High-velocity plunging water jets, appearing at the downstream end of dam weirs and spillways, can create scour of the rock. The prediction of this scour is necessary to ensure the safety of the toe of the dam as well as the stability of its abutments. A physically based engineering model has been developed at the Laboratory of Hydraulic Constructions for evaluation of the ultimate scour depth. This model is based on experimental measurements of water pressures at plunge pool bottoms and inside underlying rock joints. The pressures inside the joints revealed to be of highly transient nature and governed by the presence of free air. Hence, a numerical modelling of these pressures was performed, in collaboration with the Laboratory of Applied Hydrodynamics and Hydraulic Constructions (HACH), based on the one-dimensional transient flow equations applied to a pseudo-fluid. The amount of free air is a function of the instantaneous pressure inside the joint and has been accounted for by means of appropriate celerity-pressure relationships. These relationships are defined by the ideal gas law and Henry’s law and were optimised by means of a genetic algorithm optimisation technique. Very good agreement has been obtained between the measured and computed pressures at the end location of one-dimensional closed-end rock joints.