longer drains into the sewer pipe and the water table rises. Still the
casing leaks, so external water pressure must be resisted by the liner.
The conditions exist for buckling of the liner if external pressure is
increased. A typical scenario for failure is the following:
The empty liner floats up leaving a gap on the bottom where the
external pressure (head h) is greatest. The liner is flattened a bit on
the bottom because the perimeter shrinks under pressure.
Consequently, the radius of curvature is increased. Both the increased
radius of curvature and the loss of support, at the point where pres-
sure is greatest, are the conditions for buckling of the liner. If pressure
is increased, the liner will buckle. Because of plastic creep over the
long term, the perimeter shrinks even more over time and the condi-
tions for buckling worsen. What is the time to failure? What is the
decrease in failure pressure in fifty years—or a hundred years?
Tests at USU have given some answers to these questions. Failure was
defined as the maximum pressure when the liner is just on the verge of
buckling. Buckling is reversal of curvature. It is the result of instability
and might be initiated by a slight glitch (holiday) in the material of the
liner, by a slight deviation of the shape, or over a period of time.
Data from a report, “Long Term External Hydrostatic Pressure
Testing of Encased Insitupipes,” show that long-term failure pressure
is about half the short-term (quick-load) failure pressure. The half-ratio
of long-term to short-term failure pressures applied to all Insitupipes
test with approximately the same D/t ratio. With ample safety factor,
long-term design can be based on the half-ratio rule of thumb.
Except for an allowance for long-term plastic creep, the structural
performance and performance limits of plastic pipes are based on the
same generic properties required of all flexible pipes—including met-
als, composites, etc. Of course, pipe performance must not exceed per-
formance limits. We refer to performance limits rather than failure
because failure implies rupture or complete collapse. Performance lim-
its usually fall short of failure. Performance limit is usually defined as
excessive deformation of the pipe. Deformation includes rupture, buck-
ling, ring deflection, puncturing, denting, etc.
Design of pipe liners
For a pipe liner in a casing, internal pressure is usually of no concern.
Even if the liner inflates, it is confined by the casing like an innertube
in a tire. External pressure on the liner causes ring compression stress
of P(D
O
)/2t where P is the external pressure, D
O
is the outside
diameter, and t is the wall thickness. The ring compression stress must
be less than yield strength of the pipe wall. If steel has a yield strength
eight times as great as PVC, then the PVC pipe liner wall must be eight
Pipe Installation and Trenchless Technology 537