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Bolt reinforcement of the tunnel face
Kolloquium Bauhilfsmassnahmen im Tunnelbau
ETH Zürich
Paolo Perazzelli Pini Swiss Engineers, Zurich
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• Introduction
• On the effect of the design parametersgrounds above the water tablegrounds below the water table (drained and undrained)
• Conclusions
Outline
• Analysis method
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• Ground reinforcement using bolts is a very effective measure for stabilizing the face in conventional tunnelling
IntroductionGeneral overview
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16
total length of the bolt (L)
9.8 m
1.25 m
12 m
A
A
A-A
shotcrete and steel sets
excavation round
face bolt
pipes umbrella
bolting density (n)
installation interval (l)
Detail 1
diameter of the bolt (db)
ground
groutbolt
diameter of the borehole (d)
Detail 1
face bolt
IntroductionGeneral overview
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• Anagnostou, G., Serafeimidis, K., 2007. The dimensioning of tunnel face reinforcement. World Tunnel Congress 2007 (Prague)
• Serafeimidis, K., Ramoni, M., and Anagnostou, G. (2007). Analysing the stability of reinforced tunnel faces. Europ. Conf. on Soil Mech. and Geotech. Eng. (Rotterdam)
• Perazzelli, P., Anagnostou, G., 2013. Stress analysis of reinforced tunnel faces and comparison with the limit equilibrium method. Tunnel. Undergr. Space Techn. 38, 87–98
• Anagnostou, G., Perazzelli, P., 2015. Analysis method and design charts for bolt reinforcement of the tunnel face in cohesive-frictional soils. Tunnel. Undergr Space Techn. 47, 162–181
• Perazzelli, P., Anagnostou, G., 2017. Analysis method and design charts for bolt reinforcement of the tunnel face in purely cohesive soils. Journal of geotechnical and geoenvironmental engineering, 143 (9), American Society of Civil Engineers.
• Perazzelli, P., Cimbali, G., Anagnostou, G., 2017. Stability under seepage flow conditions of a tunnel face reinforced by bolts. EUROCK 2017 (Ostrava)
IntroductionResearch at the ETH Zurich
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• Surface load• Unit weight of the ground• Level of the water table• Overburden• Shape and dimension of the tunnel• Unsupported span
• Strength of the ground (c’, ’, su)• Bond strength of bolt/grout and grout/ground• Tensile resistance of the bolt• Bolting density• Bolting type (diameter, with/without plate,…)• Bolting length and installation interval
Load
Resistance
IntroductionRelevant design parameters
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• Surface load• Unit weight of the ground• Level of the water table• Overburden• Shape and dimension of the tunnel• Unsupported span
• Strength of the ground (c’, ’, su)• Bond strength of bolt/grout and grout/ground• Tensile resistance of the bolt• Bolting density• Bolting type (diameter, with/without plate,…)• Bolting length and installation interval
Load
Resistance
IntroductionRelevant design parameters
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Total lenght L = 12 m
(a) Large installation interval
IntroductionRelevant design parameters
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Total lenght L = 12 m
Installation interval l = 8 m
(a) Large installation interval
IntroductionRelevant design parameters
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Overlapping L’ = 4 m
Total lenght L = 12 m
Installation interval l = 8 m
(a) Large installation interval
New bolts
IntroductionRelevant design parameters
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Overlapping L’ = 4 m
Total lenght L = 12 m
New bolts
Installation interval l = 8 m
(b) Small installation interval
Installation interval l = 3 m Overlapping L1’ = 3 m, L2’ = 6 m, L3’ = 9 m
(a) Large installation interval
Total lenght L = 12 m
New bolts
IntroductionRelevant design parameters
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Analysis method
General concept - Failure mechanism
Ground above the water table
Ground below the water table – drained
Ground below the water table – undrained
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Analysis methodGeneral concept - Failure mechanism
Vtrap
Depth of cover (h)
1
2
3
2 3 1 2
• Limit equilibrium conditionTrapdoor load Vtrap = Bearing capacity of wedge Vres
B
H
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Analysis method
General concept - Failure mechanism
Ground above the water table
Ground below the water table – drained
Ground below the water table – undrained
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Analysis methodGround above the water table
x = pyGround surface
Vtrap
dTs
dT dT
dNdN
x = wy
c’, ’, dry
c’, ’, dry
• Bearing capacity of wedgeLimit equilibrium of slices
• Trapdoor loadLimit equilibrium of slices(silo theory)
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Analysis methodGround above the water table
s [kPa]
’ [°]
D
h
s
c’=0, ’
Ground surface
p = w = 1
Comparison with experimental results and other methods
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Analysis method
General concept - Failure mechanism
Ground above the water table
Ground below the water table – drained
Ground below the water table – undrained
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Analysis methodGround below the water table – drained
Ground surface
Vtrap
dTs
dT dT
dNdN
dFx
dFy
c’, ’, ’
c’, ’, ’
• Bearing capacity of wedgeLimit equilibrium of slices
• Trapdoor loadLimit equilibrium of slices
• Trapdoor loadLimit equilibrium of slices(silo theory)
x = py
x = wy
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Analysis method
General concept - Failure mechanism
Ground above the water table
Ground below the water table – drained
Ground below the water table – undrained
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Analysis methodGround below the water table – undrained
• Bearing capacity of wedgeLimit equilibrium of the entire wedge su, sat
su, sat
• Trapdoor loadUpper bound approach
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Analysis methodGround below the water table – undrained
D
h
s
su
Ground surface
Comparison with experimental results and other methods
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Analysis methodSupport pressure given by the bolts
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Analysis methodSupport pressure given by the bolts
s = n*min [Ft, max(min(dm, dbg)a, Fp), min(dm, dbg)a(L’-a)]
Bolting density
Tensile resistance of the bolt
Bearing capacity of the bolt plate
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Analysis methodSupport pressure given by the bolts
s = n*min [Ft, max(min(dm, dbg)a, Fp), min(dm, dbg)a(L’-a)]
Pull-out resistance outside the sliding wedge
Pull-out resistance inside thesliding wedge
db
m
a
overlapping length L’
m
L’-a
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Analysis methodSupport pressure given by the bolts
35°
L-l=3m150 100 50 0
n=1 bolt/m2
L=12 m l=9 m
z1
z2
s [kPa]
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Analysis methodSupport pressure given by the bolts
35°
35°
20°
L-l=3m150 100 50 0
z1
z2
n=1 bolt/m2
L=12 m l=9 m
s [kPa]
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Analysis methodSupport pressure given by the bolts
35°
L-l=3m150 100 50 0
z1
z2
35°
L-2l=3m
L-l=7.5m
n=1 bolt/m2
L=12 m l=9 m
s [kPa]
n=1 bolt/m2
L=12 m l=4.5 m
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Analysis methodComputation of the minimum required number of bolts
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Analysis methodComputation of the minimum required number of bolts
- For fixed failure mechanism i, required density of bolts ni is such that limit equilibrium condition fulfilled
- Minimum required number of bolts ncr = max (ni)
Vtrap
s (n)
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Analysis methodComputation of the minimum required number of bolts
For the special case of a homogeneous ground with uniform face reinforcement
• n = n(zf) (closed form solution)
• ncr = max [n(zf)]
c’=0, ’
n (bolts / m2)
z
c’, ’,
zf
→simple optimization problem (one-variable)
• Limit equilibrium condition
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Analysis methodComputation of the minimum required number of bolts
→complex optimization problem (multi-variable):numerical solution based on the simplex method
For the most general case of heterogeneous ground and arbitrary bolt distribution
c’=0, ’
n (bolts / m2)
z
zf
c’1, ’1, 2
c’2, ’2, 2
c’3, ’3, 3
n1
n2
• N = min ∑ nkAk
Vres (zf) ≥ Vtrap (zf)
V(zf, zi) ≥ 0zi
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Analysis methodDesign tools
• Design charts
For the special case of a homogeneous ground with uniform face reinforcement
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Tunnel+
Analysis methodDesign tools
• Tunnel+ (free App for smartphones)
For the special case of a homogeneous ground with uniform face reinforcement
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Analysis methodDesign tools
For the most general case of heterogeneous ground and arbitrary bolt distribution
• Standalone computer application with Graphical User Interface
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On the effect of the design parametersGrounds above the water table
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On the effect of the design parametersGrounds above the water table
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20
n [b
olts/
m2 ]
c [kPa]
B
C
A
h (m) =
∞∞
∞
48
= 25°
8 m
8 m
8 m4 m
8 m 4 m
A B C c’=0, ’
n (bolts / m2)
h = var
L = 12 m l = 9 m,m = 150 kPa,d = 114 mm
’ = 25°c’ = var= 20 kN/m3
z
n cr
[bol
ts/m
2 ]Overburden and shape of the face
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20
n [b
olts/
m2 ]
c [kPa]
B
C
A
h (m) =
∞∞
∞
48
= 25°
8 m
8 m
8 m4 m
8 m 4 m
A B C
53 bolts 11 + 11 = 2212 + 5 = 17
c’=0, ’
n (bolts / m2)
h = ∞
L = 12 m l = 9 m,m = 150 kPa,d = 114 mm
’ = 25°c’ = 5 kPa= 20 kN/m3
z
n cr
[bol
ts/m
2 ]
On the effect of the design parametersGrounds above the water tableOverburden and shape of the face
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c’=0, ’
n (bolts / m2)
L = 12 m l = var,m = 150 kPa,d = 114 mm
’ = 25°c’ = var= 20 kN/m3
z
On the effect of the design parametersGrounds above the water table
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20c [kPa]
= 25°
L = 12m l = 9m
L = 12m l = 4.5m
8 m
8 m
n cr
[bol
ts/m
2 ]
h = ∞
Installation interval
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c’=0, ’
n (bolts / m2)
L = 12 m l = var,m = 150 kPa,d = 114 mm
’ = 25°c’ = var= 20 kN/m3
z
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20c [kPa]
= 25°
L = 12m l = 9m
L = 12m l = 4.5m
8 m
8 m
n cr
[bol
ts/m
2 ]
h = ∞
meters of bolts installed per linear meter of tunnel102.4 m/m’
68.3 m/m’
Installation interval
On the effect of the design parametersGrounds above the water table
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c’=0, ’
n (bolts / m2)
h = 30 m
L = 12 m l = 6 m,m = 150 kPa,d = 114 mm
’ = 25°c’ = 10 kPa= 20 kN/m3
z
n (bolts / m2)
H
2H/3
H/3
H
3H/4
H/2
H/4
H
H/2
8 m
8 m10 m
e= 1 m
n (bolts / m2)n (bolts / m2)
z zz
0.35
0.28
0.39
0.23
0.59
0.040.0
0.52
0.35
0.22
28 bolts 29 bolts 34 bolts 35 bolts
10 m
On the effect of the design parametersGrounds above the water tableSpatial bolt distribution
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On the effect of the design parametersGrounds below the water table - drained
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8 m
8 m
c’=0, ’
n (bolts / m2)
h = 8 m
L = 16 m l = 8 m,m = 150 kPa,d = 114 mm
’ = varc’ = vart’ = 0’ = 12 kN/m3
z
8 m
35 bolts
h0 = 2H
On the effect of the design parametersGrounds below the water table - drainedDrainage boreholes
Without advance drainage
With advance drainage
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On the effect of the design parametersGrounds below the water table - undrained
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On the effect of the design parametersGrounds below the water table - undrainedOver-consolidation ratio
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On the effect of the design parametersGrounds below the water table - undrainedOverburden
OCR = 1.0
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On the effect of the design parametersGrounds below the water table - undrainedOverlapping length
OCR = 1.0
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Conclusions
• Experience and predictions prove that ground reinforcement using bolts is a very effective measure for stabilizing the tunnel face
• Big overlapping length are required in undrained soils
• Drainage boreholes are required in soils below the water tableunder drained conditions
• Excavation method and installation interval of the bolts affect significantly the required quantity of bolts (Top heading and Bench excavation method and small installation intervals allow to reduce the quantity of bolts)
• The uniform distribution is not the optimal one. A computational method was developed for the optimization of the face reinforcement
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Thank you for the attention!
Paolo Perazzelli Pini Swiss Engineers, Zurich