face and excavation stability - escuelaing.edu.co · anagnostou & kovari, 1994. eesc/usp...
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EESC/USP
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Face and Excavation Stability 1
Face and
Excavation
Stability
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Face and Excavation Stability 2
1 Introduction
2 Model Tests
3 Limit Analysis Model
4 Comparison with Reduced
Model Tests
5 Face stability control EPB
and slurry shield
5 Conclusions
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Face and Excavation Stability 3
1 Introduction
Importance of Stability -
recent accidents
Shallow and deep tunnels
Local and global effects
Circular cross sections - 3D
Excavation face
Analysis methods
Empirical
Force equilibrium
Theory of plasticity
Numerical analysis
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Face and Excavation Stability 4
Stability
Broms & Bennermark (1967)
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Face and Excavation Stability 5
Broms & Bennermark (1967)
Collapse: sv > (6~8) Cu
sv = total vertical stress
Cu = undrained cohesion
sT = internal pressure
N = stability number
u
Tv
CN
ss
sv
DC ss
2
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Face and Excavation Stability 6
3 Limit Analysis Models
a) Undrained Condition
Terzaghi (1947)
Broms & Bennermark (1967)
Davis et al. (1980)
Heinz (1988) - Mülhaus’
extended model
b) Drained Condition
Atkinson & Potts (1977)
Leca & Dormieux (1990)
Heinz (1988)
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Face and Excavation Stability 7
Casarin & Mair (1981)
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Face and Excavation Stability 8
N x Ld and N x C
Casarin & Mair (1981)
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Face and Excavation Stability 9
Undrained tests on
reduced models
Comparison of analytical
and experimental results
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Face and Excavation Stability 10
Lower and Upper Bound
Solutions
Davis et al. (1980)
Case 1
Lower bound
Infinite excavation
2-D problem
1
2ln2
D
C
Cu
Ts ss
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Face and Excavation Stability 11
Case 1 - Upper Bound
Upper and Lower Bound
for Case 1
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Face and Excavation Stability 12
Case 2
Lower Bound
Ewing & Hill (1967)
Upper Bound
Upper and Lower Bound for
Case 2
1ln22
D
C
Cu
Ts ss
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Face and Excavation Stability 13
Case 3
Lower Bound L/D = 0
Case 3a
Case 3b
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Face and Excavation Stability 14
Case 3
Upper Bound
Summary Case 3
Local collapse
no dependency on C
Lower Bound
Upper Bound
628.36915.42318.0
2
D
C
D
CN
63.5uC
D
28.8uC
D
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Face and Excavation Stability 15
Case 3
Heinz (1985) - Extended
Mülhals’ Model
face and unsupported span
represented by the inner sphere
evaluation of maximum
unsupported span L
1
21
4
u
Ts
Ce
D
C
D
L
ss ,
1
21ln4
2
D
L
D
C
N
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Face and Excavation Stability 16
Test Results Versus Limit Analysis
L/D = 0
L/D = 0
0
1
2
3
4
5
6
7
8
9
10
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5
C/D
N
LB1
LB2
LB3a
LB3b
UB1
UB2
UB3
Casarin (1977)
Mair (1979)
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Face and Excavation Stability 17
Test Results Versus Limit Analysis
L/D = 0.5
L/D = 0.5
0
1
2
3
4
5
6
7
8
9
10
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5
C/D
N
LB1
LB2
LB3a
Heinz
UB1
UB2
UB3
Casarin (1977)
Mair (1979)
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Face and Excavation Stability 18
Test Results Versus Limit Analysis
L/D = 1.0
L/D = 1.0
0
1
2
3
4
5
6
7
8
9
10
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5
C/D
N
LB1
LB2
LB3a
Heinz
UB1
UB2
UB3
Casarin (1977)
Mair (1979)
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Face and Excavation Stability 19
Test Results Versus Limit Analysis
L/D = 2.0
L/D = 2.0
0
1
2
3
4
5
6
7
8
9
10
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5
C/D
N
LB1
LB2
LB3a
Heinz
UB1
UB2
UB3
Mair (1979)
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Face and Excavation Stability 20
Test Results Versus Limit Analysis
L/D
L/D = infinity
0
1
2
3
4
5
6
7
8
9
10
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5
C/D
N
LB1
LB2
LB3a
UB1
UB2
Mair (1979)
Infinity
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Face and Excavation Stability 21
5 Conclusions
Broms & Bennermark’s analysis
unsafe
Discrepancy of analytical and
experimental results: caution when
choosing model
Seepage forces and gravity may
increase evaluation errors
UNDRAINED CONDITION
L/D=0
take N=max{LB3A; Heinz}
L/D>0
take N=max{LB1; Heinz}
uvT NCss
2
DCsv ss
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Face stability controlEPB and slurry shield
Face and Excavation Stability 22
Anagnostou & Kovari, 1994
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Types of shield
machines
Face and Excavation Stability 23
Compressed air
EPB
Slurry shield
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Limit equilibrium face stability analysis
Face and Excavation Stability 24
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Membrane model
no penetration
Face and Excavation Stability 25
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Slurry penetration
into the groung
Face and Excavation Stability 26
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Membrane model
typical results
Face and Excavation Stability 27
D=10m
H=10m
Hw=5m
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EPB model
seepage foces
Face and Excavation Stability 28
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3-D seepage at
tunnel face
Face and Excavation Stability 29
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Face and Excavation Stability 30
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Face and Excavation Stability 31
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Effective support
pressure
Face and Excavation Stability 32
f=30o
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Effective and total
support (c=0, f=30o)
Face and Excavation Stability 33