Page 112 - Trenchless Technology Piping Installation and Inspection

78 Cha pte r T w o

II. Deflection (spangler formula)

×
+
Y = K × ( L W W ) × 100
s
D E
+ .0 061 × E′ s
. 15 × ( DR – )1 3
where Y = vertical deflection of Liner pipe, in
Y
= deflection ratio, expressed as a percentage
D
L = empirical lag factor, taken as 1.25
K = bedding constant, taken as 0.083
W = earth load, psi
W = live load, psi (W and/or W )
s sc sd
DR = liner pipe dimension ratio = D
t

E′ = modulus of soil reaction, psi (typical value
s
700–1500 psi)
a. Determine loads
1. Earth load (modified Marston Formula)

×
×
Cw B
W = d
144
where W = earth load, psi
B = trench width, ft
d
w = soil density, pcf
– ⎛ 2ku′ H ⎞
⎜ ⎜ s ⎟ ⎟
1 – e ⎝ B d ⎠
C =
2ku′
e = 2.718
k = a ratio of horizontal to vertical pressures
u′ = coefficient of sliding friction between the backfill
and trench walls (Table 2.11)
H = soil depth to top of pipe, ft
s
B = 6.5 (Table 2.10)
d
ku′ = 0.13 (Table 2.11)
×
.
⎛ 2– × 0 130 16 ⎞
⎜ ⎝ 65 ⎟ ⎠
.
–.
C = 1 2 718 = 182.
×
.
20 13
×
.
.
.
W = 182 × 120 65 = 985 psi
144