# Numerical Simulation of Pipe-Soil Interaction by zzt18091

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```									  Numerical Simulation of Pipe-Soil Interaction

Diana Lorena Castaño Acevedo

Grupo de Investigación en Geotecnía
Universidad de Los Andes – Bogotá, Colombia
-CeiBa-

Abril 3 de 2009

Diana Lorena Castaño A. Buenos Aires                    1 / 19
Introduction
Considerations – Spangler, Marston and FEM

• Differs between kinds of Pipes
(Flexible / Rigid)
• Soil is considered to have an Elastic
behavior
• Fill is considered to have an Elastic
Behavior
• Only properties of a vertical column
of soil/fill affect results

• Model has an exact geometry, which includes trench
angle (b)
• Different constitutive models can be used in natural soil
• Different constitutive models can be used in fill
• It takes into account the different friction coefficients
that exist between materials.
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Diana Lorena Castaño A. Buenos Aires                                             2 / 19
Outline

2. Constitutive Methods
3. FEM Analysis
4. Results
5. Numerical Example – Emisario Cartagena
6. Preliminary Design Abaqus

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Diana Lorena Castaño A. Buenos Aires            3 / 19
Flexible Pipes – Spangler Theory
In flexible pipes, pipe material stiffness is negligible in
comparison with soil stiffness.
Δχ =
DL KWc r 3      Δy   (DLWc + Wl )Wc
EI + 0,061E´r 3      =
D 149 PS + 61000 M s
Where,
DL         Deflection Factor
K          Foundation Constant
Wl         Live load at top of pipe (N/m2)
E          Youngs Modulus (Elasticity)
π
I          Inertia Modulus per pipe length       I=
64
(D   4
−d4   )
E´         Soil Modulus
PS         Pipe stiffness (kPa)
Ms         Constrained soil modulus (MPa)
D          Outer pipe diameter                                               4 / 65

Δy         Vertical pipe diameter variation
Δχ         Horizontal pipe diameter variation
Diana Lorena Castaño A. Buenos Aires                                  4 / 19
Rigid Pipes – Marston Theory

In Rigid Pipes, pipe stiffness is much higher than soil stiffness.
It is necessary to determinate if pipe resistance is enough to

⎛        ′ ⎞
(V + dV ) + ⎜ 2 Kμ V ⎟dh = V + γBd dh
⎜        ⎟
⎝   Bd     ⎠
⎛        ′ ⎞
(V + dV ) + ⎜ 2 Kμ V ⎟dh − V + γBd dh = 0
⎜        ⎟
⎝   Bd     ⎠
dV ⎛        2 Kμ ′V          ⎞
= ⎜ λBd −                  ⎟
dh ⎜⎝         Bd             ⎟
⎠

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Diana Lorena Castaño A. Buenos Aires                                 5 / 19
FEM Analysis
Constitutive Models - Elastic Model

The general expression of Hooke's Law

⎡1         1            ⎤
σ ik = Ciklm ε lm = λδ ik δ lmε + 2μ ⎢ δ il δ km ε lm + δ imδ kl ε lm ⎥
⎣2         2            ⎦
lm

σ = λtr [ε ]1 + 2μ ε
σ = λe1 + 2με

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Diana Lorena Castaño A. Buenos Aires                                6 / 19
FEM Analysis
Constitutive Models - Hypoplastic Model

Hypoplasticity is a constitutive model developed for granular
soils. It is constitutive equation should be written in an
incremental way. Wollfersdorff equation (1996) improves
mathematic formulation introducing four material constants that
depend on stress and void relation and four other calibration
constants that do not vary with material.

Where,

D         Strain rate

fb        Barotropic’s factor

fe        Pyknotropy factor
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fd        Density factor

Diana Lorena Castaño A. Buenos Aires                       7 / 19
FEM Analysis
Constitutive Models - Hypoplastic vs Viscohypoplastic model

1. Barotropic Factor is modified
2. Pyknotropy and Density factor are removed.
3. Void dependecy is introduced by OCR parameter

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Diana Lorena Castaño A. Buenos Aires            8 / 19
FEM Analysis
Geometry & Boundary Condition

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Diana Lorena Castaño A. Buenos Aires            9 / 19
Results

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Diana Lorena Castaño A. Buenos Aires        10 / 19
Results
FEM Results

U2 Deformation for
elastic natural soil
material

U2 Deformation for
viscohypoplastic
natural soil material

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Diana Lorena Castaño A. Buenos Aires                        11 / 19
Results
FEM Vs Actual design

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Diana Lorena Castaño A. Buenos Aires        12 / 19
Results
Bedding Base Displacement

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Diana Lorena Castaño A. Buenos Aires        13 / 19
Results
Vertical Pipe Diameter Variation: Flexible pipe Vs Rigid pipe in FEM

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Diana Lorena Castaño A. Buenos Aires             14 / 19
Numerical Example 2 – Emisario Terrestre Cartagena
Geometry and materials

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Diana Lorena Castaño A. Buenos Aires        15 / 19
Numerical Example 2 – Emisario Terrestre Cartagena
Measurements – Data Validation

AGUAS DE CARTAGENA S.A. E.S.P.
ALC-06-BM-2006 - PROJECT EMISARIO TERRESTRE
Deflections in installation PRFV Pipes

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Diana Lorena Castaño A. Buenos Aires        16 / 19
Numerical Example 2 – Emisario Terrestre Cartagena
Results

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Diana Lorena Castaño A. Buenos Aires        17 / 19
Preliminary Design Abaqus

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Diana Lorena Castaño A. Buenos Aires        18 / 19
Acknowledgment

Thanks !

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Diana Lorena Castaño A. Buenos Aires        19 / 19

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