fuxing Rd. Tunnel10.520.48 Xiangyin Rd. Tunnel10.880.48 Shangzhong Rd. Tunnel13.900.60 South Xizang Rd. Tunnel10.860.50 Shanghai Yangtse River Tunnel14.350.65  Large section → low ratio of thickness vs. diameter  Large section → shallow embedded depth

Conventional Model

Soil resistant pressure. STEP 1 STEP 2 STEP 3 β1β1 β2β2

Deduction based on Force- Method 1st step: Force method equation

2nd step: to solve β 1 and β 2

3rd step: Internal force

Comparison Detailed information about cases adopted in analysis Cases Rrrwrw K0K0 Khwhw (m)(kN/m3) (m) Clay layer516.9100.5550000 Sand layer519.8100.25100000 Analysis of the parameters 1.Effect of horizontal soil pressure coefficient 2.Effect of soil resistance coefficient Comparison with different solutions

Effect of horizontal soil pressure coefficient

Effect of soil resistance coefficient

Comparison with different solutions R(m) Thickness( m) Embedded depth (m) r (kN/m 3 ) rw (kN/m 3 ) hw (m) 50.43719.8100 (kN/m3)K0 Compression Modulus (kN/m 3 ) SPT-NC (kPa) Φ(º)Φ(º) 200000.332200018.7138

CONCLUSION For a given soil resistance coefficient and a shallow embedded depth, the distribution of soil resistant pressure is significantly effected by the value of horizontal soil pressure coefficient, and also the ratio of thickness versus diameter is a influencing factor. For a given horizontal soil pressure coefficient and a shallow embedded depth, the distribution of soil resistant pressure is significantly effected by the value of soil resistance coefficient, and also the ratio of thickness versus diameter is a influencing factor. The results predicted by the proposed analytical solution are compared with those of numerical simulation and the conventional model solution. The comparison indicates that the proposed solution agrees more reasonably, and it provides a new approach to better predict and make the preliminary design of shield tunnel lining

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