Finite Element Analysis of Creep Buckling of CIPP Liners

Martin Zhao

10/25/2006

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 10/25/2006 Mercer University 2

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 10/25/2006 Mercer University 3

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 Finite element simulation of creep package for offshore platforms with a wave interferometry (USTC) structure with damping (BIIC) 10/25/2006 Mercer University 4

Twin Towers

: how did they collapse?

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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 ?

 

F A

 

U

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Models – Buckling in Columns

   Euler Formula (1744)

F cr



EI



L

2 2 Governing Equation

d

2

x dx

2 

F EI w

 0 Extended Euler Formula

F cr



EI

 2

L eff

2 cantilever (free clamped) clamped 10/25/2006 clamped

L eff = 2L L eff = L/2

Mercer University Simply Supported (hinged hinged) 7

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 10/25/2006 Mercer University 8

Creep Mechanism

 Dislocation: linear defect in 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 10/25/2006 Mercer University 9

Models for Creeping

   Bailey creep law – for both primary and secondary phase 

CR

 

m t n

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 

CR

 

t

(  )

t n

The significance of creep-induced buckling: critical pressure needs to be replaced by

critical time ( T cr

) 10/25/2006 Mercer University 10

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 10/25/2006 Mercer University 11

Design Practices

 Design code (ASTM-93) based on critical pressure for free standing pipe (Bresse, 1866) and enhancement effect of from the host pipe Free standing pipe

P cr

 3

EI

Encased liner

P design

3

R

 7

P cr

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Analytical Approximation

 With the assumption that the buckled portion maybe expressed as

u



u

0 cos 2    2    Glock (1977) derived that the critical pressure of encased pipe will be

P G cr

 1 

E

 2

t D

2 .

2 0 .

8 which suggests an enhancement factor

K G

 1 2

D t

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CIPP Research at TTC, LaTech

 Short-term and long-term material characterization   240 210 180 Instantaneous buckling tests 0.012

0.01

Long-term (10,000-hr) buckling tests 0.008

Ptest 1-lobe 2-lobe 0.006

0.004

0.002

0 0.01

0 0.008

150 0.006

120 0.004

90 0.002

60 30 35 40 45 50

DR

55 60 65 0 0 10/25/2006 Mercer University 1000 2000

Tim e (hr)

1000

Tim e (hr)

2000 3000 3000 14

Finite Element Method

 Minimum total potential energy principle The 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 10/25/2006 Mercer University 15

FE Modeling of CIPP Liners

   Material properties 0.012

0.01

 Elastoplasticity 0.008

0.006

 Creep 0.004

Buckling 0.002

0 0 Contact: liner with the rigid confine 0.01

0.008

0.006

0.004

0.002

0 0 1000

Tim e (hr)

2000 1000

Tim e (hr)

2000 10/25/2006 Mercer University 3000 3000 16

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

P cr

240 210 180 150 120 90 60 30 35 10/25/2006 40 45 50

DR

55 Ptest 1-lobe 2-lobe 60 65 Mercer University 17

Results:

1- to 2-lobe mode transition

 Start with a combined effect of the two competing collapse mechanisms, and end with transition into one-lobe mode 10/25/2006 Mercer University 18

Results:

Creep Buckling

 A model relating critical time and dimensionless pressure ratio is proposed

T cr



T

0 (

b

/

PR

 1 )

n

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Result:

Design Guidelines

 Critical time vs. critical pressure 10/25/2006 Mercer University 20

Q & A

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Other Training & Experience

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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 10/25/2006 Mercer University 23