Page 292 - Pipelines and Risers

Residual Strength ofDented Pipes with Cracks 265

Bursting of a pipe will happen at the uncontrolled tearing point in case the equivalent stress
exceeds the flow stress. The bursting failure will lead to the pipe rupture. The LSF based on
new fracture criterion can be formulated as:
t 20
g(~)=2---4os-' (15.31)
Dn:

where Z is the set of random variables involved in the new design format.

By introducing the normalized random variables including model error, as discussed in details
below, the new LSF is given by:

(15.32)

where P,-J is the design pressure which can be estimated from new design Equation (15.30),
parameters MS and Kmat are given by Equations (15.4) and (15.8) respectively by introducing
uncertainties into the corresponding random variables and the subscript c indicates the
characteristic values of corresponding variables.

15.4.2 Uncertainty Measure
Thoft-Christensen and Baker (1982) describes a typical classification of uncertainties.
Uncertainty can be measured by its probability distribution function and statistical values. The
major uncertainties considered in this study include:

Physical uncertainty: Caused by random nature of the actual variability of physical quantities,
such as pipe geometry (wall-thickness), etc.

Statistical uncertainty: Due to imperfect or incompletely information of the variable and can
be reduced by additional information, such as dent depth, crack size, etc.

Model uncertainty: Due to simplifications and assumptions made in establishing the analytical
model, it results in the difference between actual and predicted results.

Considering uncertainties involved in the design format, each random variable Xi can be
specified as:
Xi = B, .X, (15.33)

where Xc is the characteristic value of Xi, and Bx is a normalized variable reflecting the
uncertainty in Xi.