PPI TN-19-2010 Pipe Stiffness (PS) Ring Stiffness Constant (RSC) and Flexibility Factor (FF) for Buried Gravity Flow Pipes.pdf

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1、 105 Decker Court, Suite 825, Irving TX 75062 P: 469-499-1044 F: 469-499-1063 www.plasticpipe.org Pipe Stiffness (PS), Ring Stiffness Constant (RSC) and Flexibility Factor (FF) for Buried Gravity Flow Pipes TN-19/2010 105 Decker Court, Suite 825, Irving TX 75062 P: 469-499-1044 F: 469-499-1063 www.p

2、lasticpipe.org Foreword This report was developed and published with the technical help and financial support of the members of the PPI (Plastics Pipe Institute, Inc). The members have shown their interest in quality products by assisting independent standards-making and user organizations in the de

3、velopment of standards, and also by developing reports on an industry-wide basis to help engineers, code officials, specifying groups, and users. The purpose of this technical note is to provide general information on resistance to ring bending for buried, gravity flow pipes. This report has been pr

4、epared by PPI as a service of the industry. The information in this report is offered in good faith and believed to be accurate at the time of its preparation, but is offered without any warranty, expressed or implied, including WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. Any

5、 reference to or testing of a particular proprietary product should not be construed as an endorsement by PPI, which does not endorse the proprietary products or processes of any manufacturer. The information in this report is offered for consideration by industry members in fulfilling their own com

6、pliance responsibilities. PPI assumes no responsibility for compliance with applicable laws and regulations. PPI intends to revise this report from time to time, in response to comments and suggestions from users of the report. Please send suggestions of improvements to the address below. Informatio

7、n on other publications can be obtained by contacting PPI directly or visiting the web site. The Plastics Pipe Institute 469-499-1044 http:/www.plasticpipe.org August 20103 PIPE STIFFNESS CHARACTERISTICS FOR BURIED GRAVITY FLOW PIPES Various measures have been used to characterize a pipes resistance

8、 to ring (hoop) deflection. In the U.S., these measures include: Flexibility Factor (FF) as defined in AASHTO Bridge Design Specification Section 18, Pipe Stiffness (PS) as defined in ASTM D2412, and Ring Stiffness Constant (RSC) as defined in ASTM F894. These measures characterize the pipes resista

9、nce to ring deflection when subjected to a short-term parallel plate load. The purpose of PPI Technical Note-19 is to advise on the applicability of these measures for comparing and classifying plastic pipes. The first commonly used measure for pipe deflection resistance was “pipe stiffness” (PS). D

10、esigners found it easy to assign a minimum PS value in their specifications for plastic pipes. However, for larger diameter pipes, the validity of PS as a product specification requirement has been questioned because: (1) It was discovered that given the same handling and installation forces larger

11、diameter pipes require much lower “pipe stiffness” for proper installation than do smaller diameter pipes. (2) It was found that there was a trade-off between pipe material strain capacity and “pipe stiffness”. Pipes made from strain-limited plastics such as glass-reinforced thermoset resin required

12、 greater stiffness to resist localized deflections than that required for pipes made from thermoplastic materials having high strain capacity. 4 HANDLING AND INSTALLATION Pipe intended for buried applications must have sufficient resistance to deflection from shipping, handling, and storage loads as

13、 well as loads applied during installation. The most significant of these loads is the force exerted on the pipe during mechanical compaction of the soil. This force can cause the pipe to undergo deformations that are exacerbated by soil loads during the subsequent placement of backfill. The force e

14、xerted on the pipe during backfill compaction can be treated as a backfill compaction load that is primarily a function of the compaction method and soil type, but is relatively independent of the pipes diameter. When pipes of equal PS but different diameters are subject to equal backfill compaction

15、 loads, the deflection response in percent is a function of its diameter. For a given backfill compaction load, the deflection of a pipe can be calculated from the PS equation: 320 mD.149EI= YF= PS (1) PSF= Y (2) Where: PS = Pipe Stiffness (lbs/in2) F = Load (lbs/lineal-in) Y = Pipe Deflection (in)

16、E = Pipe Material Modulus of Elasticity (lbs/in2) I = Pipe wall Cross-Section Moment of Inertia (in4/in) Dm= Pipe Mean Diameter (in) By definition, pipes of various diameters that experience the same parallel plate load (e.g. 50 lbs / lineal-in) and experience the same absolute deflection (e.g., 1in

17、ch) have a PS of 50 psi. However, when deflection is calculated as a percentage of the initial diameter, a 1inch deflection in a small pipe is a significantly larger percentage deflection than the same 1inch deflection in a larger pipe (for 12 inch pipe, 1inch deflection equals 8.3 %; for 60 inch pi

18、pe, 1inch deflection equals 1.7%). Since control of deflection as a percent of pipe diameter is a common evaluation criterion, the conclusion can be drawn that PS is not a particularly useful measure for classifying pipes of different diameters with regard to installation forces. 5 The above discuss

19、ion leads to the conclusion that any workable minimum requirement for resistance to ring - deflection has to be diameter weighted. This can be accomplished by “weighting“ the PS equation by multiplying both sides of Eq. 1 by the mean diameter of the pipe. When terms are rearranged, the result is Eq.

20、 3. ( )20mmD.1498EI= DYF(3) If the load in Eq. 3 is expressed in lbs/ lineal-ft instead of lbs/ lineal-in and if deflection is expressed in percent, Eq. 3 becomes the mathematical expression for “ring stiffness constant”, RSC: ( )2mmD6.44EI= )10012(DYF= RSC(4) Where: RSC = Ring Stiffness Constant. W

21、hen pipes of different diameter but equal RSC are subjected to the same parallel plate loads, an equivalent percent deflection results. The AASHTO flexibility factor, FF, is simply the inverse of RSC multiplied by a constant. Therefore, FF and RSC produce equal deflection responses and can be used t

22、o classify pipes for handling and installation capacity. What minimum value of RSC is necessary to provide sufficient resistance to handling and installation forces? ASTM F 894 for example anticipates up to 3 percent out-of-roundness for pipe prior to earthloading. Therefore, the pipe should be able

23、 to withstand normal handling and installation loads, such as the force transmitted to the pipe due to machine compaction of the embedment, without exceeding 3 percent out-of-roundness. (This is not to be confused with the deflection limit applied to deflections due to backfill and live loads.) Fiel

24、d measurements reported by Petroff 1 show that RSC 40 HDPE pipes possess sufficient stiffness to resist normal handling and installation loads and remain round within 3 percent when installed in accordance with ASTM D 2321. It should be noted that the ASTM test methods for RSC and PS differ. RSC tes

25、ts are conducted at 2 in/min load rate versus 0.5 in/min for PS, and RSC is measured at 3 percent deflection where PS is measured at 5 percent. Therefore, when the expression in Eq. 4 is used to convert from RSC to PS, the F/Y value in Eq. 4 should be multiplied by an empirical factor that varies fo

26、r the material. For HDPE, the empirical factor is about 0.8. 6 In summary, as pipe diameter increases, less resistance to ring bending is required for the same handling and installation capacity. Useful measures that compare handling and installation capacity without regard to pipe size include AASH

27、TO flexibility factor, FF, and ring stiffness constant, RSC. Pipe stiffness, PS, however, is sensitive to pipe size, and is not useful for comparing the handling and installation capacities between larger and smaller pipes. STRAIN CAPACITY When subjected to earth loads, strain in the pipe wall resul

28、ts from deflection and ring compression. If the pipe material has a low tolerance for strain, it is usually necessary to limit strain by limiting pipe deformation. There are two levels of deformation in buried pipe. One is elliptical deflection due to uniform earth load; the other is a second order

29、deformation from uneven loads around the pipe circumference such as point loads that cause localized deviation from an elliptical shape. Second order deformations are generally small but may induce high strains, and they are directly proportional to the pipes stiffness. Second-order deformations are

30、 of little consequence with strain-tolerant pipes such as HDPE because of the high strain capacity. In an eight-year study of pipes made using pressure-rated HDPE material, Janson reports that for practical design purposes such as for gravity sewers, there does not appear to be an upper limit on des

31、ign strain 2. This essentially means that a design for pipes made from pressure-rated grades of HDPE does not need to address strains from second order deformations when overall deflection and buckling are controlled. BURIED PIPE PERFORMANCE Buried pipe must possess sufficient stiffness to mobilize

32、backfill soil resistance and resist buckling. Deflection must be limited to a value that will not disrupt flow or cause joint leakage. Extensive field experience with high DR stress-rated HDPE pipes and stress-rated HDPE, profile wall pipes speaks to the capability of low stiffness pipes to perform

33、under soil loads. Flexible pipe deflection depends on the combined contribution of its pipe stiffness and the embedment soil stiffness (E), but primarily on embedment soil stiffness. Considerable testing and field measurements have established that for low stiffness pipes, deflection is almost exclu

34、sively controlled by the embedment soil surrounding the pipe. This is true for any flexible pipe, whether metal or plastic. Spanglers Iowa formula can be used to demonstrate that the soils contribution to resisting deflection is much more significant than the pipes contribution. Although Spanglers I

35、owa formula was developed using pipes of 25-psi stiffness and higher, considerable field experience has demonstrated its applicability to low stiffness pipes 3. For example when pipes of 46 psi PS and 4.6 psi PS are installed with a properly selected and compacted embedment, there is little differen

36、ce in either pipes deflection. On the other hand, when pipe is not installed properly, a low embedment soil E can result in excessive deflection for both 46 psi and 4.6 psi pipes It can be shown mathematically that a 46 psi pipe supplies a stiffness to the soil/pipe system 7 equivalent to a soil wit

37、h an E of 112 psi, which offers little resistance to deflection. Therefore, embedment soil placement (installation quality), not pipe stiffness controls deflection. The principle of soil embedment controlling deflection has been illustrated over and over again in field tests and numerous soil box de

38、monstrations. Publications by Chua and Lytton 4, Watkins et al 5, Gaube and Muller 6, Taprogge 7, Janson and Molin 8, Selig 9, and Gabriel 10 all speak to the fact that the pipes stiffness makes only a minimal contribution to deflection resistance. 8 References: 1 Petroff, L.J. (1985). “Stiffness Re

39、quirements of HDPE, Profile Wall Pipe“, Proc. Int. Conf. on Advances in Underground Pipeline Engineering, ASCE, Madison, WI. 2 Janson, L.E. (1991). “Long-Term Studies of PVC and PE Pipes Subjected to Forced Constant Deflection“, Report No. 3. KP-Council, Stockholm, Sweden. 3 Chua, K.M. and Petroff,

40、L.J. (1988). “Predicting Performance of Large Diameter Buried Flexible Pipe”, Proc. Second Int. Conf. on Case Histories in Geotechnical Engineering, St. Louis. 4 Chua, K. M. and Lytton, R. L. (1987). “A New Method of Time-Dependent Analysis for Interaction of Soil and Large-Diameter Flexible Pipe.“

41、66th Annual Mtg., Transp. Res. Board, Washington, D.C. 5 Watkins, R.K., Szpak, E., and Allman, W.B. (1974). “Structural Design of PE Pipes Subjected to External Loads“, Engr. Experiment Station, Utah State Univ., Logan. 6 Gaube, E. and Muller, W. (1982). “Measurement of the long-term deformation of

42、HDPE pipes laid underground“, Kunstoffe, Vol. 72, July, pp. 420-423. 7 Taprogge, R.H. (1981). “Large Diameter Polyethylene Profile-wall Pipes in Sewer Applications“ Proc. Int. Conf. on Underground Plastic Pipe, ASCE, New Orleans. 8 Janson, L.E. and Molin, J. (1981). “Design and Installation of Under

43、ground Plastic Sewer Pipe“, Proc. Int. Conf. on Underground Plastic Pipe, ASCE, New Orleans. 9 Selig, E. T. (1990). “Flexible Pipe Design-Accomplishments and Challenges“, Conference on Flexible Pipes, Columbus, Ohio. 10 Gabriel, L.H. (1990). “Keynote address: Pipe Deflection-A Redeemable Asset“, Con

44、ference on Flexible Pipes, Columbus, Ohio. 9 APPENDIX APPROXIMATE PIPE STIFFNESS (PS) FOR SOLID-WALL HDPE DR PIPE It is occasionally convenient to know PS values for solid-wall OD-controlled HDPE pipes made to common dimension ratios (DRs). The table below was developed using Eq. 1, and assumes pipe

45、 having average outside diameter, minimum wall thickness, and made using HDPE material having 110,000 psi short-term modulus of elasticity. For the same material, pipes having the same DR have the same PS regardless of diameter. DR 7 7.3 9 11 13.5 15.5 17 21 26 32.5 PS, psi 2278.6 1968.3 961.3 492.2 252 161.4 120.2 61.5 31.5 15.7