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Probabilistic stability assessment using adaptive limit analysis and random fields

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Abstract

For deterministic scenarios, adaptive finite element limit analysis has been successfully employed to achieve tight bounds on the ultimate load of a geotechnical structure in a much more efficient manner than a dense uniform mesh. However, no probabilistic studies have so far considered finite element limit analysis with adaptive remeshing. Therefore, this research explores the benefits of combining adaptive mesh refinement with finite element limit analysis for probabilistic applications. The outcomes indicate that in order to achieve tight bounds on probabilistic results (such as the probability of failure), the ultimate load in each individual simulation (e.g. factor of safety or bearing capacity) has to be estimated with a very high level of accuracy and this can be achieved more economically using adaptive mesh refinement. The benefits, assessed here for undrained conditions, are expected to be much more pronounced in the case of frictional soils and complex geometries.

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Abbreviations

A :

Equilibrium matrix

B :

Footing width

c u :

Undrained soil shear strength

e :

Error estimate

\(e_{{\mu_{Nc} }}\) :

Error in the mean bearing capacity factor

\(e_{{p_f }}\) :

Error in the probability of failure

\(e_{{\mu_{_{FS}} }}\) :

Error in the mean factor of safety

f :

Yield function

FS :

Factor of safety

H :

Slope height

N c :

Bearing capacity factor

N c,det :

Deterministic bearing capacity factor

n sim :

Number of Monte Carlo simulations

p 0 :

Constant part of the external load

p :

External load proportional to the load multiplier α

p f :

Probability of failure

α :

Load multiplier

γ :

Unit weight of soil

θ :

Actual spatial correlation length (in units of length)

Θ:

Dimensionless spatial correlation length

\(\mu_{{c_{u} }}\) :

Mean value of undrained shear strength

\(\mu_{FS}\) :

Mean factor of safety

\(\mu_{N_{c} }\) :

Mean bearing capacity factor

\(\nu_{c_{u}}\) :

Coefficient of variation in the undrained shear strength

\(\nu_{{N_{c} }}\) :

Coefficient of variation in the bearing capacity factor

ρ :

Correlation function

\(\sigma_{{c_{u} }}\) :

Standard deviation in the undrained shear strength

\(\sigma_{{N_{c} }}\) :

Standard deviation in the bearing capacity factor

σ :

Vector of stresses

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Authors and Affiliations

  1. Australian Research Council Centre of Excellence for Geotechnical Science and Engineering, School of Engineering (ARC CGSE), The University of Newcastle, Callaghan, Australia

    Abid Ali, A. V. Lyamin, Jinsong Huang & S. W. Sloan

  2. ARC CGSE, The University of Western Australia, Perth, Australia

    J. H. Li & M. J. Cassidy

Authors
  1. Abid Ali
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  2. A. V. Lyamin
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  3. Jinsong Huang
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  4. J. H. Li
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  5. M. J. Cassidy
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  6. S. W. Sloan
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Correspondence to Abid Ali.

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Ali, A., Lyamin, A.V., Huang, J. et al. Probabilistic stability assessment using adaptive limit analysis and random fields. Acta Geotech. 12, 937–948 (2017). https://doi.org/10.1007/s11440-016-0505-1

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  • DOI: https://doi.org/10.1007/s11440-016-0505-1

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