Numerical Limit Analysis and Limit State Design

The group has strong interests in the development of Numerical Limit Analysis and Limit State Design techniques, and works closely with colleagues in the Computational Mechanics and Design group in developing innovative approaches to a broad range of problems.

Discontinuity Layout Optimization (DLO)

Background and theory

This new numerical procedure was developed by Dr Colin Smith in collaboration with Dr Matthew Gilbert and was first described in a paper published in the Proceedings of the Royal Society in 2007. Since then further developments and applications have been published in a number of journal and conference papers and the technique is now used in the LimitState:GEO commercial software application.

Discontinuity Layout Optimization is a new computational limit analysis procedure which provides visually clear failure mechanisms and accurate predictions of the associated margin of safety. At the heart of the new procedure is a simple yet robust and highly efficient algorithm that can identify the critical failure mechanism from a very large number of possibilities.

A simple MATLAB code demonstrating the essence of the procedure is available here.

Applications

The flexibility of the method allows it to provide solutions to a wide range of geotechnical stability problems:

  • Slope stability

  • Retaining walls

  • Pipelines

  • Fractured rock

Ongoing research

Research is ongoing to extend the method to:

  • 3D analysis problems
  • Analysis of non-associative problems
  • Analysis of unsaturated soil problems
  • Reinforced soils

Application in Teaching

DLO has a number of attractive attributes that makes it ideal for teaching principles of numerical limit analysis and the principles of geotechnical stability analysis.

  • simple yet robust and highly efficient algorithm
  • generation of visually clear failure mechanisms (particularly when animated)

The LimitState:GEO software which is based on DLO is available free to Universities for academic use.

The software adds a very easy to use, interactive graphical user interface to the DLO method and is also written to incorporate application of the Limit State Design approach in Eurocode 7.

It has been used at Sheffield and at a number of Universities around the world for:

  • teaching geotechnical limit analysis
  • teaching Eurocode 7
  • as an investigative tool for student projects

The Sheffield Geotechnical Engineering Group has set up a series of web pages providing resources and links relating to the teaching of Limit Analysis and Limit State Design. These are primarily based on DLO and LimitState:GEO. Further information and resources may be found here.

Research Opportunities

Research is ongoing to extend the DLO technique in a number of areas. Its comparative novelty means that there is considerable scope to extend its capability. There are PhD opportunities for strong candidates who are interested in numerical modelling and in making an impact in a new area of research with applications in geotechnical limit analysis and design and related areas. For further details, please contact Dr Colin Smith

Publications

  • Belczyk EB and Smith CC (in press). Geosynthetic landfill cap stability: comparison of limit equilibrium, computational limit analysis and finite element analyses. Geosynthetics International.
  • Lee YS, Smith CC and Cheuk CY (2011) Lateral breakout resistance of shallowly embedded offshore pipelines. Procedia Engineering, 14, pp 1690-1695. ISSN 1877-7058.
  • Smith CC and Cubrinovski M (2011) Pseudo-static limit analysis by discontinuity layout optimization: Application to seismic analysis of retaining walls. Soil Dynamics and Earthquake Engineering, 31 (10), October, pp 1311-1323. ISSN 0267-7261. DOI doi:10.1016/j.soildyn.2011.03.014
  • Gilbert M, Smith CC and Pritchard TJ (2010) Masonry arch analysis using discontinuity layout optimisation. Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics, 163 (3), September, pp 155-166. ISSN 1755-0785. DOI 10.1680/eacm.2010.163.3.155
  • Merifield RS, Smith CC (2010) The ultimate uplift capacity of multi-strip anchors in undrained clay. Computers and Geotechnics, 37(4), June, pp 540-551. DOI 10.1016/j.compgeo.2010.02.004
  • Gilbert M, Smith CC, Haslam IW and Pritchard TJ (2009) Plastic limit analysis using discontinuity layout optimization (DLO). In 17th UK Conference on Computational Mechanics (ACME-UK), 6 - 8 April 2009, Nottingham.
  • Gilbert M and Smith CC (2008) On the analogy between structural layout optimization and plastic limit analysis formulations. In 8th World Congress in Computational Mechanics, Venice.
  • Lee, YS, Smith CC and Cheuk CY (2008) Bearing capacity of embedded foundations. In 2nd International Conference on Foundations, ICOF 2008, Dundee, pp 961-972.
  • Smith CC and Gilbert M (2008) Limit analysis of the stability of foundations on inclined ground. In 2nd International Conference on Foundations, ICOF 2008, Dundee, pp 1683-1692.
  • Smith CC and Gilbert M (2007) New upper bound solutions for layered soil bearing capacity problems using discontinuity layout optimization. In 10th Australia New Zealand Conference on Geomechanics, Brisbane, October, pp 250-255.
  • Gilbert M and Smith CC (2007) Discontinuity layout optimization: a new numerical procedure for upper bound limit analysis. In IX International Conference on Computational Plasticity: COMPLAS IX, Barcelona, September, pp 170-173.
  • Smith CC and Gilbert M (2007) Application of discontinuity layout optimization to plane plasticity problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463 (2086), October, pp 2461-2484. ISSN 1364-5021. DOI 10.1098/rspa.2006.1788

Finite Element Limit Analysis

Finite Element Limit Analysis utilizes a standard Finite Element approach within a limit analysis framework. Optimization techniques are utilised to directly solve for the critical stability case, thus avoiding the need to timestep to a solution.

Work in the group has investigated use of the technique in investigating the stability of backfilled masonry arch problems and in using mobilised strength approaches in Limit Analysis.

  • Gilbert. M., Nguyen, D. and Smith, C.C. (2007) Computational limit analysis of soil-arch interaction in masonry arch bridges. In 5th International Arch Bridges Conference, Madeira, September, pp 633-640. ISBN 978-972-8692-31-5.
  • Nguyen, D., Gilbert, M. and Smith, C.C. (2007) Application of limit analysis to soil-structure interaction problems. 10th Australia New Zealand Conference on Geomechanics, Brisbane, October, pp 196-201.

Method of characteristics

The method of characteristics is a valuable limit analysis related technique for investigating specific stability problem. Work published in 2005, was the first to demonstrate rigorous lower bounds to the classic bearing capacity problem.

  • Smith CC (2005) Complete limiting stress solutions for the bearing capacity of strip footings on a Mohr-Coulomb soil. Geotechnique, 55 (8), October, pp 607-612. ISSN 0016 8505.

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