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

*Animating 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.

* 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 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

- PDF animation
- PDF file which includes all slides
**MATLAB**file for a 3D plot: matsuoka_nakai.zip

- PDF animation
- PDF file which includes all slides
**MATLAB**files for 3D plots: mohr_coulomb.zip and drucker_prager.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**

###### normally consolidated:

###### slightly overconsolidated:

###### highly overconsolidated:

**Undrained (cu) triaxial tests**

###### normally consolidated:

‘TSP’ indicates the total stress path

###### slightly overconsolidated:

###### highly overconsolidated:

**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.