Animating Soil Models – Animations as teaching and learning material for soil constitutive modeling


The project aims to increase the understanding of constitutive modeling with the help of animations by improving the visual aspect of teaching soil models.
Amongst others, the following topics are visualized: yield surfaces, stress invariants, Critical State Soil Mechanics and some related models as the Modified Cam Clay model and clay hypoplasticity.
In the sense of open education, the animations are shared under the open license CC BY to use them as teaching and learning material. The animations certainly do not replace studying the equations, computing or reading books. However, they can facilitate teaching and understanding concepts related to constitutive modeling.

Acknowledgement: I thank the geotechnical engineers on Twitter, through whom I got the idea for this project. I further thank David Mašín for his support here on the platform SoilModels.com and Hans-Peter Schröcker (University of Innsbruck) for suggesting to use asymptote.sourceforge.io for the interactive graphics. I gratefully acknowledge financial support of the University of Innsbruck: ProLehre project, AURORA Challenge Domains. Project duration: 12/2020–11/2021, amount: € 13.808.


… include the animations in LaTeX presentations:
… animate soil models:

Animations to visualize the stress invariants in principal stress space:
p’: mean effective stress
q: deviatoric stress
θ: the Lode angle to define the deviatoric direction of a stress state


Interactive WebGL graphics, created with asymptote.sourceforge.io
click to enlarge

p-q plane (scaled) for axisymm. tr. comp. is added

click to enlarge

cohesion is added

click to enlarge

vizualise plane stress, σ₃=0

click to enlarge

Rendulic plane is added

click to enlarge

p-q plane (scaled) for axisymm. tr. comp. is added

click to enlarge

cohesion is added

click to enlarge

vizualise plane stress, σ₃=0

click to enlarge

Rendulic plane is added

click to enlarge

p-q plane (scaled) for axisymm. tr. comp. is added

click to enlarge

cohesion is added

click to enlarge

vizualise plane stress, σ₃=0

 

click to enlarge

Rendulic plane is added

click to enlarge

p-q plane (scaled) for axisymm. states is added

click to enlarge

vizualise plane stress, σ₃=0

click to enlarge

p-q plane (scaled) for axisymm. states is added

click to enlarge

vizualise plane stress, σ₃=0

Useful references for 3D failure surfaces are e.g.:

  • Griffiths, D.V. (1990): Failure Criteria Interpretation Based on Mohr Coulomb Friction.
    Journal of Geotechnical Engineering, Vol. 116, Issue 6.
    doi: 10.1061/(ASCE)0733-9410(1990)116:6(986)
  • Griffiths, D.V. and Huang, J. (2009): Observations on the extended Matsuoka–Nakai failure criterion.
    Int. J. Numer. Anal. Meth. Geomech., 33: 1889-1905.
    doi: 10.1002/nag.810

The Modified Cam Clay (MCC) model by Roscoe & Burland (1968) is an elasto-plastic hardening model, assuming associated flow. It includes concepts from Critical State Soil Mechanics as the Normal Compression Line (NCL) and the Critical State Line (CSL).


Click on the images to enlarge them. You can download the GIF files directly. Below each figure, you can also download corresponding PDF files.

State boundary surface of the Modified Cam Clay model

Drained (cd) triaxial tests


Undrained (cu) triaxial tests

normally consolidated:

‘TSP’ indicates the total stress path

Linear-elasticity: How does ν affect the K₀-stress path (the stress path under oedometric compression). Mohr-Coulomb hexagon for φ = 30°, c = 0 is added; inspired by Zheng, Liu & Li (2005): doi: 10.1002/nme.1406 φ –ν inequality, sin φ ⩾1 – 2ν

How does ν affect the stress path of a plane-strain (biaxial) compression test. Linear-elastic, perfectly plastic (Mohr-Coulomb: φ = 30°, c = 0, ψ = 0°) model.

9 Comments
  1. Ahmed Salah Kamel Mohamed

    Hello Prof. Gertraud,

    Thank you so much for the great work. I have a question concerning the elliptical equation used to represent the state of the boundary surface of the cam clay model, may you please guide me to the source of this equation?

    Thank you!

    Ahmed S. Kamel
    PhD Researcher

  2. Alaa Kourdey
    Alaa Kourdey 2 months ago

    Hi Gertraud,

    Could you please provide the programming code for “3D view of the Normal Compression Line (NCL), Critical State Line (CSL) and State Boundary Surface of the MCC model “? Thank you.

    Best wishes,
    Alaa

  3. Ahmed Salah Kamel Mohamed

    Hi Gertraud,

    Thanks a lot for investing time for clarifications, this is a very appreciated efforts, actually I meant the cam clay model in p’, q, v space. I think I will figure it out from the mentioned sources.

    Thank you again for your prompt answer!

    Kind regards,
    Ahmed.

  4. Gertraud Medicus Author
    Gertraud Medicus 1 month ago

    Hi Alaa, hi Ahmed,

    sorry for the late reply.

    Here, I uploaded the script for the state boundary surface of the MCC model in p’-q-e space:
    https://soilmodels.com/wp-content/uploads/2020/12/sbs_mcc_pqe.wgl

    The surface has been created using: https://asymptote.sourceforge.io
    Just use the Asymptote Web Application and paste the lines in here:
    http://asymptote.ualberta.ca/

    Kind regards,
    Gertraud

  5. A S M RIYAD
    A S M RIYAD 3 weeks ago

    Hello Prof. Gertraud,

    Thank you so much for the great work. I have a question concerning the elliptical equation used to represent the state of the boundary surface of the bounding surface plasticity model, may you please guide me to the source of this equation?

    Thank you!

    Riyad
    Ph.D. Researcher

  6. Gertraud Medicus Author
    Gertraud Medicus 3 weeks ago

    Hello Riyad,

    Thanks for your feedback.

    If you are looking for the state boundary surface of the Modified Cam Clay model, the comments above should help. For a description of the MCC model and related equations, I suggest: Muir Wood (1990), Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press

    Regards, Gertraud

    • A S M RIYAD
      A S M RIYAD 3 weeks ago

      Thanks a lot for your reply, Prof. Gertraud. Actually, I am looking for the details of the bounding surface plasticity model (initially developed by Prof. Yannis Dafalias). Have you developed any script for the state boundary surface of the bounding surface plasticity model in the p’-q-v space during drained loading?

      • Gertraud Medicus Author
        Gertraud Medicus 3 weeks ago

        Thanks for clarification. Sorry, I didn’t read your question properly.
        So far, I have not been dealing with the boundary surface plasticity model.
        If I will, I will come back to your questions.
        All the best, Gertraud

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