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 University of Innsbruck for financial support. (ProLehre project, AURORA Challenge Domains). Project duration: 12/2020 – 11/2021, amount: € 13.808.
I further thank the geotechnical engineers on Twitter, through whom I got the idea for this project.


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

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.

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

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