Synthesis of numerical methods for the design of segmental tunnel lining

Presented by : TRAD Rim

Supervised by : MROUEH Hussein

BIAN HanbingCORMERY Fabrice

SUS 2019 , 8-10 October 2019, Lille , France

1

1. Framework2. Existing Design methods3. Development of new method4. Case study (Project): conveyance Tunnel 5. Analysis 6. Conclusion & Perspectives

Outline

2Rim TRAD – SUS 2019 – 10 October – Lille, France

Framework

3Rim TRAD – SUS 2019 – 10 October – Lille, France

• Many of tunnel are installed by TBM

• Complexity of studying the structurebehavior due to the presence of joints

• Discontinuity of joints → Reduction ofrigidity [JIN 2017]

How the numerical model can take into account this discontinuity?

Existing Design methods (1/2)

4Rim TRAD – SUS 2019 – 10 October – Lille, France

Indirectmethod

• Analytical approach , RDM• Reduced rigidity factor “η”

Direct method

• Analytical method• Longitudinal Joint : rotational springs ; circumferential joints : Shear

springs• (M – θ) linear, nonlinear? • Active and passive loads

Existing Design methods(2/2)

5Rim TRAD – SUS 2019 – 10 October – Lille, France

Is it necessary to use complex 3D models?

Numericalmethods

• Finite element analysis (2D,3D)• Interface, bolt, soil, behavior of concrete• Large computation time

Development of new method

6Rim TRAD – SUS 2019 – 10 October – Lille, France

Ø Friendly-method / macro-element : Consider the complex local behaviourof joints by the mean of global approach with globalized parameters

Ø Our study:§ Influence of number of joints.§ Comparative study for different methods

Case study (1/2)

7Rim TRAD – SUS 2019 – 10 October – Lille, France

Exploring the three-dimensional response of a water storage and sewage tunnel based on full-scale loading tests

Case study (2/2)

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modèle étudié

0

Diameter(m)

Thickness(m)

Width(m) Material Loads

(KN)

9 m 0.65 1.5Concrete

reinforced C60

1000

(Uz;Ry) (Ux;Uz;Ry)180X

Z

[HUANG 19]

Analysis (1/4)

9Rim TRAD – SUS 2019 – 10 October – Lille, France

Indirect method Direct method

Applying a reduction factor

η of EI

• Segments → Beams• Joints → Rotational

springs

Direct methodIndirect method

𝜼 =𝑬𝑰 𝒆𝒒𝑬𝑰

Joints

-10

-5

0

5

10

0 19 39 58 77 96 116

135

154

174

Conv

erge

nce

defo

rmat

ion

(cm

)

Angle (degree)

Convergence deformation

directlinear

Exp

Analysis (2/4)1. Number of joint

10Rim TRAD – SUS 2019 – 10 October – Lille, France

0

20

40

60

80

100

4000 6000 8000 10000 15000 20000 30000 40000 50000

Disp

lace

men

t (c

m)

Kθ (kN.m/rad)

Relationship between displacement and joint rotational stiffness for different number of joints

4 joints

6 joints

8 joints

-1500

-1000

-500

0

500

1000

1500

0 30 60 90 120 150 180

mom

ent r

educ

tion

fact

or

angle (degree)

Variation of moment reduction factor with number and orientation of joints.

4 joints6 joints

8 joints

Analysis (3/4)

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2. Comparative study : Direct method (using linear behavior joint)

Rim TRAD – SUS 2019 – 10 October – Lille, France

• The numerical results show a significantreduction of bending moment when theeffect of distribution of joints is taken.

• According to the indirect method, it isnoted that as the joint stiffness factorincreases, the displacement decreases.

η : reduced rigidity factor

-2500-2000-1500-1000

-5000

5001000150020002500

0 50 100 150

Bend

ing

mom

ent (

KN.m

)

angle (degree)

Variation of bending moment

ExpContinuousDirect linear

-10

-5

0

5

10

0 50 100 150

Conv

erge

nce

defo

rmat

ion

(cm

)

Angle (degree)

Convergence deformation

continous

η 0,11

η 0,25

η 0,4

η 0,6

η 0,8

direct linear

Exp

Analysis (4/4)2. Comparative study : Direct method (using elastic perfectly plastic behavior of joint)

12Rim TRAD – SUS 2019 – 10 October – Lille, France

• Very low variation• Elastic perfectly plastic behavior of jointshas a greater value than other !

-2500-2000-1500-1000

-5000

5001000150020002500

0 50 100 150

Bend

ing

mom

ent (

KN.m

)

angle (degree)

Variation of bending moment

ExpContinuousDirect linearDirect non linear

-10-8-6-4-202468

10

0 50 100 150

Conv

erge

nce

defo

rmat

ion

(cm

)

Angle (degree)

Convergence deformation

direct linear

direct nonlinear

Exp

Conclusion & Perspectives

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• Displacement obtained by different methods are not similar

• These methods can be applied but need calibration

• A real finite element calculation of joints is needed

• Introducing the concept of macro-element:

ØConsidering all material and geometrical nonlinearities of jointsØWithout using a complex three-dimensional and non-linear calculation

Rim TRAD – SUS 2019 – 10 October – Lille, France

Thank You For Your Attention

14Rim TRAD – SUS 2019 – 10 October – Lille, France

References

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• [DO 14] :N. A. Do, D. Dias, P. Oreste, I. Djeran-Maigre. J. INT J NUMER ANAL MET 38, 1617–1632(2014)

• [TEA 10]: S. Teachavorasinskun, T. Chub-uppakarn, .J. TUNN UNDERGR SP TECH 25, 490–494 (2010)• [JIN 17]: Y. Jin, W. Ding, Z. Yan, K. Soga, Z. Li. J. TUNN UNDERGR SP TECH 68, 153– 166 (2017)

• [Huang 19]: X. Huang et al. J. TUNN UNDERGR SP TECH 88, 156–168 (2019).

Rim TRAD – SUS 2019 – 10 October – Lille, France