Page 448 - Marine Structural Design

424 Part IV Structural Reliability

Time intervals of different processes are chosen such that the longer interval is an integer
multiple of the next shorter one, valid for all processes involved. This is a prerequisite for easy
calculation of the maximum value distribution of the combination of two processes because
pulse of the shorter step process are repeated exactly n-times within the pulse duration of the
longer step one.
Consider the case where three load processes XI, X2, and X3 are acting on a marine structure.
The FBC load model then considers a new variable of the maximum of X3 within an interval
~2 together with X,. This variable, in turn, is searched for its maximum during an interval 71
and added to XI. From this, finally, the maximum during the life time T is considered as the
variable representing all three processes together.
The variable Y representing the maximum combined loads of the three processes thus may be
written as follows
T { ( 21
Y =max X, +max X, +maxX, (23.30)

Herein, the XI represents the load distribution. The terms max XI represents the maximum
values of the random variable X1 within the period tl or T, respectively.

23.7 Time-Variant Reliability
Marine structures can be subjected to time-varying loads, e.g. wind loads. Structural strength
may also present a time-varying behavior, e.g. deterioration of component strength due to
corrosion attacks. The basic variables that are related to these time-dependent values are
stochastic processes. The reliability problem becomes time-variant, as defined by,
Set of basic stochastic processes: X(t) = {X, (t), X, (t),.. a, X, (f)}
Joint distribution function of X(t): Fx(t)(X(t),t)

Limit state surface: g(x(t))=O
The main interests in time-variant reliability problem lies in the time t of the first passage from
the safe domain, g(x(t))>O, to the failure domain, g(x(r)) 5 0, during the life of the structure,
t E [0, TI, as illustrated in Figure 23.5 below. T is the design life of the marine structure or the
reference period for the reliability analysis. The time t for the first excursion g(x(t))S 0 is
called time to failure and it is also a random variable.
The probability of occurrence of g(x(f)) I 0 during the design life of the marine structures, T,
is called first-passage probability. This probability may be considered equivalent to the failure
probability pdt) during a given period [O,t], defined by (Melchers, 1999).