Page 324 - Buried Pipe Design

Steel and Ductile Iron Flexible Pipe Products 295

Performance limit is ring deformation beyond which the soil-pipe
system does not perform adequately. To design the pipe ring, one can
employ the well-known, universal design criterion stress < strength,
i.e.,
PD f c
(6.2)
2A N
where P D L apparent vertical soil pressure (i. e., calculated
L L
pressure at level of top of pipe if no pipe were in place)
that compromises dead load D and live load L
L L
D H or unit weight of soil times the height of fill H
L
over the top of pipe
L vertical soil pressure at level of top of pipe due to surface
L
loads
f apparent ring compression strength that can be simply
c
picked off the plots (Fig. 6.4)
N safety factor
The ordinate in Fig. 6.4 is labeled ultimate ring compression stress.
2
The abscissa is ring flexibility (D/r) . More correctly this should be
2
(D/r) /E, where D is the diameter, r is the centroidal radius of gyration
of the longitudinal pipe wall cross-section, and E is the modulus of
elasticity of the pipe material. However, in these tests the only mater-
6
2
ial used in the pipes is steel for which E 29 10 lb/in so E is a con-
2
stant and is not included in the variable (D/r) .Within the precision of
these tests, the radius of gyration r is constant for a given corrugation
configuration (i.e., it is essentially independent of gage of steel); so the
abscissa can be displayed as a pipe diameter D for each given corru-
gation configuration.
In dense soil, the ring flexibility does not have a significant effect on
the ultimate ring compression stress. This is so because the ring
deflection is so small that any stress in the ring is pure compression
(not flexure). The performance limit is wall crushing and is indepen-
dent of ring flexibility. However, the factor of safety against reversal of
curvature is greater if the depth of corrugation is increased.
It is noteworthy that the strength envelopes dip down to the
right with increasing ring flexibility. This is due to the increased
sensitivity of the very flexible ring to nonuniform soil density. If
the soil could be placed particle by particle, the strength envelopes
would not dip down so much (especially in well-compacted soil).
However, present soil placement techniques result in nonhomoge-
neous soil that causes pressure spots and precipitates wall buck-
ling in the very flexible rings. This is shown as the ring buckling
zone.