Growth of stylolite teeth patterns depending on normal stress and finite compaction

Stylolites are spectacular rough dissolution surfaces that are found in many rock types. They are formed during a slow irreversible deformation in sedimentary rocks and therefore participate to the dissipation of tectonic stresses in the Earthʹs upper crust. Despite many studies, their genesis is still debated, particularly the time scales of their formation and the relationship between this time and their morphology. eloped 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. We also find two different spatial scaling regimes. At small spatial scales, surface energy is dominant and the growth of the roughness amplitude follows a power-law in time with an exponent of 0.5 and reaches an early saturation. Conversely, at large spatial scales, elastic energy is dominant and the growth follows a power-law in time with an exponent of 0.8. In this elastic regime, the roughness does not saturate within the given simulation time. ndings show that a styloliteʹs roughness amplitude only captures a very small part of the actual compaction that a rock experienced. Moreover the memory of the compaction history may be lost once the roughness growth saturates. We also show that the stylolite teeth geometry tracks the main compressive stress direction. If we rotate the external main compressive stress direction, the teeth are always tracking the new direction. Finally, we present a model that explains why teeth geometries form and grow non-linearly with time, why they are relatively stable and why their geometry is strongly deterministic while their location is random.