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 gratefully acknowledge financial support of the University of Innsbruck: ProLehre project, AURORA Challenge Domains. Project duration: 12/2020–11/2021, amount: € 13.808. I further thank Hans-Peter Schröcker (University of Innsbruck) for suggesting to use asymptote.sourceforge.io for the interactive graphics.


… 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.

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