Finite Element Analysis of Creep Buckling of CIPP Liners

Finite Element Analysis of Creep Buckling of

CIPP Liners

Martin Zhao10/25/2006

10/25/2006 Mercer University 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


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


Verification and enhancement of a FEA package for offshore platforms with a wave and current load generator and result visualization tool (IM/CAS)

Typical Projects in Mechanics

Residual stress distribution around cold-worked fastener holes using laser speckle interferometry (USTC)Finite element analysis of passive vibration control for an aerospace structure with damping (BIIC)

Long-term in-situ monitoring and structural dynamic analysis of a offshore production platform (W114A) located in South China Sea (IM/CAS)

Finite element simulation of creep buckling of cured-in-place plastic (CIPP) liners under hydrostatic pressure (LaTech)


Twin Towers: how did they collapse?


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?

UA

F


Models – Buckling in Columns

Euler Formula (1744)

Governing Equation

Extended Euler Formula

2

2

L

EIFcr

2

2

eff

crL

EIF

Leff = L/2

02

2

wEI

F

dx

xd

Leff = 2L

Simply-Supported(hinged-

hinged)

cantilever(free-clamped)

clamped-clamped


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


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


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)

nmCR t

nt

CR t)(


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


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

3

3

R

EIPcr

crdesign PP 7 Encased liner


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

2

cos20uu

2.2

21

D

tEPG

cr 8.0

2

1

t

DK G


Short-term and long-term material characterization Instantaneous buckling tests Long-term (10,000-hr) buckling tests

0

0.002

0.004

0.006

0.008

0.01

0.012

0 1000 2000 3000Time (hr)

Ten

sile

Str

ain

0

0.002

0.004

0.006

0.008

0.01

0 1000 2000 3000Time (hr)

Co

mp

resi

ve S

trai

n

CIPP Research at TTC, LaTech

30

60

90

120

150

180

210

240

35 40 45 50 55 60 65DR

Pcr

(psi)

Ptest

1-lobe

2-lobe


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


FE Modeling of CIPP Liners

Material properties Elastoplasticity Creep

Buckling Contact: liner with the rigid confine

0

0.002

0.004

0.006

0.008

0.01

0.012

0 1000 2000 3000Time (hr)

Ten

sile

Str

ain

0

0.002

0.004

0.006

0.008

0.01

0 1000 2000 3000Time (hr)

Co

mp

resi

ve S

trai

n


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

30

60

90

120

150

180

210

240

35 40 45 50 55 60 65DR

Pcr

(psi)

Ptest

1-lobe

2-lobe


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


Results: Creep Buckling

A model relating critical time and dimensionless pressure ratio is proposed

ncr PRbTT )1/(0


Result: Design Guidelines

Critical time vs. critical pressure


Q & A


Other Training & Experience


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

Documents

Finite Element Analysis of Creep Buckling of CIPP Liners