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Volume 39 Issue 2
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WANG Hua-ning, LUO Li-sha, JIANG Ming-jing. Analytical solutions for tunnels with any shape excavated sequentially in rheological rock at great depth[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(2): 259-268. DOI: 10.11779/CJGE201702009
Citation: WANG Hua-ning, LUO Li-sha, JIANG Ming-jing. Analytical solutions for tunnels with any shape excavated sequentially in rheological rock at great depth[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(2): 259-268. DOI: 10.11779/CJGE201702009
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Analytical solutions for tunnels with any shape excavated sequentially in rheological rock at great depth

  • 1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
    2. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;
    3. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China

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  • Received Date: November 16, 2015
  • Published Date: March 24, 2017
    Graphical Abstract
    • Abstract
  • The analytical solutions are presented for the sequential excavation of the tunnel with any shape in viscoelastic rock subjected to anisotropic stress conditions. The complex variable method and the Laplace transformation are introduced to express the displacement and stress by the two potentials, therefore the methodology and analytical solutions for displacement and stress are derived for the general viscoelastic cases. The incremental displacement after each excavation step is the summation of (1) the rheological displacement due to the released stresses along the new boundary in this step and (2) the incremental rheological displacement due to the released stresses along excavation boundaries in all previous steps. The specific analytical solution is given for the two step sequential excavations of circular tunnel. A good agreement between the results from finite element simulations and the analytical solutions is observed for the specific top-bottom excavation method. The displacement and stress distributions for two excavation methods, top-bottom and left-right excavations, are analyzed by the proposed solutions. According to the analytical solutions, a fast computational system for predicting the mechanical state during tunnel excavation can be established in the future, which may provide a more convenient way for the preliminary design of the tunnel.
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    • References (20)
  • [1]
    STERPI D, GIODA G. Visco-plastic behaviour around advancing tunnels in squeezing rock[J]. Rock Mechanics and Rock Engineering, 2009, 42(2): 319-339.
    [2]
    DUENSER C, BEER G. Simulation of sequential excavation with the boundary element method[J]. Computers and Geotechnics, 2012, 44: 157-166.
    [3]
    ROATEŞI S. Analysis of the successive phases of a tunnel excavation with support mounting[J]. Proceedings of the Romanian Academy, Series A, 2010, 11(1): 11-18.
    [4]
    ROATEŞI S. Analytical and numerical approach for tunnel face advance in a viscoplastic rock mass[J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 70: 123-132.
    [5]
    ROATEŞI S. Finite element analysis of effect of lining on damage in viscoplastic rocks[J]. Computers and Geotechnics, 2013, 49: 1-6.
    [6]
    SHARIFZADEH M R, DARAEI R, BROOJERDI M S. Design of sequential excavation tunneling in weak rocks through findings obtained from displacements based back analysis[J]. Tunnelling and Underground Space Technology, 2012, 28: 10-17.
    [7]
    FAHIMIFAR A, TEHRANI F M, HEDAYAT A, et al. Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s materialunder hydrostatic stress field[J]. Tunnelling and Underground Space Technology, 2010, 25: 297-304.
    [8]
    GRAHAM G A C, SABIN G C W. The correspondence principle of linear viscoelasticity for problems that involve time-dependent regions[J]. International Journal of Engineering Science, 1973, 11: 123-140.
    [9]
    GRAHAM G A C. The correspondence principle of linear viscoelasticity theory for mixed boundary value problems involving time-dependent boundary regions[J]. Quarterly of Applied Mathematics, 1968, 26: 167-174.
    [10]
    GRAHAM G A C. The solution of mixed boundary value problems that involve time-dependent boundary regions for viscoelastic materials with one relaxation function[J]. Acta Mechanica, 1969, 8: 188-204.
    [11]
    PYATIGORETS A V, MOGILEVSKAYA S G, MARASTEANU M O. Linear viscoelastic analysis of a semi-infinite porous medium[J]. International Journal of Solids and Structures, 2008, 45(5): 1458-1482.
    [12]
    WANG H N, LI Y, NI Q. Analytical solutions for the construction of deeply buried circular tunnels with two liners in rheological rock[J]. Rock Mechanics & Rock Engineering, 2013, 46(6): 1481-1498.
    [13]
    WANG H N, UTILI S, JIANG M J. An analytical approach for the sequential excavation of axisymmetric lined tunnels in viscoelastic rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 68: 85-106.
    [14]
    苏 锋, 陈福全, 施有志. 深埋双隧洞开挖的解析延拓法求解[J]. 岩石力学与工程学报, 2012, 31(2): 365-374. (SU Feng, CHEN Fu-quan, SHI You-zhi. Analytic continuation solution of deep twin-tunnels[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(2): 365-374. (in Chinese))
    [15]
    LEE E H. Stress analysis in viscoelastic bodies[J]. Quarterly of Appiled Mathematicas, 1955, 13: 183-190.
    [16]
    王华宁, 蒋明镜, 何 平. 流变岩体中椭圆洞室断面开挖过程的力学分析[J]. 岩土工程学报, 2013, 35(11): 1979-1987. (WANG Hua-ning, JIANG Ming-jing, HE Ping. Analytical solutions for elliptical tunnels in rheological rock considering excavation[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(11): 1979-1987. (in Chinese))
    [17]
    杨挺青. 黏弹性力学[M]. 武汉: 华中理工大学出版社, 1990. (YANG Ting-qing. Viscoelastic mechanics[M]. Wuhan: Huazhong university of sceience Press, 1990. (in Chinese))
    [18]
    祝江鸿. 隧洞围岩应力复变函数分析法中的解析函数求解[J]. 应用数学和力学, 2013, 34(4): 345-354. (ZHU Jiang-hong. Rock for caverns with the complex variable theory[J]. Applied Mathematics and Mechanics, 2013, 34(4): 345-354. (in Chinese))
    [19]
    朱大勇, 钱七虎, 周早生, 等. 复杂形状洞室映射函数新解法[J]. 岩石力学与工程学报, 1999, 18(3): 279-282. (ZHU Da-yong, QIAN Qi-hu, ZHOU Zao-sheng, et al. New method for calculating mapping function of opening with complex shape[J]. Chinese Journal of Rock Mechanics and Engineering, 1999, 18(3): 279-282. (in Chinese))
    [20]
    FENG X T, CHEN B R, YANG C X, et al. Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm[J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(5): 789-801.
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