Effect of initial normal stress on shear-induced non-linear fluid flow through fractures

This study investigated the effect of initial normal stress on the non-linear hydraulic properties of fractures during shearing. A natural rough fracture is utilised to generate the rough fracture model and a mathematical expression for predicting the normal displacement during shearing is used, after which the validity is verified. Finally, the non-linear flow rate – hydraulic gradient relationships and the empirical functions for Fochheimer coefficients and critical Reynolds number are analysed. The results show that with the increment of initial normal stress, the fractures are closed and the contact area increases, decreasing the permeability. As initial normal stress increases, both the linear and non-linear Fochheimer coefficients increase following power-law relationships with positive exponents. The non-linear Fochheimer coefficient is approximately five orders of magnitude larger than the linear Fochheimer coefficient, which is consistent with the results reported in the literature. Both Fochheimer coefficients and critical Reynolds number are strongly correlated with fracture aperture. The variation in linear Fochheimer coefficient is more robust than the variation in non-linear Fochheimer coefficient against aperture, resulting in that the critical Reynolds number increases with increasing the aperture, which follows a power-law relationship with the correlation coefficient larger than 0·91.