Moser A.P., Folkman S. Buried Pipe Design
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Plastic Flexible Pipe Products 419
t wall thickness
hydrostatic design stress
This equation can be rewritten as follows:
2
P(DR 1) (7.6)
where
DR
Equation (7.6) may be solved for DR in terms of the hydrostatic
design stress and pressure.
DR 1 (7.7)
Example 7.6—A 10-in PVC pressure pipe A 10-in PVC pipe is to be used for a
transmission pipe in a rural water system. The static pressure will not exceed
150 lb/in
2
. The pipe will be buried in a sandy clay soil with depths between 4
and 5 ft. Select the dimension ratio (DR OD/t), and design the installation
so that the vertical deflection does not exceed 5 percent.
1. The working pressure is 150 lb/in
2
—no surge pressure needs to be added
unless the engineer is aware of surge conditions.
2. Assume the material is PVC 12454B with a hydrostatic design basis
(HDB) of 4000 lb/in
2
. A safety factor of 2 is required, resulting in a hydro-
static design stress of 2000 lb/in
2
(see Chap. 4).
3. Use Eq. (7.7) to determine the dimension ratio.
DR 1
1 27.7
Choose the next-thicker wall from Table 7.7. Use
DR 26 115 lb/in
2
4. Determine required pipe zone material to limit deflection to 5 percent.
Data in Table 3.9 indicate that even for loose soil with 5 ft of cover, the
maximum deflection will not exceed the 5 percent limit imposed. This
table is for pipe with a stiffness of 46 lb/in
2
. For the pipe in this example,
F
y
2(2000)
150
2
P
OD
t
2
P
D
t
420 Chapter Seven
the stiffness is 115 lb/in
2
, so it will deflect less. Therefore, no compaction
effort is required except for the purpose of limiting surface settlement.
The soil placed around the pipe should be free of large stones or frozen
lumps.
Example 7.7—A 10-in PVC pressure pipe Resolve Example 7.6 for an internal
pressure of 100 lb/in
2
instead of 150 lb/in
2
.
1. Total pressure is 100 lb/in
2
static plus zero surge pressure, so p 100
lb/in
2
.
2. Again, PVC 12454B with a hydrostatic design stress of 2000 lb/in
2
is
selected.
3. Use Eq. (7.2) to determine the dimension ratio.
DR 1
1 41
Therefore, select a PVC pipe where
DR 41
From Table 7.7,
Pipe stiffness PS 28 lb/in
2
4. Select pipe zone material and required compaction. Vertical ring deflec-
tion is to be less than 5 percent per Example 7.6. Use Spangler’s equa-
tion to determine the required E′ [see Eq. (7.4)].
E′
For this example,
H height of cover 5 ft
0.05
PS 28 lb/in
2
Thus,
E′ 68 lb/in
2
0.56(5)/0.05 28
0.41
F
y
vertical deflection
diameter
y
D
0.56 H/(y/D) PS
0.41
F
y
OD
t
2(2000)
100
2
P
OD
t
Data in Table 3.9 indicate that a dumped or slightly compacted soil will
meet the design criteria. Only uncompacted clays may not meet the spec-
ified conditions.
Examples 7.6 and 7.7 indicate that for PVC pressure pipes in
medium soil cover, the design of the pipe embedment system is not
critical. The primary embedment objective is to protect the pipe from
large objects, such as stones, frozen lumps, and objects which could
cause impact damage or penetrate the pipe wall.
Example 7.8—DR 41 PVC pipe The DR 41 PVC pipeline operating at 100 lb/in
2
selected in Example 7.7 is to cross a roadway with only 3 ft of cover. Are
there special design considerations for this road crossing if a maximum of 2
percent deflection is allowed to protect the road surface?
1. Determine the total load.
Total load W
T
prism load live load
(See Fig. 2.19 for H-20 highway loading.) From the graph, W
T
950 lb/ft
2
.
2. Use Spangler’s equation to calculate the required soil modulus E′ [see
Eq. (7.4)].
E′
In the above equation, H represents the height of cover. For this example,
the total load is due to not just soil load, but also live load. An effective
height H can be calculated as follows:
H 7.9 ft
Use
H 8 ft 0.02
From the previous example,
PS 28
Thus
E′ 478 lb/in
2
Table 3.4 indicates that a granular material compacted to at least 85 per-
cent standard Proctor density is required. A coarse-grained material with
slight compaction will also meet the E′ requirement. Experience has shown
0.56 (8.0)/0.02 28
0.41
F
y
y
D
950 lb/ft
2
120 lb/ft
3
W
T
120
0.56 H/(y/D) PS
0.41
Plastic Flexible Pipe Products 421
422 Chapter Seven
that for such installations, little or no movement can be tolerated, or else the
road surface will break up. Therefore, a coarse granular material with high
compaction is recommended.
Example 7.9a—A 12-in PVC pressure pipe A 12-in PVC distribution line is to be
installed 5 ft deep. The line is to operate at pressures up to 200 lb/in
2
. Select
the proper dimension ratio, and comment on the backfill requirements.
1. Calculate the design stress. Distribution line AWWA C900 applies.
HDB 4000 lb/in
2
AWWA safety factor 2.0
Hydrostatic design stress 2000 lb/in
2
2. Determine the design pressure.
P static pressure surge pressure
The engineer recommends the design include a 40 lb/in
2
surge pressure.
Thus,
P 200 40 240 lb/in
2
3. Calculate the dimension ratio. Use Eq. (7.2).
DR 1
1 17.67
Choose DR 14, which has a thicker wall than required, but it produces
a conservative design.
4. Comment on the backfill requirements. Table 7.7 indicates that DR 14 PVC
pipe has a pipe stiffness of 815 lb/in
2
. This pipe will not require special com-
paction or a select soil type when placed with only 5 ft of cover. Compaction
may be necessary to prevent road or surface settlement and to provide soil
friction and soil weight, to prevent the pipe from floating in saturated soils.
Design and construction for thrust restraint will be required at fittings such
as elbows and tees (see Chap. 4 for details).
Example 7.9b—Pressure surge design A water main in a municipal water sys-
tem with temperatures below 70°F operates with a maximum sustained
pressure of 85 lb/in
2
. Design engineers predict the maximum instantaneous
surge velocity input to be 2 ft/s. For a 12-in-diameter pipe, what dimension
ratio and corresponding pressure class are required?
1. Try DR 18. From AWWA C900, average dimensions are
OD 13.200 in
2(2000)
240
2
P
4000
2.0
HDB
SF
Plastic Flexible Pipe Products 423
Wall thickness t 0.733 in
ID OD 2t 11.734 in
2. Calculate the wave speed [see Chap. 4 and Eq. (4.9)].
a
1311 ft/s
3. Calculate the surge pressure P
s
[Eq. (4.7)].
P
s
(V) (0.43)
(2) (0.43) 35 lb/in
2
4. Total pressure equals working pressure plus surge pressure.
P 85 35 120 lb/in
2
5. Calculate the DR, using Eq. (4.5).
DR 1 where 2000 lb/in
2
1 34.3
Select the next available DR which is lower. Use DR 25 which is
AWWA C900 pressure class 165.
6. Check the design with actual dimensions. Use the equation in step 2 to
recalculate the wave velocity.
ID 12.144 in
t 0.528 in
Wave speed a 1106 ft/s
Use the equation in step 3 to recalculate surge pressure.
P
s
(2) (0.43) 29.5 lb/in
2
Actual surge pressure is lower than that used in the design calculations.
Therefore, the design is okay.
Example 7.10—A 6-in PVC force main An existing 6-in sewer force main is to
be replaced with a 6-in PVC pressure pipe. The line is known to operate with
1106
32.2
2(2000)
120
4000
2.5
HDB
SF
2
P
1311
32.2
a
g
4822
1 (3
13,00
0/400
,000)
(11.73
4/0.73
3)
4822
1(K
/E)(ID
/t
–
)
424 Chapter Seven
an average pressure of 140 lb/in
2
, a minimum pressure of 100 lb/in
2
, and
cyclic pressure peaks of 180 lb/in
2
. The average number of cycles in a 24-h
period is 200. The design life of the system is to be a minimum of 100 years. Use
a factor of safety of 2.0. Determine the required dimension ratio.
1. Determine the number of cycles in the 100-year life of the system.
C cycles during life (200 cycles/day) (365 days/yr) (100 yr)
7.3 10
6
cycles
2. Determine the pressure amplitude.
P
amp
40 lb/in
2
3. Solution is the trial-and-error type. Select a DR for the PVC pipe. Try DR
18. Use Eq. (4.4) to solve for stresses in terms of pressures.
S P
Calculate the mean or average stress.
mean
P (140) 1190 lb/in
2
Calculate the stress amplitude.
amp
P (40) 340 lb/in
2
4. Use the graph in Fig. 4.18 to determine the number of cycles to failure.
(see Example 4.2 on how to use Fig 4.18)
(cycles to failure) 1.05 10
7
Safety factor:
SF 1.44
The safety factor is less than 2. Select DR = 14 which is AWWA Class 305.
It is left to the reader to show that the life of DR 14 under these cyclic
conditions is more than 300 yr.
Example 7.11. Several years ago, a city in the southwestern part of the
United States experienced numerous breaks in DR-18 PVC pipe installed in
its water system. The majority of these breaks occurred in specific areas
(not randomly). The distribution of breaks would lead one to conclude that,
for these specific areas, either system operation is at fault or faulty pipe was
installed. The AWWA Standard in effect at the time of the pipe manufacture
and during most of the breaks was AWWA C900-89.
1.05 10
7
cycles
7.3 10
6
cycles
17
2
DR 1
2
17
2
DR 1
2
DR 1
2
180 100
2
P
max
P
min
2
Plastic Flexible Pipe Products 425
Is the pipe faulty?
Samples of failed pipe were subjected to acetone
immersion testing ASTM D 2152. If a sample or samples fail this test,
additional tests such as burst tests and/or impact tests may be consid-
ered. Extrusion quality tests (acetone immersion) were conducted on
samples (see Table 7.8). Three or four specimens were prepared from
each pipe sample. The specimens were tested as per ASTM D 2152. No
flaking or wall separation was noted on any of the test samples. These
tests show that the extrusion quality for the pipe in question is good. A
sample of this pipe was subjected to the heat reversion test according
to ASTM F 1057. This sample passed this test without any wall sepa-
ration, distortion, or blistering—again indicating good quality pipe.
Heat reversion technique (as taken from ASTM F 1057). This practice is
applicable to distinguish between properly and improperly extruded
PVC plastic pipe. It can be used to (1) reveal incomplete exsiccation of
a compound before or during extrusion,
*
(2) determine presence of
stress in the pipe wall produced by the extrusion process,
†
(3) deter-
mine whether infused areas are present, and (4) reveal contamination.
The conclusion is that there is no indication of faulty pipe.
An investigation reveals the following system information:
■
There have been 19 failures over a 2-year period. This is not a high num-
ber considering that there are more than 100 mi of PVC in the system.
■
The system is complex, with many changes in elevation and numer-
ous pressure-reducing valves (PRVs), some of which are redundant.
Also, there are deep wells, pumping stations, and reservoirs. Parts of
the system are operating out of control in terms of cyclic pressures.
Operating pressures range from about 70 to 180 lb/in
2
with occa-
sional spikes to 190 lb/in
2
. However, most of the system is operating
in the 70 to 130 lb/in
2
range. A pressure range of 50 lb/in
2
is common
in the areas where failures are occurring. The cyclic rate is about
3 cycles/min.
■
In many places in the system, water temperatures were found to be
above 73.4°F. It was determined that in some of the failure zones the
pipe wall temperatures were as high as 96°F.
*Residual moisture in the compound vaporizes at extrusion temperatures and is nor-
mally evacuated as it forms vapor. Pockets of moisture trapped in the pipe wall result
from incomplete exsiccation of the compound, and may reduce the physical properties of
the pipe.
†Minor residual stress in the pipe wall will not impair field performance and han-
dleability. High residual stress has no proven effect on performance, but may impair
handleability during installation.
No statement is made about either the precision or bias of Practice F 1057 for esti-
mating the quality of PVC pipe, since the results merely state whether there is confor-
mance to the criteria for acceptability suggested by the interpretation.
This test is not required by any standards for PVC pipe whereas the acetone immer-
sion test is required by both AWWA C900 and ASTM D 2241.
426 Chapter Seven
■
Examination of failures and failed samples revealed the following:
No sample exhibited a failure due to long-term sustained pressure.
In such a failure, there is some ductile deformation associated with
the failure. The failure is usually catastrophic in nature (does not
start with a short crack that later propagates).
■
Inspection of actual breaks shows that all were breaks that took
place with virtually no ductile yielding. The inspected breaks were
all brittle, which is typical for fatigue failures and failures produced
by impact or induced by high stress intensity. An example of high-
stress-intensity crack propagation is a failure induced by tapping
when the pipe is under pressure. In this case, the crack moves very
rapidly and does so with little deformation. One of the samples
inspected had failed due to tapping. The failure was brittle in
appearance and very similar to other failures. All the samples
inspected exhibited a brittle-type failure typical of a fatigue break.
Failures due to fatigue will usually start with a short crack and will
later propagate because of the high stress intensity associated with
the crack. If the short crack exists for a time before it propagates,
there will be erosion on the pipe wall due to leaking water under
pressure. Many of the samples exhibited erosion, which is a definite
indication of fatigue failure.
The preliminary conclusion is that the pipe probably failed because of
fatigue. Will calculations concerning temperature and fatigue support
this conclusion? Or did the pipe fail because of high temperature only?
TABLE 7.8 Extrusion Quality Tests on PVC Pipe Samples
Sample identification
number Description Manufacturer Other Results
1 A VHH G21D Passed
2 12-in white A Possible megalug Passed
3 12-in white B Bell & Spigot Passed
4 8-in white A M15C4 Passed
5 12-in blue C Passed
6 8-in white A Passed
7 12-in blue C No crack Passed
8 12-in white B VHH G21D Passed
9 12-in blue C No crack Passed
10 12-in white B Passed
11 12-in white B Passed
12 12-in white B Passed
33 8-in blue C Passed
SH 8-in blue C Passed
HV I 12-in blue C Passed
HV II 12-in blue C Passed
Special sample* 12-in blue From yard Passed
*This sample was heat reversion tested.
Plastic Flexible Pipe Products 427
Check design. The design basis for AWWA C900-89 pipe includes a
safety factor of 2.5 and an allowance for occasional surges. The design
basis equation in C900 can be expressed in the following way:
2.5 (PC P
s
) (HDB) (7.8)
where 2.5 safety factor
PC pressure class (100, 150, or 200 lb/in
2
)
P
s
surge allowance, lb/in
2
, for instantaneous stoppage of
flow of 2 ft/s
t minimum wall thickness, in
D outside diameter, (inches)
HDB hydrostatic design basis 4000 lb/in
2
The actual surge allowances, in AWWA C900-89, are the increases in
pressure that result from stoppage of flow of 2 ft/s and are as follows:
Class 100, DR 25 30 lb/in
2
Class 150, DR 18 35 lb/in
2
Class 200, DR 14 40 lb/in
2
Another design parameter included in AWWA C900-89 is the effect of
sustained elevated temperatures on pressure and/or design stress. For
sustained temperature of the pipe wall above 73°F, the design stress
should be reduced. This reduction is not necessary for short-term excur-
sions of elevated temperatures, but is necessary for continuous service
at a higher temperature. The recommended percentages of allowable
pressure class for various elevated temperatures are as shown [Table 4.6
is repeated for the reader’s convenience (see Table 7.9)].
Derating a PVC pipe due to operating temperature. Temperatures were
determined to be as high as 96°F. For calculation purposes, use 100°F.
For a class 150 pipe operating at 100°F, the pipe should be derated to
62 percent of its class. Thus, the 150 lb/in
2
pipe will be effectively a 93
lb/in
2
pipe, which would then be like a DR 29 pipe operating at a tem-
perature of 73°F or below. Therefore, a DR 18 PVC pipe operating at
100°F can be analyzed as if it were a DR 29 PVC pipe operating at nor-
mal water temperatures (equal to or less than 73.4°F).
Safety factors: The design equation is
P
t
P
w
P
s
(7.9)
Solve for the factor of safety F:
F (7.10)
HDB
DR 1
2
P
w
P
s
HDB
F
2
DR 1
2t
D t
428 Chapter Seven
TABLE 7.9 Temperature Derating Factors
Percentage of allowable
Maximum continuous* pressure class or design
service temperature, °F stress at 73°F
73 100
80 88
90 75
100 62
110 50
120 40
130 30
140 22
*Note from Uni-Bell Handbook: The derating factors
assume sustained elevated service temperatures. When
the contents of a buried PVC pressure pipe are only inter-
mittently and temporarily raised above the service tem-
perature shown, a further reduction may not be needed.
where P
w
working pressure (average steady state pressure at a
given location in system)
P
s
surge pressure (occasional pressure wave due to start-
ing and stopping of pumps and closure and opening of
valves, sometimes called water hammer)
P
t
P
s
P
w
total pressure
DR dimension ratio (thickness divided by outside diameter)
HDB hydrostatic design basis (4000 Psi for AWWA C-900),
(4200 psi for ASTM D2241)
F factor of safety
The AWWA C900-89 standard is more conservative than the ASTM
D 2241 standard, for the following three reasons:
1. The AWWA standard recommends that the surge pressure be
included before applying the factor of safety. The ASTM standard
does not directly address surge pressure.
2. The AWWA standard uses a factor of safety of 2.5 whereas the
ASTM standard uses a factor of safety of 2.0.
3. The AWWA standard uses an HDB of 4000 lb/in
2
whereas the
ASTM standard uses an HDB of 4200 lb/in
2
.
The safety factor values listed in Table 7.10 were calculated using
Eq. (7.10) and temperature derating factors as given in Table 4.6 and
Table 7.9 and in AWWA C900-89. The tables show factor of safety as
a function of both temperature and pressure. They are based on a
system that has occasional surge pressures but without continuous
cyclic pressures.