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April 3, 2026Géotechnique

Differential analysis of slope stability

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Authors

JBJean‐Pierre Bardet

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Overview

Analysis uncovers numerical challenges in slope stability models, highlighting implications for engineering applications.

Key Points

  • The aim is to analyze the slope stability slice methods using ordinary differential equations to understand their numerical behavior and stability.
  • Examined the ordinary differential equations governing slice methods for slope stability.
  • Analyzed the eigenvalues of the Jacobian matrix associated with the Morgenstern–Price and Janbu models.
  • Identified conditions leading to local indeterminacy and numerical instability in the models.
  • Proposed a new model incorporating the thrust line concept and a failure criterion for internal forces.
  • Found that the Morgenstern–Price model shows greater numerical stability compared to the Janbu model.
  • Revealed positive eigenvalues can occur for the Morgenstern–Price model under certain conditions but are generally positive for the Janbu model.
  • Demonstrated the significance of numerical instability near indeterminacy points in slope stability analyses.

Cite This Study

Jean‐Pierre Bardet (2026) studied this question.

synapsesocial.com/papers/69cf5e2e5a333a821460c449https://doi.org/10.1680/jgeot.25.00014
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