Finite Element Analysis of Creep Buckling of CIPP Liners

1. Finite Element Analysis of Creep Buckling of CIPP Liners Martin Zhao 10/25/2006

2. Topics • Personal Background • An Introduction to Creep and Buckling • Cured-In-Place (CIPP) Liners & Trenchless Technology • Finite Element Model and Analysis • Results and Discussions • Q & A Mercer University

3. Training & Experiences in Mechanics • Training in Solid Mechanics • B.S. – University of Science & Technology of China (USTC) • Training in Computer Aided Structural Analysis • M.S. – Beijing Institution of Information & Control (BIIC) • Experiences with Applied Computational Structural Dynamics at the Institute of Mechanics, under the Chinese Academy of Sciences • Training in Applied & Computational Analysis & Modeling (ACAM) • Ph.D. – Louisiana Tech University Mercer University

4. Typical Projects in Mechanics Long-term in-situ monitoring and structural dynamic analysis of a offshore production platform (W114A) located in South China Sea (IM/CAS) Residual stress distribution around cold-worked fastener holes using laser speckle interferometry (USTC) Finite element simulation of creep buckling of cured-in-place plastic (CIPP) liners under hydrostatic pressure (LaTech) Verification and enhancement of a FEA package for offshore platforms with a wave and current load generator and result visualization tool (IM/CAS) Finite element analysis of passive vibration control for an aerospace structure with damping (BIIC) Mercer University

5. Twin Towers: how did they collapse? Mercer University

6. Failure Mode • The failure mode can be summarized as • Local buckling (at the locale where they got hit), plus • Dynamic loading (from the top portion of each building to the remain lower potion) • What is buckling? Mercer University

7. Models – Buckling in Columns • Euler Formula (1744) • Governing Equation • Extended Euler Formula Simply-Supported (hinged-hinged) cantilever (free-clamped) Leff = 2L clamped-clamped Leff = L/2 Mercer University

8. What is Creep? • Why do we need to know this? • Because it is the answer to the question“But why didn’t they buckle immediately after the collision?” Work hardening Mercer University

9. Creep Mechanism • Dislocation: linear defectin the crystalline may help explain both work hardening and creep • At low temperatures, a dislocation may become “jogged” by other interacting dislocations and hence hardens the material • At higher temperatures, that jog or dislocation may become mobile and climb to a direction perpendicular to the normal stress applied Mercer University

10. Models for Creeping • Bailey creep law – for both primary and secondary phase • Findley long-term model – for plastics under room temperature and constant stress. Based on 1900-hour experiment, supported by test data over a continuous time span as long as 26 years • The significance of creep-induced buckling: critical pressure needs to be replaced by critical time (Tcr) Mercer University

11. CIPP Application • Purpose • Trenchless, or no-dig • Maintain utility of sewer pipes and sanity of underground water environment • Problems • Long-term buckling under hydrostatic pressure • Design guidelines and criteria Mercer University

12. Design Practices • Design code (ASTM-93) based on critical pressure for free standing pipe (Bresse, 1866) and enhancement effect of from the host pipeFree standing pipe Encasedliner Mercer University

13. Analytical Approximation • With the assumption that the buckled portion maybe expressed as Glock (1977) derived that the critical pressure of encased pipe will be which suggests an enhancement factor Mercer University

14. CIPP Research at TTC, LaTech • Short-term and long-term material characterization • Instantaneous buckling tests • Long-term (10,000-hr) buckling tests Mercer University

15. Finite Element Method • Minimum total potential energy principleThe total potential energy, , is the sum of the elastic strain energy, U, stored in the deformed body and the potential energy, V, of the applied forces: • This energy is at a stationary position when an infinitesimal variation from such position involves no change in energy: • The equality between external and internal virtual work (due to virtual displacements) is: • Governing equilibrium equation for the system Mercer University

16. FE Modeling of CIPP Liners • Material properties • Elastoplasticity • Creep • Buckling • Contact: liner with the rigid confine Mercer University

17. Results: Instantaneous Buckling • One- and two-lobe buckling modes are found to give lower and upper bounds for critical pressures • Imperfections and yield limits have impacts on Pcr Mercer University

18. Results: 1- to 2-lobemode transition • Start with a combined effect of the two competing collapse mechanisms, and end with transition into one-lobe mode Mercer University

19. Results: Creep Buckling • A model relating critical time and dimensionless pressure ratio is proposed Mercer University

20. Result: Design Guidelines • Critical time vs. critical pressure Mercer University

21. Q & A Mercer University

22. Other Training & Experience Mercer University

23. What’s Shared in Common? • Using computing technologies to solve real world problems • Result visualization – making real truth easy to see • Game programming – make artificial images look real Mercer University