We propose a dynamical mechanism leading to the fluidization by external mechanical fluctuations of soft-glassy amorphous material driven below the yield-stress. 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. We finally propose to extend this result more generally, to a large class of glassy systems.PACS numbers: 81.40. Lm, 83.80.Fg Numerous amorphous materials such as concentrated suspensions, colloidal glasses, foams or granular materials share common global features in their mechanical response to shear [1,2]. They are characterized by a yield stress below which the material appears as a solid [3,4]. As this behaviour is shared by so many different materials, several conceptual and theoretical frameworks emerged recently [5][6][7][8][9][10] to provide a quantitative basis for the phenomenology of soft glassy rheology (SGR) above and beyond the yield stress. Even though many parallel approaches exist, sometimes at different level of description, they all share either explicitly or implicitly, the underlying idea that mesoscopic collective processes triggered by thermal or mechanical activation, contribute to the material fluidity. The direct visualization of local plastic events and the associated complex avalanching dynamics is supported by many experimental [11][12][13][14] or numerical [15][16][17] studies. In the "solid phase" corresponding to a strong dynamical arrest, soft-glassy systems display ageing properties manifesting in a slow creep relaxation process [18][19][20][21]. Ageing properties stem from a remaining thermal activation providing the possibility to cross enthalpic or entropic barriers and progressively set the system into deeper local minima where mechanical solidity is reinforced. The existence of external mechanical noise was also proposed as a substitute for thermal activation. In this sense, the behaviour of these amorphous soft glassy solids is very close phenomenologically to molecular glass-formers obtained by thermal quenching [22]. Yet, the fact that such mechanical noise truly acts as an effective temperature is presently debated [23] and indeed, deep differences in the way thermal noise and mechanical fluctuations act in amorphous systems has been recently pointed out [24].