This library provides an implementation of Terracotta - a simple hydrodynamic model for clay [1].
Terracotta is a simple and physically meaningful hydrodynamic constitutive model adept at capturing key rheological and mechanical phenomena in clays. The model is derived using the thermodynamically rigorous hydrodynamic procedure [2] and draws inspiration from granular solid hydrodynamics (GSH) [3]. Here, as in the paper [1], the model is formulated in triaxial invariants. All of the constitutive equations are included in the Figure below.
The complete code is written in Python.
In this implementation, we use the function scipy.solve_ivp() [4] to integrate the constitutive equations along a given path.
To this end, the rate formulation of the stresses given in the above Figure has to be derived.
The functions necessary for the model integration are located in Terracotta_functions.py.
The loading is defined in terms of the path called testing, the loading rate loadingRates and the target increment targetIncs.
It is possible to run a simulation over multiple paths by including a list of paths in these variables.
Possible loading paths include:
| Type of loading | testing |
loadingRates |
targetIncs |
|---|---|---|---|
| triaxial undrained compression | txu |
strain rate [1/s] | strain increment [-] |
| isotropic compression | iso |
strain rate [1/s] | strain increment [-] |
| oedometric compression | oed |
strain rate [1/s] | strain increment [-] |
| triaxial drained compression | txd |
strain rate [1/s] | strain increment [-] |
| constant pressure shear | pureDev |
strain rate [1/s] | strain increment [-] |
| isotropic compression | isoStress |
stress rate [kPa/s] | stress increment [kPa] |
| relaxation | relaxation |
time step [s] | time increment [s] |
| creep | creep |
time step [s] | time increment [s] |
| oedometric creep | creepOed |
time step [s] | time increment [s] |
| undrained creep | txuCreep |
time step [s] | time increment [s] |
A sample simulation showing how to define initial conditions and choose a loading path is given in Terracotta_main.py.
[1] M Wiebicke and I Einav (2024). "A Simple Hydrodynamic Model for Clay". Available at SSRN: https://ssrn.com/abstract=4699137
[2] L D Landau and E M Lifshitz (1987). Fluid Mechanics. Butterworth. doi:10.1016/C2013-0-03799-1.
[3] Y Jiang, M Liu (2009). Granular solid hydrodynamics. Granular Matter 11, 139–156. doi:10.1007/s10035-009-0137-3
[4] P Virtanen and SciPy 1.0 Contributors (2020). SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17(3), 261-272. doi:10.1038/s41592-019-0686-2
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