A renewed interest in fault damage zones is aimed at better understanding stress perturbation around faults, earthquake ground motions and fluid flow in the upper crust. In this study, we analyse fault/fracture systems at the outcrop and map scale and define displacement - thickness (D-T) scaling of fault damage zones using scanlines, in carbonate rocks in France and Spain. We determine fault displacement and damage zone thickness perpendicular to fault planes and far from fault tips for 12 selected faults in four study sites. The data show a logarithmic decrease of fracture frequency from the fault cores. This decrease is characterized by local frequency peaks corresponding to variably-linked secondary fault segments and abandoned tips within the fault damage zone. D-T data comprised between 0 and 100 m of net fault displacement show a nearly linear scaling with very little scattering. Including two additional data for D > 100 m, the best fit corresponds better to a power law. We propose a new model based on fault segmentation and linkage to explain the linear scaling observed up to 100 m displacement, and we discuss the non-linear behaviour with respect to the role of mechanical layer thickness and the inhibition of the segmentation process down dip for large-scale faults.