Page 84 - Buried Pipe Design

60 Chapter Two

1 2 2
A 4 R A 5 0.215R
2
1 2 1 2 2 1 1 2
A 5 R R R 0.285R
2 2 4 2
Then
2 1 (h R) 2
Total area A 2 hR 0.215R
tan
2
W W w W s W p
where W w 3.752 kips/ft buoyant uplift force per unit length of tank.
This is the weight of water per foot displaced by the pipe.
2
2
R ( w ) (52.5/12) (62.4)
W s 3.631 kips/ft effective soil wedge (ballast) on top per unit
length at f 45° /2
A b
3
52.63 (69) 3631 lb/ft for this example
W p 0.580 kip/ft weight of steel pipe
W 0.459 kip/ft net downward force
Thus, if the 17.19-ft soil wedge forms, as supposed, the pipe will not float.
However, tests show that planes are well established near the tank, but are
not well established at the ground surface. In fact, the “plane” may be more
nearly a spiral cylinder that breaks out on the ground surface at a width
less than the 17.19 ft shown. In design, a factor of safety is required and
should be at least 2.0. That is, the downward forces (soil and pipe) should
be at least 2 times the buoyant uplift force.

Liquefaction
If there is any possibility of soil liquefaction, flotation will be a major
concern and additional considerations are required. Soil can liquefy if
it is saturated and shaken, and if the density is less than about 80 per-
cent modified Proctor density (AASHTO T-180). The shaking can be a
result of seismic activity. If the soil is completely saturated to ground
level and the pipe is empty, there will be little resistance to flotation
and the empty pipe will rise through the liquid soil.
The concept of liquefaction is as follows: Pour loose sand into a quart
jar to the top, then carefully fill to the top with water. Put on the lid
and shake the soil-water mixture. Remove the lid and turn the jar
upside down, and the liquefied soil will run out. Now repeat the
process, but this time carefully compact the sand in layers. The density
must be greater than 80 percent modified Proctor. Another way of say-
ing this is that the void ratio must be less than the critical void ratio.
After the jar is completely full with compacted sand, again carefully