A verified numerical simulator for hydro-geomechanical heterogeneity based on MOOSE

About

RHEA (Real HEterogeneity App), is an open-source fully coupled finite element application capable of including element-resolution hydro-geomechanical properties in coupled simulations. The code was developed by José Bastías with small additions from Andy Wilkins in a collaboration between Karlsruhe Institute of Technology (KIT) and the Commonwealth Scientific and Industrial Research Organisation (CSIRO).

RHEA is a MOOSE based application, for more information visit MOOSE Framework. To use RHEA, you will need to have installed MOOSE, which can take some time.

RHEA is released under the GNU Lesser General Public License Version 2.1. See the LICENSE file for details.

Getting started

For system requirements and MOOSE installation visit Getting Started page of the MOOSE framework.

Clone RHEA

The stable version of RHEA can be cloned directly for the GitHub repository. As usual in any MOOSE based app, RHEA will be located by default in the cd ~/projects folder generated during the installation of MOOSE.

cd ~/projects
git clone https://github.com/josebastiase/RHEA.git
cd ~/projects/RHEA

Compile and test RHEA

As any MOOSE based app, you first need to compile RHEA

cd ~/projects/RHEA
make -j4

and then test RHEA

cd ~/projects/RHEA
./run_tests

If RHEA has compiled successfully, you should see various output, ending with the line

2 passed, 0 skipped, 0 pending, 0 failed

Examples

Terzaghi's consolidation problem

In Terzaghi’s original theoretical work (von Terzaghi, 1923), which was inspired by the measurements of delayed deformations in a compression test on a clay sample, the pore fluid and the soil particles were both assumed to be incompressible, so that the only mechanism of deformation was a rearrangement of the particles. In modern presentations, these assumptions are no longer made, and this generalised theory will be used here. The relevant parameters used in this model are as follows.

Hydraulic properties

Parameter	Symbol	Value	Unit
Hydraulic conductivity	k	1.0E-4	m/s
Porosity	n	0.2	-

Mechanical properties

Parameter	Symbol	Value	Unit
Shear modulus	G	6.25E7	Pa
Bulk modulus	K	8.4E7	Pa
Biot's coefficient	a	0.9	-

Fluid properties

Parameter	Symbol	Value	Unit
Water bulk modulus	K_f	2.2E7	Pa
Volumetric weigth	y	1.0E4	m/s

System's characteristics

Parameter	Symbol	Value	Unit
Load	q	1.0E3	Pa
System's depth	h	1.0E2	m
time	t	-	s

The RHEA files for this scenario are found in test/tests/terzaghi/. There are three important files:

1. test/tests/terzaghi/Workflow_TerzaghiImportData.ipynb. This is a Jupyter notebook that creates files that define the hydraulic conductivity, porosity, bulk modulus and shear modulus throughout the Terzaghi soil sample. In this case, these properties are homogeneous. The files created are K.data, p.data, L.data and G.data (which are part of this repository, so you don't need to create them yourself).

2. test/tests/terzaghi/TerzaghiImportData.i. This is the RHEA input file. Run it using the rhea-opt executable you created during compilation: cd ~/projects/RHEA/test/tests/terzaghi ; ../../../rhea-opt -i TerzaghiImportData.i.

3. test/tests/terzaghi/plot_results.py. This is a python file that plots the results, demonstrating agreement between RHEA and the analytical formulae derived by Terzaghi, as shown below. If you require more precise agreement, simply decrease the time-step size in TerzaghiImportData.i.

Consolidation of a heterogeneous sample

The Terzaghi consolidation problem may be generalised to hterogeneous, layered samples. The aim is to test Rhea's import data material properties with different layers and sharp gradients. Contrasting values of hydraulic conductivities are considerated

Parameter	Symbol	Value	Unit
Hydraulic conductivity layer 1	k	1.0E-4	m/s
Hydraulic conductivity layer 2	k	1.0E-8	m/s

The RHEA files for this scenario are found in test/tests/terzaghi_layers/. The important files are:

1. test/tests/terzaghi_layers/Workflow_TerzaghiImportDataLayers.ipynb. Jupyter notebook that creates the files containing the sptially-varying properties that are going to be used by RHEA. The files created are K.data, p.data, L.data and G.data.

2. test/tests/terzaghi_layers/TerzaghiImportDataLayers.i. This is the RHEA input file. Run it using the rhea-opt executable you created during compilation: cd ~/projects/RHEA/test/tests/terzaghi_layers ; ../../../rhea-opt -i TerzaghiImportDataLayers.i.

3. test/tests/terzaghi_layers/plot_results.py. This is a python file that plots the results, demonstrating agreement between RHEA and the analytical formulae derived by Hickson et al., as shown below. If you require more precise agreement, simply decrease the time-step size in TerzaghiImportDataLayers.i.

Support

If you encounter difficulties at any step, you can ask for help on the MOOSE GitHub discussions.

References

von Terzaghi, K.: Die Berechnug der Durchlassigkeit des Tones aus dem Verlauf der hydromechanischen Spannungserscheinungen, Sitzungs-470ber. Akad. Wiss.(Wien). Math.-Naturwiss. Kl., Abt. Iia, 132, 125–138, 1923

Hickson, R., Barry, S., and Mercer, G.: Critical times in multilayer diffusion. Part 1: Exact solutions, International Journal of Heat and MassTransfer, 52, 5776–5783, 2009.

Cite

Bastías Espejo, J. M., Wilkins, A., Rau, G., & Blum, P. (2021). RHEA v1. 0: Enabling fully coupled simulations with hydro-geomechanical heterogeneity. Geoscientific Model Development Discussions, 1-21.