Environmental Engineering Reference
In-Depth Information
Fig. 2.44 Action affects on a gravity base caused by wave loads [32]
The solution to the diffraction problem is generally based on a potential theory
formulation (see Section 2.6.3) and calls for the solution space to be discretised.
Suitable numerical methods for this are the boundary element method or the singularity
method (see Section 2.6.4). Figure 2.44 shows the interaction between the hydro-
dynamic analysis according to the singularity method and the structural analysis
according to the finite element method.
Suitable software packages are very expensive because of the numerical complexity.
In addition, owing to the boundary conditions that have to be maintained at the
structure, it is not possible to separate the mathematical description of the wave
kinematics from the actual calculation of the hydrodynamic loading. This leads to a
small bandwidth of applicable wave theories.
On the other hand, the wave loads on resolved slender offshore structures (e.g.
monopiles, jackets) may be calculated using the empirical Morison formula (see
Section 2.6.2). Diffraction effects are not included in the Morison approach, that is the
wave kinematics and the hydrodynamics are separated from each other. Consequently,
in contrast to diffraction theory, the complete range of available wave theories can be
used to calculate the wave loads.
Owing to their simpler implementation, programs based on the Morison formula are
often less expensive and thus more widely used. Therefore, such programs are
frequently employed to obtain rough estimates of the wave loads on large-volume
offshore structures. This can lead to inappropriate results because critical diffraction
effects are ignored.
The numerical sensitivity analysis of a simple typical structure is ideal for clarifying
just how much the results of the Morison formula and diffraction theory differ from
each other [32]. Let us consider a simple cylinder (Figure 2.45) that extends from the
seabed to the still water level. The relevant application ranges for diffraction theory and
