Field Performance of Corrugated Pipe Manufactured with Recycled Polyethylene Content (2018)

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F-1 Calculations for Peak Bending Strain in Pipe Wall for Simulated Field Test The combined tensile strain in the outer fiber of the pipe wall is calculated from Equation 12.12.3.10.2b-1 of the AASHTO LRFD Bridge Design Specifications, 7th Edition, as shown below in Equation F.1. (F.1)Combined f ucε = ε − ε where εCombined = Combined tensile strain in pipe wall εf = Tensile strain due to flexure εuc = Factored compressive strain due to thrust The tensile strain due to flexure, εf, is calculated from Equa- tion 12.12.3.10.2b-3 of the AASHTO LRFD Bridge Design Specifications, as shown in Equation F.2. (F.2)D c R D f EV f f( )( )ε = γ ∆ where εf = Strain due to flexure γEV = Load factor for vertical pressure from dead load of earth fill Df = Shape factor from Table 12.12.3.10.2b-1 of AASHTO LRFD Bridge Design Specifications c = Distance from neutral axis of wall profile to extreme fiber, in. R = Centroidal radius of pipe, in. Δf = Deflection of pipe due to flexure, in. D = Centroidal diameter of pipe, in. For the loading conditions in the simulated field test (namely, a pipe installed on firmly compacted bedding with an ASTM Class III backfill material compacted to around 87% standard Proctor density), the Shape Factor was inter- polated to 5.7. The average centroidal diameter of the test pipes was around 31.8 in. and the centroidal radius 15.9 in. based on an analysis of the wall profiles. Similarly, the aver- age distance from the neutral axis to the extreme fiber for the wall profiles in the test pipes was 1.63 in. The AASHTO recommended load factor of 1.3 for vertical pressure from the fill was used to account for any uncertainties or varia- tions in loading pressure due to exposure to precipitation and other environmental conditions. The deflection of the pipe due to flexure, Δf, was deter- mined based on the measured deflection of pipes in the sim- ulated field test and offset slightly to account for deflection due to circumferential shortening. An average value of 3.4 in. deflection was used. Based on these measurements, the strain due to flexure is calculated in Equation F.3 (values have been rounded up). 1.3 5.7 1.6 15.9 3.4 31.8 8.2% (F.3)D c R D f EV f f( )( ) ( )( )ε = γ ∆ = =i i The factored compressive strain due to thrust is calculated from Equation 12.12.3.10.1c-1 in the AASHTO LRFD Bridge Design Specifications, as shown in Equation F.4. ( )ε = (F.4) T A E uc U Eff P where εuc = Factored compressive strain due to thrust TU = Factored thrust per unit length, lb/in. AEff = Effective area of pipe wall per unit length of pipe, in.2/in. Ep = Average modulus during loading period, psi For the wall profiles in this study, the typical effective area was calculated to be 0.256 in.2/in. The average mod- ulus during a 100-day loading period was shown to be 43,660 psi (see Chapter 2). The factored wall thrust per unit length was calculated using Equation 12.12.3.5-1 from the A P P E N D I X F

F-2 AASHTO LRFD Bridge Design Specifications, as shown in Equation F.5. 2 (F.5)T K VAFP D U EV EV E SP O( )( )= η γ γ where TU = Factored thrust per unit length, lb/in. ηEV = Load modifier for vertical earth loads = 1.05 γEV = Load factor for vertical pressure from dead load of earth fill = 1.3 KγE = Installation factor = 1.0 (due to controlled installation) VAF = Vertical arching factor (Equation F.6) PSP = Soil prism pressure, psi. (Equation F.7) DO = Outside diameter of pipe, in. = 35.1 in. = − − +     =0.76 0.71 1.17 2.92 0.881 (F.6)VAF S S H H ( )= + γ =0.11 25.3 (F.7)P H D psiSP O S Based on these values, the factored thrust per unit length is calculated as shown in Equation F.8. 1.05 1.3 1.0 0.881 25.3 35.1 2 533 (F.8)( )( )= =• • •T lbinU The factored compressive strain due to thrust is then cal- culated as shown in Equation F.9. i( ) ( )ε = = = 533 0.256 43,660 4.7% (F.9) T A E uc U Eff P Applying Equation F.1, we can calculate the net combined tensile strain in the extreme fiber of the wall as shown in Equation F.10. ε = ε − ε = − =8.2 4.7 3.5% (F.10)Combined f uc Assuming an equivalent average modulus of 43,660 psi, the equivalent average stress for a 100-day loading period is 43,660 * 0.035 = 1528 psi.