Page 52 - Buried Pipe Design

30 Chapter Two

(2.11)
W p PB t HB t
W t C t B t ( B t 2C) (2.9)

The prism load in this case will be very conservative because it
neglects not only friction but also the cohesion of the soil. If C t is taken
as H/B t and the cohesion coefficient is zero, then the two methods of cal-
culating loads give the same results.

Longitudinal Loading

Certain types of pipe failures which have been observed over the years
are indicative of the fact that only under ideal conditions is a pipeline
truly subjected to only vertical earth loading. There are other forces that
in some way produce axial bending stresses in the pipe. These forces can
be large, highly variable, and localized and may not lend themselves to
quantitative analysis with any degree of confidence. Some of the major
causes of axial bending or beam action in a pipeline area are
1. Nonuniform bedding support
2. Differential settlement
3. Ground movement for such external forces as earthquakes or frost
heave

Nonuniform bedding support
A nonuniform bedding can result from unstable foundation materials,
uneven settlement due to overexcavation and nonuniform compaction,
and undermining, such as might be produced by erosion of the soil into
a water course or by a leaky sewer.
One of the advantages of a flexible conduit is its ability to deform
and move away from pressure concentrations. The use of flexible joints
also enhances a pipe’s ability to yield to these forces and reduces the
risk of rupture. These advantages, coupled with good engineering and
a proper installation, virtually eliminate axial bending as a cause of
failure in a flexible pipe. The examples which follow in Figs. 2.14, 2.15,
and 2.16 give an indication of the magnitude of bending moments that
might be induced.
Axial bending of a long tube in a horizontal plane will produce vertical
ring deflection ( y/D) due to the bending moments created. Reissner 20
has amplified the work of others in this area, and the following formula
results from his work on pure bending of a long pressurized tube:
y 1 D 2 D 2

(2.12)
D 16 t R