Page 203 - Buried Pipe Design

Design of Gravity Flow Pipes 177

of the pipe-strain plot does not match the measured values as well as
for the cases with 90 percent density.

Discussion of results. The incorporation of the compaction simulation
for comparison of the response of the FRP pipe improved the compari-
son for the homogeneous condition for most cases that were attempted.
For the nonhomogeneous installation conditions, the compaction sim-
ulation did not improve the correlation of FEA and test results. It is
possible that nonhomogeneous conditions dominate the response,
masking the compaction simulation response. This could be due to the
nature of the compaction simulation sequence. Had the compaction
sequence individually modeled the backfill condition (poor haunch,
soft top, and so forth), the results might have improved. For most
cases, the compaction simulation does not improve the results enough
to justify the additional computational effort required.
The FEA data and experimental data generally correlated better for
the dense installation conditions than for the loose conditions. This is
probably due to a combination of numerical difficulties with the finite
element method and difficulties in obtaining a uniform soil condition for
low to medium density in the test cell. Entries in the stiffness matrix
become sensitive to the magnitudes of the elastic and bulk modulus
parameters at low stiffnesses. To achieve larger deflections, lower values
of the bulk modulus parameters are required. This, however, can result
in singular matrix warnings, which indicates that entries in the stiffness
matrix will not produce reliable results. More work is needed in this area
with respect to modeling soil behavior under loose conditions.
The geometric nonlinear analysis (where the formulation of the stiff-
ness matrix accounts for the nodal deflections at each loading incre-
ment) does not significantly change the results for installation
condition modeling. The inclusion of the geometric nonlinear analysis
would generally predict somewhat higher deflections. For example, an
analysis that did not include geometric nonlinearities might predict a
vertical ring deflection of 4 percent. The same conditions including
geometric nonlinearities would predict ring deflections of around 5
percent. However, for the other types of loading conditions (for
instance, rerounding), the formulation of the stiffness matrix must
reflect the shape of the pipe. Note that geometric nonlinearities would
play a much bigger role in modeling deflection bigger that 5% (a 5%
deflection is borderline of a small deflection).

Summary and conclusions
Good correlation of finite element modeling of flexible pipes with test
data requires modeling capabilities not readily available in most existing