Abstract
On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together. The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure, surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.
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References
CHEN W F. Limit analysis and soil plasticity [M]. Florida: J. Ross Publishing, Inc, 2007: 47–99.
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, 2011, 35(12): 1363–1388.
DAVIS E H, GUNN M J, MAIR R J, SENEVIRATINE H N. The stability of shallow tunnels and underground openings in cohesive material [J]. Geotechnique, 1980, 30(4): 397–416.
KLAR A, OSMAN A S, BOLTON M. 2D and 3D upper bound solutions for tunnel excavation using elastic flow fields [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(12): 1367–1374.
HUANG Fu, ZHANG Dao-bing, SUN Zhi-bin, JIN Qi-yun. Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique [J]. Journal of Central South University, 2012, 19(7): 2008–2015.
ZHENG Y R, DENG C J, WANG J L. The study of slip line field and upper bound method based on associated flow and non-associated flow rules [J]. Engineering Sciences, 2010, 28(3): 21–40.
DRESCHER A, DETOURNZY E. Limit load in translational failure mechanics for associative and non-associative materials [J]. Geotechnique, 1993, 43(3): 443–456.
YIN J H, WANG Y J, SELVADURAI A P S. Influence of non-associativity on the bearing capacity of a strip footing [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2001, 127(11): 985–989.
WANG Y J, YIN J H, LEE C F. The influence of a non-associated flow rule on the calculation of the factor of safety of soil slopes [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25(13): 1351–1359.
YANG Xiao-li, HUANG Fu. Slope stability analysis considering joined influences of nonlinearity and dilation [J]. Journal of Central South University of Technology, 2009, 16(2): 292–296.
YANG Xiao-li, SUI Zhi-rong. Seismic failure mechanisms for loaded slopes with associated and nonassociated flow rules [J]. Journal of Central South University of Technology, 2008, 15(2): 276–279.
SHI Ting-feng, ZHAO Lian-heng. Upper bound analysis for the ultimate pullout capacity of vertically loaded strip plate anchors considering the nonlinearity of shear strength characteristics of geomaterials [J]. Electronic Journal of Geotechnical Engineering, 2011, 16(G): 729–739.
YANG X L, PAN Q J. Three dimensional seismic and static stability of rock slopes [J]. Geomechanics and Engineering, 2015, 8(1): 97–111.
YANG X L, QIN C B. Limit analysis of rectangular cavity subjected to seepage forces based on Hoek-Brown failure criterion [J]. Geomechanics and Engineering, 2014, 6(5): 503–515.
PARK T, CHUNG K. Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing [J]. International Journal of Solids and Structures, 2012, 49(25): 3582–3593.
YANG X L. Seismic bearing capacity of a strip footing on rock slopes [J]. Canadian Geotechnical Journal, 2009, 46(8): 943–954.
CHAABA A, BOUSSHINE L, De SAXCE G. Kinematic limit analysis of nonassociated perfectly plastic material by the bipotential approach and finite element method [J]. Journal of Applied Mechanics, 2010, 77(3): 1–11.
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.
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, 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, ZOU J F. Cavity expansion analysis with non-linear failure criterion [J]. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 2011, 164(1): 41–49.
SAADA Z, MAGHOUS S, GARNIER D. Pseudo-static analysis of tunnel face stability using the generalized Hoek-Brown strength criterion [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(18): 3194–3212.
TANGARAMVONG S, TIN-LOI F. A constrained non-linear system approach for the solution of an extended limit analysis problem [J]. International Journal for Numerical Methods in Engineering, 2010, 82(8): 995–1021.
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.
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 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.
BISHOP A W. The use of pore-pressure coefficients in practice [J]. Geotechnique, 1954, 4(4): 148–152.
MICHALOWSKI R L, NADUKURU S S. Three-dimensional limit analysis of slopes with pore pressure [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2012, 139(9): 1604–1610.
VIRATJANDR C, MICHALOWSKI R L. Limit analysis of submerged slopes subjected to water drawdown [J]. Canadian Geotechnical Journal, 2006, 43(8): 802–814.
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, YIN J H. Slope stability analysis with nonlinear failure criterion [J]. Journal of Engineering Mechanics, 2004, 130(3): 267–273.
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.
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.
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Foundation item: Project(2013CB036004) supported by the National Basic Research Program of China; Projects(51178468, 51378510) supported by the National Natural Science Foundation of China; Project(CX2013B077) supported by Hunan Provincial Innovation Foundation for Postgraduate, China
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Zhang, Jh., Wang, Cy. Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion. J. Cent. South Univ. 22, 1070–1078 (2015). https://doi.org/10.1007/s11771-015-2618-3
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DOI: https://doi.org/10.1007/s11771-015-2618-3