Effective elasticity of a medium with many parallel fractures

TL;DR

This paper introduces a novel model for effective elastic properties of cracked media using embedded thin layers, relaxing classical assumptions, and demonstrating improved accuracy for media with more than 1% crack fill.

Contribution

It presents a new approach based on Backus averaging with finite-thickness layers to better model highly fractured media, extending classical linear-slip models.

Findings

Model accurately describes media with >1% crack fill

Numerical experiments show improved performance over linear-slip models

Effective tensor captures higher crack concentrations more precisely

Abstract

We consider an alternative way of obtaining the effective elastic properties of a cracked medium. Similarly, to the popular linear-slip model, we assume flat, parallel fractures, and long wavelengths. However, we do not treat fractures as weakness planes of displacement discontinuity. In contrast to the classical models, we represent fractures by a thin layer embedded in the background medium. In other words, we follow the Schoenberg-Douma matrix formalism for Backus averaging, but we relax their assumptions of infinite weakness and marginal thickness of a layer so that it does not correspond to the linear-slip plane. To represent the properties of a fracture, we need a fourth order elasticity tensor and a thickness parameter. The effective tensor becomes more complicated, but it may describe a higher concentration of parallel cracks more accurately. Apart from the derivations of the effective elasticity tensors, we perform numerical experiments in which we compare the performance of our approach with a linear-slip model in the context of highly fractured media. Our model becomes pertinent if filled-in cracks occupy more than one percent of the effective medium.