Limit Analysis of Anchor Trapdoor Embedded in Nonhomogeneous and Nonlinear Soils
Publication: International Journal of Geomechanics
Volume 19, Issue 8
Abstract
The anchor trapdoor provides a simple and economical system widely used to study the stability of similar geotechnical engineering structures, such as foundations and tunnels. In this study, the passive and active failure mechanisms were proposed to estimate the uplift capacity for anchor-trapdoor design. The nonhomogeneous soil properties were investigated with the help of the slice method, which was inspired by interpretations of integration. Within the framework of the upper-bound theorem, a nonlinear slip-line layout optimization procedure with classical tools of variational calculus was presented for a single layer to provide the basis for multilayer analysis. This approach was extended to put forward an innovative failure mechanism describing the curvilinear function for circular anchor plates in a three-dimensional space. To investigate the effects of nonhomogeneity on the stability of the anchor trapdoor, case studies were conducted for soils with linear changing cohesion and layered soils. To make safe guidance for engineers facing geotechnical limit-state problems, considering both linear and nonlinear failure modes, the stability factor calculated by a few examples was validated by lower-bound solutions and results in commercial packages.
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Acknowledgments
Financial support was received from the Innovation Foundation for postgraduates of Central South University (Grant 2017zzts157) for the preparation of this manuscript. This financial support is greatly appreciated.
References
Anyaegbunam, A. 2015. “Nonlinear power-type failure laws for geomaterials: Synthesis from triaxial data, properties, and applications.” Int. J. Geomech. 15 (1): 04014036. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000348.
Baker, R. 2004. “Nonlinear Mohr envelopes based on triaxial data.” J. Geotech. Geoenviron. Eng. 130 (5): 498–506. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(498).
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Chen, W., N. Snitbhan, and H. Fang. 1975. “Stability of slopes in anisotropic, nonhomogeneous soils.” Can. Geotech. J. 12 (1): 146–152. https://doi.org/10.1139/t75-014.
Davis, E. H., and J. R. Booker. 1973. “The effect of increasing strength with depth on the bearing capacity of clays.” Géotechnique 23 (4): 551–563. https://doi.org/10.1680/geot.1973.23.4.551.
Elsgolc, L. E. 1962. Calculus of variations. London: Pergamon Press.
Fraldi, M., and F. Guarracino. 2009. “Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 46 (4): 665–673. https://doi.org/10.1016/j.ijrmms.2008.09.014.
Ghaly, A., and A. Hanna. 1994. “Ultimate pullout resistance of single vertical anchors.” Can. Geotech. J. 31 (5): 661–672. https://doi.org/10.1139/t94-078.
Giampa, J., A. Bradshaw, and J. Schneider. 2017. “Influence of dilation angle on drained shallow circular anchor uplift capacity.” Int. J. Geomech. 17 (2): 04016056. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000725.
Hirai, H. 2012. “A Winkler model approach for vertically and laterally loaded piles in nonhomogeneous soil.” Int. J. Numer. Anal. Methods Geomech. 36 (17): 1869–1897. https://doi.org/10.1002/nag.1078.
Hirai, H. 2014. “Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach.” Int. J. Numer. Anal. Methods Geomech. 38 (12): 1298–1320. https://doi.org/10.1002/nag.2270.
Hirai, H. 2015. “Analysis of rectangular piles subjected to lateral loads in nonhomogeneous soil using a Winkler model approach.” Int. J. Numer. Anal. Methods Geomech. 39 (9): 937–968. https://doi.org/10.1002/nag.2345.
Hoek, E., and E. T. Brown. 1997. “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci. 34 (8): 1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X.
Huang, F., X. L. Yang, and T. H. Ling. 2014. “Prediction of collapsing region above deep spherical cavity roof under axis-symmetrical conditions.” Rock Mech. Rock Eng. 47 (4): 1511–1516. https://doi.org/10.1007/s00603-013-0455-y.
Ilamparuthi, K., E. A. Dickin, and K. Muthukrisnaiah. 2002. “Experimental investigation of the uplift behaviour of circular plate anchors embedded in sand.” Can. Geotech. J. 39 (3): 648–664. https://doi.org/10.1139/t02-005.
Jiang, J. C., R. Baker, and T. Yamagami. 2003. “The effect of strength envelope nonlinearity on slope stability computations.” Can. Geotech. J. 40 (2): 308–325. https://doi.org/10.1139/t02-111.
Khuntia, S., and J. Prasad Sahoo. 2018. “Vertical uplift capacity of strip plate anchors embedded horizontally adjacent to cohesive-frictional soil slopes.” Int. J. Geomech. 18 (3): 06018001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001088.
Koutsabeloulis, N. C., and D. V. Griffiths. 1989. “Numerical modelling of the trap door problem.” Géotechnique 39 (1): 77–89. https://doi.org/10.1680/geot.1989.39.1.77.
Li, Y. X., and X. L. Yang. 2019a. “Soil-slope stability considering effect of soil-strength nonlinearity.” Int. J. Geomech. 19 (3): 04018201. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001355.
Li, Z. W., and X. L. Yang. 2019b. “Active earth thrust considering tension crack, pore-water pressure and soil nonlinearity.” KSCE J. Civ. Eng. 23 (1): 56–62. https://doi.org/10.1007/s12205-018-1098-z.
Lin, Y. L., Z. Yang, G. L. Yang, Y. Li, and L. H. Zhao. 2017. “A closed-form solution for seismic passive pressure behind a retaining wall supporting cohesive-frictional backfill.” Acta Geotech. 12 (2): 453–461. https://doi.org/10.1007/s11440-016-0472-6.
Merifield, R. S., A. V. Lyamin, S. W. Sloan, and H. S. Yu. 2003. “Three-dimensional lower bound solutions for stability of plate anchors in clay.” J. Geotech. Geoenviron. Eng. 129 (3): 243–253. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:3(243).
Merifield, R. S., and S. W. Sloan. 2006. “The ultimate pullout capacity of anchors in frictional soils.” Can. Geotech. J. 43 (8): 852–868. https://doi.org/10.1139/t06-052.
Merifield, R. S., S. W. Sloan, and H. S. Yu. 2001. “Stability of plate anchors in undrained clay.” Géotechnique 51 (2): 141–153. https://doi.org/10.1680/geot.2001.51.2.141.
Meyerhof, G. G., and J. I. Adams. 1968. “The ultimate uplift capacity of foundation.” Can. Geotech. J. 5 (4): 225–244. https://doi.org/10.1139/t68-024.
Murray, E. J., and J. D. Geddes. 1989. “Resistance of passive inclined anchors in cohensionless medium.” Géotechnique 39 (3): 417–431.
Nian, T. K., G. Q. Chen, M. T. Luan, Q. Yang, and D. F. Zheng. 2008. “Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils.” Can. Geotech. J. 45 (8): 1092–1103. https://doi.org/10.1139/T08-042.
Pan, Q. J., and D. Dias. 2016. “Face stability analysis for a shield-driven tunnel in anisotropic and nonhomogeneous soils by the kinematical approach.” Int. J. Geomech. 16 (3): 04015076. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000569.
Pan, Q. J., and D. Dias. 2018. “Three-dimensional static and seismic stability analysis of a tunnel face driven in weak rock masses.” Int. J. Geomech. 18 (6): 04018055. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001174.
Perazzelli, P., and G. Anagnostou. 2017. “Uplift resistance of strip anchors in cohesive frictional mediums of limited tensile strength.” Int. J. Geomech. 17 (9): 04017042. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000901.
Qin, C. B., and S. C. Chian. 2017. “Kinematic stability of a two-stage slope in layered soils.” Int. J. Geomech. 17 (9): 06017006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000928.
Qin, C. B., and S. C. Chian. 2018. “Seismic ultimate bearing capacity of a Hoek-Brown rock slope using discretization-based kinematic analysis and pseudodynamic methods.” Int. J. Geomech. 18 (6): 04018054. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001147.
Reddy, A. S., and K. N. Rao. 1981. “Bearing capacity of strip footing on anisotropic and nonhomogeneous clays.” Soils Found. 21 (1): 1–6. https://doi.org/10.3208/sandf1972.21.1.
Rowe, R. K., and E. H. Davis. 1982. “The behaviour of anchor plates in clay.” Géotechnique 32 (1): 9–23. https://doi.org/10.1680/geot.1982.32.1.9.
Smith, C. C. 1998. “Limit loads for an anchor-trapdoor embedded in an associative Coulomb soil.” Int. J. Numer. Anal. Methods Geomech. 22 (11): 855–865. https://doi.org/10.1002/(SICI)1096-9853(199811)22:11%3C855::AID-NAG945%3E3.0.CO;2-4.
Smith, C. C., and M. Gilbert. 2007. “Application of discontinuity layout optimization to plane plasticity problems.” Proc. R. Soc. A 463 (2086): 2461–2484. https://doi.org/10.1098/rspa.2006.1788.
Terzaghi, K. 1936. “Stress distribution in dry and saturated sand above a yielding trap-door.” In Vol. 1 of Proc., Int. Conf. on Soil Mechanics, 307–316. Rotterdam, Netherlands: A. A. Balkema.
Toyota, H., A. Susami, and S. Takada. 2014. “Anisotropy of undrained shear strength induced by K0 consolidation and swelling in cohesive soils.” Int. J. Geomech. 14 (4): 04014019. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000344.
Vesic, A. S. 1971. “Breakout resistance of objects embedded in ocean bottom.” J. Soil Mech. Found. Div. 97 (9): 1183–1205.
Wang, L., B. Leshchinsky, T. M. Evans, and Y. Xie. 2017. “Active and passive arching stresses in c′-ϕ′ soils: A sensitivity study using computational limit analysis.” Comput. Geotech. 84 (Apr): 47–57. https://doi.org/10.1016/j.compgeo.2016.11.016.
Xu, J. S., and X. L. Yang. 2019. “Seismic stability of 3D soil slope reinforced by geosynthetic with nonlinear failure criterion.” Soil Dyn. Earthquake Eng. 118 (Mar): 86–97. https://doi.org/10.1016/j.soildyn.2018.12.019.
Yang, X. L., and Z. W. Li. 2018. “Comparison of factors of safety using a 3D failure mechanism with kinematic approach.” Int. J. Geomech. 18 (9): 04018107. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001235.
Yang, X. L., and Z. A. Liu. 2018. “Reliability analysis of three-dimensional rock slope.” Geomech. Eng. 15 (6): 1183–1191.
Zhang, R., and C. C. Smith. 2019. “Upper bound limit analysis of soils with a non-linear failure criterion.” Can. Geotech. J. https://doi.org/10.1139/cgj-2018-0513.
Zhang, R., and X. L. Yang. 2018. “Limit analysis of active and passive mechanisms of shallow tunnels in nonassociative soil with changing water table.” Int. J. Geomech. 18 (7): 04018063. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001167.
Zhang, X. J., and W. F. Chen. 1987. “Stability analysis of slopes with general nonlinear failure criterion.” Int. J. Numer. Anal. Methods Geomech. 11 (1): 33–50. https://doi.org/10.1002/nag.1610110104.
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Published In
International Journal of Geomechanics
Volume 19 • Issue 8 • August 2019
Copyright
© 2019 American Society of Civil Engineers.
History
Received: May 24, 2018
Accepted: Mar 15, 2019
Published online: May 20, 2019
Published in print: Aug 1, 2019
Discussion open until: Oct 20, 2019
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