Abstract
Based on nonlinear failure criterion, a three-dimensional failure mechanism of the possible collapse of deep tunnel is presented with limit analysis theory. Support pressure is taken into consideration in the virtual work equation performed under the upper bound theorem. It is necessary to point out that the properties of surrounding rock mass plays a vital role in the shape of collapsing rock mass. The first order reliability method and Monte Carlo simulation method are then employed to analyze the stability of presented mechanism. Different rock parameters are considered random variables to value the corresponding reliability index with an increasing applied support pressure. The reliability indexes calculated by two methods are in good agreement. Sensitivity analysis was performed and the influence of coefficient variation of rock parameters was discussed. It is shown that the tensile strength plays a much more important role in reliability index than dimensionless parameter, and that small changes occurring in the coefficient of variation would make great influence of reliability index. Thus, significant attention should be paid to the properties of surrounding rock mass and the applied support pressure to maintain the stability of tunnel can be determined for a given reliability index.
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FRALDI M, GUARRACINO F. Evaluation of impending collapse in circular tunnels by analytical and numerical approaches [J]. Tunnelling and Underground Space Technology, 2011, 26(4): 507–516.
FRALDI M, GUARRACINO F. Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections [J]. International Journal of Solids and Structures, 2010, 47(2): 216–223.
FRALDI M, GUARRACINO F. Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(3): 665–673.
YANG X L, HUANG F. Collapse mechanism of shallow tunnel based on nonlinear Hoek-Brown failure criterion [J]. Tunnelling and Underground Space Technology, 2011, 26(6): 686–691.
YANG X L, HUANG F. Three-dimensional failure mechanism of a rectangular cavity in a Hoek–Brown rock medium [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 61: 189–195.
YANG Xiao-li, QIN Chang-bing. Limit analysis of supporting pressure in tunnels with regard to surface settlement [J]. Journal of Central South University, 2015, 22(1): 303–309.
YANG Xiao-li, LONG Ze-xiang. Roof collapse of shallow tunnels with limit analysis method [J]. Journal of Central South University, 2015, 22(5): 1929–1936.
MOLLON G, DIAS D, SOUBRA A H. Range of the safe retaining pressures of a pressurized tunnel face by a probabilistic approach [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2013, 139(11): 1954–1967.
MOLLON G, DIAS, D, SOUBRA, A. Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield [J]. International Journal for Numerical and Analytical Methods in Geomechancs, 2011, 35(12): 1363–1388.
MOLLON G, DIAS D, SOUBRA A H. Probabilistic analysis and design of circular tunnels against face stability [J]. International Journal of Geomechanics, 2009, 9(2): 237–249.
HOEK E, BROWN E T. Practical estimates of rock mass strength [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8): 1165–1186.
HOEK E, CARRANZA-TORRES C, CORKUM B. Hoek-Brown failure criterion [M]. Toronto: University of Toronto Press, 2002: 267–273.
YANG X L, YIN J H. Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2005, 42(4): 550–560.
YANG X L, YIN J H. Slope equivalent Mohr-Coulomb strength parameters for rock masses satisfying the Hoek-Brown criterion [J]. Rock Mechanics and Rock Engineering, 2010, 43(4): 505–511.
SENENT S, MOLLON G, JIMENEZ R. Tunnel face stability in heavily fractured rock masses that follow the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 60(1): 440–451.
YANG X L, WANG J M. Ground movement prediction for tunnels using simplified procedure [J]. Tunnelling and Underground Space Technology, 2011, 26(3): 462–471.
YANG X L. Seismic passive pressures of earth structures by nonlinear optimization [J]. Archive of Applied Mechanics, 2011, 81(9): 1195–1202.
YANG X L. Seismic bearing capacity of a strip footing on rock slopes [J]. Canadian Geotechnical Journal, 2009, 46(8): 943–954.
YANG X L, LI L, YIN J H. Seismic and static stability analysis for rock slopes by a kinematical approach [J]. Geotechnique, 2004, 54(8): 543–549.
YANG Xiao-li, LI Wen-tao, PAN Qiu-jing. Influences of anisotropy and in homogeneity on supporting pressure of tunnel face with kinematical approach [J]. Journal of Central South University, 2015, 22(9): 3536–3543.
SOUBRA A H. Three-dimensional face stability analysis of shallow circular tunnels [C]// International Conference on Geotechnical and Geological Engineering. Melbourne, Australia: ICGGE, 2000: 19–24.
SOUBRA A H, DIAS D. Three-dimensional face stability analysis of circular tunnels by a kinematical approach [J]. Geotechqiuue, 2008, 30(5): 894–901.
YANG X L, YIN J H. Slope stability analysis with nonlinear failure criterion [J]. Journal of Engineering Mechanics, 2004, 130(3): 267–273.
YANG X L, LONG Z X. Seismic and static 3D stability of two-stage rock slope based on Hoek-Brown failure criterion [J]. Canadian Geotechnical Journal, 2016, 53(3): 551–558.
YANG X L. Seismic displacement of rock slopes with nonlinear Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(6): 948–953.
YANG X L. Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion [J]. Theoretical and Applied Fracture Mechanics, 2007, 47(1): 46–56.
GEREMEW A M. Pore-water pressure development caused by wave-induced cyclic loading in deep porous formation [J]. International Journal of Geomechanics, 2011, 13(1): 65–68.
VIRATJANDR C, MICHALOWSKI R L. Limit analysis of submerged slopes subjected to water drawdown [J]. Canadian Geotechnical Journal, 2006, 43(8): 802–814.
PAUL M, Hoek E. Estimating the geotechnical properties of heterogeneous rock masses such as flash [J]. Bulletin of Engineering Geology and the Environment, 2001, 60(2): 85–92.
ZHANG D B, SUN Z B, ZHU C Q. Reliability analysis of retaining walls with multiple failure modes [J]. Journal of Central South University, 2013, 20(10): 2879–2886.
YANG X L, XU J S, LI Y X, YAN R M. Collapse mechanism of tunnel roof considering joined influences of non linearity and non-associated flow rule [J]. Geomechanics and Engineering, 2016, 10(1): 21–35.
LOW B K, LACASSE S, NADIM F. Slope reliability analysis accounting for spatial variation [J]. Assessment and Management of Risk for Engineered Systems and Geohazards, 2007, 11(4): 177–189.
ABDEL Y, MASSIH D S, SOUBRA A H. Reliability based analysis of strip footings using response surface methodology [J]. International Journal of Geomechanics, 2008, 8(2): 134–143.
SU Y H, LI X, XIE Z Y. Probabilistic evaluation for the implicit limit-state function of stability of highway tunnel in China [J]. Tunnelling and Underground Space Technology, 2011, 26(2): 422–434.
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Foundation item: Project(2013CB036004) supported by National Basic Research Program of China
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Luo, Wh., Li, Wt. Reliability analysis of supporting pressure in tunnels based on three-dimensional failure mechanism. J. Cent. South Univ. 23, 1243–1252 (2016). https://doi.org/10.1007/s11771-016-0374-7
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DOI: https://doi.org/10.1007/s11771-016-0374-7