The wave forces on an offshore structure are determined by a wave theory (e.g., Stokes or Stream Function) which relates the water kinematics (velocity and acceleration) to the wave parameters (height and period), and a theory which relates the resulting pressures on the structure to the predicted water kinematics (e.g., Morison Equation or Refraction Theory). Generally, the Morison Equation is used which incorporates two force coefficients-the drag and inertia coefficients.

The wave parameters experienced by a structure during a storm are random. Also, inferred values of the force coefficients from field measurements indicate a random scatter from wave to wave due to the random nature of the processes involved and imperfect wave and hydrodynamic theories. Therefore, for offshore structures the prediction of wave forces and ultimately the selection of design criteria involve both the random nature of the wave parameters (e.g., height) and the uncertainty in the force coefficients. Procedures for selecting wave heights for design criteria have received considerable attention and are well established; however, the problem of considering the uncertainty in the force coefficients has received little attention. Currently there is no rational procedure to generally account for coefficient uncertainty except to use arbitrary, and potentially unrealistic, guidelines such as the mean value plus a multiple of the standard deviation.

The purpose of this paper is to provide a rational framework for dealing with the uncertainty in force coefficients. This framework is statistical and incorporates into the force statistics the uncertainty of the force coefficients and the random occurrence of the wave parameters.


The wave forces on an offshore structure are generally determined by the Morison equation

(Mathematical Equation Available in Full Paper)

and QD and Qr are the drag and inertia forces (respectively) per unit length acting normal to a structural element; CD and Cr are the drag and inertia coefficients (i.e., the force coefficients), v and v are the water velocity and acceleration normal to the element, D is the element diameter and P is the mass density of water.

As shown in Appendix I, the maximum total horizontal forces on a vertical cylinder during a wave cycle are

(Mathematical Equation Available in Full Paper)

which are obtained by integrating (1) over the water depth. FD is the total drag force; Fr is the total inertia force; H is the wave height and s is the wave steepness (height/wave length). The assumptions used to derive (2) are deepwater waves and linear wave theory. Similar expressions have been presented in Ref. 1. Except for the properties of the water and cylinder (p,D), (2) depends only on the force coefficients, CD and Cr, and wave height, H, if the steepness is small (exp(2ns)=1) or constant. It is noted that for these conditions the total forces are independent of wave period.

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