Page 176 - Reliability and Maintainability of In service Pipelines

Case Studies on the Application of Structural Reliability 161

of these three random variables for low values of t has a more significant effect
on the reliability index.

5.4.2 MULTIFAILURE MODE ASSESSMENT

In this section, the case of the concrete sewer pipeline in Harrogate UK is ana-
lyzed by considering more than one possible failure mode. This study which is
called multifailure mode reliability analysis will eventually end up with a more
reliable service life estimation.

5.4.2.1 Problem Formulation

Limit State Functions
For concrete sewers, failure does not necessarily imply structural collapse (ulti-
mate strength failure) but in most cases is indicated by loss of structural service-
ability, as characterized by concrete cracking and/or concrete cover loss. In a
comprehensive reliability analysis it is of interest to take into account both ser-
viceability failure and ultimate strength failure.
In some cases of reliability analysis of a structure, various limit states such as
bending, shear, cracking, and deflection may apply in a composition referred to
as a “system.” The detail of system reliability analysis was explained in
Section 3.4. As was mentioned in that section, in a series system, attainment of
any limit state constitutes failure of the structure. All components of a parallel
system must fail for system failure to occur.
A concrete sewer can fail in multiple modes due to different limit state viola-
tions. Therefore, the probability of the sewer failure should be determined using
the methods of systems reliability analysis.
Considering design codes of practice and manuals for reinforced concrete pipe
design (ASCE 15 98, 2000; ASCE 60, 2007), the four following failure modes
(limit state functions) should all be considered for buried concrete sewers:

Flexural limit state: G 1 M u ; M s ; tð Þ 5 M u ðtÞ 2 M s ðt ð5:33aÞ

Shear limit state: G 2 V b ; V s ; tð Þ 5 V b tðÞ 2 V s tðÞ ð5:33bÞ
Excessive crack limit state: G 3 F; F cr ; tð Þ 5 FtðÞ 2 F cr tðÞ ð5:33cÞ

Cover loss limit state :G 4 Δ; a o ; tð Þ 5 ΔðtÞ 2 a o ðtÞ ð5:33dÞ
where M u ; V b ; F; and Δ are flexural strength, shear strength, crack control factor,
and concrete thickness reduction, respectively, which are considered as thresholds
for limit state functions. Formulization of these four resistance modes for a rein-
forced concrete pipe are presented in Table 5.9.