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
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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
