Simulated Crack and Slip Plane Propagation in Soil Slopes with Embedded Discontinuities Using XFEM
Publication: International Journal of Geomechanics
Volume 18, Issue 12
Abstract
To simulate the onset and growth of strong discontinuities (cracks or slip planes) and the failure mechanism in soil slopes with reasonable accuracy, a program was developed based on the existing extended finite-element method (XFEM). This program consists of a new analytical algorithm for strong-discontinuity initiation and propagation in soils considering the stress concentration and redistribution around the discontinuity tip and an integration scheme for the XFEM enriched discontinuities. Two different types of interfacial contact constitutive models are used to describe the interface behavior of the cracks or slip planes. Analyses of two slope failure examples are presented to demonstrate the reliability of this program and the reference values for engineering measurements.
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Acknowledgments
This work was supported by the National Key R&D Program of China (Grant 2017YFC0804602) and the National Natural Science Foundation of China (Grants 51379103 and 51479099).
References
Alfano, G., and M. A. Crisfield. 2001. “Finite element interface models for the delamination analysis of laminated composites: Mechanical and computational issues.” Int. J. Numer. Methods Eng. 50 (7): 1701–1736. https://doi.org/10.1002/nme.93.
Baker, R., and M. Garber. 1978. “Theoretical analysis of the stability of slopes.” Géotechnique 28 (4): 395–411. https://doi.org/10.1680/geot.1978.28.4.395.
Belytschko, T., and T. Black. 1999. “Elastic crack growth in finite elements with minimal remeshing.” Int. J. Numer. Methods Eng. 45 (5): 601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5%3C601::AID-NME598%3E3.0.CO;2-S.
Bishop, A. W. 1955. “The use of the slip circle in the stability analysis of slopes.” Géotechnique 5 (1): 7–17. https://doi.org/10.1680/geot.1955.5.1.7.
Bjerrum, L. 1967. “Progressive failure in slopes of overconsolidated plastic clay and clay shales.” J. Soil Mech. Found. Div. 93 (5): 1–49.
Dolbow, J., N. Moës, and T. Belytschko. 2001. “An extended finite element method for modeling crack growth with frictional contact.” Comput. Methods Appl. Mech. Eng. 190 (51–52): 6825–6846. https://doi.org/10.1016/S0045-7825(01)00260-2.
Eberhard, P., and B. Hu. 2003. Advanced contact dynamics. Nanjing, China: South-East University.
Fang, X. J., F. Jin, and J. T. Wang. 2007. “Simulation of mixed-mode fracture of concrete using extended finite element method.” Eng. Mech. 24 (S1): 46–52.
Griffiths, D. V., and P. A. Lane.1999. “Slope stability analysis by finite elements.” Géotechnique 49 (3): 387–403. https://doi.org/10.1680/geot.1999.49.3.387.
Janbu, N. 1954. “Application of composite slip surfaces for stability analysis.” In Vol. 3 of Proc., European Conf. on Stability of Earth Slopes, 43–49. Stockholm, Sweden: International Society of Soil Mechanics and Foundation Engineering.
Jones, R. E., and P. Papadopoulos. 2000. “A yield-limited Lagrange multiplier formulation for frictional contact.” Int. J. Numer. Methods Eng. 48 (8): 1127–1149. https://doi.org/10.1002/(SICI)1097-0207(20000720)48:8%3C1127::AID-NME937%3E3.0.CO;2-C.
Khosravi, M., D. Leshchinsky, C. L. Meehan, and A. Khosravi. 2013. “Stability analysis of seismically loaded slopes using finite element techniques.” In Proc., Geo-Congress 2013, 1310–1319. Reston, VA: ASCE.
Leonardos, M., and N. Terezopoulos. 2003. “Rim slope failure mechanism in the Greek deep lignite mines—A case study.” Min. Technol. 112 (3): 197–204. https://doi.org/10.1179/037178403225001656.
Li, M. 2012. “Research on failure mechanism and deformation rules of cohesive slopes under excavation conditions.” Ph.D. thesis, Tsinghua Univ.
Li, M., G. Zhang, J.-M. Zhang, and C. F. Lee. 2011. “Centrifuge model tests on a cohesive soil slope under excavation conditions.” Soils Found. 51 (5): 801–812. https://doi.org/10.3208/sandf.51.801.
Liu, X., A. Scarpas, C. Kasbergen, and E. Kondo. 2012. “Numerical analysis characterizing the influence of the evolution of the length scale on strain localization in Cosserat media.” Int. J. Geomech. 12 (3): 272–280. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000148.
Oliver, J., A. E. Huespe, and P. J. Sánchez. 2006. “A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM.” Comput. Methods Appl. Mech. Eng. 195 (37–40): 4732–4752. https://doi.org/10.1016/j.cma.2005.09.020.
Planas, J., M. Elices, G. V. Guinea, F. J. Gómez, D. A. Cendón, and I. Arbilla. 2003. “Generalizations and specializations of cohesive crack models.” Eng. Fract. Mech. 70 (14): 1759–1776. https://doi.org/10.1016/S0013-7944(03)00123-1.
Sanborn, S. E., and J. H. Prévost. 2011. “Frictional slip plane growth by localization detection and the extended finite element method (XFEM).” Int. J. Numer. Anal. Methods Geomech. 35 (11): 1278–1298. https://doi.org/10.1002/nag.958.
Skempton, A. W. 1964. “Long-term stability of clay slopes.” Géotechnique 14 (2): 77–102. https://doi.org/10.1680/geot.1964.14.2.77.
Song, J.-H., P. M. A. Areias, and T. Belytschko. 2006. “A method for dynamic crack and shear band propagation with phantom nodes.” Int. J. Numer. Methods Eng. 67 (6): 868–893. https://doi.org/10.1002/nme.1652.
Troncone, A. 2005. “Numerical analysis of a landslide in soils with strain-softening behaviour.” Géotechnique 55 (8): 585–596. https://doi.org/10.1680/geot.2005.55.8.585.
Ugai, K. 1989. “A method of calculation of total safety factor of slope by elasto-plastic FEM.” [In Japanese.] Soils Found. 29 (2): 190–195. https://doi.org/10.3208/sandf1972.29.2_190.
Willner, K. 1995. “A statistical model for the contact of metallic bodies.” Ph.D. thesis, Dept. of Engineering Mechanics, Universität der Bundeswehr Hamburg.
Wriggers, P. 1995. “Finite element algorithms for contact problems.” Arch. Comput. Methods Eng. 2 (4): 1–49. https://doi.org/10.1007/BF02736195.
Yang, G. H., Z. H. Zhong, Y. C. Zhang, and E. Q. Wang. 2012. “Identification of landslide type and determination of optimal reinforcement site based on stress field and displacement field.” [In Chinese.] Chin. J. Rock Mech. Eng. 31 (9): 1879–1887.
Yu, J. L., X. Sun, Y. Z. Yu, and L. Chai. 2010a. “Experimental study of the evolution of shear bands in structured soil.” [In Chinese.] J. Tsinghua Univ. Sci. Tech. 50 (3): 367–371.
Yu, J. L., Q. G. Zhang, Y. Z. Yu, and X. Sun. 2009. “An integration scheme for discontinuities in the extended finite element method.” [In Chinese.] J. Tsinghua Univ. Sci. Tech. 49 (3): 351–354.
Yu, Y. Z., J. L. Yu, B. Y. Zhang, and H. Lv. 2010b. “Analysis of the evolution of shear bands considering stress concentrations and redistribution around the tip.” [In Chinese.] J. Tsinghua Univ. Sci. Tech. 50 (3): 372–375.
Zervos, A., I. Vardoulakis, and P. Papanastasiou. 2007. “Influence of nonassociativity on localization and failure in geomechanics based on gradient elastoplasticity.” Int. J. Geomech. 7 (1): 63–74. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:1(63).
Zhang, Y., and M. Y. Chen. 2015. “Tensile strength of compacted clay.” [In Chinese.] Hydrogeol. Eng. Geol. 42 (4): 56–60.
Zhou, X., and H. Cheng. 2017. “Multidimensional space method for geometrically nonlinear problems under total Lagrangian formulation based on the extended finite-element method.” J. Eng. Mech. 143 (7): 04017036. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001241.
Zi, G., and T. Belytschko. 2003. “New crack-tip elements for XFEM and applications to cohesive cracks.” Int. J. Numer. Methods Eng. 57 (15): 2221–2240. https://doi.org/10.1002/nme.849.
Zienkiewicz, O. C., C. Humpheson, and R. W. Lewis. 1975. “Associated and non-associated visco-plasticity and plasticity in soil mechanics.” Géotechnique 25 (4): 671–689. https://doi.org/10.1680/geot.1975.25.4.671.
Zipf, R. K. 2005. “Failure mechanics of multiple-seam mining interactions.” In Proc., 24th International Conf. on Ground Control in Mining, 93–106. Washington, DC: National Institute for Occupational Safety and Health.
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Published In
International Journal of Geomechanics
Volume 18 • Issue 12 • December 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Oct 9, 2017
Accepted: May 21, 2018
Published online: Oct 3, 2018
Published in print: Dec 1, 2018
Discussion open until: Mar 3, 2019
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