Abstract
A probability distribution, which incorporates the random occurrence of wave heights and the uncertainty in the force coefficients of the Morison equation, was derived for the forces on offshore structures.
The random occurrence of wave heights was assumed to be described by a Weibull distribution, and the uncertainty in the force coefficients was assumed to be represented by a normal distribution. Wave force was assumed to be proportional to wave height raised to a power.
The assumed distributions and force relationship may not describe exactly the actual problem within a general framework, but the assumptions are believed to be applicable to the range of wave heights and conditions occurring for the selection of static design criteria for the forces on offshore structures. The applicability of the assumptions is enhanced because the primary results are expressed as ratios, which require only relative accuracy and not quantitative accuracy.
Introduction
The wave forces on an offshore structure are determined by a wave theory (e.g., Stokes or stream function) that relates the water kinematics (velocity and acceleration) to the wave parameters (height and period) and a theory that relates the resulting pressures on the structure to the predicted water kinematics (e.g., the Morison equation or refraction theory). Generally, the Morison equation, which incorporates two force coefficients - the drag and inertia coefficients - is used.
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 caused by the random nature of the processes involved and imperfect wave and hydrodynamic theories. Therefore, the prediction of wave forces and, ultimately, the selection of design criteria for offshore structures 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 account generally 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.
Background
The wave force, Q, on an offshore structure is generally determined by the Morison equation,Equation 1
QD and QI are defined as the drag and inertia forces, respectively, per unit length acting normal to a structural element; CD and CI 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 ?w is the mass density of water.
THE DYNAMIC RESPONSE OF OFFSHORE STRUCTURES TO TIME-DEPENDENT FORCES