Page 54 - Marine Structural Design

Chapter 2 Wave Loach for Ship Design and Classification 31

analysis leading up to Eq. (2.29). In the case of bottom slamming, empirical formulae are used,
see Zhao and Faltinsen (1 993).
For green water on deck to occur, the relative immersion of the section of the ship must be
larger than the distance between the water level and the deck (freeboard). The actual force the
green water exerts on the deck is difficult to assess because of the complicated flow of the
water. Wang, Jensen, and Xia (1 998) derived the following equation to calculate the sectional
force, qnw (x, t) resulting from green water on deck:

(2.30)

where,
m,, = Sectional mass of water on the deck
Z,: = Modified relative vertical motion depending on z and a parameter known as
the Smith correction factor K
The first term on the right hand side of Eq. (2.30) represents the gravity force, while the
second term is analogous to a momentum slamming force. Eq. (2.30) may also be included in
a global wave load equation, such as Eq. (2.23).
Green water has caused damage to bow super-structure and FPSO topsides along the length of
the ship. A prediction theory for the green water on deck and the resulting green water loading
have been developed by Zhou, De Kat and Buchner (1 999). The green water or deck wetness
slamming phenomena is highly non-linear. Wang, Leitch and Bai (2001) proposed the
following design procedures for greenwater impact on FPSOs:

Estimate the possibility of greenwater occurrence using past experience and approximate
methods. Ideally, some preliminary analysis using computer software should be done to
get a more reliable estimation.
If the estimation indicates that greenwater likely to occur in a significant manner, model
tests should be performed. Greenwater model tests can be arranged as part of global
performance model testing program. The critical parameters should be identified during
planning stage of the model tests. If the greenwater impact is judged to be a serious
problem and must be designed on, height, occurrence frequencies and the impact pressure
of greenwater should be carefilly measured.
If the model tests do not or cannot cover sufficient number of the values of the identified
critical parameters, some complementary numerical simulations using benchmarked
software should be performed to identify the critical value of each critical parameter for
design consideration.
Analyze the results of model tests and numerical simulations to judge if the greenwater
needs to be dealt with in design and engineering. Risk analysis may be conducted to help
decision making if the judgment is difficult make directly from the results of model tests
and numerical simulation.
If it is found that greenwater must be considered, model test results should be used for
design. In case no applicable model test results are available, the impact pressure can be
calculated using some approximate formulas. For instance, the formulas summarized in
reference 1 may be used to estimate the horizontal pressure of greenwater impact while
classification societies rules may be used for calculation of the pressure vertically acting
on vessel deck. Due to the complexity of greenwater analysis and the limitation of those