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Buried Corrugated Thermoplastic Pipe: Simulation and Design

Buried Corrugated Thermoplastic Pipe: Simulation and Design. B.W. Schafer, T.J. M c Grath. Simulation of buried pipe. Simulation methodology Strain demands – CANDE Strain capacity – ABAQUS Depth of fill predictions Comparison with AASHTO design method Conclusions. Simulation methodology.

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Buried Corrugated Thermoplastic Pipe: Simulation and Design

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

  2. Simulation of buried pipe • Simulation methodology • Strain demands – CANDE • Strain capacity – ABAQUS • Depth of fill predictions • Comparison with AASHTO design method • Conclusions

  3. Simulation methodology Strain Demand - CANDE Strain Capacity – ABAQUS

  4. max depth of filldemand curve from CANDE crosses capacity curve from ABAQUS 16’ 12’ 8’ 4’ Limiting curve defined by series of ABAQUSanalyses performed to determine strainswhen 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! depth of fill methodology crest in compression thrust strain (compression) bending strain 0 valley in compression

  5. CANDE modeling • 2D plane strain model • Nonlinear “hyperbolic” soil models • Model is “built” by adding soil layers and the pipe • Surcharge 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 theory eout= P/(EA) + Mcout/(EI)

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

  7. -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 Vertical soil stress • model state • 20 ft of fill • uniform ML90 soil (g = 120) • long-term pipe modulus psi

  8. 0 PIPE 90 180 Pipe bending strain depth of fill = 41 ft 4 3 2 1 outside fiber bending strain (%) 0 -1 -2 -3 -4 0 20 40 60 80 100 120 140 160 180 theta (deg.) 0º = crown

  9. 0 PIPE 90 180 Pipe hoop strains depth of fill = 41 ft 12 10 8 axial strain (%) 6 4 2 0 0 20 40 60 80 100 120 140 160 180 theta (deg.) 0º = crown

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

  11. ABAQUS model (cont.) • Pipe geometry • based on one manufacturer’s 60 in. diameter pipe • Model 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 included • Elastic material models • Epipe=Ei, Esoil=1,000 psi (lowerbound ML90) • Loading • applied axial and bending deformations, straindemands determined from resulting forces

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

  13. Thrust-bending capacity 8 6 (a) 4 (b) 2 (c) outside bending strain (%) (d) 0 - 2 (e) - 4 - 6 (f) - 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 thrust strain (%)

  14. Thrust-bending capacity (a) (b) (c) 8 8 6 6 (a) (b) 4 4 (c) (d) 2 2 (d) 0 0 outside bending strain (%) outside bending strain (%) (e) - - 2 2 - - 4 4 - - 6 6 (e) - - 8 8 0 0 0.5 0.5 1 1 1.5 1.5 2 2 2.5 2.5 3 3 3.5 3.5 4 4 4.5 4.5 5 5 thrust strain (%) thrust strain (%)

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

  16. 0 PIPE 90 180 Demand vs. capacity OUTSIDE STRAIN AT 6.4 FT 6 Buckling Yielding 4 2 0 180 120 30 0 outside bending strain (%) 150 90 60 -2 -4 -6 0 1 2 3 4 5 thrust strain (%) uniform ML90 backfill, Epipe = long-term modulus

  17. 0 PIPE 90 180 Demand vs. capacity OUTSIDE STRAIN AT 12.5 FT 6 Buckling Yielding 4 2 0 180 30 120 0 outside bending strain (%) 90 60 150 -2 -4 -6 0 1 2 3 4 5 thrust strain (%) uniform ML90 backfill, Epipe = long-term modulus

  18. 0 PIPE 90 180 Demand vs. capacity OUTSIDE STRAIN AT 15.6 FT 6 Buckling Yielding 4 2 0 30 180 120 0 outside bending strain (%) 90 60 150 -2 -4 -6 0 1 2 3 4 5 thrust strain (%) uniform ML90 backfill, Epipe = long-term modulus

  19. Depth of fill predictions Depth of fill, m (ft), at limit of Backfill Soil Pipe Modulus Buckling Strain of Profile Limit NOMINAL PREDICTION (ALL SAFETY FACTORS = 1) Uniform E 6.4 (21) 7.9 (26) 50 Non - Uniform E 4.9 (16) 5.5 (18) 50 ML90 Uniform E >20.4 (> 67) >20.4 (> 67) i Non - Uniform E >20.4 (> 67) >20.4 (> 6 7) i DESIGN PREDICTION (WITH SAFETY FACTORS*) Uniform E 2.7 (9) 3.7 (12) 50 Non - Uniform E 2.6 (8.5) 2.9 (9.5) 50 ML90 Uniform E 9.1 (30) 20.1 (66) i Non - Uniform E 9.8 (32) 13.4 (44) i * 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: Soil Type Condition SW95 SW95 SW90 SW90 ML90 ML90 Considering Local Buckling Design Design 6.4 (21.1) 6.4 (21.1) 4.2 (13.9) 4.2 (13.9) 3.0 (9.7) 3.0 (9.7) Ultimate Ultimate 16.3 (53.4) 16.3 (53.4) 9.7 (31.7) 9.7 (31.7) 6.3 (20.6) 6.3 (20.6) Ignoring Local Buckling Design Design 8.8 (28. 8.8 (28. 9) 9) 5.7 (18.7) 5.7 (18.7) 3.9 (12.8) 3.9 (12.8) Ultimate Ultimate 21.3 (>70) 21.3 (>70) 13.1 (43.0) 13.1 (43.0) 8.3 (27.3) 8.3 (27.3)

  21. Comparison • Depth of fill predictions • AASHTO with ML90 fill • 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) • Simulation model with non-uniform ML90 • 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. • 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.

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