We report experimental results on the maximum angle of stability, i.e., the so-called avalanche angle, of a granular medium subjected to an inner water flow controlled by a constant pressure drop. A unique avalanche threshold is derived by two alternative theoretical developments, namely a continuum and a discrete approach, and is successfully confronted to many measurements in a large experimental range. A qualitative analysis of the instability triggering reveals different dynamical behaviors depending on whether the water flow is downward or upward in the granular layer, namely stabilizing versus destabilizing regime. Contrary to the purely hydrostatic situation, the free surface following an avalanche departs from a linear shape because the dynamical pressure gradient is no longer constant in the medium. A simple model is proposed that can satisfactorily predict the postavalanche height profile as well as its subsequent evolution for higher inclinations.