  Stylolites are spectacular rough dissolution surfaces that are found in many
rock types. Despite many studies, their genesis is still debated, particularly
the time scales of their formation and the relationship between this time and
their morphology. We developed a new discrete simulation technique to explore
the dynamic growth of the stylolite roughness, starting from an initially flat
dissolution surface. We demonstrate that the typical steep stylolite teeth
geometry can accurately be modelled and reproduce natural patterns. The growth
of the roughness takes place in two successive time regimes: i) an initial
non-linear increase in roughness amplitude that follows a power-law in time up
to ii) a critical time where the roughness amplitude saturates and stays
constant.
