Page 173 - Buried Pipe Design

Design of Gravity Flow Pipes 147

thermodynamics, geotechnical engineering, groundwater analysis,
aerodynamics, and many other areas of science. The approach has
evolved into a rather sophisticated mathematical analysis technique.
It has proved to be a very useful tool in research and development as
well as in everyday analysis.
One area of development for the use of FEA that has been promoted is
in soil-structure interaction mechanics. One-, two-, and three-dimen-
sional finite elements can be combined into a global matrix. Each ele-
ment type may be defined with different stiffness properties. The
modeling of the nonlinear stress-strain properties of soil has been accom-
modated through incremental analysis and an iterative solution scheme.
This approach has been widely used in the past for the analysis of earth
structures, buried pipes, and earth-retaining structures. It has allowed
the development and use of some very large and/or complex structures.
Various loading conditions, subsurface conditions, and structural prop-
erties can be modeled mathematically. This is an advantage over physi-
cal testing of such structures. However, the user must be forewarned
that the FEA results are only as good as the ability to model the behav-
ior of soil-structure interaction. For flexible pipes, the results are pri-
marily governed by the behavior of the soil and not the pipe. Predicting
the behavior of the pipe is usually quite straight forward. Accurate mod-
els of soil behavior can be difficult to obtain. Note that, the finite element
method often has to be calibrated by comparing FEA results with results
from physical tests. Additional FEA limitations may include inaccurate
input data, convergence, and roundoff error.
A variety of commercial finite element programs are currently avail-
able for structural analysis. A linear finite element model is a capability
supported by any analysis package. A linear solution requires that dis-
placements be small and the materials be linear elastic. This restriction
limits application of these linear models to well compacted soils (e.g. soil
density in excess of 95% standard proctor) and small burial depths (e.g.
less than 20 feet). By judicious selection of soil modulus values, good
insight into the expected behavior can be obtained. To model deep burial
conditions or any installation in moderate to poor soil conditions, a non-
linear finite element solution is required. Finite element packages that
support nonlinear analyses are also quite common, but their built-in
material models typically do not give good results for culverts installed
in native materials. For native soils, a hyperbolic soil model such as a
Duncan or Duncan/Selig 30,42 is recommended. A description of the
6
Duncan soil model is given below. Only a few nonlinear finite element
programs support hyperbolic soil models. Two of those that are available
4
are CANDE and PLAXIS. 40 PLAXIS is a commercial program than
handles a variety of geotechnical problems. CANDE-89 is available from
the U.S. Federal Highway Administration. A new version of CANDE to