Page 169 - Pipelines and Risers

142 Chapier IO

P(*) is the probability of a combined wave and current induced flow event. f, is the
dominating vibration frequency of the considered pipe response and Tfif, is the time of
exposure to fatigue load effects.

Applying the partial safety factors, the above equations my be re-expressed as
DM = +~f”(YSS(Y, ,Yi...))”P(*) 5 ?l (10.4)

where yf, yk and ys denote partial safety factors for natural frequency, damping (stability
parameter) and stress range, respectively. For normal safety class, it is suggests that
and
y~p=~=1.3 yd.6.
10.2.4 Fatigue Damage Calculated using Time-Domain Solution
The fatigue damage may be evaluated independently for each sea-state of the scatter diagram
in terms of R, Tp and 6, as below.
(10.5)

where:
P(*) is the joint probability of occurrence for the given sea state in terms of significant
wave height H,, wave peak period Tp, mean wave direction.

dFuC denotes the long term distribution function for the current velocity. The notation
“max” denotes that the mode associated with the largest contribution to the fatigue
damage must be applied when several potential vibration modes may be active at
a given current velocity.

In the Time Domain analysis, the irregular wave induced short term particle velocity at pipe
level is represented by regular waves for a range of wave frequencies.

The stress range is calculated in the Time Domain Force model for each sea-state with a
constant value of wave induced velocity amplitude but for a range of current velocities, from
zero to a maximum value with nearly zero probability of occurrence. The calculated stress
ranges are used when evaluating the integral in Equation (10.5). For each sea-state, the fatigue
damage associated with each current velocity is multiplied by the probability of occurrence of
the current velocity. When stress ranges for all sea-states are obtained through the force
model, the fatigue damage is calculated using Equation (10.5).
10.2.5 Fatigue Damage Calculated Using Frequency Domain Sofution
- Fatigue Damage for One Sea-State