Hydro-Mechanical Modelling of Infiltration Test for a
Bentonite-Sand Mixture: Model Verification and
Parameter Identification
M. Hasal 1 , R. Hrtus 1 , Z. Michalec 1 , R. Blaheta 1
1 Institute
of Geonics AS CR, Ostrava, Czech Republic
Abstract
Introduction:
The first aim of our work is to create a hydro-mechanical model of unsaturated fluid flow in the
bentonite-sand mixture (BSM) MX-80. Such model is important for modelling of the flow in the
case when BSM is used to stop or slow down the fluid flow, as when BSM is used as a plug e.g.
in the design of underground nuclear waste repository. The second aim is to validate and
calibrate the developed model by using the data from a laboratory infiltration test of bentonitesand mixture MX-80, see Figure 1, [1.]. Variations of relative humidity (RH) at four distances
from the wetted end (h = 50, 100, 150, 200 mm) is monitored during the hydration. We formulate
the mathematical description of the infiltration, based on flow of water, air and water vapour in
porous media. Moreover, we couple the unsaturated flow with mechanical response, which
include swelling and constant volume restriction [2].
Use of COMSOL Multiphysics® and Results:
The COMSOL Multiphysics® software is used for implementation of the developed model. The
model of unsaturated flow of water and water vapour is implemented within the Heat Equation
Model framework from Mathematics Models. For the mechanics part, we use Linear Elastic
Model from the Solid Mechanics interface. It can be also adapted to include changes of elastic
moduli. The hydro-mechanical coupling is based on swelling, effective stress concept, water
source due to deformation and deformation induced permeability changes, Figure 2.
COMSOL Multiphysics® is used for simulation of the infiltration process and the results are
compared with data from the infiltration experiment. The laboratory data can be also used for
identification of the model parameters. Especially, we used a generalized Irmay's expression,
i.e. the relative permeability is a power of relative saturation [3.]. The exponent in this power is
determined by minimization of a norm of the difference between computed and measured data.
The minimization procedure is written in MATLAB® and the COMSOL model is invoked from
MATLAB® by using the LiveLink™ for MATLAB® Module [5.]. The correspondence of the
computed and measured data and optimization of this correspondence can be seen in Figure 3.
Conclusions:
The COMSOL Multiphysics® is used for numerical simulation of evolution of the relative
humidity in the infiltration experiment for a period of 6000 hours. The results show applicability
of COMSOL Multiphysics® for the simulation of a complex model of unsaturated flow
coupled with mechanical processes. A future work is planned for both model improvement and
identification of model parameters.
Reference
1. A. Millard, Decovalex 2015, Task A Description, 16 (2012)
2. Son Nguyen et al., DECOVALEX-THMC Project - SKI Report 2007:07, 144 (2007)
3. S. Irmay, On the hydraulic conductivity of unsaturated soils. Trans. Amer. Geophys. Union
35(1954), 463-468
4. COMSOL GM Geomechanics Module. User guide. Comsol 4.2a, Oct. 2011
5. COMSOL LL LiveLink for Matlab. User´s Guide. Comsol 4.3, 2012
Figures used in the abstract
Figure 1: Schematic setup of the infiltration tests under constant volume condition
Figure 2: Relative humidity at the last step of time discretization.
Figure 3: Comparison of the time evolution of relative humidity: dotted - measurement, dashed computed with Irmay’s expression for relative permeability, thin solid – optimized Irmay’s
expression