Management of energy waste such as high-level waste (HLW) disposal in deep geological repositories is one of most pressing challenges in the context of nuclear energy. The general research question addressed in the present work is how to represent coupled physical processes after the emplacement of heat-emitting waste in such a repository in claystone at multiple scales by numerical models and how can they validated by experimental results in underground research laboratories. Numerical modelling of the coupled thermal hydraulic mechanical (THM) processes to assess the long-term safety of deep geological repositories rests on adequate constitutive laws and quantification of in-situ host rock material properties during long-term heating as well as a reliable numerical approach for solving the underlying governing equations. For this purpose, various in-situ experiments have been conducted in the Callovo-Oxfordian claystone (COx) at the Meuse/Haute-Marne (M/HM) Underground Research Laboratory (URL) by the French National Radioactive Waste Management Agency (ANDRA) since 2003. A subset of these is investigated here using a numerical THM model employed at different spatial scales. Two main results were achieved. First, the previously developed numerical THM model (Wang et al., 2021) has been compared agains in-situ experimental data from the full-scale heating (ALC) experiment at the M/HM URL in an attempt to validate the model. The numerically simulated temperature and pore pressure data of the ALC experiment are in good agreement with in-situ measured data. This model was then employed to simulate fully coupled THM processes of an entire repository section for High-Level Waste (HLW) in a COx clay formation according to the Cigeo project by ANDRA. This upscaling was enabled by running the numerical code on high-performance-computing platforms. Three-dimensional, fully coupled and efficient THM models for the numerical simulation of deep geological repositories such as the one presented in this study will help in the design of nuclear waste repositories under realistic geological conditions. Moreover, the present work is a contribution to Task E of the DECOVALEX-2019 project for model validation and comparison against experimental results (Plúa et al., 2021; Seyedi et al., 2020).