Roughness of fracture surfaces in numerical models and laboratory experiments

Steffen Abe,Hagen Deckert

doi:10.5194/se-12-2407-2021

Abstract

Abstract. We investigate the influence of stress conditions during fracture formation on the geometry and roughness of fracture surfaces. Rough fracture surfaces have been generated in numerical simulations of triaxial deformation experiments using the discrete element method and in a small number of laboratory experiments on limestone and sandstone samples. Digital surface models of the rock samples fractured in the laboratory experiments were produced using high-resolution photogrammetry. The roughness of the surfaces was analyzed in terms of absolute roughness measures such as an estimated joint roughness coefficient (JRC) and in terms of its scaling properties. The results show that all analyzed surfaces are self-affine but with different Hurst exponents between the numerical models and the real rock samples. Results from numerical simulations using a wide range of stress conditions to generate the fracture surfaces show a weak decrease of the Hurst exponents with increasing confining stress and a larger absolute roughness for transversely isotropic stress conditions compared to true triaxial conditions. Other than that, our results suggest that stress conditions have little influence on the surface roughness of newly formed fractures.

Highlights

It is well known that surfaces of faults and fractures in rocks are rough at all scales (Brown and Scholz, 1985; Hobbs, 1993; Power and Durham, 1997; Candela et al, 2012)
Based on the data produced by a total of 131 numerical simulations, the geometrical properties of 388 fracture surfaces have been analyzed
While the roughness produced by the numerical models is outside the range for which the fitting equations collected by Li and Zhang (2015) were originally intended, Fig. 1a in their work suggests that Eq (5) would be the best option to extend the range of approximate joint roughness coefficient (JRC) to the surface geometries observed here because it provides a good fit at large values (i.e., Z2 ≈ 0.35–0.4, JRC ≈ 20)

Summary

Introduction

It is well known that surfaces of faults and fractures in rocks are rough at all scales (Brown and Scholz, 1985; Hobbs, 1993; Power and Durham, 1997; Candela et al, 2012). The degree of roughness of a surface can be described in a number of different ways, ranging from visual, semi-quantitative approaches such as the “joint roughness coefficient” (JRC) (Barton, 1973; Barton and Choubey, 1977) to fully quantitative measures derived directly from the geometrical properties of the surface such as the root mean square of the first deviation (slope) along a profile Z2 (Myers, 1962) or the “structure function” (SF) proposed by Sayles and Thomas (Sayles and Thomas, 1977). A roughness measure of particular interest due to its possible use in the parametrization of the fluid flow properties of rock fractures is the “effective surface area S” proposed by Kottwitz et al (2020), which can be considered as an extension of the “areal roughness index” defined by El-Soudani (1978) and a 2-D analog of the “roughness profile index” defined there (Rp in Li and Zhang, 2015). The roughness can be described by a scaling parameter such as a fractal dimension or a Hurst exponent (Candela et al, 2009) in addition to a geometric roughness measure such as the Published by Copernicus Publications on behalf of the European Geosciences Union

Methods

Results

Discussion

Conclusion