Moser A.P., Folkman S. Buried Pipe Design
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pull the pipe away from the soil. The FEA model was successful for
tests where the soil density was at least 90 percent Proctor density.
There was some difficulty in modeling rerounding for a poor haunch
condition in loose soils. Figure 4.19 is a graphical comparison of
bending strain as predicted by FEA with test data. There is reasonable
agreement. The bending strains shown are for the pipe’s outside surface.
Figure 4.20 shows FEA data only. It clearly shows the change in both
bending and thrust strains as the internal pressure is changed from 0 to
120 lb/in
2
.
Residual bending strain data. The data are tabulated in Tables 4.10
and 4.11 and plotted in Figs. 4.21 to 4.25 for rerounding coefficient
R
P
/
I
, where
P
is the bending strain at a given pressure and
I
is
the initial bending strain. As expected, the general trend is that R
decreases as pressure increases. Note that the strains given in
Tables 4.10 and 4.11 do not necessarily occur at the same circumfer-
ential location on the pipe as pressure increases. As the pipe
rerounded, it could change shape slightly, causing the maximum
strain to shift location. Thus, the rerounding coefficient is computed
using the ratio of the maximum measured strain at any given pressure
to the maximum initial bending strain.
Other data. A review of literature shows data from rerounding tests
conducted on full-scale installations
7,8,19
correlate well with test data
Design of Pressure Pipes 229
×
×
–
Figure 4.19 Rerounding data for pipe buried 20 ft deep in silty-sand soil com-
pacted to 80 percent of Proctor density. Pipe stiffness 36 lb/in
2
. Internal
pressure is 100 lb/in
2
.
230 Chapter Four
×
×
–
Figure 4.20 FEA rerounding data for pipe buried 20 ft deep in silty-sand
soil compacted to 80 percent of Proctor density. Pipe stiffness 36
lb/in
2
.
obtained from the Utah State University experiments. Table 4.12 data
from these references are plotted in Fig. 4.25.
For the Cole and Timblin data,
8
the rerounding coefficients were
computed by backing out the calculated pressure strain from the total
measured strain plotted in Fig. 4.25.
8
For the Sears data,
19
the
rerounding coefficient was computed by using deflection data and dif-
ferential bending stress data given in Table 4.11, both giving similar
results. These coefficients are shown in Table 4.12. For the Carlstrom
data
7
the rerounding coefficients were taken from his Picture-12.
Observations. Observations from the data tables and the rerounding
plots are as follows:
1. Poor and complete haunches permit about the same rerounding to
slightly more for the poor haunch type, as shown in Tables 4.10 and
4.11. Note that initial bending strain will be less for complete
haunch since it will have a more elliptical shape and a lower D
f
fac-
tor for use in the bending strain equation.
b
D
f
(4.21)
2. The maximum residual bending strains occur when the starting
deflections are highest, as shown in Tables 4.10 and 4.11.
t
D
y
D
231
TABLE 4.10 Poor Haunch
Proctor Pipe Initial
Test density, stiffness, Cover, deflection, Internal pressure, lb/in
2
no. percent lb/in
2
ft percent 0 25 50 75 100 125
Strain
PH1 90 13 10.00 2.90 4,533 3,373 3,776 3,312 2,058 1,649
PH2 85 92 10.00 7.90 11,094 14,601 10,131 8,074 8,222 7,318
PH3 80 92 10.00 10.20 9,916 10,356 9,883 8,500 8,456 6,759
PH4 80 5 3.00 3.00 3,839 3,376 2,355 1,929 1,367 1,239
PH5 80 13 3.00 4.00 6,425 5,559 5,604 5,201 4,769 4,052
PH6 80 35 6.50 7.70 12,331 11,068 11,083 8,330 7,303 6,493
PH7 80 92 5.58 5.38 8,103 8,246 6,977 7,423 6,697 6,759
PH8 80 35 6.50 7.70 11,028 9,732 6,405 8,438 8,486 7,299
PH9 80 35 6.50 6.50 10,381 9,529 9,228 8,727 6,960 6,360
PH10 80 92 5.50 8.70 17,776 16,777 12,988 12,157 9,946 9,255
PH11 85 92 6.50 5.20 11,716 11,597 10,925 8,915 7,749 7,533
Rerounding coefficient R
P
/
I
PH1 90 13 10.00 2.90 1.00 0.74 0.83 0.73 0.45 0.36
PH2 85 92 10.00 7.90 1.00 1.32 0.91 0.73 0.74 0.66
PH3 80 13 10.00 10.00 1.00 1.04 1.00 0.86 0.85 0.68
PH4 80 5 3.00 3.80 1.00 0.88 0.61 0.50 0.36 0.32
PH5 80 13 3.00 4.00 1.00 0.87 0.67 0.81 0.74 0.63
PH6 80 35 6.50 7.70 1.00 0.90 0.50 0.68 0.59 0.53
PH7 80 92 5.50 5.30 1.00 1.02 0.85 0.92 0.83 0.83
PH8 80 35 6.50 7.70 1.00 0.88 0.58 0.77 0.76 0.66
PH9 80 35 6.50 6.50 1.00 0.92 0.89 0.84 0.67 0.61
PH10 80 92 5.50 5.70 1.00 0.94 0.73 0.68 0.55 0.52
PH11 85 92 6.50 5.20 1.00 0.99 0.93 0.76 0.66 0.64
232
TABLE 4.11 Complete Haunch
Proctor Pipe Initial
Test density, stiffness, Cover, deflection,
Internal pressure, lb/in
2
no. percent lb/in
2
ft percent 0 25 50 75 100 125
Strain
CH1 80 5 3.00 1.60 1,700 1,700 1,800 1,200 1,000 —
CH2 85 13 6.50 4.50 4,954 5,300 4,669 4,526 3,691 3,326
CH3 85 13 6.50 4.90 5,377 4,672 4,095 3,956 3,557 3,453
CH4 85 13 6.50 4.40 3,651 3,247 3,469 3,587 3,359 4,664
CH5 85 92 6.50 3.20 4,807 4,363 3,921 333 2,589 2,348
CH6 85 92 10.00 7.60 2,763 6,222 4,333 2,923 — —
CH7 95 13 10.00 1.90 2,288 1,947 1,897 1,789 1,488 1,426
CH8 95 92 10.00 2.40 5,037 4,769 4,805 4,516 4,206 3,634
Rerounding coefficient R
P
/
I
CH1 80 5 3.00 1.60 1.00 1.00 1.06 0.71 0.59 0.36
CH2 85 13 6.50 4.50 1.00 1.07 0.94 0.91 0.75 0.67
CH3 85 13 6.50 4.50 1.00 0.87 0.76 0.74 0.65 0.64
CH4 85 13 6.50 4.40 1.00 0.89 0.95 0.98 0.92 —
CH5 85 92 6.50 3.28 1.00 0.51 0.82 0.69 0.54 0.49
CH6 85 92 10.00 7.60 1.00 2.25 1.57 1.05 — —
CH7 95 13 10.00 1.50 1.00 0.85 0.83 0.78 0.65 0.62
CH8 95 92 10.00 2.40 1.00 0.95 0.95 0.90 0.84 0.72
Design of Pressure Pipes 233
R
R
R
R
P
n
P
n
P
n
Figure 4.22 Rerounding coefficient from test data—poor haunch condition.
R
R
R
R
P
n
P
n
P
n
Figure 4.21 Rerounding coefficient from test data—poor haunch condition.
234 Chapter Four
R
R
R
R
P
n
P
n
P
n
Figure 4.24 Rerounding coefficient from test data—complete haunch condition.
R
R
R
R
P
n
P
n
P
n
Figure 4.23 Rerounding coefficient from test data—poor haunch condition.
Design of Pressure Pipes 235
R
R
R
R
P
n
P
n
1
P
n
Figure 4.25 Rerounding coefficient from test data on both ductile iron and FRP
pipes.
3. Rerounding is generally insensitive to soil type, compaction, or pipe
stiffness, as shown by all data sets.
4. Rerounding increases steadily, as an approximately linear function
of internal pressure, as shown by all data sets. The rerounding fac-
tor R may be conservatively approximated as
R 1 (4.21)
where P
n
internal pressure, lb/in
2
(0 < P
n
< 435).
5. The rerounding coefficients reduce somewhat with time, as seen
from the Carlstrom data.
7
Discussion. A combined loading analysis is outlined in App. A of
AWWA C950-81. Two methods are given for calculating the combined
stresses and strains. One method has been attributed to Spangler and
the other to Molin. Both equations are to be used, and the lowest
value is the resulting combined stress and/or strain. This lowest value
must not exceed the long-term bending strength of the product
reduced by a design factor. The method permits the rerounding of a
deflected pipe due to internal pressure to be considered when com-
puting the total combined strain in the pipe. The combined strain is
P
n
435
236
TABLE 4.12 Rerounding Coefficient
Pipe Cover Pressure, lb/in
2
stiffness, depth, 50 100 200 300 400
Ref. /DD lb/in
2
Pipe mat. Backfill ft Rerounding coefficient R Remarks
8 3.17 48 30.5 FRP Loose 12.8 1.04 0.98 0.47 0.25
dry sand 0.90 0.89 0.45 0.16
19 2.0 36 247.0 Ductile Native 8.0 0.87 0.67 0.44 0.29 0.18 1961
iron soil 0.96 0.90 0.60 0.38 0.23 1963
90%
Proctor
7 2.2 35 97.3 FRP Native 6.6 R 0.43 @ 350 lb/in
2
(initial)
soil 11.5 R 0.39 @ 350 lb/in
2
(2 weeks)
taken as the lesser value computed using Eqs. (4.23) and (4.24) by
Molin and Spangler.
6
(4.23)
(4.24)
Figure 4.26 shows a typical plot of the AWWA C950-81 combined
strains versus internal pressure. Research indicate that this procedure
is conservative. The dashed line is typical pipe behavior as observed in
all data sets from actual tests. The correlation between test data and
the AWWA C950 method is generally acceptable. However, at low to
intermediate pressure, particularly in the region where the Spangler
and Molin curves cross, there is some discrepancy.
Also shown on Fig. 4.26 (dashed line) is typical pipe behavior as
observed in all data sets. There is generally good correlation between
the AWWA C950-81 method and the observed pipe behavior except at
the lower pressures and particularly in the region where the Spangler
and Molin curves intersect.
3K
b
WDt
3K
x
PD
3
Et
3
PD
2tE
y
D
t
D
PD
2tE
Design of Pressure Pipes 237
Figure 4.26 Typical plot for combined strains.
Conclusions
1. Rerounding is influenced mostly by internal pressure and possibly
to some extent by time.
2. It has been shown that rerounding is generally insensitive to soil
density, burial depth, pipe stiffness, and pipe material.
3. Maximum combined strains occur when starting deflections are
highest.
4. Rerounding generally increases linearly with increasing internal
pressure and may be represented by the rerounding factor R com-
puted as follows:
R 1 (4.25)
It was found that rerounding is primarily a function of pressure,
and a rerounding relationship is proposed which accounts for the
reduction of bending strain as pressure increases. It was also found
that the highest allowable deflection for a pipe determines the cal-
culated behavior since the residual bending strain for an initial
highly deflected pipe is more than the residual strain for a low initial
deflected pipe.
Recommendation. Combined strain should be calculated as follows:
C
RD
f
(4.26)
where
C
combined strain
D
f
shape factor, range 3 to 8 (3 for uniform compaction and a
pipe stiffness greater than 40 lb/in
2
, 6 for poor haunch or
nonuniform compaction, 8 for nonuniform compaction and
pipe stiffness less than 15 lb/in
2
)
R rerounding factor 1 P
n
/435
P internal pressure
t wall thickness
E Young’s modulus
D pipe diameter
y vertical pipe deflection
P
n
internal pressure, lb/in
2
(0 P
n
435)
Thrust restraint
Unbalanced hydrostatic and hydrodynamic forces in piping systems
are called thrust forces. In the range of pressures and fluid velocities
found in waterworks or wastewater piping, the hydrodynamic thrust
y
D
t
D
PD
2tE
P
n
435
238 Chapter Four