We investigate friction memory effects in the chaotic stick-slip motion of a plate shearing a granular bed. By analyzing separately trajectories' portions having increasing or decreasing instantaneous velocity, it is found that there are two quantitatively distinct granular friction–velocity curves for positive or negative acceleration, which cross one another in the weakening region. Interpreting acceleration dependence as an indirect consequence of contact ageing, we try to explain these effects by including rate-and-state (RS) friction equations in the stochastic model describing the plate motion. Preliminary results on a study case show that the main experimental features can be reproduced in this way, although quantitative agreement is partial. From the value obtained for the RS parameters we conclude that sliding friction decorrelation takes place at the length-scale of the solid-on-solid micro-contacts between grains and plate. In addition, the contemporary presence of noise and RS effects influences the average friction curve at large shear rate.