Seismic risk management for water pipeline networks - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 625

where

1 cosh β − cos γ

1 1

α = , λ = [23.7]

1

1
2

+ (

)

2

1 γβ

β sinh β

11

1 1

K
EA l

2 π l

g 1

d

β = , γ = [23.8]

1 d 1

L ′

in which E , A , and K g1 are the elastic rigidity, cross-section area, and spring
modulus of a segmented pipe, respectively; L

′ is the apparent wavelength

along the pipe; and L ′ = 2 L for the incident wavelength L . Δ u G is the rela-

tive ground displacement which is given by

u 2 π

⎡
⎢

⎛
⎜

⎞
⎟

⎤
⎥

G

[23.9]

Δ u = 1 − cos l d

G

L

2 ′

in which U G is the horizontal displacement at the ground surface and can
be calculated by the following equation:

2
2

( ⋅

u = S T T [23.10]

G V G G

π

where T G is the characteristic site period of the soil deposit in which a
buried pipeline is installed, and S V is the spectral response velocity at the
characteristic site period, respectively.
In the seismic design procedure for unrestrained DCIP, the seismic dis-
placement of a single DCIP joint is assessed by

ΔΔ
joint

≥+ u additional load displacements [23.11]

J

in which Δ joint is the critical joint displacement.

Figure 23.5 shows a fl owchart of JWWA's seismic design procedure, in
which the calculation steps for the unrestrained joints are described in
detail, but those for the restrained joints request non-linear structural anal-
ysis to obtain the seismic stress of pipe joints without any detailed instruc-
tion on its calculation methods.
In this design procedure, the following steps must be executed:

1. Assume the seismic load conditions at the site; T G , L , S V .

2. Assume the structural design conditions; D , l d , Δ joint , θ cr .

3. Calculate the apparent wavelength L , the horizontal displacement u G

in Equation (23.10), the transverse displacement v G , and its corre-
sponding angle

′

θ G .

4. Calculate the bending angle Δ θ at an unrestrained joint.