1. Buried Corrugated Thermoplastic Pipe: Simulation and Design B.W. Schafer, T.J. M c Grath

2. Simulation of buried pipe Simulation methodologySimulation methodology Strain demands – CANDEStrain demands – CANDE Strain capacity – ABAQUSStrain capacity – ABAQUS Depth of fill predictionsDepth of fill predictions Comparison with AASHTO design methodComparison with AASHTO design method ConclusionsConclusions

3. Simulation methodology Strain Demand - CANDEStrain Capacity – ABAQUS

4. depth of fill methodology thrust strain (compression) crest in compression 0 valley in compression max depth of fill demand curve from CANDE crosses capacity curve from ABAQUS 4’ 8’ 12’ 16’ Limiting curve defined by series of ABAQUS analyses performed to determine strains when failure occurs for a given pipe profile. Limit curve defined by selection of yield strains. Demand curve, CANDE analysis prediction of strain demand of a section of pipe as depth of fill increases, example shows hypothetical demand at crown. demand curve must be compared to capacity curve for all critical pipe locations! bending strain

5. CANDE modeling 2D plane strain model2D plane strain model Nonlinear “hyperbolic” soil modelsNonlinear “hyperbolic” soil models Model is “built” by adding soil layers and the pipeModel is “built” by adding soil layers and the pipe Surcharge loads simulate increasing depth of fillSurcharge loads simulate increasing depth of fill Model predicts stress state in the soil and forces in the pipe, forces are used to determine strains via engineering beam theoryModel predicts stress state in the soil and forces in the pipe, forces are used to determine strains via engineering beam theory  out = P/(EA) + Mc out /(EI)

6. CANDE model models considered uniform ML90 soil non-uniform soil short-term E pipe long-term E pipe 12-20 surcharge load ML90 CL85 ML90 CL50 ML90 in situ medium stiffness

7. Vertical soil stress -0.9 -2.7 -4.6 -6.4 -8.3 -10.2 -12.0 -13.9 -15.7 -17.6 -19.5 -21.3 -23.2 -25.0 -26.9 -28.8 -30.6 model state 20 ft of fill uniform ML90 soil (  = 120) long-term pipe modulus psi

8. 020406080100120140160180 -4 -3 -2 0 1 2 3 4 theta (deg.) 0º = crown outside fiber bending strain (%) Pipe bending strain Pipe bending strain depth of fill = 41 ft 0 PIPE 90 180

9. Pipe hoop strains 020406080100120140160180 0 2 4 6 8 10 12 axial strain (%) depth of fill = 41 ft 0 PIPE 90 180 theta (deg.) 0º = crown

10. ABAQUS model 30º symmetry radial support pipe-soil interface compression only (gap elements) no friction

11. ABAQUS model (cont.) Pipe geometryPipe geometry –based on one manufacturer’s 60 in. diameter pipe Model and mesh sizeModel and mesh size –eigen analysis to determine mesh sensitivity –arc size: compromise between allowing buckling to form, vs. strain gradients around the pipe Initial imperfections includedInitial imperfections included Elastic material modelsElastic material models –E pipe =E i, E soil =1,000 psi (lowerbound ML90) LoadingLoading –applied axial and bending deformations, strain demands determined from resulting forces

12. ABAQUS results cutaway isometric of deformed shape at failure with applied thrust and small negative bending

13. Thrust-bending capacity 00.511.522.533.544.55 -8 -6 -4 -2 0 2 4 6 8 thrust strain (%) outside bending strain (%) (a) (b) (c) (d) (e) (f)

14. Thrust-bending capacity 00.511.522.533.544.55 -8 -6 -4 -2 0 2 4 6 8 thrust strain (%) outside bending strain (%) (a) (b) (c) (d) (e) 00.511.522.533.544.55 -8 -6 -4 -2 0 2 4 6 8 thrust strain (%) outside bending strain (%) (a)(b)(c) (d) (e)

15. Strain demands ABAQUS pipe-soil model applied crest/web any location strain* corner min max condition  total  average  tension  compression (a) positive moment 4.0 3.1 -9.5 14.9 (b) positive moment and moderate thrust 5.2 4.8 -5.5 8.5 (c) positive moment and large thrust 4.7 4.4 -5.0 6.6 (d) thrust 4.6 4.4 -9.7 10.3 (e) negative moment and large thrust 0.7 -0.8 -7.3 6.9 (f) negative moment -4.9 -6.6 -9.1 7.6 ABAQUS strains direct from analysis in a given condition. Applied strains based on

16. Demand vs. capacity Demand vs. capacity 012345 -6 -4 -2 0 2 4 6 OUTSIDE STRAIN AT 6.4 FT 0 30 60 90 120 150 180 thrust strain (%) outside bending strain (%) Buckling Yielding 0 PIPE 90 180 uniform ML90 backfill, E pipe = long-term modulus

17. Demand vs. capacity Demand vs. capacity 012345 -6 -4 -2 0 2 4 6 OUTSIDE STRAIN AT 12.5 FT 0 30 60 90 120 150 180 thrust strain (%) outside bending strain (%) Buckling Yielding 0 PIPE 90 180 uniform ML90 backfill, E pipe = long-term modulus

18. Demand vs. capacity Demand vs. capacity 012345 -6 -4 -2 0 2 4 6 OUTSIDE STRAIN AT 15.6 FT 0 30 60 90 120 150 180 thrust strain (%) outside bending strain (%) Buckling Yielding 0 PIPE 90 180 uniform ML90 backfill, E pipe = long-term modulus

19. Depth of fill predictions Depth of fill, m(ft), at limit of Buckling Strain Backfill Soil Pipe Modulus of Profile Limit NOMINAL PREDICTION (ALL SAFETY FACTORS = 1) Uniform E 50 6.4 (21) 7.9 (26) Non-Uniform E 50 4.9 (16) 5.5 (18) Uniform E i >20.4 (> 67) ML90 Non-Uniform E i >20.4 (> 67) >20.4 (> 67) DESIGN PREDICTION (WITH SAFETY FACTORS*) Uniform E 50 2.7 (9) 3.7 (12) Non-Uniform E 50 2.6 (8.5) 2.9 (9.5) Uniform E i 9.1 (30) 20.1 (66) ML90 Non-Uniform E i 9.8 (32) 13.4 (44) * Safety factors: 2 for buckling, 2 for the yielding in thrust strain limit, and 1.5 for the combined yielding strain limit, “>” indicates that the strain limit was not reached in the CANDE analysis conducted.

20. AASHTO design method Depth of fill predictions, m (ft), using the newly adopted AASHTO design method for this pipe were determined as follows:Depth of fill predictions, m (ft), using the newly adopted AASHTO design method for this pipe were determined as follows: Soil Type ConditionSW95SW90ML90 Design6.4 (21.1)4.2 (13.9)3.0 (9.7) Ultimate16.3 (53.4)9.7 (31.7)6.3 (20.6) Design8.8 (28.9)5.7 (18.7)3.9 (12.8) Ultimate21.3 (>70)13.1 (43.0)8.3 (27.3) SW95SW90ML90 Considering Local Buckling Design6.4 (21.1)4.2 (13.9)3.0 (9.7) Ultimate16.3 (53.4)9.7 (31.7)6.3 (20.6) Ignoring Local Buckling Design8.8 (28.9)5.7 (18.7)3.9 (12.8) Ultimate21.3 (>70)13.1 (43.0)8.3 (27.3)

21. Comparison Depth of fill predictionsDepth of fill predictions –AASHTO with ML90 fill design: 3.0 m (9.7 ft) ultimate: 6.3 m (20.6 ft)design: 3.0 m (9.7 ft) ultimate: 6.3 m (20.6 ft) –Simulation model with uniform ML90 fill design: 2.7 m (9 ft) ultimate: 6.4 m (21 ft)design: 2.7 m (9 ft) ultimate: 6.4 m (21 ft) –Simulation model with non-uniform ML90 design: 2.6 m (8.5 ft) ultimate: 4.9 m (16 ft)design: 2.6 m (8.5 ft) ultimate: 4.9 m (16 ft)

22. Conclusion A new model for simulation of buried pipe design with local buckling limit states is presented.A new model for simulation of buried pipe design with local buckling limit states is presented. This new model represents an opportunity to more fully explore the complex relationship between the pipe and soil for a large variety of conditions relevant to corrugated thermoplastic pipe design.This new model represents an opportunity to more fully explore the complex relationship between the pipe and soil for a large variety of conditions relevant to corrugated thermoplastic pipe design. The agreement of the AASHTO method with the comprehensive numerical analysis supports continued use of the AASHTO method for design depth of fill predictions.The agreement of the AASHTO method with the comprehensive numerical analysis supports continued use of the AASHTO method for design depth of fill predictions.