Analysis of Vessels Moored in Shallow, Unprotected Waters
Authors: Schellin Thomas E. , Scharrer Manfred E. , Matthies Hermann G. 
Published: October 2008

Abstract
Safe mooring of structures such as construction vessels, crane barges or pipe laying barges in shallow, unprotected waters presents unique problems. This is a consequence of the limited allowable horizontal excursion of the moored vessel due to relatively small displacement capability of the mooring system on the one hand and relatively large horizontal vessel displacements induced by waves extending into the range of rapidly increasing nonlinear mooring restoring forces on the other. This can result in highly peaked line tensions.
The mathematical model used in this analysis attempts to accurately account for this phenomenon. This precludes linear or linear zed methods and, therefore, the analysis presented here is done with two different nonlinear methods. The first method models the vessel behavior directly by solving the motion equations under the influence of the combined first-order wave and second-order wave (drift) forces. The second method calculates first-order oscillating wave motions and second-order drift motions of the moored vessel separately and superimposes them to obtain total vessel motions. Line tensions due to the total vessel motions are calculated quasistatically with both methods.
A sample analysis of a crane barge moored in shallow, unprotected waters shows results obtained with the two methods.
Both methods predict highly peaked line tensions of similar magnitude and occurrence frequency, yet the calculated horizontal motions of the moored vessel are significantly different with the two methods.

Introduction
This study is concerned with the analysis of moored vessels in shallow, unprotected waters. Such situations arise, for example, during the mooring of construction vessels, crane barges or pipe laying barges in areas in which not necessarily the worst environmental conditions are to be encountered, however, which pose unique problems that affect operating performance.
In such an analysis the environmental forces acting on the vessel are of central consideration. These are usually due to wind, current and waves and they each have special characteristics. Although wind velocities can vary drastically over a few seconds (e.g. wind gusts), the vessel in general does not respond noticeably to these gusts except as they contribute to the average wind force. Winds tend to be unidirectional over periods of a storm and current forces do not generally vary greatly with time. Therefore, both wind and current forces are taken as constant in the present analysis. The forces due to the irregular seaway must be treated as dynamically acting forces. These forces can be divided into first-order wave forces, oscillating with frequencies of the passing waves, and second order slowly varying wave (drift) forces.
In order to analyze the response of the moored vessel it is necessary to specify vessel response characteristics as follows:–wind and current force characteristics–frequency response functions of hydrodynamic first-order wave forces acting on the vessel–frequency response functions of first-order vessel motions in waves–second order wave (drift) force coefficients vessel mass and inertia, including hydrodynamic "added" mass–vessel damping coefficients–vessel restoring force coefficients–mooring system characteristics.
The analysis of mooring systems used to station offshore vessels tends to be complicated. Mooring system characteristics are influenced by numerous parameters.