Page 167 - Reliability and Maintainability of In service Pipelines

152 Reliability and Maintainability of In-Service Pipelines

To incorporate the effect of increments in populations of residents and essen-
tially the increase in the flow rate during the system’s lifetime, the modeling
assumes flow rates corresponding to relative depths (i.e., depth/diameter) of 0.2,
0.4, and 0.6, each occurring over a period of 25 years.
Reliability analysis and service life prediction of this concrete sewer pipeline
is of interest for asset managers in North Yorkshire, England, to develop a risk-in-
formed and cost-effective strategy in the management and maintenance of con-
crete sewers. The analysis can also help infrastructure managers to develop reha-
bilitation or replacement strategies for existing pipe networks with a view to
better management of the pipe asset.

5.4.1.1 Problem Formulation

Limit State Function
According to the ASCE manual No.69 (1989), one of the performance criteria
related to the stability of concrete sewers is to control the wall thickness reduction
under an acceptable limit (normally concrete cover). In the theory of structural
reliability this criterion can be expressed in the form of a limit state function as
follows:

Gd max ; d; tð Þ 5 d max ðtÞ 2 dðtÞ ð5:28Þ
where:
d: Reduction in wall thickness due to corrosion (or corrosion depth), (mm)
d max : Maximum permissible reduction in wall thickness (structural resistance
or limit), (mm)
t: elapsed time

d max may change with time although in most practical cases it has a constant
value prescribed in design codes of practice and manuals.

Corrosion Model
The corrosion mechanism in concrete sewers was discussed in Section 1.6.1 and
models for the rate of corrosion and wall thickness reduction were presented in
the form of Equations 1.19 and 1.20, respectively.
Recalling Equation 1.20, the reduction in wall thickness in elapsed time t, is:

b
3=8
½
dtðÞ 5 c:t 5 8:05k:ðsuÞ j: DSŠ 3 0 :t ð1:20Þ
P A
where k is the factor representing the proportion of acid reaction, s is pipe slope,
u is the velocity of stream (m/s), j is pH-dependent factor for proportion of H 2 S,