Some applications of numerical limit analysis to geotechnical problems
DOI:
https://doi.org/10.14195/2184-8394_100_22Keywords:
Stability problem, Limit analysis, Reinforced soil, Fracturated media, Mathematical programmingAbstract
Various formulations for the numerical limit analysis have been proposed for the solution of stability problems in geotechnical engineering, formulated as a Mathematical Programming problem. Toe problem can be solved directly as a Non - linear Mathematical Programming problem or approximated by a Linear Mathematical programming problem. This paper presents a mixed formulation for limit analysis to solve stability problems in continuum, fractured, and reinforced geological (soil or rock) media under the condition of plane strain and using the Finite Element Method. For the description of the rock mass, Hoek and Brown criterion is used as yield function. For the soil description, Mohr-Coulomb criterion is used in a linearized form. Toe yield condition for the interfaces is described by the Coulomb criterion. The soil, the interfaces and the reinforcement are idealized as rigid-plastic materiais with an associated flow rule. Toe results obtained in the examples indicate that the methodology presented has considerable potential to be applied to the solution of geotechnical problems.
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References
Araújo, L. G. (1997) Estudo numérico de problemas de estabilidade em materiais geotécnicos através da análise limite. Tese de Doutorado, PUC/Rio.
Bathe, K. J. (1982) Finite element procedures in engineering analysis. Prentice Hall.
Borges, L. A. (1991) Formulação e solução para análise limite com superfície de escoamento não linear. Tese de Doutorado, PUC/Rio.
Casciaro, R. e Cascini, L. (1982) A mixed formulation and mixed finite elements for limit analysis. Int. J. num. Meth. E ngng, v.18, p .211- 243.
Chen, W. F. e Liu, X. L. (1990) Limit Analysis in Soil Mechanics. Elsevier, 477 p.
Chen, W. F. (1975) Limit analysis and soil plasticity. Elsevier Science Publishers, B V, Amsterdam, The Netherlands.
Christiansen, E. (1981) Computation of limit loads. lnt. J. Num. Meth. Engng, v.17, pp. 1547-1570.
Cook, R. D.; Malkus, D. S.; e Plesha, M. E. (1989) Concepts and applications of finite element analysis. Wiley & Sons, lnc.
Davis, E. H. (1980) A Note on Some Plasticity Solutions Relevant to the Bearing Capacity of Brittle and Fissured Materials. Proc. Int. Conf. on Structural Foundations on Rock, Vol. 3.
Drucker, D. C., Greenberg, H. J. e Prager, W. (1952) Extended limit Design Theorems for Continuous Media. Quartely Applied Mathematic., Vol. 9.
Durand, A. F. (2000) Aplicação da Análise Limite a Problemas Geotécnicos Modelados como meios Contínuos Convencionais e Meios de Cosserat. Tese de Doutorado, Pontifícia Universidade Católica do Rio de Janeiro.
Faria, P. O. (1992) Análise limite de problemas geotécnicos. Dissertação de Mestrado, PUC/Rio.
Finn, W. D. L. (1967) Application of limit plasticity in soil mechanics. J. of Soil Mechanics and Foundation Division. ASCE.
Francescato, P. e Pastor, J. (1997) Lower and upper numerical bounds to the off-axis strength of unidirectional fiber-reinforced composites by limit analysis methods. Eur. J. Mech., A/Solids, v.16. n.2, p.213-234.
Gerrard, G. M. e Pande, G. N. (1985) Numerical Modelling of Reinforced Jointed Rock Masses. Computers and Geomechanics, vol. 1.
Hoek, E. e Brown, E. T. (1980) Empírical Strength Criterion for Rock Masses. J. Geoth. Eng. Division.
Jaeger, J. C. e. Cook, N. G. W. (1979) Fundamentals of Rock Mechanics , Ed. Chapman and Hall.
Jiang, G. L. (1995) Non-linear finite element formulation of kinematic limit analysis. lnt. J. for Num. And Anal. Meth. in Eng.
Lemos, P. A. (2002) Estudo numérico pela análise limite de problemas geotécnicos em solos reforçados. Dissertação de mestrado UFOP.
Livesley, R. L. (1978) Limit analysis of structures formed from rigid blocks. Int. J. Num. Met. Eng, Vol. 12.
Lysmer, J. (1970) Limit analysis of plane problems in soil mechanics. J. of Soil Mech. and Foundations Div., ASCE, v. 96, SM4, pp. 1311- 1334.
Michalowski, R. L. (1998) Limit analysis in stability calculations of reinforced soil structures. Geotextiles and Geomembranes, v.16, p.311-331.
Murtagh, B. A. e Saunders M. A. (1987) MINOS 5. user's guide. Technical Report SOL 83-20R, Stanford University: California.
Porbaha, A.; Zhao, A.; Kobayashi, M. e Kishida, T. (2000) Upper bound estimate of scaled reinforced soil retaining walls. Geotextiles and Geomembranes, v.18, p.403-413.
Schrage, L. (1991) lindo User's Manual. The Scientific Press.
Serrano, A. e Olalla, C. (1994) Ultimate bearing capacity of rock. Int J. Mech. Sei. & Gomech. Elsevier Science Ltd.: Vol. 31, No 2, pp 93-106.
Singh, D. N. e Basudhar, P. K. (1993a) Determination of the optimal lower bound bearing capacity of reinforced soil-retaining walls by using finíte elements and non-linear programming. Geotextiles and Geomembranes, v.12, p.665-686.
Singh, D. N. e Basudhar, P. K. (1993b) Optima/ lower bound bearing capacity of strip footings. Soils and Foundations, v.33, n.4, p.18-25.
Sloan, S. W. (1987a) Lower bound limit analysis using finite elements and linear programming. Report Nº 020.01.87, The University Of New Castle, Australia.
Sloan, S. W. (1987b) Upper bound limit analysis using finite elements and linear programming. Report Nº 025.01.1987, Toe University Of New Castle, Austrália.
Sousa, L. S. M. R. (2001) Estudo numérico de problemas de estabilidade de solos reforçados via análise limite. Dissertação de Mestrado, UFOP.
Tamura, T.; Kobayashi, S. e Sumi, T. (1987) Rigid plastic finite element method for frictional materiais. Soils and Foundations, v.27, n.3, p.1- 12.
Terzaghi, K. (1943) Theoretical soil mechanics. Wiley.
Yu, H. S. e Sloan, S. W. (1994) Bearing capacity of Jointed rock. Computer Methods and Advances in Geomechanics, pp. 2403-2408.
Yu, H. S. e Sloan, S. W. (1997) Finite element limit analysis of reinforced soi/s. Computers & Structures, v.63, n.3, pp. 567-577.
Zienkiewicz, O. C. e Pande, G. N. (1977) Time Dependent Multilaminated Model of Rocks - A Numerical Study of Deformation and Failure of Rock Masses. lnt. J. for Num. and. Anal. Meth. in Geomech, vol. 1.
