  We propose a dynamical mechanism leading to the fluidization of soft-glassy
amorphous mate-rial driven below the yield-stress by external mechanical
fluctuations. The model is based on the combination of memory effect and
non-linearity, leading to an accumulation of tiny effects over a long-term. We
test this scenario on a granular packing driven mechanically below the Coulomb
threshold. We bring evidences for an effective viscous response directly
related to small stress modulations in agreement with the theoretical
prediction of a generic secular drift.
