1. Structural Design of Flexible Pipe

2. Pipe Info Pipe ID = 48 inches RCP – B-Wall OD = 58 inches = 4.83 ft.2
Pipe Info
Pipe ID = 48 inches
RCP – B-Wall OD = 58 inches = 4.83 ft.
HDPE – Manufacture = in. = 4.52 ft.

3. Soil Parameters What is the insitu soil?3
Soil Parameters
What is the insitu soil?
Firm silt
What is the embedment material?
Silt
90% proctor compaction
How wide is the trench?
Positive projecting embankment - NA
How deep is the installation?
8 feet

4. Plastic Pipe Design Considerations4
Plastic Pipe Design Considerations
Determine Installation Conditions
Determine the Overburden Pressure
Determine the Earth Load
Determine the Hoop Thrust
Determine the Pipe’s Capability
Hoop Compression Strain
Global Buckling
Deflection
Bending Strain
Compression
Tension

5. Soil Load – Plastic Pipe
Service Load ( )
Ts = [K2 VAF Psp +Pw] (Do/2)
Ts = service thrust per unit length (lb/in)
K2 = coefficient to account for variation of thrust around circumference of pipe
= 1.0 springline
= 0.60 crown
VAF = vertical arching factor
Psp = soil prism pressure (psi)
Pw = hydrostatic water pressure at springline (psi)
Do = outside diameter of pipe (in)

6. Soil Load – Plastic Pipe
Factored Load ( )
Tu = [ηEV(γEVKγEK2 VAF Psp + γWAPw](Do/2)
Tu = factored thrust per unit length (lb/in)
ηEV = load modifier for earth loads
γEV = load factor for earth fill dead load
KγE = installation factor
= 1.5 if installation is not monitored
= 1.0 if installation is monitored
γWA = load factor for hydrostatic pressure

7. Hydrostatic Pressure Pipe is above the water table Pw = 0.0 psi 7

8. Soil Prism Pressure - Flexible8
Soil Prism Pressure:
Psp = [[H (Bc)] w]/144
Psp = [[(8 ft.) (4.52)] (120 pcf)]/144
Psp = psi
Soil Prism Load
PL = Psp x Do x 12
PL = (7.08 psi)(54.26 in.)(12)
PL = 4,610 lbs/ft

9. Soil Load – Plastic Pipe9
Soil Load – Plastic Pipe
Service Load ( )
Ts = [K2 VAF Psp +Pw] (Do/2) ( )
SH – 1.17
VAF = 0.76 – 0.71
( ) SH
SH = hoop stiffness factor

10. Soil Load – Plastic Pipe10
Soil Load – Plastic Pipe ( )
SH – 1.17
VAF = 0.76 – 0.71
( ) SH
ɸsMsR
SH =
( )
EpAg
ɸs =resistance factor for soil stiffness
Ms = secant constrained soil modulus (ksi)
R = radius from center of pipe to center of profile
Ep = long-term modulus of pipe material (ksi)
Ag = gross area of pipe wall (in2/in)

11. HDPE Arching Factor Bending Hoop Deflection Compression +

12. Strength Over Time Ec0 = 2.781 x 104 MPa Epe0 = 758 MPa
Epvc0 = 3030 MPa
Ec50 = x 104 Mpa
Epe50 = 152 Mpa
Epvc50 = 1090 MPa
Graphs for Modulus of Elasticity based on equations found in Final Report of NCHRP 20-7, Task 89, “LRFD Specifications For Plastic Pipe and Culverts”

13. Hoop Stiffness Parameters13
Hoop Stiffness Parameters
ɸs =resistance factor for soil stiffness
ɸs = 0.90 (Table )
Ms = secant constrained soil modulus (ksi)
R = radius from center of pipe to center of profile
R = in (From the pipe supplier)
Ep = long-term modulus of pipe material (ksi)
E50 = 22 ksi (Table )
Ag = gross area of pipe wall (in2/in)
Ag = 0.44 in2/in (From the pipe supplier)

14. Constrained Soil Modulus14

15. Constrained Soil Modulus15
Constrained Soil Modulus
Soil Prism Pressure:
Psp = [[H (Bc)] w]/144
Psp = [[(12 ft.) (4.52)] (120 pcf)]/144
Psp = 7.08 psi
Ms = ksi

16. Hoop Stiffness Factor ɸsMsR SH = (12.12.3.5-4) EpAg16
Hoop Stiffness Factor
ɸsMsR
SH =
( )
EpAg
0.90 (0.744 ksi) (25.27 in.)
SH =
(22 ksi) (0.44 in2/in))
SH = 1.75

17. Soil Load – Plastic Pipe17
Soil Load – Plastic Pipe ( )
SH – 1.17
VAF = 0.76 – 0.71
( ) SH
1.75 – 1.17
VAF = 0.76 – 0.71
VAF = 0.67

18. Soil Load – Plastic Pipe
Factored Load ( )
Tu = [ηEV(γEVKγEK2 VAF Psp + γWAPw] (Do/2)
Tu = factored thrust per unit length (lb/in)
ηEV = load modifier for earth loads
1.05 For nonredundant earth loads ( & 1.3.2)
γEV = load factor for earth fill dead load
1.3 (Table )
KγE = installation factor ( )
= 1.5 if installation is not monitored
= 1.0 if installation is monitored
γWA = load factor for hydrostatic pressure
1.0 (Table )

19. Soil Load – Plastic Pipe
Factored Load ( )
Tu = [ηEV(γEVKγEK2 VAF Psp + γWAPw] (Do/2)
Tu = [1.05((1.3)(1.5)(1.0)(0.67)(7.08 psi))](54.26 in/2)
Tu = lbs/in
WEu = (263.5 lbs/in)(2)(12) = 6,324 lbs/ft
WEs = 6,324 lbs/ft/[(1.05)(1.3)(1.5)] = 3,089 lbs/ft

20. Live Load – Plastic Pipe
Factored Load (with Live) ( )
Tu = [ηEV(γEVKγEK2 VAF Psp + γWAPw) + ηLLγLLPLCLF1F2](Do/2)
ηLL = load modifier for live loads (1.0)
γLL = load factor for live loads (1.75)
PL = live load pressure
CL = live load distribution coefficient
F1 = (0.75D0)/Lw
F2 = 0.95/( SH)
Note: SH = 0 for no soil

21. Plastic Pipe Design Considerations21
Plastic Pipe Design Considerations
Hoop Compression Strain
Global Buckling
Deflection
Bending Strain
Compression
Tension

22. Plastic Pipe Design - Hoop Compression StrainTu
εuc =
( c-1)
1000(AeffEp)
Tu = factored thrust per unit length (lbs/in)
Tu = lbs/in
Ep = pipe modulus (ksi) – long-term for soil loading
Ep = 22 ksi
Aeff = effective area of pipe wall (in2/in)

23. 23
Hoop
Compression
Strain

24. Evaluate Local Buckling24
Aeff = 0.31 in2/in
Ag = 0.44 in2/in
%eff = 70%

25. Effective Pipe Wall Area25

26. Stub Compression Test

27. Plastic Pipe Design - Hoop Compression StrainTu
εuc =
( c-1)
1000(AeffEp)
263.5 lbs/in
εuc =
1000(0.31 in2/in)(22 ksi)
εuc =

28. Thrust Strain Limits εuc < ɸT εyc (12.12.3.10.1d-1)28
Thrust Strain Limits
εuc < ɸT εyc ( d-1)
εuc = factored compressive strain due to thrust =
ɸT = resistance factor for thrust effects = 1.0 (Table )
εyc = factored compressive strain limit = (Table )
< (1.0)(0.041) O.K.

29. Waviness Hoop Compression at Valley29
Hoop Compression at Valley
Di x εcu x 1 = 48 in x = in
Hoop Compression at Liner
Di x εcu x 0.38 = 48 in x x 0.38 = in
Difference in Hoop Compression under Service Loads
(1.856 in – in)/1.95 = 0.59 in

30. Waviness 30
A’ = (0.59 in)/2
A’ = 0.3 in

31. Buckling Strain Limit 1.2 Cn(EpIp)1/3 ɸsMs(1-2ʋ) Rh εbck = Aeff Ep31 2
1.2 Cn(EpIp)1/3 3
ɸsMs(1-2ʋ) Rh
εbck =
Aeff Ep
(1-ʋ)2
εbck = nominal strain capacity for general buckling
Cn = calibration factor to account for nonlinear effects = 0.55
ʋ = Poisson’s ratio of soil
Rh = correction factor for backfill soil geometry
11.4
11.4
Rh = =
= 0.99 D
50.54 in
11+
11+
12H
(12)(8 ft)

32. Buckling Strain Limit 1.2 Cn(EpIp)1/3 ɸsMs(1-2ʋ) Rh εbck = Aeff Ep32 2
1.2 Cn(EpIp)1/3 3
ɸsMs(1-2ʋ) Rh
εbck =
Aeff Ep
(1-ʋ)2 2 3
(0.9)(0.744 ksi)(1-2(0.3))
1.2(0.55)[(22 ksi)/(0.65 in4/in]1/3
0.99
εbck =
(0.31 in2/in)(22 ksi)
(1-0.3)2
εbck = > O.K

33. Reverse Curvature/Snap-Through Buckling

34. Check Deflection Δt < ΔA (12.12.2.2-1) KB(DLPsp + CLPL)Do Δt =34
Check Deflection
Δt < ΔA ( )
KB(DLPsp + CLPL)Do
Δt =
+ εscD ( )
1000(EpIp/R Ms)
KB = bedding coefficient (typical)
DL = Deflection Lag Factor – 1.5 (typical)
Psp = Soil Prism
εsc = εuc/1.95 = /1.95 =

35. Check Deflection Δt = 57.62 Δt = + 0.95 46.235
Check Deflection
0.10[1.5(7.08 psi) + 0]54.26 in
Δt =
(48 in)
1000[(22 ksi)(0.65 in4/in)/(25.27 in) (0.744 ksi)]
57.62
Δt =
+ 0.95
46.2
Δt = 2.2 in < ΔA = 0.05 x 48 in = 2.4 in
(2.2/48)/100 = 4.6% Deflection

36. Determine the Bending Strain36
Δf = ΔA – εcsD ( b-4)
Δf = 2.4 – 0.95 = 1.45 in
εf = γEVDf(c/R)(Δf/D)
γEV = load factor for earth fill dead load1.3 (Table )
Df = shape factor (Table b-1)
c = larger of the distance from the neutral axis
c = cmax = 1.86 in

37. Bending and Shortening

38. Determine the Bending Strain38
Δf = ΔA – εcsD ( b-4)
Δf = 2.4 – 0.95 = 1.45 in
εf = γEVDf(c/R)(Δf/D)
γEV = load factor for earth fill dead load1.3 (Table )
Df = shape factor (Table b-1)
c = larger of the distance from the neutral axis
c = cmax = 1.86 in

39. Well Compacted Soil

40. Shape Factor PS = [(22 ksi)(0.65 in4/in)]/[(0.149)(25.27)3]40
PS = [(22 ksi)(0.65 in4/in)]/[(0.149)(25.27)3]
PS = ksi
Df = 8 – 1 = 7 ( b)

41. 36 inch pipe Profile Wall Solid Wall 1.71” 2.7”” 1.62” 0.99” 0.81”

42. Compression/Tension in Bending 3

43. R1 Traffic Load Earth Load Final Backfill Initial Backfill Haunching
Bedding
Foundation

44. Determine the Bending Strain44
εf = (1.3)(7.0)(1.86 in/25.27 in)(1.45 in/50.54 in)
εf =
Tension = εcu – εf
– =
Compression = εcu + εf =

45. Allowable Bending Strain45
εyt = 0.050
εyc = 0.041

46. Allowable Bending Strain46
Allowable Bending Strain
Tension
εcu – εf < ɸfεyt ( b-1)
< 1.0 (0.050) Great!
Compression
εcu + εf < ɸT(1.5εyc)
< 1.0[(1.5)(0.041)]
< Great!
ɸf = ɸT = 1.0 (Table )

47. Conclusion 47 Slides 14 Necessary Equations Pipe Producer Provides
Not including live load
Not including Aeff Calculations
Not including service load calculations
Pipe Producer Provides
Outside Diameter
Aeff
c – Distance to the neutral axis