Skip to main content
SpringerLink
Log in

Limit Analysis

  • Chapter
Book cover Plasticity and Geotechnics

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 13))

  • 3357 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Alehossein H., Carter J.P. and Booker J.R. (1992). Finite element analysis of rigid footings on jointed rock. Proc. 3rd Int. Conf. Computational Plasticity, Vol. 2, 935–945.

    Google Scholar 

  • Anderheggen, E. and Knopfel, H. (1972). Finite element limit analysis using linear programming. Int. J. Solids and Structures., Vol. 8, 1413–1431.

    Article  Google Scholar 

  • Bishop, A.W. (1955). The use of the slip circle in the stability of slopes. Geotechnique., Vol 5, 7–17.

    Google Scholar 

  • Bottero, A., Negre, R., Pastor, J. and Turgeman, S. (1980). Finite element method and limit analysis theory for soil mechanics problems. Comput. Meth. Appl. Mech. Eng., Vol. 22, 131–149.

    Article  Google Scholar 

  • Chen, W.E (1975). Limit Analysis and Soil Plasticity, Elsevier, Amsterdam.

    Google Scholar 

  • Chen W.F. and Drucker D.C. (1969). Bearing capacity of concrete blocks or rock. J. Eng. Mech. Div., ASCE, Vol 95, 955–979.

    Google Scholar 

  • Chen, W.E and Liu, X.L. (1990). Limit Analysis in Soil Mechanics, Elsevier, Amsterdam.

    Google Scholar 

  • Collins, I.F. (1974). A note on the interpretation of Coulomb’s analysis of the thrust on a rough retaining wall in terms of the limit theorems of plasticity theory. Geotechnique., Vol. 24, 106–108.

    Google Scholar 

  • Cousins, B.E (1978). Stability charts for simple earth slopes. J. Geotech. Eng. Div., ASCE, Vol. 104, GT2, 267–279.

    Google Scholar 

  • Davis, E.H. (1968). Theories of plasticity and the failure of soil masses, In: Soil Mechanics: Selected Topics, (Editor: I. K. Lee), Butterworths, London, 341–380.

    Google Scholar 

  • Davis E.H. (1980). A note on some plasticity solutions relevant to the bearing capacity of brittle and fissured materials. Proc. Int. Conf. Struct. Foundations on Rock, Vol. 3, 83–90.

    Google Scholar 

  • Davis, R.O. and Selvadurai, A.P.S. (2002). Plasticity and Geomechanics, Cambridge University Press.

    Google Scholar 

  • Drescher, A. and Detournay, E. (1993). Limit load in translational failure mechanisms for associative and non-associative materials. Geotechnique., Vol. 43, 443–456.

    Google Scholar 

  • Drucker, D.C., Greenberg, H.J. and Prager, W. (1952). Extended limit design theorems for continuous media. Quart. J. Appl. Maths., Vol. 9, 381–389.

    Google Scholar 

  • Duncan, J.M. and Wright, S.G. (1980). The accuracy of equilibrium methods of slope stability analysis, Eng. Geology, Vol. 16, 5–17.

    Article  Google Scholar 

  • Duncan, J.M., Buchignani, A.L. and de Wet, M. (1987). An engineering manual for slope stability studies, Internal Research Report, Department of Civil Engineering, Virginia Tech, USA.

    Google Scholar 

  • Fellenius, W.O. (1926). Mechanics of Soils, Statika Gruntov, Gosstrollzdat.

    Google Scholar 

  • Fredlund, D.G. and Krahn, J. (1977). Comparison of slope stability methods of analysis, Can. Geotech. J., Vol. 14, 429–439.

    Google Scholar 

  • Gao, Y. (1988). Panpenalty finite element programming for plastic limit analysis, Comput. Struct., Vol. 28, 749–755.

    Article  Google Scholar 

  • Gibson, R.E. and Morgenstern, N. (1962). A note on the stability of cuttings in normally consolidated clays. Geotechnique., Vol. 12, 212–216.

    Google Scholar 

  • Graham, J. (1984). Methods of stability analysis. Chapter 6 In: Slope Instability, (Editors: D. Brunsden and D.B. Prior), Wiley.

    Google Scholar 

  • Himmelblau, D.M. (1972). iApplied Nonlinear Programming, McGraw-Hill Book Company, New York.

    Google Scholar 

  • Huh, H. and Yang, W.H. (1991). A general algorithm for limit solutions of plane stress problems. Int. J. Solids and Structures, Vol. 28, 727–738.

    Article  Google Scholar 

  • Hunter, J.H. and Schuster, R.L. (1968). ‘Stability of simple cuttings in normally consolidated clays’. Geotechnique, Vol. 18, 372–378.

    Google Scholar 

  • Janbu, N. (1954). Stability analysis of slopes with dimensionless parameters, Harvard Soil Mechanics Series, No. 46.

    Google Scholar 

  • Kim, J.K., Salgado, R. and Lovell, C.W. (1997). STABL-Instructions for Use. School of Civil Engineering, Purdue University.

    Google Scholar 

  • Kim, J.M., Salgado, R. and Yu, H.S. (1999). Limit analysis of soil slopes subjected to pore pressures. J. Geotech. Geoenviron. Eng., ASCE, Vol 125, 49–58.

    Article  Google Scholar 

  • Li, H.X. and Yu, H.S. (2005). Kinematic limit analysis of frictional materials using nonlinear programming. Int. J. Solids and Structures, Vol 42, 4058–4076.

    Article  Google Scholar 

  • Li, H.X. and Yu, H.S. (2006a). Limit analysis of composite materials based on an ellipsoid yield criterion. Int. J. Plasticity (in press).

    Google Scholar 

  • Li, H.X. and Yu, H.S. (2006b). Limit analysis of 2D and 3D structures based on an ellipsoid yield criterion. Int. J.Mech. Sci. (in press).

    Google Scholar 

  • Liu, Y.H., Cen, Z.Z. and Xu, B.Y. (1995). A numerical method for plastic limit analysis of 3D structures. Int. J. Solids and Structures, Vol 32, 1645–1658.

    Article  Google Scholar 

  • Lyamin, A. and Sloan S.W. (2002a). Upper bound limit analysis using linear finite elements and nonlinear programming. Int. J. Nurn. Analy. Meth. Geomech, Vol 26, 181–216.

    Article  Google Scholar 

  • Lyamin, A. and Sloan S.W. (2002b). Lower bound limit analysis using nonlinear programming. Int. J. Nurn. Meth. Eng., Vol 55, 573–616.

    Article  Google Scholar 

  • Lyamin, A., Yu, H.S., Sloan, S.W and Hossain, M.Z. (1998). Lower bound limit analysis of jointed rocks using the Hoek-Brown criterion. Australian Geomech. J., Vol 33, 46–62.

    Google Scholar 

  • Lysmer, J. (1970). Limit analysis of plane problems in soil mechanics. J. Soil Mech. and Found. Div., ASCE, Vol. 96, SM4, 1131–1334.

    Google Scholar 

  • Maier, G, Carvelli, G. and Cocchetti, G. (2000). On direct methods of shakedown and limit analysis. Plenary Lecture, 4th Euromech Solid Mechanics Conference, Metz, June.

    Google Scholar 

  • Merifield, R.S., Sloan, S.W. and Yu, H.S. (1999). Rigorous plasticity solutions for the bearing capacity of two layered clays. Geotechnique, Vol. 49,471–490.

    Google Scholar 

  • Merifield, R.S., Sloan, S.W. and Yu, H.S. (2001). Stability of plate anchors in undrained clay. Geotechnique, Vol. 51, 141–153.

    Article  Google Scholar 

  • Michalowski, R.L. (1989). Three-dimensional analysis of locally loaded slopes. Geotechnique., Vol. 39, 27–38.

    Google Scholar 

  • Michalowski, R.L. (1994). Limit analysis of slopes subjected to pore pressure. Computer Methods and Advances in Geomechanics, (Editors: Siriwardane and Zaman), 2477–2482.

    Google Scholar 

  • Miller, T.W. and Hamilton, J.H. (1989). A new analysis procedure to explain a slope failure at the Martin Lake mine. Geotechnique, Vol. 39, also see Discussion, Vol. 40, 145–147.

    Google Scholar 

  • Morgenstern, N.R. and Price, V.E. (1965). The analysis of the stability of generalized slip surfaces. Geotechnique, Vol. 15, 79–93.

    Article  Google Scholar 

  • Nagtegaal, J., Parks, D.M. and Rice, J.R. (1974). On numerically accurate finite element solutions in the fully plastic range. Comput. Meth. Appl. Mech. Eng., Vol. 4, 153–177.

    Article  Google Scholar 

  • Nash, D. (1987). A comparative review of limit equilibrium methods of stability analysis. Chapter 2 In: Slope Stability, (Editors: M.G. Anderson and K.S. Richards), John Wiley.

    Google Scholar 

  • Ponter, A.R.S. and Boulbibane, M. (2006). The linear matching method for limit load and shakedown analysis, In: Modern Trends in Geomechanics, (Editors: W. Wu and H.S. Yu), Springer.

    Google Scholar 

  • Potts, D. M. and Zdravkovic, L. (1999). Finite Element Analysis in Geotechnical Engineering: Theory, Thomas Telford, London.

    Google Scholar 

  • Prager, W. and Hodge, P.G. (1951). The Theory of Perfectly Plastic Solids, John Wiley and Sons, New York.

    Google Scholar 

  • Shield, R.T. (1954). Stress and velocity fields in soil mechanics, Quart. Appl. Math., Vol 12, 144–156.

    Google Scholar 

  • Sloan, S.W. (1988a). A steepest edge active set algorithm for solving sparse linear programming problems. Int. J. Num. Meth. Eng., Vol. 26, 2671–2685.

    Article  Google Scholar 

  • Sloan, S.W. (1988b). Lower bound limit analysis using finite elements and linear programming. Int. J. Num. Analy. Meth. Geomech., Vol. 12, 61–77.

    Article  Google Scholar 

  • Sloan, S.W. (1989). Upper bound limit analysis using finite elements and linear programming. Int. J. Num. Analy. Meth. Geomech., Vol. 13, 263–282.

    Article  Google Scholar 

  • Sloan, S.W. (1995). ‘Limit analysis in geotechnical engineering’. in: Modern Developments in Geomechanics (Editor: C.M. Haberfield), Proc. of Ian Donald Symposium, Monash University, Australia, 167–199.

    Google Scholar 

  • Sloan, S.W. and Kleeman, P.W. (1995). Upper bound limit analysis using discontinuous velocity fields. Computer Meth. Appl. Mech. Eng., Vol. 127, 293–314.

    Article  Google Scholar 

  • Sloan S.W. and Randolph M.F. (1982). Numerical prediction of collapse load using finite elements and linear programming. Int. J. Num. Analy. Meth. Geomech, Vol 6, 47–76.

    Article  Google Scholar 

  • Spencer, E. (1967). A method of analysis of the stability of embankments assuming parallel inter-slice forces. Geotechnique., Vol. 17, 11–26.

    Google Scholar 

  • Sutcliffe, D.J., Yu, H.S. and Page, A.W. (2001). Lower bound limit analysis of unreinforced masonry shear walls, Comput. Struct., Vol. 79, 1295–1312.

    Article  Google Scholar 

  • Sutcliffe, D.J., Yu, H.S. and Sloan, S.W. (2004). Lower bound solutions for bearing capacity of jointed rock. Comput. Geotech., Vol. 31, 23–36.

    Article  Google Scholar 

  • Taylor, D.W. (1948). Fundamentals of Soil Mechanics, Wiley, New York.

    Google Scholar 

  • Terzaghi, K. (1943). Theoretical Soil Mechanics, Wiley, New York.

    Google Scholar 

  • Whitman, R.W. and Bailey, W.A. (1967). Use of computers for slope stability analysis. J. Soil Mech. and Found. Div., ASCE, Vol. 93, SM4, 475–498.

    Google Scholar 

  • Yu, H.S. and Netherton, M. (2000). Performance of displacement finite elements for modelling incompressible materials. Int. J. Num. Analy. Meth. Geomech., Vol. 24, 627–653.

    Article  Google Scholar 

  • Yu, H.S. and Sloan, S.W. (1991a). Lower bound limit analysis of axisymmetric problems using finite elements and linear programming, Proc. 6th Int. Conf. in Australia on Finite Elements, Sydney, Vol.I, 48–52.

    Google Scholar 

  • Yu, H.S. and Sloan, S.W. (1991b). Lower bound limit analysis of plane problems in soil mechanics, Proc. Int. Conf. of Nonlinear Engineering Computations, Swansea, 329–338.

    Google Scholar 

  • Yu, H.S. and Sloan, S.W. (1994a). A note on bearing capacity of soft clays under embankments, J. Geotech. Eng., ASCE, Vol. 120 (I), 246–255.

    Google Scholar 

  • Yu, H.S. and Sloan, S.W. (1994b). Upper bound limit analysis of a rigid-plastic body with frictional interfaces. Int. J. Mech. Sci., Vol. 36, 219–229.

    Article  Google Scholar 

  • Yu, H.S. and Sloan, S.W. (1994). Bearing capacity of jointed rock. In: Compter methods and Advances in Geomechanics, (Editors: Siriwardane and Zaman), 2403–2408.

    Google Scholar 

  • Yu, H.S. and Sloan, S.W. (1995). Limit analysis of anisotropic soils using finite elements and linear programming. Mech. Res. Comrnu., Vol. 21 545–554.

    Article  Google Scholar 

  • Yu, H.S. and Sloan, S.W. (1997). Finite element limit analysis of reinforced soils. Comput. Struct., Vo1 63, 567–577.

    Article  Google Scholar 

  • Yu H.S., Houlsby, G.T. and Burd, H.J. (1993). A novel isoparametric finite element displacement formulation for axisymmetric analysis of nearly incompressible materials. Int. J. Num. Meth. Eng., Vol 36, 2453–2472.

    Article  Google Scholar 

  • Yu, H.S., Salgado, R., Sloan, S.W. and Kim, J.M. (1998). Limit analysis versus limit equilibrium for slope stability. J. Geotech. Geoenviro. Eng., ASCE, Vol 124, 1–11.

    Article  Google Scholar 

  • Yu, H.S., Sloan, S.W. and Kleeman, P.W. (1994). A quadratic element for upper bound limit analysis. Engineering Computations, Vol. 11, 195–212.

    Google Scholar 

  • Zhang, P.X., Lu, M.W. and Hwang, K. (1991). A mathematical programming algorithm for limit analysis. Acta Mechanica Sinica., Vol. 7, 267–274.

    Article  Google Scholar 

  • Zouain, N., Herskovits, J. and Borges, L.A. (1993). An iterative algorithm for limit analysis with nonlinear yield functions. Int. J. Solids and Structures., Vol. 32, 1645–1658.

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

(2006). Limit Analysis. In: Plasticity and Geotechnics. Advances in Mechanics and Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-33599-5_12

Download citation

Publish with us

Policies and ethics

Search

Navigation