Modeling the growth of stylolites in sedimentary rocks

in press, Journal of Geophysical Research - Solid EarthStylolites are ubiquitous pressure-solution seams found in sedimentary rocks. Their morphology is shown to follow two self-affine regimes: analyzing the scaling properties of their height over their average direction shows that at small scale, they are self-affine surfaces with a Hurst exponent around 1, and at large scale, they follow another self-affine scaling with Hurst exponent around 0.5. In the present paper we show theoretically the influence of the main principal stress and the local geometry of the stylolitic interface on the dissolution reaction rate. We compute how it is affected by the deviation between the principal stress axis, and the local interface between the rock and the soft material in the stylolite. The free energy entering in the dissolution reaction kinetics is expressed from the surface energy term, and via integration from the stress perturbations due to these local misalignments.The resulting model shows the interface evolution at different stress conditions. In the stylolitic case, i.e. when the main principal stress is normal to the interface, two different stabilizing terms dominate at small and large scales which are linked respectively to the surface energy and to the elastic interactions. Integrating the presence of small scale heterogeneities related to the rock properties of the grains in the model leads to the formulation of a Langevin equation predicting the dynamic evolution of the surface. This equation leads to saturated surfaces obeying the two observed scaling laws. Analytical and numerical analysis of this surface evolution model shows that the cross-over length separating both scaling regimes depends directly on the applied far-field stress magnitude. This method gives the basis for the development of a paleostress magnitude marker. We apply the computation of this marker, i.e. the morphological analysis, on a stylolite found in the Dogger limestone layer located in the neighborhood of the Andra Underground Research Laboratory at Bure (Eastern France). The results are consistent with the two scaling regimes expected, and the practical determination of the major principal paleostress, from the estimation of a cross-over length, is illustrated on this example