Page 318 - Buried Pipe Design

Steel and Ductile Iron Flexible Pipe Products 289

Then
1 1
M
EI
R R
i o
To use this formula, the radius of curvature R of the deformed pipe ring
i
must be known. The pipe wall is not crushed just because the stress S
reaches yield point. Stress S is the stress in the most remote fiber only,
and it may already be at the yield point due to cold-forming. See Fig. 6.3.
The design limit is performance limit divided by a safety factor. The
performance limit is excessive distortion of the soil-pipe system so that
either the pipe or the soil cannot perform adequately its designed func-
tion. Performance limits do not include a yield point stress in the most
remote fiber, or necessarily a specific ring deflection.
The performance limit of a buried corrugated steel pipe ring is defor-
mation of the ring beyond which the system can no longer perform the
purpose for which it was designed. If an unacceptable hump or dip or
crack develops in the soil surface above the pipe, the performance limit
is exceeded. If the flow characteristics of the pipe are reduced below
designed values because of ring deformation, the performance limit is
exceeded. The final definition of performance limit must be left up to
the design engineer.
For most installations, the definition of the performance limit is
incipient ring failure, as shown in Fig. 6.4. Incipient ring failure is
defined as some deformation of the ring beyond which the ring would
continue to deform (to collapse) if loads on it were not relieved by the
arching action of the soil. This is an arbitrary performance limit. It does
not mean collapse. The proposed strength envelopes shown in Fig. 6.4
become a design chart for this performance limit. The strength enve-
lope for dense soil exceeds the yield point for steel because part of the
vertical soil pressure is supported by the soil in arching action. An addi-
tional safety factor is built in because the ring does not collapse even
though it is deformed to incipient ring failure.

M 1
R o d = M = R i – R 1 o
EI
R i 1 1
M = EI –
R i R o Figure 6.3 Relationship of
moment to change in radius of
M curvature of pipe ring.