14Stylolites are spectacular rough dissolution surfaces that are found in many rock types. 15They are formed during a slow irreversible deformation in sedimentary rocks and therefore 16 participate to the dissipation of tectonic stresses in the Earth's upper crust. Despite many 17 studies, their genesis is still debated, particularly the time scales of their formation and the 18 relationship between this time and their morphology. 19We developed a new discrete simulation technique to explore the dynamic growth of 20 the stylolite roughness, starting from an initially flat dissolution surface. We demonstrate that 21 the typical steep stylolite teeth geometry can accurately be modelled and reproduce natural 22 patterns. The growth of the roughness takes place in two successive time regimes: i) an initial 23 non-linear increase in roughness amplitude that follows a power-law in time up to ii) a critical 24 time where the roughness amplitude saturates and stays constant. We also find two different 25 spatial scaling regimes. At small spatial scales, surface energy is dominant and the growth of 26 the roughness amplitude follows a power-law in time with an exponent of 0.5 and reaches an 27 early saturation. Conversely, at large spatial scales, elastic energy is dominant and the growth 28 follows a power-law in time with an exponent of 0.8. In this elastic regime, the roughness 29 does not saturate within the given simulation time. 30Our findings show that a stylolite's roughness amplitude only captures a very small 31 part of the actual compaction that a rock experienced. Moreover the memory of the 32 * Manuscript Click here to download Manuscript: Styloteeth_EPSL.doc -2 -compaction history may be lost once the roughness growth saturates. We also show that the 33 stylolite teeth geometry tracks the main compressive stress direction. If we rotate the external 34 main compressive stress direction, the teeth are always tracking the new direction. Finally, we 35 present a model that explains why teeth geometries form and grow non-linearly with time, 36 why they are relatively stable and why their geometry is strongly deterministic while their 37 location is random. 38

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Stylolites are rough surfaces that form by localized stress-induced dissolution. Using a set of limestone rock samples collected at different depths from a vertical section in Cirque de Navacelles (France), we study the influence of the lithostatic stress on the stylolites morphology on the basis of a recent morphogenesis model. We measured the roughness of a series of bedding-parallel stylolites and show that their morphology exhibits a scaling invariance with two self-affine scaling regimes separated by a crossover-length (L) at the millimeter scale consistent with previous studies. The importance of the present contribution is to estimate the stylolite formation stress σ from the sample position in the stratigraphic series and compare it to the crossover-length L using the expected relationship: L ∼ σ −2 . We obtained a successful prediction of the crossover behavior and reasonable absolute stress magnitude estimates using relevant parameters: depth of stylolite formation between 300 to 600 m with corresponding normal stress in the range of 10-18 MPa. Accordingly, the stylolite morphology contains a signature of the stress field during formation and we thus suggest that stylolites could be used as paleo-stress gauges of deformation processes in the upper crust.

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