1 Structural Design of Flexible Pipe www flexiblepipe
1 Structural Design of Flexible Pipe www. flexible-pipe. omg
2 Pipe Info • Pipe ID = 48 inches § RCP – B-Wall OD = 58 inches = 4. 83 ft. § HDPE – Manufacture = 54. 26 in. = 4. 52 ft. www. flexible-pipe. omg
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 www. flexible-pipe. omg
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 www. flexible-pipe. omg 4
5 Soil Load – Plastic Pipe • Service Load (12. 3. 5 -2) § Ts = [K 2 VAF Psp +Pw] (Do/2) • Ts = service thrust per unit length (lb/in) • K 2 = 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) www. flexible-pipe. omg
6 Soil Load – Plastic Pipe • Factored Load (12. 3. 5 -1) § Tu = [ηEV(γEVKγEK 2 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 www. flexible-pipe. omg
7 Hydrostatic Pressure • Pipe is above the water table § Pw = 0. 0 psi www. flexible-pipe. omg
8 Soil Prism Pressure - Flexible • Soil Prism Pressure: § Psp = [[H + 0. 11(Bc)] w]/144 § Psp = [[(8 ft. ) + 0. 11(4. 52)] (120 pcf)]/144 § Psp = 7. 081 psi • Soil Prism Load § PL = Psp x Do x 12 § PL = (7. 08 psi)(54. 26 in. )(12) § PL = 4, 610 lbs/ft www. flexible-pipe. omg
9 Soil Load – Plastic Pipe • Service Load (12. 3. 5 -2) § Ts = [K 2 VAF Psp +Pw] (Do/2) ( SH – 1. 17 VAF = 0. 76 – 0. 71 SH + 2. 92 SH = hoop stiffness factor www. flexible-pipe. omg ) (12. 3. 5 -3)
10 Soil Load – Plastic Pipe ( SH – 1. 17 VAF = 0. 76 – 0. 71 SH + 2. 92 ɸs. Ms. R SH = E p. A g ) (12. 3. 5 -3) (12. 3. 5 -4) 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 (in 2/in) www. flexible-pipe. omg
11 HDPE Arching Factor Hoop Compression www. flexible-pipe. omg + Bending Deflection
12 Strength Over Time Ec 0 = 2. 781 x 104 MPa Epe 0 = 758 MPa Epvc 0 = 3030 MPa Ec 50 = 2. 781 x 104 Mpa Epe 50 = 152 Mpa Epvc 50 = 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” www. flexible-pipe. omg
13 Hoop Stiffness Parameters • ɸs =resistance factor for soil stiffness § ɸs = 0. 90 (Table 12. 5. 5 -1) • Ms = secant constrained soil modulus (ksi) • R = radius from center of pipe to center of profile § R = 25. 27 in (From the pipe supplier) • Ep = long-term modulus of pipe material (ksi) § E 50 = 22 ksi (Table 12. 3. 3 -1) • Ag = gross area of pipe wall (in 2/in) § Ag = 0. 44 in 2/in (From the pipe supplier) www. flexible-pipe. omg
14 Constrained Soil Modulus www. flexible-pipe. omg
Constrained Soil Modulus • Soil Prism Pressure: § Psp = [[H + 0. 11(Bc)] w]/144 § Psp = [[(12 ft. ) + 0. 11(4. 52)] (120 pcf)]/144 § Psp = 7. 08 psi Ms = 0. 744 ksi www. flexible-pipe. omg 15
16 Hoop Stiffness Factor ɸs. Ms. R SH = E p. A g (12. 3. 5 -4) 0. 90 (0. 744 ksi) (25. 27 in. ) SH = (22 ksi) (0. 44 in 2/in)) SH = 1. 75 www. flexible-pipe. omg
17 Soil Load – Plastic Pipe ( SH – 1. 17 VAF = 0. 76 – 0. 71 SH + 2. 92 ) 1. 75 – 1. 17 VAF = 0. 76 – 0. 71 1. 75 + 2. 92 VAF = 0. 67 www. flexible-pipe. omg (12. 3. 5 -3)
Soil Load – Plastic Pipe • Factored Load (12. 3. 5 -1) § Tu = [ηEV(γEVKγEK 2 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 (12. 5. 4 & 1. 3. 2) • γEV = load factor for earth fill dead load § 1. 3 (Table 3. 4. 1 -2) • KγE = installation factor (12. 3. 5) § = 1. 5 if installation is not monitored § = 1. 0 if installation is monitored • γWA = load factor for hydrostatic pressure www. flexible-pipe. omg § 1. 0 (Table 3. 4. 1 -1) 18
19 Soil Load – Plastic Pipe • Factored Load (12. 3. 5 -1) § Tu = [ηEV(γEVKγEK 2 VAF Psp + γWAPw] (Do/2) § Tu = [1. 05((1. 3)(1. 5)(1. 0)(0. 67)(7. 08 psi))](54. 26 in/2) § Tu = 263. 5 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 www. flexible-pipe. omg
20 Live Load – Plastic Pipe • Factored Load (with Live) (12. 3. 5 -1) § Tu = [ηEV(γEVKγEK 2 VAF Psp + γWAPw) + ηLLγLLPLCLF 1 F 2](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 F 1 = (0. 75 D 0)/Lw F 2 = 0. 95/(1 + 0. 6 SH) § Note: SH = 0 for no soil www. flexible-pipe. omg
21 Plastic Pipe Design Considerations • • Hoop Compression Strain Global Buckling Deflection Bending Strain § Compression § Tension www. flexible-pipe. omg
22 Plastic Pipe Design Hoop Compression Strain εuc = Tu 1000(Aeff. Ep) (12. 3. 10. 1 c-1) Tu = factored thrust per unit length (lbs/in) Tu = 263. 5 lbs/in Ep = pipe modulus (ksi) – long-term for soil loading Ep = 22 ksi Aeff = effective area of pipe wall (in 2/in) www. flexible-pipe. omg
Hoop Compression Strain www. flexible-pipe. omg 23
24 Evaluate Local Buckling Aeff = 0. 31 in 2/in Ag = 0. 44 in 2/in %eff = 70% www. flexible-pipe. omg
25 Effective Pipe Wall Area www. flexible-pipe. omg
Stub Compression Test 26
27 Plastic Pipe Design Hoop Compression Strain εuc = Tu 1000(Aeff. Ep) εuc = 263. 5 lbs/in 1000(0. 31 in 2/in)(22 ksi) εuc = 0. 0386 www. flexible-pipe. omg (12. 3. 10. 1 c-1)
28 Thrust Strain Limits • εuc < ɸT εyc (12. 3. 10. 1 d-1) § εuc = factored compressive strain due to thrust = 0. 0386 § ɸT = resistance factor for thrust effects = 1. 0 (Table 12. 5. 5 -1) § εyc = factored compressive strain limit = 0. 041 (Table 12. 3. 3 -1) § 0. 0386 < (1. 0)(0. 041) O. K. www. flexible-pipe. omg
29 Waviness Hoop Compression at Valley Di x εcu x 1 = 48 in x 0. 03866 = 1. 856 in Hoop Compression at Liner Di x εcu x 0. 38 = 48 in x 0. 03866 x 0. 38 = 0. 705 in Difference in Hoop Compression under Service Loads (1. 856 in – 0. 705 in)/1. 95 = 0. 59 in www. flexible-pipe. omg
Waviness A’ = (0. 59 in)/2 A’ = 0. 3 in www. flexible-pipe. omg 30
31 Buckling Strain Limit εbck = 1. 2 Cn(Ep. Ip)1/3 Aeff Ep ɸs. Ms(1 -2ʋ) (1 -ʋ)2 2 3 Rh 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 Rh = D 11+ 12 H www. flexible-pipe. omg = 11. 4 = 0. 99 in 11+ 50. 54 (12)(8 ft)
32 Buckling Strain Limit εbck = 1. 2 Cn(Ep. Ip)1/3 Aeff Ep ɸs. Ms(1 -2ʋ) (1 -ʋ)2 1. 2(0. 55)[(22 ksi)/(0. 65 in 4/in]1/3 (0. 9)(0. 744 ksi)(1 -2(0. 3)) εbck = (0. 31 in 2/in)(22 ksi) (1 -0. 3)2 εbck = 0. 155 > 0. 03866 www. flexible-pipe. omg O. K 2 3 Rh 2 3 0. 99
Reverse Curvature/Snap. Through Buckling www. flexible-pipe. omg 33
34 Check Deflection Δt < ΔA (12. 2. 2 -1) KB(DLPsp + CLPL)Do Δt = + εsc. D (12. 2. 2 -2) 3 1000(Ep. Ip/R + 0. 061 Ms) KB = bedding coefficient - 0. 10 (typical) DL = Deflection Lag Factor – 1. 5 (typical) Psp = Soil Prism εsc = εuc/1. 95 = 0. 0386/1. 95 = 0. 0198 www. flexible-pipe. omg
35 Check Deflection Δt = 0. 10[1. 5(7. 08 psi) + 0]54. 26 in + 0. 0198(48 in) 1000[(22 ksi)(0. 65 in 4/in)/(25. 27 in)3 + 0. 061(0. 744 ksi)] Δt = 57. 62 + 0. 95 46. 2 Δt = 2. 2 in < ΔA = 0. 05 x 48 in = 2. 4 in (2. 2/48)/100 = 4. 6% Deflection www. flexible-pipe. omg
36 Determine the Bending Strain Δf = ΔA – εcs. D (12. 3. 10. 2 b-4) Δf = 2. 4 – 0. 95 = 1. 45 in εf = γEVDf(c/R)(Δf/D) γEV = load factor for earth fill dead load 1. 3 (Table 3. 4. 1 -2) Df = shape factor (Table 12. 3. 10. 2 b-1) c = larger of the distance from the neutral axis c = cmax = 1. 86 in www. flexible-pipe. omg
37 Bending and Shortening
38 Determine the Bending Strain Δf = ΔA – εcs. D (12. 3. 10. 2 b-4) Δf = 2. 4 – 0. 95 = 1. 45 in εf = γEVDf(c/R)(Δf/D) γEV = load factor for earth fill dead load 1. 3 (Table 3. 4. 1 -2) Df = shape factor (Table 12. 3. 10. 2 b-1) c = larger of the distance from the neutral axis c = cmax = 1. 86 in www. flexible-pipe. omg
39 Well Compacted Soil www. flexible-pipe. omg
40 Shape Factor PS = [(22 ksi)(0. 65 in 4/in)]/[(0. 149)(25. 27)3] PS = 0. 0059 ksi Df = 8 – 1 = 7 www. flexible-pipe. omg (12. 3. 10. 2 b)
41 36 inch pipe Profile Wall Solid Wall 1. 71” 0. 99” 1. 62” 2. 7”” www. flexible-pipe. omg 0. 81”
Compression/Tension in Bending t 3 t 3 www. flexible-pipe. omg 42
43 Traffic Load Earth Load Final Backfill R 1 Initial Backfill Haunching Bedding Foundation www. flexible-pipe. omg
44 Determine the Bending Strain εf = (1. 3)(7. 0)(1. 86 in/25. 27 in)(1. 45 in/50. 54 in) εf = 0. 0192 Tension = εcu – εf 0. 0386 – 0. 0192 = 0. 0194 Compression = εcu + εf 0. 0386 + 0. 0192 = 0. 0578 www. flexible-pipe. omg
45 Allowable Bending Strain εyt = 0. 050 εyc = 0. 041 www. flexible-pipe. omg
46 Allowable Bending Strain • Tension § εcu – εf < ɸfεyt (12. 3. 10. 2 b-1) § 0. 0194 < 1. 0 (0. 050) Great! • Compression § εcu + εf < ɸT(1. 5εyc) § 0. 0578 < 1. 0[(1. 5)(0. 041)] § 0. 0578 < 0. 0615 Great! • ɸf = ɸT = 1. 0 www. flexible-pipe. omg (Table 12. 5. 5 -1)
47 Conclusion • 47 Slides • 14 Necessary Equations § 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 • www. flexible-pipe. omg
- Slides: 47