(1. Institute of Geotechnical Engineering，Zhejiang University，Hangzhou，Zhejiang 310058，China；2. Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education，Zhejiang University，Hangzhou，Zhejiang 310058，China；3. Shenzhen Municipal Engineering Corp，Shenzhen，Guangdong 518034，China)
Abstract：In shield-driven tunnel，too large support pressure may lead to the upheaval of ground surface，even blow-out failure of tunnel face. In order to reveal the mechanism of blow-out failure and to obtain the limit supporting force，based on Mohr-Coulomb model，the blow-out failure of shield tunnels in sand is simulated using ABAQUS. Accordingly，the prism part of three-dimensional wedge model，which is based on limit equilibrium method，is modified to an inverted truncated pyramid，which is consistent with the actual upheaval zone better. The formulas of limit supporting force with regard to the angle of wedge are deduced. The minimum value，which is obtained by trial calculation，is the limit supporting force. The results obtained from the modified limit equilibrium model are well consistent with the numerical simulations results，and just fall in upper and lower bound solutions calculated by E. Leca et al. The model will provide reference for determining the upper value of supporting force of shield tunnels in sand.
[1] 张庆贺，朱忠隆. 21世纪地铁施工技术展望[J]. 施工技术，1999，28(1)：9–10.(ZHANG Qinghe，ZHU Zhonglong. Prospect on technology of subway construction in the 21st century[J]. Construction Technology，1999，28(1)：9–10.(in Chinese))
[2] 李 君. 盾构开挖面稳定性理论与试验研究[硕士学位论文][D]. 杭州：浙江大学，2010.(LI Jun. Theoretical and test studies on face stability of shallow tunnel[M. S. Thesis][D]. Hangzhou：Zhejiang University，2010.(in Chinese))
[3] CHAMBON P，CORTE J F. Shallow tunnels in cohesionless soil：Stability of tunnel face[J]. Journal of Geotechnical Engineering，1994，120(7)：1 148–1 165.
[4] ANGNOSTOU G，KVOARL K. Face stability conditions with earth-pressure-balanced shields[J]. Tunnelling and Underground Space Technology，1996，11(2)：165–173.
[5] 李 昀. 软土中超大直径泥水平衡盾构开挖面稳定性研究[博士学位论文][D]. 上海：同济大学，2008.(LI Yun. Stability analysis of large slurry shield-driven tunnel in soft clay[Ph. D. Thesis][D]. Shanghai：Tongji University，2008.(in Chinese))
[6] WONG K S，NG C W W，CHEN Y M，et al. Three-dimensional analysis of passive failure of circular tunnel face in layered ground[C]// Proceedings of the 2nd International Conference on Computational Methods in Tunnelling. Bochum，German：Ruhr University Bochum，2009：841–848.
[7] BEZUIJEN A，BRASSINGA H E. Tunnelling：a decade of progress：GeoDelft 1995–2005[M]. Abingdon：Taylor and Francis，2006：143–148.
[8] 竺维彬，鞠世健. 地铁盾构施工风险源及典型事故的研究[M]. 广州：暨南大学出版社，2009：80.(ZHU Weibin，JU Shijian. Study of risk source and typical cases in shield tunneling[M]. Guangzhou：Jinan University Press，2009：80.(in Chinese))
[9] 裴红军. 城市隧道盾构法施工开挖面稳定性研究[硕士学位论文][D]. 南京：河海大学，2005.(PEI Hongjun. Research for face stability at shield tunneling[M. S. Thesis][D]. Nanjing：Hohai University，2005.(in Chinese))
[10] LECA E，DORMIEUX L. Upper and lower bound solutions for the face stability of shallow circular tunnels infrictional material[J]. Géotechnique，1990，40(4)：581–606.
[11] MOLLON G，DIAS D，SOUBRA A H. Probabilistic analysis and design of circular tunnels against face stability[J]. International Journal of Geomechanics，ASCE，2009，9(6)：237–249.
[12] MOLLON G，DIAS D，SOUBRA A H. Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2010，35(12)：1363–1 388.
[13] LI Y，EMERIAULT F，KASTNER R，et al. Stability analysis of large slurry shield-driven tunnel in soft clay[J]. Tunnelling and Underground Space Technology，2009，24(4)：472–481.
[14] MAIR R J，TAYLOR R N. Bored tunnelling in the urban environment[C]// Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering. Hamburg；A. A. Balkema Publishers，1997：2 353–2 385.
[15] 周小文，濮家骝. 砂土中隧洞开挖引起的地面沉降试验研究[J]. 岩土力学，2002，23(5)：559–563.(ZHOU Xiaowen，PU Jialiu. Centrifuge model test on ground settlement induced by tunneling in sandy soil[J]. Rock and Soil Mechanics，2002，23(5)：559–563.(in Chinese))
[16] ATKINSON J H，POTTS D M. Stability of a shallow circular tunnel in cohesionless soil[J]. Geotechnique，1997，27(2)：203–215.
[17] 齐立志. 盾构隧道开挖面被动破坏支护力研究[硕士学位论文][D]. 杭州：浙江大学，2012.(QI Lizhi. Study on blow-out face pressure of shield tunnels[M. S. Thesis][D]. Hangzhou：Zhejiang University，2012.(in Chinese))
[18] LEE C J，WU B R，CHEN H T，et al. Tunnel stability and arching effects during tunneling in soft clayey soil[J]. Tunnelling and Underground Space Technology，2006，21(2)：119–132.
[19] HORN M. Horizontal earth pressure on perpendicular tunnel face[C]// Proceedings of the Hungarian National Conference of the Foundation Engineer Industry. Hungarian：Budapest，1961：7–16.
2013, Vol. 32 
