Page 150 - Buried Pipe Design

124 Chapter Three

If live load W is assumed to be a distributed surface pressure, the
Newmark integration can be used. Soil cover must be greater than
minimum by the pyramid/cone analysis of Chap. 2. After an adequate
pipe has been selected, the soil column can be designed.
The following analysis is for flexible pipes. The vertical load supported
by the two flexible pipe walls at section AA is no less than 2PD/2
PD. So, in the design of the soil column, it is assumed, conserva-
tively, that the pipe wall cladding takes a vertical load of PD. The
remainder of the load must be supported by the soil. The greatest
load on the soil occurs when the heavy live load W is centered above
section AA—centered between the two pipes. At this location, not
only is the live load pressure on the soil maximum, but the portion
supported by the pipe walls is minimum. Pipe walls carry dead load
P d D HD. The live load P l on the pipes is small enough to be
neglected. The live load on section AA cannot be neglected. This is
the Boussinesq soil stress
y , and must be less than strength S′.
Vertical stress is soil load per length divided by the distance
between pipes X:

V′ S′

y
X SF
Per unit length of pipe V is the sum of the deadweight of the cross-
hatched soil mass w d and that portion w l of the surface live load
W that reaches section AA. See Fig. 3.26. The dead load w d per unit
length of pipe is the soil unit weight times the cross-hatched area;
i.e.,

r 2
w d (X 2r)(H r) (3.26)
2
The live load w l is the volume under the live load pressure diagram of
Fig. 3.26 at section AA. It is calculated by means of the Boussinesq live
load w l per unit length.

0.477WX
w l
(H r) 2
Example Problem 3.3 What is the vertical soil stress at section AA of
Fig. 3.26? The pipes are 24-in-diameter DR 35 PVC. There is 12 in of soil
between the two at the spring line. Soil cover is 1.5 ft of soil at a unit weight
3
of 120 lb/ft . A surface wheel load of W 20 kips is anticipated. Thickness
t 24/35 0.686 in.
1. Find the maximum ring compression stress in the pipe wall.
2. Evaluate the soil stress at section AA.