Page 172 - Buried Pipe Design

146 Chapter Three

The Iowa formula versus the Burns and Richard solution. Since it has
been shown here that both methods produce the same vertical deflec-
tion when applied with the same soil modulus, it no longer needs to be
debated as to which solution is better. Both solutions are linear elastic
solutions with theoretical bases. Both methods are in error when com-
pared to test data and with finite element data but are easily corrected
to give accurate results. However, the Burns and Richard method pro-
duces results such as strain, deflection, and thrust at any point around
the pipe that are not directly available from the Iowa formula.

Conclusions

1. The FEA method can produce results that most closely represent
test data.
2. Full-scale testing and finite element analysis used together are the
preferred methods for research and product testing, evaluation, and
qualification.
3. The overburden-dependent soil modulus that is presently used in
the Burns and Richard solution is incorrect and should not be used
in analysis, design, or evaluation of flexible pipe installations.
4. The Iowa formula and the Burns and Richard solution predict
essentially the same vertical deflections when the same soil modulus
and correction are used in each theory.
5. On a theoretical basis, both the Burns and Richard solution and the
Iowa formula are incorrect since they assume an elastic soil.
Further, the Burns and Richard solution assumes symmetry about
the horizontal axes, which is usually not a valid assumption.
6. If a corrected soil modulus is used, results from either solution
closely match test results. The corrected soil modulus is such that a
bilinear load-deflection curve results.
7. With the corrected soil modulus, the Burns and Richard solution
has advantages over the Iowa formula as it will directly produce
horizontal deflection, stress, and strains.

Finite Element Methods
Introduction
The finite element analysis technique was developed primarily for the
analysis of complex structural systems. The technique was developed to
analyze structural responses to different loading conditions. Through
the years, the technique has been extended through mathematical
relationships and developed in other areas such as fluid mechanics,