Page 159 - Reliability and Maintainability of In service Pipelines

144 Reliability and Maintainability of In-Service Pipelines

TABLE 5.7 Models for Stresses on Buried Pipes Considered in this Study
Stress Type Model a References
σ F , hoop stress due to internal fluid pressure pD Rajani et al. (2000)
2d
2
3K m γB C d E P dD
σ S , soil pressure d Ahammed & Melchers (1994)
3
E P d 1 3K d pD 3
σ V , Traffic stress 3K m I c C t FE P dD Ahammed & Melchers (1994)
AE P d 3 1 3K d pD 3 Þ
ð
, Thermal stress Rajani et al. (2000)
σ T e 2 E P α P ΔT e

σ P , axial stress due to internal fluid pressure p D Rajani et al. (2000)
2 d 2 1 ν p
a
Notations are in Table 5.6.
5.3.1.3 Toughness Limit State
For localized stress concentration caused by defects, e.g., corrosion pits, the term
stress intensity factor, K I , is used (as it was mentioned in Section 2.2.2) to more
accurately predict the stress state (“stress intensity”) near the tip of a crack
(caused by applied or residual stresses).
The formulations presented by Laham (1999) are used for calculation of stress
intensity factors for crack pits in a pipe under different stresses. According to
Laham (1999), the stress intensity factor for a crack pit in a pipe under hoop
stress is as follows:
3
p ffiffiffiffiffiffi X a 2c R
K I2h 5 πa σ i f i ; ; ð5:23Þ
d a d
i50
and the stress intensity factor for a crack pit in a pipe under axial stress:
!
3
p ffiffiffiffiffiffi X a 2c R a 2c R
K I2a 5 πa σ i f i ; ; 1 σ bg f bg ; ; ð5:24Þ
d a d d a d
i50
where
K I-h 5 Stress intensity factor for longitudinal crack in mode I, caused by hoop
stress;
K I-a 5 Stress intensity factor for circumferential crack in mode I, caused by
axial stress;
a 5 Depth of the crack, i.e., corrosion pit;
σ i 5 Stress normal to the crack plane;
f i and f bg 5 Geometry functions, depend on a, c (half-length of crack) and R
(inner radius of pipe);
σ bg 5 the global bending stress, i.e.; the maximum outer fiber bending stress
For internal and/or external crack pits, the difference in formulations of stress
intensity factor (Eqs. 5.23 and 5.24) lies in geometry functions (i.e., f i and f bg ), which