Slope stability analysis in 3D using numerical limit analysis (NLA) and elasto-plastic analysis (EPA)

References

• Araújo, L.G. (1997). Numerical study of stability problems in rock mass using limit analysis. PhD Thesis. Department of Civil Engineering, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil. [in Portuguese]
   Google Scholar
• Arora, J., 2011. Introduction to optimum design. 3rd. New York, NY: Academic Press.
   Google Scholar
• Ben-Tal, A. and Nemirovski, A., 2001. Lectures on modern convex optimization: analysis, algorithms, engineering applications, MPS-SIAM series on optimization. Philadelphia: SIAM.
   Google Scholar
• Bhattacharyya, C., 2004. Second Order Cone Programming formulation for Feature Selection. Journal of Machine Learning Research, 5, 1417–1433.
   Web of Science ®Google Scholar
• Borges, L. (1991). Formulation and solution for limit analysis with nonlinear yield surface. PhD. Thesis. Department of Mechanical Engineering, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil. [in Portuguese].
   Google Scholar
• Borges, L.A., Zouain, N., and Huespe, A.E., 1996. A nonlinear optimization procedure for limit analysis. European Journal Mechanics A - Solids, 15, 487–512.
   Web of Science ®Google Scholar
• Borja, R.I., Liu, X., and White, J.A., 2012. Multiphysics hillslope processes triggering landslides. Acta Geotechnica, 7 (4), 261–269. doi:10.1007/s11440-012-0175-6
   Web of Science ®Google Scholar
• Botero, A., et al., 1980. Finite element method and limit analysis theory for soil mechanics problems. Computer Methods in Applied Mechanics and Engineering, 22(1), 131–149.
   Google Scholar
• Camargo, J., Velloso, R., and Vargas Jr., E.A., 2016. Numerical limit analysis of three-dimensional slope stability problems in catchment areas. Acta Geotechnica, 11, 1369–1383. Presently available online. doi:10.1007/s11440-016-0459-3
   Web of Science ®Google Scholar
• Carrión, P.M. (2004). Three-dimensional deterministic and non deterministic Limit Analysis. MSc dissertation, Department of Civil Engineering, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil. [in Portuguese].
   Google Scholar
• Carrión, P.M. (2009). Limit Analysis with Large Scale Optimizer and Reliability Analysis. PhD. Thesis, Department of Civil Engineering, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil [in Portuguese].
   Google Scholar
• Carrión, P.M., et al. (2008). Geotechnical limit analysis and optimization. EngOpt 2008, International Conference on Engineering Optimization, Rio de Janeiro, Brazil.
   Google Scholar
• Chandra, T.R., Prakash, B.N., and Ryuichi, Y., 2013. High-Order FEM Formulation for 3-D Slope Instability. Applied Mathemathics, 4, 8–17. doi:10.4236/am.2013.45A002
   Google Scholar
• Chen, W.F. and Baladi, G.Y., 1985. Soil plasticity: theory and implementation. New York, NY: Elsevier.
   Google Scholar
• Chen, J., Yin, J., and Lee, C.F., 2003. Upper bound limit analysis of slope stability using rigid finite elements and non linear programming. Canadian Geotechnical Journal, 40 (4), 742–752. doi:10.1139/t03-032
   Web of Science ®Google Scholar
• Chen, W., 1975. Limit analysis and soil plasticity. Amsterdam, Oxford, New York: Elsevier Scientific Publishing Company.
   Google Scholar
• Chen, W. and Liu, X., 1990. Limit analysis in soil mechanics. New York, NY: Elsevier Scientific Publishing Company.
   Google Scholar
• Chen, Z., et al., 2001. A three-dimensional slope stability analysis method using the upper bound theorem. International Journal Rock Mechanisms Mining Sciences, 38 (3), 379–397. doi:10.1016/S1365-1609(01)00013-2
   Web of Science ®Google Scholar
• Christiansen, E., 1981. Computation of limit loads. International Journal for Numerical Methods in Engineering, 17, 1547–1570. doi:10.1002/(ISSN)1097-0207
   Web of Science ®Google Scholar
• CIMNE. GID 10.09, 2011. Reference manual. Barcelona: International Center for Numerical Methods in Engineering.
   Google Scholar
• Dassault Systèmes, 2011. Abaqus/Standard User’s Manual (Version 6.11). Providence, RI, USA: Dassault Systèmes Simulia Corp.
   Google Scholar
• Drucker, D. and Prager, W., 1952. Soil mechanics and plastic analysis on limit design. Quarterly Applied Mathematics, 10, 157–165. doi:10.1090/qam/1952-10-02
   Web of Science ®Google Scholar
• Drucker, D.C., Greenberg, H.J., and Prager, W., 1952. Extended limit design theorems for continuous media. Quarterly Applied Mathematics, 9, 381–389.
   Web of Science ®Google Scholar
• Durand, A.F. (2000). Applications of limit analysis as conventional continuum and Cosserat continua to geotechnics problems. PhD Thesis, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil. [in Portuguese]
   Google Scholar
• Durand, A.F., Vargas Jr., E.A., and Vaz, L.E., 2006. Applications of numerical limit analysis (NLA) to stability problems of rock e soil masses. International Journal of Rock Mechanics and Mining Sciences, 43 (3), 408–425. doi:10.1016/j.ijrmms.2005.07.010
   Web of Science ®Google Scholar
• Eerheggen, E. and Knöpfel, H., 1972. Finite element limit analysis using linear programming. International Journal of Solids and Structures, 8, 1413–1431. doi:10.1016/0020-7683(72)90088-1
   Google Scholar
• Eersen, E.D., Roos, C., and Terlaky, T., 2003. On implementing a primal-dual interior-point method for conic quadratic optimization. Mathematical Programming, Series B, 95, 249–277. doi:10.1007/s10107-002-0349-3
   Web of Science ®Google Scholar
• Gharti, H.N., et al., 2012. Application of an elastoplastic spectral-element method to 3D slope stability analysis. International Journal for Numerical Methods in Engineering, 91, 1–26. doi:10.1002/nme.v91.1
   Web of Science ®Google Scholar
• Goldfarb, D. and Yin, W., 2005. Second-order cone programming methods for total variational-based image restoration. Society for industrial and applied mathematics. SIAM Journal SCI Computation, 27 (2), 622–645. doi:10.1137/040608982
   Web of Science ®Google Scholar
• Griffiths, D.V. and Marquez, R.M., 2007. Three-dimensional slope stability analysis by elasto-plastic finite elements. Géotechnique, 57 (6), 537–546. doi:10.1680/geot.2007.57.6.537
   Web of Science ®Google Scholar
• Gvozdev, A.A., 1960. The determination of the collapse load for statically indeterminate system undergoing plastic deformations. International Journal Mechanisms Sciences, 1, 322–335. translated from the original in 1938. doi:10.1016/0020-7403(60)90051-5
   Google Scholar
• Huang, C.C. and Tsai, C.C., 2000. New method for 3D and axisymmetric slope stability analysis. Journal of Geotechnical and Environmental Engineering, 126 (10), 917–927. doi:10.1061/(ASCE)1090-0241(2000)126:10(917)
   Web of Science ®Google Scholar
• Huang, C.C., Tsai, C.C., and Chen, Y.H., 2002. Generalized method for three-dimensional slope stability analysis. Journal of Geotechnical and Environmental Engineering, 128 (10), 836–848. doi:10.1061/(ASCE)1090-0241(2002)128:10(836)
   Web of Science ®Google Scholar
• Hungr, O., Salgado, F.M., and Byrne, P.M., 1989. Evaluation of a three-dimensional method of slope stability analysis. Canadian Geotechnical Journal, 26, 679–686. doi:10.1139/t89-079
   Web of Science ®Google Scholar
• Kim, S., Kojima, M., and Yamashtia, M. (2002). Second order cone programming relaxation of positive semidefinite constraint. Research Report on Mathematical and Computing Sciences. Department of Mathematical and Computing Sciences Tokyo Institute of Technology, Japan.
   Google Scholar
• Lam, L. and Fredlund, D.G., 1993. A general limit equilibrium model for three-dimensional slope stability analysis. Canadian Geotechnical Journal, 30, 905–919. doi:10.1139/t93-089
   Web of Science ®Google Scholar
• Li, H.X. and Yu, H. S., 2006. Limit analysis of 2-D and 3-D structures based on an ellipsoid yield criterion. Acta Geotechnica, 1, 179–193. doi:10.1007/s11440-006-0020-x
   Web of Science ®Google Scholar
• Lobo, M.S., et al., 1998. Applications of second-order cone programming. Linear Algebra and Its Applications, 284, 193–228. doi:10.1016/S0024-3795(98)10032-0
   Web of Science ®Google Scholar
• Lysmer, J., 1970. Limit analysis of plane problems in soil mechanics. Journal of the Soil Mechanics E Foundations Division, 96, 1311–1334.
   Google Scholar
• Maier, G., 1969. Shakedown theory in perfect elastoplasticity with associated and non-associated flow laws: a finite element linear programming approach. Meccanica, 4, 250–260. doi:10.1007/BF02133439
   Google Scholar
• Makrodimopoulos, A. and Martin, C.M., 2006. Lower bound limit analysis of cohesive-frictional materials using second-order cone programming. International Journal for Numerical Methods in Engineering, 66, 604–634. doi:10.1002/(ISSN)1097-0207
   Web of Science ®Google Scholar
• MOSEK ApS, 2012. The MOSEK C API manual Version 6.0 (Revision 148). Denmark: Copyright (c) 1998-2012. Available from http://www.mosek.com
   Google Scholar
• Pastor, J., 1978. Analyse limite: détermination numérique de solutions statiques complètes. Application Au Talus Vertical. Journal De Mécanique Appliquée., 2, 167–196.
   Google Scholar
• Shivaswamy, P.K., Bhattacharyya, C., and Smola, A.J., 2006. Second order cone programming approaches for handling missing and uncertain data. Journal of Machine Learning Research, 7, 1283–1314.
   Web of Science ®Google Scholar
• Sloan, S.W., 1988. A steepest edge active set algorithm for solving sparse linear programming problems. International Journal for Numerical Methods in Engineering, 26, 2671–2685. doi:10.1002/(ISSN)1097-0207
   Web of Science ®Google Scholar
• Sloan, S.W., 2013. Geotechnical stability analysis. Geotechnique, 63, 531–572. doi:10.1680/geot.12.RL.001
   Web of Science ®Google Scholar
• Sun, G., Zheng, H., and Jiang, W., 2011. A global procedure for evaluating stability of three-dimensional slopes. Natural Hazards, 61, 1083–1098. doi:10.1007/s11069-011-9963-9
   Web of Science ®Google Scholar
• Tecgraf/PUC-Rio, 2013. Mtool3D 3.01 User Manual. In: Computer graphics technology. Brazil: PUC-Rio.
   Google Scholar
• Tiwari, R.C., Bhandarya, N.P., and Yatabea, R., 2015. 3-D elasto-plastic spectral element application to evaluate the stability of large-scale landslides. Geomechanics and Geoengineering, 10, 271–289. doi:10.1080/17486025.2014.985337
   Web of Science ®Google Scholar
• Tseng, P., 2007. Second-order cone programming relaxation of sensor network localization. Society for industrial and applied mathematics. SIAM Journal OPTIM, 18 (1), 156–185. doi:10.1137/050640308
   Web of Science ®Google Scholar
• Turgeman, S. and Pastor, J., 1982. Limit analysis: a linear formulation of the kinematic approach for axisymetric mechanic problems. International Journal for Numerical and Analytical Methods in Geomechanics, 6, 109–128. doi:10.1002/nag.1610060108
   Web of Science ®Google Scholar
• Xing, Z., 1988. Three-dimensional stability analysis of concave slopes in plan view. Journal Geotechnology Engineering, 114 (6), 658–671. doi:10.1061/(ASCE)0733-9410(1988)114:6(658)
   Google Scholar
• Yang, X. and Chi, S., 2013. Upper bound finite element analysis of slope stability using a nonlinear failure criterion. Computers and Geotechnics, 54, 185–191. doi:10.1016/j.compgeo.2013.06.007
   Web of Science ®Google Scholar
• Zhang, Y., et al., 2013. Effects of geometries on three-dimensional slope stability. Canadian Geotechnical Journal, 50, 233–249. doi:10.1139/cgj-2012-0279
   Web of Science ®Google Scholar
• Zheng, H., 2009. Eigenvalue problem from the stability analysis of slopes. Journal of Geotechnical and Geoenviromental Engineering, 135, 647–656. doi:10.1061/(ASCE)GT.1943-5606.0000071
   Web of Science ®Google Scholar
• Zienkiewicz, O.C., Humpheson, C., and Lewis, R.W., 1975. Associated and non-associated visco-plasticity in soil mechanics. Géotechnique, 25 (4), 671–689. doi:10.1680/geot.1975.25.4.671
   Web of Science ®Google Scholar
• Zouain, N., et al., 1993. An iterative algorithm for limit analysis with nonlinear yield functions. International Journal of Solids and Structures, 30, 1397–1417. doi:10.1016/0020-7683(93)90220-2
   Web of Science ®Google Scholar