Seismic risk management for water pipeline networks - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 630

( )

Δ= − 1

qu

* α [23.16]

G

where α 0 is the conversion factor of the pipe

strain from the ground strain without slippage,

ε G is the ground strain,

* is the conversion
factor of the segmented pipe by considering it as a continuous pipe, and
q eff is the slippage factor for the segmented pipe. In particular, q * is
computed as follows by assuming that it is a continuous pipe:

α

πξ ξξ

2 2

⎛
⎜

⎞
⎟ −

q * in = ξ ⋅ + 1 − cos [23.17]

82

where

τ
τ

2 EA

D

⎛
⎜

⎞
⎟

cr

ξ = arcsin , τ = α ε [23.18]

G 0 G

L

G

As a simplifi ed assumption, the following formula can be used as a con-
servative estimate:

SDl =⋅ π ⋅ τ

cr

[23.19]

eff

The resisting force for pull-out, which is produced by the compression
force at the contact surface between the locking ring and the stopper shown
in Fig. 23.3, is given by the following equation:

RDr
Y

=⋅ ⋅ π

cr

[23.20]

where

cr is the critical axial stress to initiate pull-out failure from the pipe
joint, and r is the height of the locking ring.
The pull-out failure of the new DCIP is initiated when the joint displace-
ment

σ

Δ joint . Therefore, the
pull-out failure can be assessed using the following criteria:

Δ u G,eff exceeds the critical pull-out displacement

Δ
Δ

<
>

Δ
Δ

u
u

pull-out failure occurs
pull-ou

joint G,eff

t failure does not occur

[23.21]

joint G,eff

where the joint displacement is given by:

Δ u ≅⋅ε l [23.22]

G,eff eff G

Fragility curves for segmented pipelines

The pipe damage severity due to an earthquake can be measured in terms
of the ratio of pipe damage numbers per kilometer. There are many obser-
vation data on the pipe damage ratio from the past earthquakes in Japan.
From these site investigation data, fragility curves for segmented pipelines