Page 115 - Buried Pipe Design

Design of Gravity Flow Pipes 91

Many research efforts have attempted to measure E without
much success. The most useful method has involved the measure-
ment of deflections of a buried pipe for which installation conditions
are known, followed by a back calculation through the Iowa formula
to determine the effective value of E . This requires assumed values
for the load, the bedding factor, and the deflection lag factor.
Inconsistent assumptions have led to a variation in reported values
of E .
One attempt to acquire information on values of E was conducted
by Amster K. Howard of the U.S. Bureau of Reclamation. 12 Howard
used data from laboratory and field tests to compile a table of average
E values for various soil types and densities (see Table 3.4). He
assigned values to E , K, and W c and then used the Iowa formula to cal-
culate a theoretical value of deflection. This theoretical deflection was
then compared with actual measurements. By assuming the E values
of Table 3.4 and a bedding constant K 0.1, Howard was able to cor-
relate the theoretical and empirical results to within 2 percent
deflection when he used the prism soil load. This means that if theo-
retical deflections using Table 3.4 were approximately 5 percent, mea-
sured deflections would range between 3 and 7 percent. Howard is
reported to have used a deflection lag factor D L 1.5 in his calcula-
tions. However, if the prism load were used as reported, a lag factor
D L 1.0 would have to have been used to be theoretically correct. In
any case, the data in Table 3.4 are consistent with field and laboratory
data taken over a 20-year period at Utah State University if the prism
load is used along with a value of 1.0 for the deflection lag factor.
Although the vast majority of data from Howard’s study were taken
from tests on steel and reinforced plastic mortar pipe with diameters
greater than 24 in, they do provide some useful information to guide
designers of all flexible pipe, including PVC pipe, since the data help
to give an understanding of the Iowa deflection formula.

Use of the constrained soil modulus
for flexible pipe design
In design of buried flexible pipe, the soil stiffness has traditionally
been modeled using the modulus of soil reaction E . This is a semiem-
pirical parameter required as input to the Iowa formula for predicting
deflection of buried pipe. An alternate would be to use the one dimen-
sional constrained modulus M s . The relationship between E and M s
has often been discussed in the literature, with a few researchers con-
cluding that the two parameters are interchangeable. Design values for
M s as used in finite element programs are derived using the hyperbolic
model for Young’s modulus developed by Duncan. The development of