Bolt reinforcement of the tunnel face

Kolloquium Bauhilfsmassnahmen im Tunnelbau

ETH Zürich

Paolo Perazzelli Pini Swiss Engineers, Zurich

• Introduction

• On the effect of the design parametersgrounds above the water tablegrounds below the water table (drained and undrained)

• Conclusions

Outline

• Analysis method

• Ground reinforcement using bolts is a very effective measure for stabilizing the face in conventional tunnelling

IntroductionGeneral overview

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

• 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

• 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

• 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

Total lenght L = 12 m

(a) Large installation interval

IntroductionRelevant design parameters

Total lenght L = 12 m

Installation interval l = 8 m

(a) Large installation interval

IntroductionRelevant design parameters

Overlapping L’ = 4 m

Total lenght L = 12 m

Installation interval l = 8 m

(a) Large installation interval

New bolts

IntroductionRelevant design parameters

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

Analysis method

General concept - Failure mechanism

Ground above the water table

Ground below the water table – drained

Ground below the water table – undrained

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

Analysis method

General concept - Failure mechanism

Ground above the water table

Ground below the water table – drained

Ground below the water table – undrained

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)

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

Analysis method

General concept - Failure mechanism

Ground above the water table

Ground below the water table – drained

Ground below the water table – undrained

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

Analysis method

General concept - Failure mechanism

Ground above the water table

Ground below the water table – drained

Ground below the water table – undrained

Analysis methodGround below the water table – undrained

• Bearing capacity of wedgeLimit equilibrium of the entire wedge su, sat

su, sat

• Trapdoor loadUpper bound approach

Analysis methodGround below the water table – undrained

D

h

s

su

Ground surface

Comparison with experimental results and other methods

Analysis methodSupport pressure given by the bolts

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

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

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]

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]

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

Analysis methodComputation of the minimum required number of bolts

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)

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

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

Analysis methodDesign tools

• Design charts

For the special case of a homogeneous ground with uniform face reinforcement

Tunnel+

Analysis methodDesign tools

• Tunnel+ (free App for smartphones)

For the special case of a homogeneous ground with uniform face reinforcement

Analysis methodDesign tools

For the most general case of heterogeneous ground and arbitrary bolt distribution

• Standalone computer application with Graphical User Interface

On the effect of the design parametersGrounds above the water table

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

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

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

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

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

On the effect of the design parametersGrounds below the water table - drained

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

On the effect of the design parametersGrounds below the water table - undrained

On the effect of the design parametersGrounds below the water table - undrainedOver-consolidation ratio

On the effect of the design parametersGrounds below the water table - undrainedOverburden

OCR = 1.0

On the effect of the design parametersGrounds below the water table - undrainedOverlapping length

OCR = 1.0

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

Thank you for the attention!

Paolo Perazzelli Pini Swiss Engineers, Zurich