Page 111 - Trenchless Technology Piping Installation and Inspection

Existing Pipeline Renewal and Replacement Methods 77

a. Calculate coefficient of elastic support
⎡ 1 ⎤
.
B ′ = ⎢ 0 065 × 16 ⎥ = 0 414
.
⎣1 + 4 ( × 2 178 ⎦ )
.
b. Calculate ovality reduction factor
⎡ ⎛ ⎞ ⎤ 3
⎢ ⎜1 – 20 . ⎟ ⎥
⎢ ⎝ 100 ⎠ ⎥
C = ⎢ ⎥ = = 0 836
.
⎢ ⎛ 20 . ⎞ 2 ⎥
⎢ ⎜1 – 100 ⎟ ⎠ ⎦ ⎥
⎝ ⎣
c. Calculate E
L
E = E – (E × reduction factor to account for long-term effects)
L
E = 250,000 – (250,000 × 0.5) = 125,000 psi
L
d. Determine minimum CIPP thickness in buckling
1
⎡ ⎛ 2 ⎤ 3
⎢ ⎜ N × q ⎞ ⎟ ⎥
t
⎢ ⎜ ⎝ 1 ⎟ ⎠ ⎥
=
t 0 721 × D × ⎢ ⎥
.
⎢ E × R × B′ × C × E′ s⎥
w
L
⎢ ⎢ ⎥
⎣ ⎢ ⎦ ⎥
1
⎡ ⎞ 2 ⎤ 3
×
.
⎢ ⎛ 2 0. 14 90 ⎟ ⎥
⎜
t 0 721 48 00 ⎢ ⎢ ⎝ 1 ⎠ ⎥ ⎥
×
=
×
.
.
×
×
×
,
.
.
⎢ 125 000 × 0.835 × 0 414 0 836 1000 ⎥
⎢ ⎣ ⎥ ⎦
t = 1.01 in. (external pressure, deteriorated conduit)
e. Check minimum stiffness requirement
×
EI E
≥
3 = 3 0 093.
×
D 12 ( DR)
where DR = Dimension Ratio, DR = D/t
Solve for t,
1
⎡ ⎤ 3
⎢ 3 ⎥
=
t ⎢ 48 ⎥
⎛ ⎢ 250 000 ⎞⎥
,
⎜ ⎢ ⎟⎥
.
⎝ ⎣ 12 × 0 093 ⎠⎦
t = 0.790 in. (min. stiff. limitation, deteriorated conduit)