Page 165 - Buried Pipe Design

Design of Gravity Flow Pipes 139

and soil consolidation—not due to creep in the pipe material. Thus, as
previously stated, the creep properties of pipe materials have little
effect on the long-term deflection behavior of flexible pipe. It should be
noted that for some profile-walled pipes, controlling vertical deflection
may not control localized buckling as a performance limit.

Methods for predicting pipe performance
Full-scale testing. Full-scale testing has been used with great success
at various research laboratories such as at Utah State University, the
U.S. Bureau of Reclamation, and Ohio University. Techniques have
evolved whereby a prototype pipe is tested until failure occurs, and
then the total performance of the pipe is studied.

Model testing. Model testing is as described above but often involves
smaller-scale pipes. Dimensional analysis is used to predict the per-
formance of larger pipes. Pipe models are sometimes put in centrifuges
where g-forces are generated to simulate high depths of cover. Model
testing has been used with some success, but centrifuge testing has its
problems and has not been universally accepted.

Spangler’s Iowa Formula. This equation is discussed earlier in this
chapter.
D L KW
x y (3.33)
EI/r 0.061E′
3
Spangler assumed symmetry about the vertical centerline but did not
assume symmetry about the horizontal centerline. A review of the
derivation of the Iowa formula shows that it has an excellent theoret-
ical foundation. The derivation uses the exact relations of moment,
shear, and thrust in the pipe ring. It is an excellent linear theory.

Burns and Richard’s elastic solution. 3,9 Burns and Richard published
their solution at the Symposium on Soil-structure Interaction at the
University of Arizona in 1964. There was little interest shown in their
solution, since it is an elasticity solution. In fact, it was largely ignored
until the mid-1990s when some renewed attention was given to this
solution. This solution is nothing more than an adaptation of the theory
of elasticity solution published by Michell in 1899. Michell’s solution is
for a circular hole in a semi-infinite isotropic elastic medium. Burns and
Richard modified the Michell solution by placing a circular isotropic
elastic shell in the hole and used thin-shell theory to match boundary
conditions between the circular hole and circular shell. This solution is
linear. It assumes both the soil and the pipe structure to be linear elastic