Assessment of Existing Structures and Repairs - Offshore Structures: Design, Construction and Maintenance - page 513

as a system in series. In most cases, the failure of the topsides subsystem does
not occur in advance of failure of the jacket/foundation subsystem, even with
large wave force effect on the topsides under extreme storm conditions. The
failure of the topsides subsystem is not considered acceptable criteria against
environmental overload.

Limit State Function
The limit state function for estimating the failure probability may be defined as

g ð X Þ = R − L (7.28)

where R is the platform capacity in terms of maximum lateral load that the plat-
form can withstand before system failure or collapse. L is the total environmen-
tal load, which consists of wave and current load, W v and wind load, W l , i.e.,

g ð X Þ = R − W v − W l (7.29)

The limit state function g(X) defines a failure criterion that is a function of
all random variables X. Failure occurs when the load L exceeds the capacity R
or when g(X)

< 0.

First-Order Reliability Method (FORM)
With the establishment of a limit state function, the conventional formula for
computing the probability of failure is:

Z ∞

P f = ð 1 − F s ð x ÞÞ f R ð x Þ: dx (7.30)

0

where F s is the cumulative distribution function (CDF) for the total environmen-
tal load variable S,andf R is the probability density function (PDF) for the
capacity variable R.
The probability of failure can be calculated using the Rackwitz-Fiessler
FORM method. In this method, the probability of failure is estimated using
first-order approximation to the limit state at the design point. The Rackwitz-
Fiessler FORM method includes the following steps:

1. Transform non-normal-distribution random variables that are used to define
the limit state function to equivalent normal-distribution variables. The
CDFs and the PDFs of the actual variables and the equivalent normal vari-
ables are equal at the iteration point on the failure surface.
2. Iteratively search the most probable point (MPP) of failure in the limit state
surface based on Newton-type recursive formula.
3. Compute the reliability index

β

.