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  1. Home
  3. Implicit Sub-stepping Scheme For Critical State Soil Models.
  1. Home
  3. Implicit Sub-stepping Scheme For Critical State Soil Models.

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Implicit sub-stepping scheme for critical state soil models.

Hoang-Giang Bui1,2, Jelena Niníc1, Günther Meschke3

  • 1Department of Engineering, Durham University, Durham, UK.

Engineering with Computers
|April 3, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces an efficient consistent tangent operator formulation for implicit sub-stepping integration in critical soil models. This method enhances convergence for large load steps, crucial for complex simulations like tunnel analysis.

Keywords:
CASMImplicit integrationModified Cam-ClaySub-stepping scheme

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Area of Science:

  • Geotechnical Engineering
  • Computational Mechanics
  • Soil Mechanics

Background:

  • Implicit Euler algorithm and return mapping are standard for critical soil models.
  • Large load steps can cause convergence issues in local nonlinear systems.
  • Sub-stepping schemes improve convergence but increase tangent operator complexity.

Purpose of the Study:

  • To develop a consistent tangent operator formulation for implicit sub-stepping integration.
  • To address convergence challenges in critical soil models under large load steps.
  • To enhance the efficiency of numerical simulations for geotechnical problems.

Main Methods:

  • Developed a formulation for the consistent tangent operator.
  • Applied the formulation to implicit sub-stepping integration.
  • Validated the approach for modified Cam-Clay and unified Clay and Sand models.

    • Main Results:

    • The proposed formulation is highly efficient.
    • Achieved convergence for arbitrary large load steps.
    • Successfully integrated with modified Cam-Clay and unified Clay and Sand models.

    Conclusions:

    • The developed consistent tangent operator formulation overcomes convergence issues in large load steps.
    • This method is efficient and applicable to complex geotechnical simulations, including tunnel analysis.
    • Enhances the robustness of numerical integration for critical soil models.