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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 727964, 11 pages
Research Article

Upper Bound Solution for the Face Stability of Shield Tunnel below the Water Table

1Department of Geotechnical Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China
2Shanghai Urban Construction Design & Research Institute, Shanghai 200125, China

Received 16 May 2014; Revised 15 August 2014; Accepted 22 August 2014; Published 9 October 2014

Academic Editor: Hang Xu

Copyright © 2014 Xilin Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By FE simulation with Mohr-Coulomb perfect elastoplasticity model, the relationship between the support pressure and displacement of the shield tunnel face was obtained. According to the plastic strain distribution at collapse state, an appropriate failure mechanism was proposed for upper bound limit analysis, and the formula to calculate the limit support pressure was deduced. The limit support pressure was rearranged to be the summation of soil cohesion , surcharge load , and soil gravity multiplied by their corresponding coefficients , , and , and parametric studies were carried out on these coefficients. In order to consider the influence of seepage on the face stability, the pore water pressure distribution and the seepage force on the tunnel face were obtained by FE simulation. After adding the power of seepage force into the equation of the upper bound limit analysis, the total limit support pressure for stabilizing the tunnel face under seepage condition was obtained. The total limit support pressure was shown to increase almost linearly with the water table.