Understanding fluid flow in rough fractures is of high importance to large scale geologic processes and to most anthropogenic geo-energy activities. Here, we conducted fluid transport experiments on Carrara marble fractures with a novel customized surface topography. Transmissivity measurements were conducted under mechanical loading conditions representative of deep geothermal reservoirs (normal stresses from 20 to 70 MPa and shear stresses from 0 to 30 MPa). A numerical procedure simulating normal contact and fluid flow through fractures with complex geometries was validated towards experiments. Using it, we isolated the effects of roughness parameters on fracture fluid flow. Under normal loading, we find that i) the transmissivity decreases with normal loading and is strongly dependent on fault geometry ii) the standard deviation of heights (RMS) and macroscopic wavelength of the surface asperities control fracture transmissivity. Transmissivity evolution is non-monotonic, with more than 4 orders of magnitude difference for small variations of macroscopic wavelength and RMS roughness. Reversible shear loading has little effect on transmissivity, it can increase or decrease depending on the combined contact geometry and overall stress state on the fault. Finally, irreversible shear displacement (up to 1 mm offset) slightly decreases transmissivity contrary to common thinking. The transmissivity variation with irreversible shear displacements can be predicted geometrically at low normal stress only. Finally, irreversible changes in surface roughness (plasticity and wear) due to shear displacement result in a permanent decrease of transmissivity when decreasing differential stress. We discuss the implications for Enhanced Geothermal Systems stimulation.