Ship berthing to a vertical quay-wall: Fender forces and ship motion

In this report a mathematical model is formulated which is sufficiently accurate to describe the typical behaviour of a ship berthing to a vertical quay-wall fitted with fenders as well as to determine the response of the fenders themselves. In order to achieve this a three-dimensional set of governing equations is drawn up by which the lateral transient motions of shiplike bodies nearby a closed wall with a vertical front can be described adequately. To this end use is made of two separate methods both originating from the mathematical model presented, viz. the so-called 'impulse response function'-technique, which has the restriction that the ship-fluid system is supposed to be linear, and a direct 'timedomain approach' where non-linearities can be taken into account. Both methods enable the inclusion of external forces of arbitrary nature. The 'impulse response function'-technique makes allowance for the fluid reactive forces by means of the hydrodynamic coefficients which are incorporated in the impulse response functions representing the properties of the linear ship-fluid system. Application of the 'timedomain approach' amounts to a direct solution of the governing set of equations which is simplified to a two-dimensional situation (strip theory). The ship is schematized to a prismatic body with a rectangular crosssection so that coupling between the respective ship motions is not present. The closed berthing structure consists of a long, straight wall with an impermeable, vertical front and fitted with one fender, the reaction force of which acts perpendicular to the front side of the berth. Although not essential, the fender applied is ndamped and linear. The influence of a restrictive water depth is taken into account. Since berthing manoeuvres and ship-fender interactions take mainly place in the horizontal plane and the ship is supposed to maintain a lateral motion with its longitudinal axis of symmetry parallel to the face of the berth, only the sway mode of motion needs to be considered; the effect of a forward speed is not included. The 'impulse response function'-technique as well as the direct 'time-domain approach' are applied to the case of shallow water with a horizontal bottom and relatively large horizontal dimensions in front of the berthing structure. Only centric impacts are considered. Each of both methods presented describes the behaviour of the schematized ship during the berthing operation as well as the behaviour of the fender itself. An extensive experimental verification was carried out by means of model tests. Four water depths were regarded. The results of theoretical calculations and model tests show a reasonably good agreement.Hydraulic EngineeringCivil Engineering and Geoscience