Analytical Formulae for Lock Levelling and Overtravel – Application to the Kieldrecht Lock (Belgium)

When levelling a navigation lock with a culvert-based system, overtravel occurs due to the inertia of the water flowing in the culverts. This paper provides first an overview of known analytical formulae for the levelling time and characteristics of the surges around the equalization level, based upon a simplified model governed by a second order differential equation for a quadratically damped oscillator. New analytical formulae for lock levelling are then presented, based upon recent work on the mass oscillations in a simple surge tank problem, which is governed by the same equation. When the damping parameter is relatively small, the new formulae are more accurate solutions to the simplified lock levelling problem than the known formulae. Finally, it is illustrated how the formulae can be applied outside the simplified modelling framework, in particular to the Kieldrecht lock (Belgium), which is equipped with two unequal bypass culverts per lock head. By calibrating the total head losses of the two culverts independently, making use of available measurements for one-sided fillings, and replacing the two culverts by one equivalent culvert in case of two-sided fillings, predictions with the analytical formulae can be made. The filling time predictions of the new and the known formula agree reasonably well with the measurements, except in case of fillings characterized by a relatively small damping parameter (small lift height), where the known formula yields an underprediction. The new and the known formulae agree reasonably well with the measured time of the first up-surge, but overpredict its height.