  We investigate the problem of fluid injection at constant pressure in a 2D
Discrete Fracture Network (DFN) with randomly oriented and uniformly
distributed frictionally-stable fractures. We show that this problem shares
similarities with the simpler scenario of injection in a single planar shear
fracture, investigated by Bhattacharya and Viesca (2019); Viesca (2021) and
whose results are here extended to include closed form solutions for aseismic
moment as function of injected volume Vinj. Notably, we demonstrate that the
hydro-mechanical response of the fractured rock mass is at first order governed
by a single dimensionless parameter T associated with favourably oriented
fractures: low values of T (critically stressed conditions) lead to fast
migration of aseismic slip from injection point due to elastic stress transfer
on critically stressed fractures. In this case, therefore, there is no effect
of the DFN percolation number on the spatio-temporal evolution of aseismic
slip. On the other hand, in marginally pressurized conditions (T > 1), the
slipping patch lags behind the pressurized region and hence the percolation
number affects to a first order the response of the medium. Furthermore, we
show that the aseismic moment scales Vinj^2 in both limiting conditions,
similarly to the case of a single planar fracture subjected to the same
injection condition. The factor of proportionality, however, depends on the DFN
characteristics in marginally pressurized conditions, while it appears to be
only mildly dependent on the DFN properties in critically stressed conditions.
