Page 166 - Buried Pipe Design

140 Chapter Three

materials. The elastic assumption for the pipe structure is acceptable for
most pipe materials. However, in this solution and in the Iowa formula,
the assumption that the soil is elastic can lead to large errors.
Burns and Richard used only a constant elastic modulus for the soil.
The possibility for the soil modulus to change as the depth of cover
increases has been added to the linear elastic theory proposed by Burns
and Richard. In this modified version, the effective soil modulus
increases as the soil height over the top of the pipe is increased. This is
sometimes called the overburden-dependent soil modulus. Again, this
overburden-dependent soil modulus was not proposed by Burns and
Richard but was added later. The justification for an increasing modulus
with depth of cover comes from the confined compression test for soil. In
such a test, the stress-strain curve is concave upward. The slope of the
line (modulus) increases with increasing stress. However, in a buried
flexible pipe situation the soil next to the pipe is not confined and the
load deflection curve is concave downward.
It has been shown that when the overburden-dependent model is
applied to steel, solid wall PVC, FRP, RPM, or HDPE pipes, the pre-
dicted vertical deflection is often in large error. The primary difficulty
lies in having the proper soil modulus to make the solution work. The
assumed increase in the effective soil modulus with depth of cover usu-
ally does not take place for flexible pipes, but may be valid for rigid
pipes. If the overburden-dependent feature is not used, the Burns and
Richard solution produces almost identical results to those produced
by the Iowa formula. Also, if the same overburden-dependent modulus
is used in both the Iowa formula and the Burns and Richard solution,
then the calculated vertical deflections are essentially the same from
either theory. A version of the Burns and Richard solution is available
on a spreadsheet.
The advantages of the Burns and Richard solution are that

1. It has been programmed on a spreadsheet and is easy to use.
2. It produces pipe wall thrust and strain, and horizontal deflection
directly.
3. It allows for full slip or no slip at the soil-pipe interface.

The greatest short-comings of the Burns and Richard solution are that

1. The solution assumes double symmetry. That is, it assumes that the
soil-pipe system is symmetric about both the horizontal and the ver-
tical axes. It is normal to assume symmetry about the vertical axes;
however, both test results and finite element methods show that
symmetry about the horizontal axis is not the norm. Spangler rec-
ognized (based on tests) that symmetry about the horizontal axes