Three‐dimensional roughness of stylolites in limestones

Abstract

[1] Stylolites are dynamic roughly planar surfaces formed by pressure solution of blocks of rocks into each other. The three-dimensional geometry of 12 bedding-parallel stylolites in several limestones was measured using laser and mechanical profilometers, and statistical characteristics of the surfaces were calculated. All the stylolites analyzed turn out to have self-affine fractal roughness with a well-characterized crossover length scale separating two self-affine regimes. Strikingly, this characteristic length scale falls within a very narrow range for all the stylolites studied, regardless of the microstructure sizes. To explain the data, we propose a continuous phenomenological model that accounts for the development of the measured roughness from an initially flat surface. The model postulates that the complex interface morphology is the result of competition between the long-range elastic redistribution of local stress fluctuations, which roughen the surface, and surface tension forces along the interface, which smooth it. The model accounts for the geometrical variability of stylolite surfaces and predicts the dependence of the crossover length scale on the mechanical properties of the rock.

Variety of stylolites' morphologies and statistical characterization of the amount of heterogeneities in the rock

“…2), 121 H = 0.5 for the large length scales and H = 1.1 for small length scales (Figure 3, see also 122 Renard et al, 2004). 123…”

Stress sensitivity of stylolite morphology

“…These data have allowed quantitative approaches based on fractal analysis tools (Drummond and Sexton, 1998) and demonstrated fractal scaling invariance over several orders of magnitude of stylolite roughness Schmittbuhl et al, 2004;Gratier et al, 2005;Karcz and Scholz, 2003;Brouste et al, 2007). In addition Schmittbuhl et al (2004) and Renard et al (2004) observed the existence of a crossover-length (L) that separates two scaling regimes with different roughness exponents for small and large scales. These scaling regimes are consistent with an interface morphogenesis model Renard et al, 2004) that describes the growth of a stylolite surface as a competition between two stabilizing forces: long range elastic fluctuations and local surface tension, and a destabilizing force due to the presence of heterogeneities in the material.…”

Compaction creep of wet granular calcite by pressure solution at 28°C to 150°C

“…Such microstructures are widely found in carbonate and sandstone rocks, often in association with evidence for grain scale microfracturing and cracking healing [Renard et al, 2000, Gratier et al, 2003. However, evidence for IPS and localized zones of pressure solution, such as stylolites, is perhaps most common in carbonate rocks [Bathurst, 1958;Tada and Siever, 1989;Renard et al, 2004]. About 60% of the world's oil and 40% of its gas reserves are found in carbonate reservoirs [Liteanu and Spiers, 2009; Schlumberger market analysis at http://www.slb.com/services/industry-challenges/ carbonates.aspx.].…”