A geometrical aperture-width relationship for rock fractures

TL;DR

This paper proposes a theoretical linear relationship between fracture aperture and width based on fractal geometry and fracture mechanics, supported by literature data, with implications for flow prediction in rock fractures.

Contribution

It introduces a first-order approximation that fracture aperture is linearly related to fracture width, supported by theoretical and experimental evidence.

Findings

Linear relationship between aperture and width supported by literature data

Model predicts flow rate scaling over 14 orders of magnitude

Supports use of cubic law with aperture-width relationship for flow modeling

Abstract

The relationship between fracture aperture (maximum opening; dmax) and fracture width (w) has been the subject of debate over the past several decades. An empirical power law has been commonly applied to relate these two parameters. Its exponent (n) is generally determined by fitting the power-law function to experimental observations measured at various scales. Invoking concepts from fractal geometry we theoretically show, as a first- order approximation, that the fracture aperture should be a linear function of its width, meaning that n = 1. This finding is in agreement with the result of linear elastic fracture mechanics (LEFM) theory. We compare the model predictions with experimental observations available in the literature. This comparison generally supports a linear relationship between fracture aperture and fracture width, although there exists considerable scatter in the data. We also discuss the limitations of the proposed model, and its potential application to the prediction of flow and transport in fractures. Based on more than 170 experimental observations from the literature, we show that such a linear relationship, in combination with the cubic law, is able to scale flow rate with fracture aperture over ~14 orders of magnitude for variations in flow rate and ~5 orders of magnitude for variations in fracture width.