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

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E-1 Finite Element Analysis from Ohio University Constant Strain Pipe Test Finite Element Analysis The objective of this task was to perform a three-dimensional (3D) finite element analysis (FEA) of the constant strain test and compare the results with the experimental work discussed earlier. The FEA modeled the response of a 30 in. (76 cm) high-density polyethylene (HDPE) 100% virgin resin pipe subjected to forced long-term deflection. The force needed to keep the pipe continuously deflected has been calculated in the analysis. All the finite element analyses in this investiga- tion were performed using finite element program ‘ABAQUS’. The detailed dimensions of the cross section of the pipe are shown in Table E-1. The inner and outer diameter of the undeflected pipe are given in Figure E-1. The analyses were performed using a linear 3D stress 8-node brick element with reduced integration to represent the pipe, steel beams, and steel plates. The meshes consisted of 103240 nodes and 60342 elements. The FEA diagrams in Figure E-2 represent the meshed pipe before and after deflec- tion with different views. Figure E-3 shows a front view and Figure E-4 a side view of the pipe, while Figure E-5 shows details of the pipe cross-section in the mesh. The dimensions of the pipe after deflection are shown in Figure E-6. An HDPE pipe was analyzed for time periods of 60 min- utes and 100 days using finite element analysis. The pipe was subjected to a 20% [6 in. (15 cm)] deflection. The Young’s modulus and Poisson’s ratio of the steel beams and plates were assigned values of 29,000,000 psi (200 GPa) and 0.3, respectively. The HDPE corrugated pipe was mod- eled using viscoelastic properties with a Young’s modulus and Poisson’s ratio of 116,000 psi (800 MPa) and 0.45. The steel beams and plates had a density of 0.28 lb/in3 (7750 kg/m3) whereas the HDPE pipe was given a density of 0.035 lb/in3 (969 kg/m3). The analyses were performed using viscoelastic proper- ties for the HDPE pipe to represent its viscoelastic response with time. In order to find the best material behavior of HDPE, modified model type 1 and modified model type 2 of Hengprathanee [2000], depicted in Figure E-7, were used for converting the creep compliance term to a relaxation modulus. The creep compliance equation is: 10 1D D D ei t i n i∑ ( )= + − ∝ = The relaxation modulus equation is: 10 1E E E ei t i n i∑ ( )= − − β = The exponent terms are given in Table E-2. According to J.D. Ferry [1980] and D.R. Hiltunen and R. Roque [1995], creep compliance data can be converted to relaxation modulus data analytically using a Laplace transform: 1 0 D t dE d d∫ ( ) ( )− τ ττ τ = ∞ 1 2 L D t L E t s [ ] [ ]( ) ( )× = 1 1 2 E t L s L D t[ ]( ) ( )= ×  − 2 1 Shear Modulus E v( )µ = + 3 1 2 Bulk Modulus K E v( )= + Using the relaxation modulus from the table above and v = 0.45, the shear modulus and bulk modulus of HDPE were calculated, with results in Table E-3. By normalizing the bulk modulus and shear modulus, the coefficients in the Prony series for the viscoelastic properties were calculated, as given in Table E-4. This normalization is required by ABAQUS. A P P E N D I X E

E-2 Inner Diameter Width Crest Width Liner Width Valley Width Web Thickness Crest Thickness Liner Thickness Valley Thickness Web (in.) 30 1.575 2.559 1.181 1.969 0.118 0.079 0.197 0.177 (cm) 76.2 4.000 6.500 3.000 5.001 0.300 0.201 0.500 0.450 Table E-1. Detailed dimensions of HDPE pipe based on AASHTO calculations. Figure E-1. Pipe dimensions before applying the load [inner diameter 30 in. (76 cm), outer diameter 35 in. (89 cm)]. Figure E-2. 3D FEA mesh model before and after deflection.

E-3 Figure E-3. FEA mesh of pipe front view before and after deflection. Figure E-4. FEA mesh of pipe side and top view.

E-4 Figure E-5. FEA of pipe cross section. Figure E-6. Pipe dimensions after applying a 20% [6 in. (15 cm)] vertical deflection [inside 24 in. (61 cm), outside 29 in. (74 cm)].

E-5 Comparison of FEA Results to Experimental Data The FEA was first used to simulate the initial application of the load. The FEA and experimental results for the first 60 minutes for Frame 8 (virgin resin) are compared in Fig- ure E-8, and the long-term results are simulated in Figure E-9. In the experiment, the load was applied in six 1 in. (2.54 cm) increments of deflection, with 1 minute pauses in between, so the total deflection reached 20% [6 in. (15 cm)]. The deflection was then kept constant and the strain monitoring continued until the present. The entire loading process took 672 seconds, including pauses. The finite element analysis model of the experiment showed a good correlation with the experimental results. However, it was noticed that after loading the pipe to a 3 in. (7.6 cm) deflec- tion (10%), there was a small difference in the initial results of the experimental test from the FEA, as can be seen in Fig- ure E-8; this discrepancy is due to the nonlinear behavior of the pipe when the deflection exceeded 10%. This difference in the initial results dissipated over time and the experimental values and long-term FEA results converged, as shown in Figure E-9. Previous researchers have studied the behaviors of visco- elastic polymer pipes response to parallel plate loading [Moore and Zhang, 1995]. Their analyses were successful for pipe deflections with small strains up to 5%, but their predictions were poor for pipes with 20% deflection. This is due to the nonlinear material behaviors at some locations on the pipe wall. It was found that linear behavior limit of HDPE pipes was about 0.8% of material strain. Strain Using the finite element model, the strain as a function of position along the length of the pipe was computed at the crown, inner springline, and outer springline. From these graphs, it was computed by FEA that the maximum strain in the pipe for the 30 in. (76 cm) pipe at 20% deflection was 3.75% at the crown as seen in Figure E-10. The lowest strain was noticed at the inner springline. Short-term and long-term FEA strain results for the 30 in. (76 cm) pipe with 20% deflection are shown in Figures E-11, E-12, and E-13. Experimental strain results for the 30 in. (76 cm) pipe with 20% deflection are shown in Figure E-14. Using finite element analyses, the maximum strain on the pipe was calculated to be 3.75%, which was close to the exper- imental value of 3.1%, as shown in Table E-5. HDPE stress/strain curves are mostly linear up to a value of 2% strain, and beyond that the relationship becomes nonlinear. Most polymers have a linear viscoelastic strain limit of 0.5%. There is a transition from linear viscoelastic to a nonlinear viscoelastic between 0.5% and 1% [Lai, 1995]. This nonlinear effect poses difficulties in interpreting experimental results. Figure E-7. Modified models for HDPE [Hengprathanee, 2000]. i Di (psi−1) i (second) Ei (psi) i (second) 0 3.52E-06 - 2.84E+05 - 1 1.11E-07 10 9.84E+03 10 2 1.71E-06 100 9.48E+04 67 3 2.58E-06 1000 5.95E+04 672 4 4.51E-06 10000 4.34E+04 6378 5 7.23E-06 100000 2.58E+04 64760 Table E-2. Creep components and relaxation moduli for HDPE pipe (1 psi = 6895 Pa) [Lai, 1995; Hengprathanee, 2000]. Shear Modulus Bulk Modulus (psi) (MPa) (psi) (MPa) G0 97931 675.21 K0 946666.7 6527.04 G1 3393.1 23.395 K1 32800 226 G2 32689.6 225.39 K2 316000 2179 G3 20517.2 141.46 K3 198333.3 1367 G4 14965.5 103.18 K4 144666.7 997 G5 8896.6 61.340 K5 86000 593 Table E-3. Shear and bulk modulus components for HDPE. Normalized Shear Modulus Normalized Bulk Modulus Relaxation Time, i 0.0346 0.0346 10 0.3338 0.3338 67 0.2095 0.2095 672 0.1528 0.1528 6378 0.0908 0.0908 64760 Table E-4. Coefficients in the Prony series used in ABAQUS.

E-6 Figure E-8. FEA and experimental results comparison for the first 60 minutes (20% deflection). Figure E-9. FEA and experimental results long-term comparison (20% deflection).

E-7 Figure E-10. Strain in the pipe using FEA. Figure E-11. Strain at crown of pipe using FEA.

E-8 References Ferry J. D. (1980). Viscoelastic Properties of Polymers, 3rd Edition, John Wiley & Sons, New York. Hengprathanee, S. (2000). Evaluation of the Geometry Effect of the Profile of High Density Polyethylene Pipes. Master’s thesis. Ohio University. Hiltunen, D. R. and Roque, R. (1995). “The Use of Time-Temperature Superposition to Fundamentally Characterize Asphaltic Concrete Mixtures at Low Temperatures,” STP1265, American Society for Testing and Materials, Philadelphia. Lai, J. (1995). Non-linear Time-dependent Deformation Behaviour of High Density Polyethylene. Delft University Press, Delft, The Netherlands. Moore, I. D., and Zhang, C. (1995). “Computer Models for Predicting HDPE Pipe Stiffness.” Annual Conference of the Canadian Society for Civil Engineering, Ottawa, Canada, p. 565–575. Figure E-12. Strain at outer springline of the pipe using FEA. Figure E-13. Strain at inner springline of the pipe using FEA. Figure E-14. Experimental strain results. 20% deflection Experimental FEA Maximum strain 3.1% 3.75% Table E-5. Experimental and FEA strain results comparison.