Page 438 - Marine Structural Design

414 Part IVSiructuraI Reliabiliiy

assess the relative importance of the various types of uncertainties. For example, one of the
conclusions drawn from a study on offshore structures was that the uncertainty in the lifetime
extreme wave height is the most significant one. The error in predicting the most severe sea
condition over the design lifetime is one of the major ingredients of the uncertainty.
The reliability of a structural system depends on load and strength variables. Each variable can
be calculated with different degree of accuracy. For example, for most of the cases, the
response of an offshore platform to dead loads can be evaluated with high accuracy, while
wave induced response may not be predicted with the same confidence. Therefore, when
assessing structural safety and making design decisions, we must take into account the
differences in the confidence levels associated with each load and strength variable. For
example, in a reliability based design code for offshore structures, the load factor for wave
loads is larger than that for dead loads, because the modeling uncertainty associated with the
former is larger.

23.2.2 Natural vs. Modeling Uncertainties
Uncertainties in analysis of marine structures can be categorized into natural (random) and
modeling types. The former is due to the statistical nature of the environment and the resulting
loads. The latter are due to the imperfect knowledge of various phenomena, and idealizations
and simplifications in analysis models. These uncertainties introduce bias and scatter. An
example of a natural uncertainty is that associated with the wave elevation at a given position
in the ocean. An example of a modeling uncertainty is the error in calculating the stresses and
strength in a structure, when the applied loads are known. For this case, the error is only due to
the assumptions and simplifications in structural analysis.
Modeling uncertainties can be reduced as the mathematical models representing them become
more accurate. This is not the case with random uncertainties that do not decrease as we gather
more information. Both random and modeling uncertainties must be quantified and accounted
for in reliability analysis and development of reliability based design codes.
Let X be the actual value of some quantity of interest and XO the corresponding value specified
by a design code. According to Ang and Cornel1 (1974),
X = BI BII Xo (23.1)

where BI = Xp /Xo and where X, is the theoretically predicted value for this quantity, and
BII = X/xp . BI is a measure of natural (random) variability and BII is a measure of
modeling uncertainty.
The mean values of random variables B, and BII , E(BI) and E(BII) , are the biases
corresponding to natural and modeling uncertainties, respectively. Assuming that the random
and modeling uncertainties are statistically independent, and by using a linear expansion of the
expression for B about the mean value of the random variables, we can quantify the total
uncertainty in X as follows:

E@) =E(BI)E(BII) and COVB =(COVBI~ + COVB$)*’~ (23.2)
where B = BfBIf and COV stands for the coeficient of variation of the quantity specified by
the subscript.