Abstract
The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
KIM J, SALGADO R, YU H S. Limit analysis of slopes subjected to pore-water pressures [J]. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125(1): 49–58.
MICHALOWSKI R L. Stability charts for uniform slopes [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(4): 351–355.
SOUBRA A H. Static and seismic passive earth pressure coefficients on rigid retaining structure [J]. Canadian Geotechnical Journal, 2000, 37(2): 463–478.
AGAR J G, MORGENSTERN N R, SCOTT J. Shear strength and stress-strain behavior of Athabasca oil sand at elevated temperatures and pressure [J]. Canadian Geotechnical Journal, 1985, 24(1): 1–10.
BAKER R. Nonlinear Mohr envelopes based on triaxial data [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(5): 498–506.
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 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, 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. Estimation of seismic passive earth pressures with nonlinear failure criterion [J]. Engineering Structures, 2006, 28(3): 342–348.
LAM L, FREDLUND D G. A general limit equilibrium model for three-dimensional slope stability analysis [J]. Canadian Geotechnical Journal, 1993, 30(6): 905–919.
CHEN Z Y, WANG X G, HABERFIEDL C. A three-dimensional slope stability analysis method using the upper bound theorem [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(1): 69–378.
DONALD I B, CHEN Z Y. Slope stability analysis by the upper bound approach: Fundamentals and methods [J]. Canadian Geotechnical Journal, 1997, 34(6): 853–862.
ANAGNOSTOU G, KOVÁRI K. Face stability conditions with earth-presssure-balanced shields [J]. Tunnelling and Underground Space Technology, 1996, 11(2): 165–173.
LECA E, DORMIEUX L. Upper and lower solutions for the space stability of shallow circular tunnels in frictional material [J]. Geotechnique, 1990, 40(4): 581–606.
SOUBRA A H, DIAS D, EMERIAULT F. Three-dimensional face stability analysis of circular tunnels by a kinematical approach [C]// Proceedings of the Geocongress Characterization Monitoring and Modelling of Geosystems, New Orleans, 2008: 9–12.
CHAMBON P, CORTÉ J F. Shallow tunnels in cohesionless soil: Stability of tunnel face [J]. Journal of Geotechnical Engineering, 1994, 120(7): 1148–1165.
YANG X L, ZHANG J H, JIN Q Y, MA J Q. Analytical solution to rock pressure acting on three shallow tunnels subjected to unsymmetrical loads [J]. Journal of Central South University, 2013, 20(2): 528–535.
YANG X L, JIN Q Y, MA J Q. Pressure from surrounding rock of three shallow tunnels with large section and small spacing [J]. Journal of Central South University, 2012, 19(8): 2380–2385.
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, 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.
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, 25(12): 1363–1388.
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(4): 665–673.
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.
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.
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.
LEE I M, NAM S W. The study of seepage forces acting on the tunnel lining and tunnel face in shallow tunnels [J]. Tunnelling and Underground Space Technology, 2001, 16(1): 31–40.
HOEK E, BROWN E T. Practical estimate the rock mass strength [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8): 1165–1186.
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, 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.
SAADA Z, MAGHOUS S, GARNIER D. Stability analysis of rock slopes subjected to seepage forces using the modified Hoek-Brown criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 55(1): 45–54.
CHEN W F. Limit analysis and soil plasticity [M]. Amsterdam: Elsevier, 1975: 85–96.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project(2013CB036004) supported by the National Basic Research Program of China; Project(51178468) supported by the National Natural Science Foundation of China; Project(2013zzts235) supported by Innovation Fund of Central South University of China
Rights and permissions
About this article
Cite this article
Qin, Cb., Sun, Zb. & Liang, Q. Limit analysis of roof collapse in tunnels under seepage forces condition with three-dimensional failure mechanism. J. Cent. South Univ. 20, 2314–2322 (2013). https://doi.org/10.1007/s11771-013-1739-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-013-1739-9