Model order reduction of coupled thermo-hydro-mechanical processes in geo-environmental applications

In a large number of geo-environmental applications, it is essential to model coupled processes that depend on several design parameters such as material properties and geometrical features. Thermo-hydro-mechanical (THM) processes are, among others, key effects to consider in critical applications such as deep geological repository of hazardous waste. This thesis proposes novel model order reduction strategies to evaluate the thermo-hydro-mechanical response of the material, taking into account the complexities involved in the coupled processes for such applications.
To include variability of some design parameters, an a-posteriori model order reduction approach with reduced basis methods is applied to solve the high-dimensional parametric THM system. The reduction is based on an offline-online stage strategy.
In the offline stage, reduced subspaces are constructed by a greedy adaptive procedure and in the online stage, multi-subspace projection is performed to quickly obtain the coupled THM response at any value of the design parameter. At the core of the greedy adaptive strategy is a goal-oriented error estimator that guides the selection of optimal design parameters where snapshots are evaluated. To tackle nonlinearity in the form of elasto-plastic material behaviour, the multi-subspace reduced basis method is combined with sub-structuring by domain decomposition.
The effectiveness of the model reduction strategies are demonstrated on inverse problems involving large-scale geomodels that depict the coupled response of host rocks in potential deep geological repository sites. Two types of scenarios are considered: (i) the host rock undergoing geomorphological process is investigated as glacier advances over it for a period lasting over thousands of years and (ii) the clay response of an underground research laboratory is modelled numerically to support and validate in-situ heating experiments.