Page 109 - Trenchless Technology Piping Installation and Inspection

Existing Pipeline Renewal and Replacement Methods 75

Design Calculations for CIPP
I. Buckling analysis (modified AWWA formula)
1
⎡ ⎛ E × ⎞ ⎤ 2
I
q = 1 ⎢32 × R × B′ × E′ × C × ⎜ L ⎟ ⎥
t N ⎣ w s ⎝ D 3 ⎠ ⎦
Solve for t,
1
⎡ ⎛ N × q ⎞ 2 ⎤ 3
⎢ ⎜ t ⎟ ⎥
⎢ ⎝ 1 ⎠ ⎥
= .
t 0 721 × D ×
⎢ E × R × B′ × C E′ ⎥
×
⎢ ⎢ L w s ⎥
⎣ ⎢ ⎦ ⎥
where q = total external pressure on pipe, psi
t
w × H × R
×
s
.
= 0 433 H w + 144 w +W s
H = height of water above top of pipe, ft
w
w = soil density, lb/ft 3
H = height of soil above top of pipe, ft
s
R = water buoyancy factor
w
⎛ H ⎞
= 1 – 0.33 × ⎜ w ⎟ , minimum value = 0.67
⎝ H s ⎠
W = live load, psi (W and/or W )
s sc sd
D = mean inside diameter of existing pipe (or liner pipe
outside diameter), in.
C = ovality factor
⎡ ⎛ ⎤ 3
⎢ ⎜ 1– q ⎞ ⎟ ⎥
⎢ ⎝ 100 ⎠ ⎥
= ⎢ 2 ⎥
⎢ ⎛ 1+ q ⎞ ⎥
⎟
⎢ ⎜ ⎝ ⎣ 100 ⎠ ⎦ ⎥
q = ovality
⎛ maximum diameter – mean diameter ⎞
q = 100 × ⎜ ⎟
⎝ mean diameter ⎠
a
N = factor of safety, typical value = 1.5 to 2
B′ = coefficient of elastic support
1
= ( + − 0.65 H s )
14e
E = flexural modulus of elasticity of liner pipe, psi, reduced
L
to account for long-term effects
I = moment of inertia, in.(4/in.) = t 3/12
t = liner pipe thickness, in.