In the context of studies on deep geological disposal of radioactive waste, the overpressures whose origin is still debated raise the question of the relevant transport processes to be taken into account in clay media. An anomaly of about 13 bars was identified during the Deep Borehole (DB) experiment at the Mont Terri URL (Switzerland) whose objective was to identify the impact of hydraulic and chemical transient behavior on fluid and solute transfers. The first stage of DB experiment consisted in drilling BDB-1, a 250 m long-inclined borehole across the entire Opalinus Clay (OPA). The second stage of the work aimed at determining the driving forces (pressure, temperature, and salinity gradients) and transport coefficients (diffusion, hydraulic conductivity, chemical and thermal osmotic coefficients) using a multi-packer hydraulic system. The last step of this fully experimental and modelling integrated study was the development of 1D transport models either in fully transient or in pseudo-steady state to reproduce the measured pressure and salinity profiles. Pure hydraulic calculations evaluated a Darcy velocity in the order of 10−14 m s−1, related to a downward flow. However the best agreement with the data was obtained by introducing osmotic processes. Chemical osmosis slightly increased the advective flow in the same direction, but its effect is minor compared to that of thermo-osmosis which inverts the water movement with a mean Darcy velocity of about 10−13 m s−1. However, the Peclet number still confirmed the dominance of diffusion with respect to advection at Mont Terri.