Animating Soil Models – Animations as teaching and learning material for soil constitutive modeling
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.
Contact: Gertraud Medicus – gertraud.medicus@uibk.ac.at
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
- PDF animation
- PDF file which includes all slides
- MATLAB scripts for 3D plots of Matsuoka-Nakai, Mohr-Coulomb and Drucker-Prager: MN_MC_DP.zip
Interactive WebGL graphics, created with asymptote.sourceforge.io
click to enlarge
p-q plane (scaled) for axisymm. tr. comp. is added
- 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
Interactive WebGL graphics, created with asymptote.sourceforge.io
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
- Here is the PDF animation where you can use control buttons (pause/speed up/…). It can be viewed for example in Acrobat Reader (except on mobile devices).
- here is the PDF file which includes all slides.
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
- Here is the PDF animation where you can use control buttons (pause/speed up/…). It can be viewed for example in Acrobat Reader (except on mobile devices).
- here is the PDF file which includes all slides.
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.
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
Hi Ahmed,
thank you for your feedback.
I added some comments to it and uploaded the script to create the state boundary surface of the MCC model in stress space:
https://soilmodels.com/wp-content/uploads/2020/12/sbsMCC.txt
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/
Was this the surface you were interested in?
A description of the MCC model and equations can e.g. be found in
(i) Muir Wood (1990), Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press,
(ii) Muir Wood (2003), Geotechnical modelling, CRC Press
Kind regards,
Gertraud
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
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.
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
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
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
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?
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