Technical Papers
Apr 18, 2014

Simplified Numerical Implementation in Slope Stability Modeling

Publication: International Journal of Geomechanics
Volume 15, Issue 3

Abstract

This paper mainly focuses on numerical implementations in slope instability computations through three simplified numerical procedures, i.e., FEM, mesh-free method (MFM), and spectral-element method (SEM), in one sample problem that was originally solved by the FEM. This work validates all three numerical procedures through comparison of the results with the sample problem, and also briefly describes all three numerical procedures and their scopes and limitations. Among the three procedures, the SEM-based procedure is found to be more effective in handling simple to complex problems of a small- to large-scale size because of its effective computational capacity as well as higher degree of work accuracy. For this, a newly released open-source program has been used along with two other programming codes developed in FEM and MFM platforms. This work also presents a sample simulation of large-scale slope stability using the h-refinement (i.e., meshing), p-refinement (i.e., mapping), and hp-refinement (i.e., meshing and mapping) technique of the SEM approach in different instability conditions, such as soil saturation and pseudostatic seismic loading. Furthermore, the SEM procedure can be effectively applied to slope stability modeling for numerical stability and accuracy in small- to large-scale mountain failure.

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Acknowledgments

The author acknowledges the support and suggestions provided by Professor R. Yatabe and Assistant Professor N. P. Bhandary from Ehime University, Matsuyama, Japan, and Professor P. B. Khadka from Tribhuvan University, Institute of Engineering, Lalitpur, Nepal.

References

Ahmed, A., Ugai, K., and Yang, Q. Q. (2012). “Assessment of 3D slope stability analysis methods based on 3D simplified Janbu and Hovland methods.” Int. J. Geomech., 81–89.
Bathe, K. J. (1996). Finite element procedures, Prentice Hall, Upper Saddle River, NJ.
Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., and Krysl, P. (1996). “Meshless methods: An overview and recent developments.” Comput. Meth. Appl. Mech. Eng., 139(1–4), 3–47.
Chen, J. X., Ke, P. Z., and Zhang, G. (2007). “Slope stability analysis by strength reduction elasto-plastic FEM.” Key Eng. Mater., 345–346, 625–628.
Chen, Z., Mi, H., Zhang, F., and Wang, X. (2003a). “A simplified method for 3D slope stability analysis.” Can. Geotech. J., 40(3), 675–683.
Chen, Z., Wang, J., Wang, Y., Yin, J.-H., and Haberfield, C. (2001b). “A three-dimensional slope stability analysis method using the upper bound theorem: Part II: numerical approaches, applications and extensions.” Int. J. Rock Mech. Min. Sci., 38(3), 379–397.
Chen, Z., Wang, X., Haberfield, C., Yin, J. H., and Wang, Y. (2001a). “A three-dimensional slope stability analysis method using the upper bound theorem: Part I: Theory and method.” Int. J. Rock Mech. Min. Sci., 38(3), 369–378.
Chen, J., Yin, J.-H., and Lee, C. F. (2003b). “Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming.” Can. Geotech. J., 40(4), 742–752.
Chen, J., Yin, J.-H., and Lee, C. F. (2004). “Rigid finite element method for upper bound limit analysis of soil slopes subjected to pore water pressure.” J. Eng. Mech., 886–893.
Cheng, Y. M., Lansivaara, T., and Siu, J. (2008). “Impact of convergence on slope stability analysis and design.” Comput. Geotech., 35(1), 105–113.
Cheng, Y. M., Lansivaara, T., and Wei, W. B. (2007). “Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods.” Comput. Geotech., 34(3), 137–150.
Cheng, Y. M., and Lau, C. K. (2008). Slope stability analysis and stabilization: New methods and insight, Taylor & Francis, London.
Chevalier, C., and Pellegrini, F. (2008). “PT-SCOTCH: A tool for efficient parallel graph ordering.” Parallel Comput., 34(6–8), 318–331.
Chowdhury, R., and Rao, B. N. (2010). “Probabilistic stability assessment of slopes using high dimensional model preparation.” Comput. Geotech., 37(7–8), 876–884.
Chung, A. K. (2003). “On the boundary conditions in slope stability analysis.” Int. J. Numer. Anal. Methods Geomech., 27(11), 905–926.
Clausen, J., Damkilde, L., and Andersen, L. (2006). “Efficient return algorithms for associated plasticity with multiple yield planes.” Int. J. Numer. Methods Eng., 66(6), 1036–1059.
Clausen, J., Damkilde, L., and Andersen, L. (2007). “An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space.” Comput. Struct., 85(23–24), 1795–1807.
CUBIT 13.0 [Computer software]. Albuquerque, NM, Sandia National Laboratories.
Cupillard, P., et al. (2012). “RegSEM: A versatile code based on the spectral element method to compute seismic wave propagation at the regional scale.” Geophys. J. Int., 188(3), 1203–1220.
Cygwin 1.7.29 [Computer software]. Raleigh, NC, Red Hat.
Dawson, E. M., Roth, W. H., and Drescher, A. (1999). “Slope stability analysis by strength reduction.” Geotechnique, 49(6), 835–840.
De Basabe, J. D., and Sen, M. K. (2010). “Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping.” Geophys. J. Int., 181(1), 577–590.
Donald, I. B., and Chen, Z. (1997). “Slope stability analysis by the upper bound approach: Fundamentals and methods.” Can. Geotech. J., 34(6), 853–862.
Easymesh 1.4 [Computer software]. Cambridge, MA, Massachusetts Institute of Technology.
EMU-3D [Computer software]. Hong Kong, Hong Kong Polytechnic Univ.
Gharti, H. N., Komatitsch, D., Oye, V., Martín, R., and Tromp, J. (2012). “Application of an elastoplastic spectral-element method to 3D slope stability analysis.” Int. J. Numer. Methods Eng., 91(1), 1–26.
Griffiths, D. V., Huang, J., and deWolfe, G. F. (2011). “Numerical and analytical observations on long and infinite slopes.” Int. J. Numer. Anal. Methods Geomech., 35(5), 569–585.
Griffiths, D. V., and Lane, P. A. (1999). “Slope stability analysis by finite elements.” Geotechnique, 49(3), 387–403.
Griffiths, D. V., and Marquez, R. M. (2007). “Three-dimensional slope stability analysis by elasto-plastic finite elements.” Geotechnique, 57(6), 537–546.
Griffiths, D. V., and Smith, I. M. (1991). Numerical methods for engineers, Blackwell, Oxford, U.K.
Griffiths, V. D., and Gioda, G., eds. (2001). Advanced numerical applications and plasticity in geomechanics, Springer, New York.
Hamdhan, I. N., and Schweiger, H. F. (2013). “Finite element method–based analysis of an unsaturated soil slope subjected to rainfall infiltration.” Int. J. Geomech., 653–658.
Jeldes, I. A., Vence, N. E., and Drumm, E. C. (2013). “An approximate solution to the Sokolovskiĭ concave slope at limiting equilibrium.” Int. J. Geomech., (Jun. 8, 2013).
Jennings, A., and Mckeown, J. (1992). Matrix computation for engineers and scientists, Wiley, London.
Khan, A. I., and Topping, B. H. V. (1996). “Parallel finite element analysis using Jacobi-conditioned conjugate gradient algorithm.” Adv. Eng. Software, 25(2–3), 309–319.
Kim, J. Y., and Lee, S. R. (1997). “An improved search strategy for the critical slip surface using finite element stress fields.” Comput. Geotech., 21(4), 295–313.
Kim, S. (1995). “Parallel multidomain iterative algorithms for the Helmholtz wave equation.” Appl. Numer. Math., 17(4), 411–429.
Komatitsch, D., and Tromp, J. (1999). “Introduction to the spectral element method for three-dimensional seismic wave propagation.” Geophys. J. Int., 139(3), 806–822.
Komatitsch, D., and Tromp, J. (2002). “Spectral-element simulations of global seismic wave propagation—I. Validation.” Geophys. J. Int., 149(2), 390–412.
Komatitsch, D., Tsuboi, S., and Tromp, J. (2005). “The spectral-element method in seismology.” Seismic earth: Array analysis of broadband seismograms, A. Levander and G. Nolet, eds., Vol. 157, American Geophysical Union, Washington, DC, 205–227.
Komatitsch, D., and Vilotte, J.-P. (1998). “The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures.” Bull. Seismol. Soc. Am., 88(2), 368–392.
Krahenbuhl, J., and Wagner, A. (1983). Survey, design, and construction of trail suspension bridges for remote areas, Swiss Center for Appropriate Technology, St. Gallen, Switzerland.
Kramer, S. L. (2003). Geotechnical earthquake engineering, Pearson Education, Singapore.
Lam, L., and Fredlund, D. G. (1993). “A general limit equilibrium model for three-dimensional slope stability analysis.” Can. Geotech. J., 30(6), 905–919.
Li, X. (2007). “Finite element analysis of slope stability analysis using a nonlinear failure criterion.” Comput. Geotech., 34(3), 127–136.
Liu, G. R. (2003). Mesh free methods, CRC Press, Boca Raton, FL.
Liu, J., and Marfurt, K. J. (2007). “Instantaneous spectral attributes to detect channels.” Geophysics, 72(2), 23–31.
Low, B. K., and Tang, W. H. (1997). “Probabilistic slope analysis using Janbu’s generalized procedure of slices.” Comput. Geotech., 21(2), 121–142.
Matsui, T., and San, K.-C. (1992). “Finite element slope stability analysis by shear strength reduction technique.” Soils Found., 32(1), 59–70.
Open MPI 1.4.3 [Computer software]. Bloomington, IN, Indiana Univ.
ParaView 3.7 [Computer software]. Clifton Park, NY, Kitware.
Pasquetti, R., and Rapetti, F. (2006). “Spectral element methods on unstructured meshes: Comparisons and recent advances.” J. Sci. Comput., 27(1–3), 377–387.
Pellegrini, F. (2010). “Scotch and libScotch 5.1 user's guide (version 5.1.11).” 〈https://gforge.inria.fr/docman/view.php/248/7104/scotch_user5.1.pdf〉 (Sep. 8, 2011).
Pellegrini, F., and Roman, J. (1997). “Scotch: A software package for static mapping by dual recursive bipartitioning of process and architecture graphs.” Lect. Notes Comput. Sci., 1067, 493–498.
Sandia National Laboratory. (1999). “CUBIT mesh generation environment—Volume 1: Users manual.” 〈http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.43.3793&rep=rep1&type=pdf〉 (Sep. 15, 2011).
Seriani, G. (1998). “3-D large-scale wave propagation modeling by spectral-element method on Cray T3E multiprocessors.” Comput. Methods Appl. Mech. Eng., 164(1–2), 235–247.
Smith, I. M., and Griffiths, D. V. (2003). Programming the finite element method, 3rd Ed., Wiley, New York.
Specfem3D-Slope 1.1 [Computer software]. Kjeller, Norway, NORSAR.
Steward, T., Sivakugan, N., Shukla, S. K., and Das, B. M. (2011). “Taylor’s slope stability charts revisited.” Int. J. Geomech., 348–352.
Swan, C. C., and Seo, Y.-K. (1999). “Limit state analysis of earthen slopes using dual continuum/ FEM approaches.” Int. J. Numer. Anal. Methods Geomech., 23(12), 1359–1371.
Tecplot Focus [Computer software]. Bellevue, WA, Tecplot.
Tautges, T. J. (2001). “The generation of hexahedral meshes for assembly geometry: Survey and progress.” Int. J. Numer. Methods Eng., 50(12), 2617–2642.
Taylor, M. A., and Wingate, B. A. (2000). “A generalized diagonal mass matrix spectral element method for non-quadrilateral elements.” Appl. Numer. Math., 33(1–4), 259–265.
Tiwari, R. C., Bhandary, N. P., Yatabe, R., and Bhat, D. R. (2013). “New numerical scheme in the finite-element method for evaluating root-reinforcement effect on soil slope stability.” Geotechnique, 63(2), 129–139.
Tromp, J., Komatitsch, D., and Liu, Q. (2008). “Spectral-element and adjoint methods in seismology.” Commun. Comput. Phys., 3(1), 1–32.
TrueGrid [Computer software]. Livermore, CA, XYZ Scientific Applications.
Vaughan, D., Griffiths, D. V., and Giancarlo, G. (2001). “Advanced numerical applications and plasticity in geomechanics.” CISM International Centre for Mechanical Sciences, No. 426, Springer, New York.
Wang, Y.-J., Yin, J.-H., Chen, Z., and Lee, C. F. (2004). “Analysis of wedge stability using different methods.” Rock Mech. Rock Eng., 37(2), 127–150.
Wei, W. B., Cheng, Y. M., and Li, L. (2009). “Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods.” Comput. Geotech., 36(1–2), 70–80.
Yagawa, G., and Furukawa, T. (2000). “Recent developments of free mesh method.” Int. J. Numer. Methods Eng., 47(8), 1419–1443.
Zheng, H., Sun, G., and Liu, D. (2009). “A practical procedure for searching critical slip surfaces of slopes based on the strength reduction technique.” Comput. Geotech., 36(1–2), 1–5.
Zheng, H., Tham, L. G., and Liu, D. (2006). “On two definitions of the factor of safety commonly used in the finite element slope stability analysis.” Comput. Geotech., 33(3), 188–195.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 15Issue 3June 2015

History

Received: Nov 30, 2012
Accepted: Mar 4, 2014
Published online: Apr 18, 2014
Published in print: Jun 1, 2015

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R. C. Tiwari [email protected]
Lecturer, Master of Science Program in Geotechnical Engineering, Dept. of Civil Engineering, Tribhuvan Univ., Institute of Engineering, Pulchowk Lalitpur 44700, Nepal. E-mail: [email protected]

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