Effective elastic properties of fractured rocks considering fracture interactions

Fracture interactions are an important factor that affects rock effective elastic properties. We study the fracture interaction effects by combinations of theoretical modelling, numerical simulations and experiments in this work. First, we propose a simplified differential effective medium scheme and self-consistent approximation for effective elastic properties of rocks with aligned fractures, and we compare their results to those of non-interaction approximation. The results show that the predictions by differential effective medium scheme and self-consistent approximation are lower than those by non-interaction approximation. This indicates that the differential effective medium scheme and self-consistent approximation quantify the stress amplification effects but not stress shielding effects. To validate this, we carry out numerical simulations for cases with coplanar cracks and stacked cracks, respectively. We find that the stress shielding effect (stacked cracks) causes a significant increment of effective elastic stiffnesses of fractured rocks. However, the stress amplification (coplanar cracks) has the opposite effect, which induces a slight reduction in rock effective elastic stiffnesses. The differential effective medium scheme quantifies the lower bound for this effect well. Besides numerical simulations, applying theoretical models in experimental measurements also shows a pronounced effect of stress shielding but a small influence of stress amplification on fractured rock elastic properties. This work indicates that the stress shielding is an important effect that affects fractured rock elastic properties. Without considering this effect, the fracture density may be largely underestimated by the seismic or sonic logging inversion. Hence, the models accounting for stress shielding effects need to be developed in the future, which can combine with the above models for the seismic or sonic logging inversion of fracture properties.