Permafrost covers one-fifth of the planet's land surface. It consists of a first layer a few meters below the surface, known as the active layer, which freezes in winter and thaws in summer, situated above a thicker layer of soil constantly below the freezing point. The presence and displacement of a solidification front in the soil can cause underground water flows and change the soil structure, leading to the emergence of surprising shapes on the surface, some examples of which are illustrated in the figure below (left). With global warming and thawing permafrost, this type of event will become increasingly frequent, altering landscapes, their ecosystems, and infrastructures. All these behaviors are poorly understood. Indeed, the associated physical mechanisms are still unclear, and we lack consistent predictive models for heat transport, phase change dynamics, and induced groundwater flows in these complex media. The aim of this work is therefore to gain a better understanding of solidification in porous media and induced flows.