Page 160 - Reliability and Maintainability of In service Pipelines

Case Studies on the Application of Structural Reliability 145

have been presented in different tables by Laham (1999). Due to the propagation of
corrosion, a changes with time so the stress intensity factors are time variant.
If K C is the critical stress intensity factor, known as fracture toughness,
beyond which the pipe cannot sustain propagation of the crack pit, the two limit
state functions for fracture toughness can be established as follows:

Axial fracture limit state : G 3 K C ; K I2h ; tð Þ 5 K C 2 K I2h ðtÞ ð5:25Þ

Hoop fracture limit state : G 4 K C ; K I2a ; tð Þ 5 K C 2 K I2a ðtÞ ð5:26Þ

5.3.1.4 Corrosion Model
It has been well known that the predominant deterioration mechanism for cast
iron pipes is electrochemical corrosion in the form of corrosion pits. Each spot of
metal loss represents a corrosion pit that grows with time and reduces the thick-
ness and mechanical resistance of the pipe wall. This process eventually leads to
the collapse of the pipe.
As it was mentioned in Section 1.6.2, a number of models for corrosion of cast
iron pipes have been proposed to estimate the depth of corrosion. There are
debates in the research community as to whether the corrosion rate can be assumed
linear or otherwise (e.g., Kucera and Mattsson, 1987; Sheikh and Hansen, 1996;
Ahammed and Melchers, 1997; Rajani et al., 2000; Sadiq et al., 2004). The widely
used model for corrosion pit is expressed in the form of the following:

a 5 kt n ð5:25Þ
where t is the exposure time and K and n are empirical coefficients which in prac-
tice are obtained by fitting the model to experimental data.
The modeling of corrosion pit is based on the experimental data from a UK
Water Industry Research report (Marshall, 2001). This corrosion rate data used in
this case study has been illustrated in Fig. 5.14. As the regression of available
2
data fits a power law very well with high R-square value (Fig. 5.14, R 5 0:959
2
for internal corrosion and R 5 0:857 for external corrosion), the corrosion can be
modeled, for both external and internal corrosion, as follows:
μ 5 2:54t 0:32 for external corrosion ð5:26Þ
a
μ 5 0:92t 0:4 for internal corrosion ð5:27Þ
a
where μ denotes the mean value for the depth of corrosion pit.
a
The widely used corrosion model (i.e., Eq. (5.25)) is selected for the multifai-
lure mode reliability analysis of the cast iron pipe. Therefore the statistical values
(mean and standard deviation) for k and n in Eq. (5.25) are again taken from the
mathematical regression (Fig. 5.14) to the data from Marshall (2001). Based on