Page 70 - Buried Pipe Design

46 Chapter Two

equations is conservative. A safety factor of 1.5 is usually adequate,
and it does not need to be greater than 2 for highway culverts. With M
and T known, Eq. (2.16) can be solved for the maximum stress when-
ever stress (or strain) is of concern, as in the case of bonded linings in
pipes. And H does not appear in Eqs. (2.18) and (2.19) because the
weight of the soil is negligible.

Example Problem 2.5 Find the minimum cover of granular soil over corru-
gated polyethylene pipe with 460-mm (18-in) inside diameter (ID). The poly-
ethylene is HDPE (high-density polyethylene). The soil cover is compacted
to 85 percent density (AASHTO T-99, ASTM D 698). The yield strength of
HDPE at sudden inversion is 21 MPa (3 ksi). The surface load is a highway
truck dual wheel for which the area of the tire print is 180 mm (7 in) by 560
mm (22 in). The procedure is to substitute values of P from Eq. (2.15) into
Eq. (2.18). By including values of r and I/c for 460-mm (18-in) HDPE pipe,
the resulting equation becomes a quadratic, (H 14.5 in) 56.25 in
2
2
2
25W in /kip. Solutions are as follows:
W, kN (kips) 25 (5.5) 31 (7) 48 (9) 71 (16)
H, mm (in) 15 ( 0.6) 18 (0.7) 58 (2.3) 175 (6.9)
W dual-wheel load of 70 kN (16 kips H-20 load)

H rutted soil cover—no surface pavement
A safety factor of two is often applied to H because loads are dynamic—
not static. Some specifications require a minimum cover of 1 ft of compact-
ed granular backfill. The negative H 15 mm at W 25 kN indicates that
soil cover is not needed for such a light load. The pipe can carry a 25-kN
dual-wheel even though the top of the pipe is exposed. Of course, enough soil
cover should be provided to allow for rutting, prevent surface rocks from
denting the pipe, and prevent crushing of corrugations. This example is con-
firmed by field tests. A similar analysis for 610-mm (24-in) HDPE pipes is
almost identical. Apparently manufacturers provide equivalent properties
for their pipes in both sizes. Installation techniques are about the same for
460-mm (18-in) and 610-mm (24-in) corrugated HDPE pipes.
Flotation. When pipes are buried in soil under water, the minimum
height of soil cover to prevent flotation of an empty pipe is about H
D/2. But the soil should be denser than the critical density in order to
prevent liquefaction. Because a safety factor is advisable, specifications
often call for minimum H D.

Rigid pipe. Two performance limits for buried rigid pipes subjected to
surface loads are longitudinal fractures and broken bells.
Circumferential fractures can occur, but less frequently. They occur at
midlength of a pipe acting as a simply supported beam under a heavy
load at midspan.