Page 109 - Buried Pipe Design

Design of Gravity Flow Pipes 85

M. G. Spangler, Circa 1979.
to determine an adequate design procedure. His research and testing led
to the derivation of the Iowa formula, which he published in 1941. 46
Spangler incorporated the effects of the surrounding soil on the
pipe’s deflection. This was accomplished by assuming that Marston’s
theory of loads applied and that this load would be uniformly distrib-
uted at the plane at the top of the pipe. He also assumed a uniform
pressure over part of the bottom, depending upon the bedding angle.
On the sides, he assumed the horizontal pressure h on each side would
be proportional to the deflection of the pipe into the soil. The constant
of proportionality was defined as shown in Fig. 3.6 and was called the
modulus of passive resistance of the soil. The modulus would presum-
ably be a constant for a given soil and could be measured in a simple
lab test. He derived the Iowa formula through analysis as follows:

D L KW c r 3
X (3.4)
EI 0.061er 4
where D L deflection lag factor
K bedding constant
W c Marston’s load per unit length of pipe, lb/in
r mean radius of pipe, in
E modulus of elasticity of pipe material, lb/in 2
4
I moment of inertia of pipe wall per unit length, in /in in 3
2
e modulus of passive resistance of sidefill, lb/(in ) (in)
X horizontal deflection or change in diameter, in