Page 138 - Buried Pipe Design

112 Chapter Three

The limiting value of the above equation as the pipe thickness
becomes small is
Et 3

4R 3
which is less than Eq. (3.14). In fact, in all cases Eq. (3.15) is less than

yt

R
or less than the pressure corresponding to the yield point stress. The
above equations apply only to a hydrostatic condition, i.e., for a conduit
completely submerged in a medium that has zero shear strength. The
above equations would therefore be valid for checking buckling resis-
tance of a pipeline used for a river crossing, for a liner pipe, for a pipe
in a saturated soil, or a line subjected to an internal vacuum. This
analysis does not include initial ellipticity of the conduit.
Most conduits are buried in a soil medium that does offer consider-
able shear resistance. An exact rigorous solution to the problem of
buckling of a cylinder in an elastic medium would call for some
advanced mathematics, and since the performance of a soil is not very
predictable, an exact solution is not warranted. Meyerhof and Baike
developed the following formula for computing the critical buckling
force in a buried circular conduit: 27

2 KEI
P cr 1 (3.16)

R 2
If the “subgrade modulus” K is replaced by the soil stiffness E /R, we have
1
E′
EI

P cr 2 R 3 (3.17)
2
In both Eqs. (3.16) and (3.17), initial out-of-roundness is neglected,
but this reduction in P cr because of this is assumed to be no greater
than 30 percent. As a result, it is recommended that a safety factor of
2 be used with the above formula in the design of a flexible conduit to
resist buckling. The Scandinavians have rewritten the above formula
for critical buckling pressure as follows:
2E

t

P cr 1.15 P b E P b 3 (3.18)
1 2 D
Actual tests show that while the above equations work fairly well
for steel pipe, the equations are conservative for either plastic pipe