Environmental Engineering Reference
In-Depth Information
The type and size of the arrangement of the structure relative to the wave parameters
have a decisive influence on the mechanism of the sea state actions. Inertia, drag and
diffraction forces occur in this context.
- Inertia and drag effects are critical for structures that are slender in hydrodynamic
terms and have structural member dimensions (D) that are small in relation to the
wavelength (
l
1/5, for example jackets, tripods, monopiles). Their action
effects are therefore considered semi-empirically (see Section 2.6.2).
- The inertia and diffraction effects dominate in the case of structures that are compact
in hydrodynamic terms (D/
l
) (D/
1/5, for example gravity bases). Their action effects
can be calculated really quite accurately using potential theory with approximations
based on diffraction theory (see Sections 2.6.3, 2.6.4, 2.6.5 and 2.6.7).
- Non-linear effects, for example viscosity-related drag forces, wave forces of a higher
order, loads due to waves with a finite steepness or large deformations, may not be
neglected when it is necessary to consider sea state actions that exhibit a strong non-
linear dependence on the wave height (see Section 2.6.6).
Depending on the structure to be designed, the design sea state can either be entered as
a characteristic solitary wave (deterministic method), considered as a characteristic
wave time series, from which a time series of loads on the structure is generated
(stochastic method), or be incorporated as a total distribution in order to determine the
probabilities of failure for various limit states (probabilistic method).
Deterministic design methods are generally favoured in practice [26], and these will be
dealt with below.
l>
2.6.2 Morison formula
Wave loads on narrow bodies are mostly calculated with the help of the Morison
formula. Let us consider a rigid vertical cylinder in a harmonic primary wave
(Figure 2.32). The wave force per unit length of the cylinder is then expressed as
the sum of an inertia force and an unsteady drag force (index I: inertia; D: drag):
dz
¼
c
M
r
p
D
2
dF
x
ðÞ
dz
¼
dF
Ix
ðÞ
dz
þ
dF
Dx
ðÞ
@
u
ðÞ
@
1
2
r
D
u
ðÞ
t
þ
c
D
j
j
u
ðÞ
4
Fig. 2.32 Wave forces on a pile, notation [17]
