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Strength design of underground GRP pipes for unpressurized applications
Strength design of underground G RP pipes for unpressurized applications BORGE INGMAR CARLSTROM* and KA RL-AXEL RUMBERG* Formulae have been established for the calculation of buckling pressure and strains of underground flexible pipes. Test methods have been worked out for the determination of those long-term properties, which are needed for the design calculations, For minimum wall thickness the buckling pressure and its relation to the pipe creep modulus is critical. For the amount of circumferential deflection which can be tolerated for the pipe in the ground the allowed strain is critical. The behaviour in the ground of a flexible pipe, such as a plastics pipe, is different from that of a rigid one made of concrete or clay, for example. A flexible pipe in the ground is deflected circumferentially by several percent and the stresses in the pipe are mainly compressive stresses. If the pipe has a very high deflection there can also be considerable bending stresses. Failure of the pipe will occur when the compressive stresses are too high with regard to the stiffness properties of the pipe wall - the pipe will fail due to buckling. Failure can also occur when the vertical deflection of the pipe is so great that it causes bending rupture. RPM-pipes (reinforced plastics mortar pipes), like other flexible pipes, must be designed so that they will withstand certain deflections without failure when buried in the ground at various depths. This means that certain mechanical propery criteria must be complied with. This report will give some information about how the Swedish RPM pipe FSP-69 - a glass fibre reinforced pipe with sand-filled polyester - has been tested and designed with regard to those long-term properties which are related to its performance in the ground.
BUCKLING RESISTANCE The buckling pressure for a flexible pipe in the ground is calculated according to Molinl :
Pk = 2.3 [E}E c (s/D) 3 ] y'-
(1)
where
Pk = the critical pressure in N/m 2 at which the pipe will buckle due to the external pressure from the surrounding soil E t' = the tangential soil modulus in N/m 2 E c = the creep modulus of the pipe in N/m 2 s = wall thickness in metres D = average pipe diameter in metres As we can see from equation (1) the pipe properties which influence the buckling pressure are the creep modulus,
* Hoganas AB, 263 00, H6ganas, Sweden
68
the wall thickness and the pipe diameter; it is the pipe stiffness
Eel/D3 (N/m 2) The creep modulus is the modulus value after subjecting the sample to stress for a given time. In order to design a flexible pipe safely against buckling it is necessary to know the creep modulus of the pipe for as long periods of time as 5 0 - 1 0 0 years. This creep modulus must relate to conditions in the ground, therefore the pipe must be completely saturated with water. Creep modulus of FSP-69 pipes with an inside diameter of 40 cm have been determined on 12 cm wide test rings, which have been saturated with water by soaking for 1000 hours at 50°C in water containing 0"1% di-2ethylhexylsodiumsulphosuccinate. Creep tests have been made in water at 20°C, 50°C and 75°C after the soaking. In Fig 1 the test results of the creep studies are shown. As can be seen, the measurements indicate straight lines even at so high a temperature as 75°C. With regard to this it might be allowed to extrapolate the room temperature curve to at least 50 years, which will give a creep modulus of about 8000 MN/m 2. In calculating the wall thickness a value of 7350 MN/m 2 is used. A safety factor of two is used for the buckling pressure and a value of 1 MN/m 2 is used for E l . This means another safety factor of x/2 if the soil compaction is minimum 85% modified proctor and the soil consists of granular material. For FSP-69 pipes this gives a minimum value ofs/D = 0"009 at a backfill height of 4 m.
Original deflection =5°/o
c~-~,,.~.,~¢ars ..... 75oc "150°C 20°C
.~...__Z=~= =.-..-=_ --.-1
O
I t IO "t
~ I
I
IO
I
I
IO2 IO3 Days
J] IO 4'
I,
IO5
IO6
F1G 1 Test results o f creep studies on FSP-69 reinforced plastics mortar pipe
COMPOSITES. MARCH 1973
DEFL ECTION PROPER TIES
x~ O .=O
The vertical deflection of a flexible pipe in the ground is calculated according to a modified Spangier formula 1,2 :
6v -
s =
--
D
0"083 X
.
e;
.
.
.
~o
(2)
.
s;+0-122
M I
I
I0 "t
I
i
]
I0
where 6v D q Es
= = = =
Sf
= the stiffness factor = 3
E s
= pipe modulus in N/m 2 = wall thickness in metres
. ~-
Es
0.036) s 3 + . . . . .
~2~
sf
9
(4)
D
s 6v D D
(5)
The pipe cannot be considered as flexible i f S f is higher than 0.012. Therefore, the strain has its maximum at this value, which corresponds to a critical wall thickness
s( )lj3 =
O-OlS
D
....
(6)
Ec
where
From equations (5) and (6) the relationship between deflection after 50 years and the pipe properties and soil conditions can be obtained: ............ D
6(0"0
eallowed ] 8
r~-
(7)
J~s/~'c) 3
where eallowe d = allowed flexural strain of the pipe after 50 years In order to specify which deflection the pipe can withstand and to give instructions on how to install the pipe so that this specified deflection will not be exceeded, it is necessary to know which strain can be allowed in the pipe for 50 years' use, This has been determined for FSP-69 pipes by so called relaxation tests. Pipe rings 12 cm wide have been saturated with water in the same way as for the creep tests. The wet rings have been deflected and the strain measured with strain guages at different deflections. Then
COMPOSITES. MARCH 1973
106
3
Y'
II
4
, I 075 °Io
[
I
I
IO -t
I
IO
I
IO 2
I
IO 3
I
IO4
I
IO5
io 6
Hours
FIG 3 Relaxation test on 12 cm wide pipe rings showing log(strain) plotted against log{ time) rings have been kept at constants deflections in a water bath. The load needed to keep the rings deformed to these different degrees of deflection has been measured and recorded as in Fig 2. After some time a sudden decrease in load can be noted in the load -time curve as can be seen in Fig 2. This corresponds to a failure of the pipe or to a rupture in some of the reinforcement fibres in the wall. The rings 4 and 5 show after about 104 hours an abrupt decrease in load of about 10% but no failure in the pipe can be observed. Some reinforcement close to the surface has probably failed. The strain and the time at failure or sudden loaddecrease is plotted in a l o g - l o g diagram as shown in Fig 3. A straight line can be drawn to connect the points. The line is extrapolated to 50 years and at this time coordinate a value of allowed strain = 0"75% is read. This value is valid for pipes under constant deflection and not for pipes with internal pressure. For pipes with internal pressure the necessary safety factor can be estimated from the following formula
E c = creep modulus o f the pipe after 50 years in N/m 2
6v
2
5
i f S f is lower than 0-012 the value o f 0"012 is used in eqtiation (4), which then will be c=6
J
•
6u
I
IOs
_,o|
The deflection causes a bending stress in the pipe. If the deflection is constant the stress decreases due to relaxation. If the deflection increases the stress may increase depending on what is greatest, deflection rate or relaxation rate. For design purposes it is simpler to calculate with strain than with stress. The strain is calculated accordlug to a Molin Spangler formula modified by the authors:
e=
l
104
FIG 2 Relaxation test on 12 cm wide pipe rings showing log(load) plo tted against log(time) 5 0 eors
the vertical deflection in metres pipe diameter in metres soil pressure in N/m 2 the secant soil modulus in N/m 2 ---
J
10`9. 103 Hours
Oflex eallowe d . . . . nE c where Ofle x = ultimate flexural strength of the pipe n = minimum safety factor Actual figures in this test give a minimum safety factor of about four. Reducing the value of eallowe d to 0"5 in order to add an extra safety factor of 1-5 gives a value o f 6 v / D = 0'075 for 50 years using equation (7). With a time lag factor of 1'5 this means an allowed initial deflection of 5% when burying the pipe. For a backfill height of 4 m this means that a packing of 85% modified proctor should be specified for granular materials.
REFERENCES Molin, Svenska Vatten och A vloppsverkens Forening. Publication No 16 2 Spangler, M. G. Btdletin No 153, Iowa Eng Experiment Station, Ames 1941 l
69
BUCKLING RESISTANCE The buckling pressure for a flexible pipe in the ground is calculated according to Molinl :
Pk = 2.3 [E}E c (s/D) 3 ] y'-
(1)
where
Pk = the critical pressure in N/m 2 at which the pipe will buckle due to the external pressure from the surrounding soil E t' = the tangential soil modulus in N/m 2 E c = the creep modulus of the pipe in N/m 2 s = wall thickness in metres D = average pipe diameter in metres As we can see from equation (1) the pipe properties which influence the buckling pressure are the creep modulus,
* Hoganas AB, 263 00, H6ganas, Sweden
68
the wall thickness and the pipe diameter; it is the pipe stiffness
Eel/D3 (N/m 2) The creep modulus is the modulus value after subjecting the sample to stress for a given time. In order to design a flexible pipe safely against buckling it is necessary to know the creep modulus of the pipe for as long periods of time as 5 0 - 1 0 0 years. This creep modulus must relate to conditions in the ground, therefore the pipe must be completely saturated with water. Creep modulus of FSP-69 pipes with an inside diameter of 40 cm have been determined on 12 cm wide test rings, which have been saturated with water by soaking for 1000 hours at 50°C in water containing 0"1% di-2ethylhexylsodiumsulphosuccinate. Creep tests have been made in water at 20°C, 50°C and 75°C after the soaking. In Fig 1 the test results of the creep studies are shown. As can be seen, the measurements indicate straight lines even at so high a temperature as 75°C. With regard to this it might be allowed to extrapolate the room temperature curve to at least 50 years, which will give a creep modulus of about 8000 MN/m 2. In calculating the wall thickness a value of 7350 MN/m 2 is used. A safety factor of two is used for the buckling pressure and a value of 1 MN/m 2 is used for E l . This means another safety factor of x/2 if the soil compaction is minimum 85% modified proctor and the soil consists of granular material. For FSP-69 pipes this gives a minimum value ofs/D = 0"009 at a backfill height of 4 m.
Original deflection =5°/o
c~-~,,.~.,~¢ars ..... 75oc "150°C 20°C
.~...__Z=~= =.-..-=_ --.-1
O
I t IO "t
~ I
I
IO
I
I
IO2 IO3 Days
J] IO 4'
I,
IO5
IO6
F1G 1 Test results o f creep studies on FSP-69 reinforced plastics mortar pipe
COMPOSITES. MARCH 1973
DEFL ECTION PROPER TIES
x~ O .=O
The vertical deflection of a flexible pipe in the ground is calculated according to a modified Spangier formula 1,2 :
6v -
s =
--
D
0"083 X
.
e;
.
.
.
~o
(2)
.
s;+0-122
M I
I
I0 "t
I
i
]
I0
where 6v D q Es
= = = =
Sf
= the stiffness factor = 3
E s
= pipe modulus in N/m 2 = wall thickness in metres
. ~-
Es
0.036) s 3 + . . . . .
~2~
sf
9
(4)
D
s 6v D D
(5)
The pipe cannot be considered as flexible i f S f is higher than 0.012. Therefore, the strain has its maximum at this value, which corresponds to a critical wall thickness
s( )lj3 =
O-OlS
D
....
(6)
Ec
where
From equations (5) and (6) the relationship between deflection after 50 years and the pipe properties and soil conditions can be obtained: ............ D
6(0"0
eallowed ] 8
r~-
(7)
J~s/~'c) 3
where eallowe d = allowed flexural strain of the pipe after 50 years In order to specify which deflection the pipe can withstand and to give instructions on how to install the pipe so that this specified deflection will not be exceeded, it is necessary to know which strain can be allowed in the pipe for 50 years' use, This has been determined for FSP-69 pipes by so called relaxation tests. Pipe rings 12 cm wide have been saturated with water in the same way as for the creep tests. The wet rings have been deflected and the strain measured with strain guages at different deflections. Then
COMPOSITES. MARCH 1973
106
3
Y'
II
4
, I 075 °Io
[
I
I
IO -t
I
IO
I
IO 2
I
IO 3
I
IO4
I
IO5
io 6
Hours
FIG 3 Relaxation test on 12 cm wide pipe rings showing log(strain) plotted against log{ time) rings have been kept at constants deflections in a water bath. The load needed to keep the rings deformed to these different degrees of deflection has been measured and recorded as in Fig 2. After some time a sudden decrease in load can be noted in the load -time curve as can be seen in Fig 2. This corresponds to a failure of the pipe or to a rupture in some of the reinforcement fibres in the wall. The rings 4 and 5 show after about 104 hours an abrupt decrease in load of about 10% but no failure in the pipe can be observed. Some reinforcement close to the surface has probably failed. The strain and the time at failure or sudden loaddecrease is plotted in a l o g - l o g diagram as shown in Fig 3. A straight line can be drawn to connect the points. The line is extrapolated to 50 years and at this time coordinate a value of allowed strain = 0"75% is read. This value is valid for pipes under constant deflection and not for pipes with internal pressure. For pipes with internal pressure the necessary safety factor can be estimated from the following formula
E c = creep modulus o f the pipe after 50 years in N/m 2
6v
2
5
i f S f is lower than 0-012 the value o f 0"012 is used in eqtiation (4), which then will be c=6
J
•
6u
I
IOs
_,o|
The deflection causes a bending stress in the pipe. If the deflection is constant the stress decreases due to relaxation. If the deflection increases the stress may increase depending on what is greatest, deflection rate or relaxation rate. For design purposes it is simpler to calculate with strain than with stress. The strain is calculated accordlug to a Molin Spangler formula modified by the authors:
e=
l
104
FIG 2 Relaxation test on 12 cm wide pipe rings showing log(load) plo tted against log(time) 5 0 eors
the vertical deflection in metres pipe diameter in metres soil pressure in N/m 2 the secant soil modulus in N/m 2 ---
J
10`9. 103 Hours
Oflex eallowe d . . . . nE c where Ofle x = ultimate flexural strength of the pipe n = minimum safety factor Actual figures in this test give a minimum safety factor of about four. Reducing the value of eallowe d to 0"5 in order to add an extra safety factor of 1-5 gives a value o f 6 v / D = 0'075 for 50 years using equation (7). With a time lag factor of 1'5 this means an allowed initial deflection of 5% when burying the pipe. For a backfill height of 4 m this means that a packing of 85% modified proctor should be specified for granular materials.
REFERENCES Molin, Svenska Vatten och A vloppsverkens Forening. Publication No 16 2 Spangler, M. G. Btdletin No 153, Iowa Eng Experiment Station, Ames 1941 l
69