Structural Design of Flexible Pipe www.flexible-pipe.omg

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 = 54.26 in. = 4.52 ft. www.flexible-pipe.omg

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 www.flexible-pipe.omg

Plastic Pipe Design Considerations 4 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

Soil Load – Plastic Pipe Service Load (12.12.3.5-2) 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) www.flexible-pipe.omg

Soil Load – Plastic Pipe Factored Load (12.12.3.5-1) 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 www.flexible-pipe.omg

Hydrostatic Pressure Pipe is above the water table Pw = 0.0 psi 7 www.flexible-pipe.omg

Soil Prism Pressure - Flexible 8 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

Soil Load – Plastic Pipe 9 Soil Load – Plastic Pipe Service Load (12.12.3.5-2) Ts = [K2 VAF Psp +Pw] (Do/2) ( ) SH – 1.17 VAF = 0.76 – 0.71 (12.12.3.5-3) SH + 2.92 SH = hoop stiffness factor www.flexible-pipe.omg

Soil Load – Plastic Pipe 10 Soil Load – Plastic Pipe ( ) SH – 1.17 VAF = 0.76 – 0.71 (12.12.3.5-3) SH + 2.92 ɸsMsR SH = (12.12.3.5-4) 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) www.flexible-pipe.omg

HDPE Arching Factor Bending Hoop Deflection Compression + www.flexible-pipe.omg

Strength Over Time Ec0 = 2.781 x 104 MPa Epe0 = 758 MPa Epvc0 = 3030 MPa Ec50 = 2.781 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” www.flexible-pipe.omg

Hoop Stiffness Parameters 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) E50 = 22 ksi (Table 12.12.3.3-1) Ag = gross area of pipe wall (in2/in) Ag = 0.44 in2/in (From the pipe supplier) www.flexible-pipe.omg

Constrained Soil Modulus 14 www.flexible-pipe.omg

Constrained Soil Modulus 15 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

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

Soil Load – Plastic Pipe 17 Soil Load – Plastic Pipe ( ) SH – 1.17 VAF = 0.76 – 0.71 (12.12.3.5-3) SH + 2.92 1.75 – 1.17 VAF = 0.76 – 0.71 1.75 + 2.92 VAF = 0.67 www.flexible-pipe.omg

Soil Load – Plastic Pipe Factored Load (12.12.3.5-1) 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 (12.5.4 & 1.3.2) γEV = load factor for earth fill dead load 1.3 (Table 3.4.1-2) KγE = installation factor (12.12.3.5) = 1.5 if installation is not monitored = 1.0 if installation is monitored γWA = load factor for hydrostatic pressure 1.0 (Table 3.4.1-1) www.flexible-pipe.omg

Soil Load – Plastic Pipe Factored Load (12.12.3.5-1) 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 = 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

Live Load – Plastic Pipe Factored Load (with Live) (12.12.3.5-1) 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/(1 + 0.6SH) Note: SH = 0 for no soil www.flexible-pipe.omg

Plastic Pipe Design Considerations 21 Plastic Pipe Design Considerations Hoop Compression Strain Global Buckling Deflection Bending Strain Compression Tension www.flexible-pipe.omg

Plastic Pipe Design - Hoop Compression Strain Tu εuc = (12.12.3.10.1c-1) 1000(AeffEp) 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 (in2/in) www.flexible-pipe.omg

23 Hoop Compression Strain www.flexible-pipe.omg

Evaluate Local Buckling 24 Aeff = 0.31 in2/in Ag = 0.44 in2/in %eff = 70% www.flexible-pipe.omg

Effective Pipe Wall Area 25 www.flexible-pipe.omg

Stub Compression Test

Plastic Pipe Design - Hoop Compression Strain Tu εuc = (12.12.3.10.1c-1) 1000(AeffEp) 263.5 lbs/in εuc = 1000(0.31 in2/in)(22 ksi) εuc = 0.0386 www.flexible-pipe.omg

Thrust Strain Limits εuc < ɸT εyc (12.12.3.10.1d-1) 28 Thrust Strain Limits εuc < ɸT εyc (12.12.3.10.1d-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 12.12.3.3-1) 0.0386 < (1.0)(0.041) O.K. www.flexible-pipe.omg

Waviness Hoop Compression at Valley 29 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 30 A’ = (0.59 in)/2 A’ = 0.3 in www.flexible-pipe.omg

Buckling Strain Limit 1.2 Cn(EpIp)1/3 ɸsMs(1-2ʋ) Rh εbck = Aeff Ep 31 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) www.flexible-pipe.omg

Buckling Strain Limit 1.2 Cn(EpIp)1/3 ɸsMs(1-2ʋ) Rh εbck = Aeff Ep 32 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 = 0.155 > 0.03866 O.K www.flexible-pipe.omg

Reverse Curvature/Snap-Through Buckling www.flexible-pipe.omg

Check Deflection Δt < ΔA (12.12.2.2-1) KB(DLPsp + CLPL)Do Δt = 34 Check Deflection Δt < ΔA (12.12.2.2-1) KB(DLPsp + CLPL)Do Δt = + εscD (12.12.2.2-2) 1000(EpIp/R3 + 0.061Ms) 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

Check Deflection Δt = 57.62 Δt = + 0.95 46.2 35 Check Deflection 0.10[1.5(7.08 psi) + 0]54.26 in Δt = + 0.0198(48 in) 1000[(22 ksi)(0.65 in4/in)/(25.27 in)3 + 0.061(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 www.flexible-pipe.omg

Determine the Bending Strain 36 Δf = ΔA – εcsD (12.12.3.10.2b-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 3.4.1-2) Df = shape factor (Table 12.12.3.10.2b-1) c = larger of the distance from the neutral axis c = cmax = 1.86 in www.flexible-pipe.omg

Bending and Shortening

Determine the Bending Strain 38 Δf = ΔA – εcsD (12.12.3.10.2b-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 3.4.1-2) Df = shape factor (Table 12.12.3.10.2b-1) c = larger of the distance from the neutral axis c = cmax = 1.86 in www.flexible-pipe.omg

Well Compacted Soil www.flexible-pipe.omg

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 = 0.0059 ksi Df = 8 – 1 = 7 (12.12.3.10.2b) www.flexible-pipe.omg

36 inch pipe Profile Wall Solid Wall 1.71” 2.7”” 1.62” 0.99” 0.81” www.flexible-pipe.omg

Compression/Tension in Bending  3 www.flexible-pipe.omg

R1 Traffic Load Earth Load Final Backfill Initial Backfill Haunching Bedding Foundation www.flexible-pipe.omg

Determine the Bending Strain 44 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

Allowable Bending Strain 45 εyt = 0.050 εyc = 0.041 www.flexible-pipe.omg

Allowable Bending Strain 46 Allowable Bending Strain Tension εcu – εf < ɸfεyt (12.12.3.10.2b-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 (Table 12.5.5-1) www.flexible-pipe.omg

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 www.flexible-pipe.omg