AGS/IMM Technical Meeting 2002 on “Underground Excavation in Urban Environment”

Principles of Tunnel Lining Design

Dr. Morgan W. W. Yang Maunsell Geotechnical Services Ltd.

Basics GROUND

equilibrium

Interaction

SUPPORTS

compatibility

Tunneling is An Art GROUND TUNNELING

PLANNING

DESIGN

CONSTRUCTION

Interaction Among Planning, Studies and Design Process PLANNING •FINANCIAL •PROJECT •LOGISTICS •LAYOUT •OPERATION

P

S

D

STUDIES •GROUND •DEMAND •ACCESS •AD HOC

DESIGN •PERMANENT SUPPORTS •TEMPORARY SUPPORTS •METHODS OF CONSTRUCTION •MEANS OF CONSTRUCTION

Tunneling Procedure Geology Geotechnical investigations

Site investigation Line and orientation of the tunnel Ground characteristics: Primary stress, strength, water Fissures, anisotropy, etc Excavation method Structural method

Experience, estimation

Statical system analysis

Mechanical model By pass

Design criteria

Safety concept, failure hypothese Yes

Risk assessment

No

Concept aspects

Driving the tunnel

Field measurements

In situ monitoring: deformations stop?

Yes

For actual state only, Unknown safety margin

No ‘Safe’

After H. Duddeck, “Guidelines for the design of tunnels”

Options for Tunneling

A. M. Muir Wood (2000), “Tunnelling: Management by design”

Weak rock

Str onger ground

----------------------------------------------------------------------------------------------------Ground type Excavation Support ----------------------------------------------------------------------------------------------------Strong rock Drill-&-blast or TBM Nil or rockbolts + TBM or roadheader

Rockbolts, shorcrete etc.

OC clay

Open-face shielded TBM roadheader

Weak clay, silty clay

EPB closed-face machine

Sands, gravels

Closed-face slurry machine

Str onger support

Squeezing rock Roadheader

Varity of means of support depending on conditions Segmental lining or shotcrete etc. Segmental lining Segmental lining

After A. M. Muir Wood (2000), “Tunnelling: Management by design”

Development of Design Model -----------------------------------------------------------------------------------------------------

1. Research model

Explanation of phenomena Study actual loads and materials Analysis of parameters Establishing correspondence between theory and experiment

2. Technical model Developed for practical design Selection of dominant factors Idealization of loading, physical characteristics and safety criteria No attempt precisely to model reality Lack of precise correspondence between theory and full scale test accepted After A. M. Muir Wood (2000), “Tunnelling: Management by design”

Types of Ground Model ----------------------------------------------------------------------------------------------------1. Geological structure Fundamentally a descriptive model which establishes limits of variability of salient factors 2. As (1) + simple qualitative factors

RQD or similar simplified representation of rock quality or selected relevant parameters for soil

3. As (2) + monitoring

Simplest basis for informal support

4. As (3) + quantitative

Adequate for analysis based on continuumdiscontinuum or on elasto-plastic models of increasing complexity -----------------------------------------------------------------------------------------------------

After A. M. Muir Wood (2000), “Tunnelling: Management by design”

Fundamental of Tunneling Stress States of Ground Initial

Secondary

Tertiary

Convergence-Confinement NMT

NATM

TBM

Characteristics of Ground

Elastic Solution of Initial Stresses Ground surface

x σy

z σz y

Governing Equations

∂σ x ∂τ xy + =0 ∂x ∂y

∂σ x ∂τ xy + =r ∂y ∂x

∇ 2 (σ x + σ y ) = 0

σy σx

x y

σx=λσy y

Solutions

σ y = ry σz =σx =

µ 1− µ

σy

Elastic Solution of Secondary Stresses σy

σr τrθ

r aa

θ

σθ

σx=λσy

Kirsch’s solutions

σ r = σ y [(1 − α − 2 )(1 + λ ) + (1 − 4α − 2 + 3α − 4 )(1 − λ ) cos( 2θ )] 1 2

σ θ = σ y [(1 + α − 2 )(1 + λ ) − (1 + 3α − 4 )(1 − λ ) cos( 2θ )] 1 2

τ rθ = σ y [− (1 + 2α − 2 − 3α − 4 )(1 − λ ) sin( 2θ )] 1 2

α=

r a

Radial Stress Distribution 1.5 Radial stress λ=1.5, θ=90 deg. λ=1.0, θ=90 deg. λ=0.5, θ=90 deg. λ=0.0, θ=90 deg.

1.0

λ=1

σr /σy

Stress

λ=1.5

r=5a 0.5

λ=0.5 λ=0 0.0 1

2

3

4

5

r/a

6

7

8

9

10

Radial distance Kirsch’s solutions

σr

Tangential Stress Distribution 3.0 Tangential stress λ=1.5, θ=90 deg.

σθ /σy

Stress

λ=1.0, θ=90 deg. λ=0.5, θ=90 deg.

2.5

λ=0.0, θ=90 deg.

r=5a

2.0

σθ

λ=1.5, 1, 0.5, 0

1.5

1.0 1

2

3

4

5

r/a

6

7

8

9

10

Radial distance Kirsch’s solutions

Secondary Stress States At the periphery of the opening : Only tangential stress but zero radial stress Biaxial stress state => uni-axial stress state

σ1

A

B

σ1

σ3

Rb

r lu i Fa

A

e in l e

B

σ3

0

Coulomb Criteria

Plastic Solutions of Secondary Stresses σ rp

Rb  r  =   ξ − 1  a 

σ θp =

Rb  r    ξ − 1  a 

σ r0 =

ξ −1

ξ −1

σy

 − 1 

σr0 r0



ξ − 1 

a

2σ y − Rb

ξ +1

Plastic zone

1 + sin φ ξ= 1 − sin φ

Elastic zone

τ

σ y (ξ − 1) + Rb   2 × r0 = a   + ξ 1 R b  

1 /(ξ −1)

Mohr Coulomb Model

c

σ

φ

0

σrp

Rb

σθp

Plasticity Radius

Radius of Plastic Zone 3.0 Plastic zone

θ=250

λ=1, θ=25 deg. λ=1, θ=30 deg. λ=1, θ=35 deg.

2.5

θ=300

λ=1, θ=40 deg. λ=1, θ=50 deg. λ=1, θ=60 deg. λ=1, θ=70 deg.

θ=350

σy

r0 /a

λ=1, θ=80 deg.

2.0

σr0

θ=400

r0 1.5

θ=500

a

Plastic zone Elastic zone

1.0 0

1

2

3

4

σy /Rb

5

6

7

Initial stress

8

Stress Distribution (λ=1) 2.0 Elastic solution: σθ

σ0=Rb

1.8

Plastic solution (φ=25 deg, σ0 /R b =1): σ

∆σ

Plastic solution (φ=25 deg, σ0 /R b =2): σ

Stress

1.5

σ/σy

σy

σ0=2Rb

1.0

Radial Stress Plastic solution (φ=25 deg, σ0 /R b =1): σ

r0 0.5

a

Plastic zone Elastic zone

θ

Tangential Stress r=5a

1.3

0.8

σr0

θ

r

Elastic solution: σr Plastic solution (φ=25 deg, σ0 /R b =2): σ

r

0.3

0.0 1

2

3

4

5

r/a

6

7

Radial distance

8

Solutions of Tertiary Stresses σy σr0 r0

pa a

Plastic zone Elastic zone

σ rp

ξ −1   r  ξ −1 Rb  r  =   − 1 +   p a ξ − 1  a    a 

σ θp

ξ −1 ξ −1  Rb  r  r =   ξ − 1 + ξ   p a ξ − 1  a  a 

σ y (ξ − 1) + Rb   2 × r0 = a   ξ + 1 p a (ξ − 1) + Rb 

1 /(ξ −1)

pa =

2σ y 2R − Rb a +( + 2 b )( ) ξ −1 ξ −1 ξ +1 ξ −1 r

 2 σ y (ξ − 1) + Rb  (1 + µ ) ua = (σ y − σ r 0 )   E  ξ + 1 p a (ξ − 1) + Rb 

2 /(ξ −1)

P a / σ y Support

pressure

Characteristic Curve of Ground 1.0 Characteristic curve

0.9

σ y /R b =0.5, φ=35 deg

σy=2Rb

0.8

σ y /R b =2, φ=35 deg σ y /R b =2.8, φ=35 deg

0.7

σy

σy=2.8Rb

0.6

σr0 r0

0.5

pa

σy=0.5Rb

0.4

a

0.3 0.2

Plastic zone

0.1

Elastic zone

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

[E/(1+u)R b ]*(u a /a)

3.5

4.0

4.5

5.0

Radial displacement

Support pressure

Typical Characteristic Curve of Ground pa A

Initial stress of ground B

Elastic

Plastic stable ground

Plastic unstable ground

C Pamin uamax

0

Ground deformation pressure

D

ua

Ground loosening pressure

Radial displacement Elastic deformation => Development of plastic zone => Initiation of instability

Support pressure

Convergence-Confinement Method pa

Characteristic curve of ground Characteristic curve of support Psmax Pa1

0

ua0

ua1

ua

Radial displacement

1. Limit convergence to acceptable values, compatible with excavation and the ultimate purpose of the structure 2. Control decompression of the surrounding ground, which always leads to a serious deterioration in its mechanical properties 3. Optimize support quantities and cost by applying only enough confining pressure to keep convergence within acceptable limits

Fundamental Principles of NATM 1. Maintain strength of the rock mass Avoid detrimental loosening by careful excavation and by immediate application of support and strengthening means. Shotcrete and rockbolts applied close to the excavation face help to maintain the rock mass.

2. Rounded tunnel shapes Avoid stress concentrations in corners where progressive failure mechanisms start.

Fundamental Principles of NATM 3. Flexible thin lining The primary support shall be flexible in order to minimise bending moments and to facilitate the stress rearrangement process without exposing the lining to unfavourable sectional forces. Additional support requirement shall not be added by increasing lining thickness but by bolting.

4. In situ measurements Observation of tunnel behaviour during construction is an integral part of NATM. With the monitoring and interpretation of deformations, strains and stresses it is possible to optimise working procedures and support requirements.

New Austrian Tunneling Method The NATM constitutes a method where the surrounding rock or soil formations of a tunnel are integrated into an overall ring-like support support structure. Thus the formations will themselves be part of this supporting structure.

Behavior of ground mass 1. Ground mass is the most important material for the stability of a tunnel.

Tate’s Cairn Tunnel, HK

Behavior of ground mass 2. Tunnel support contributes mostly by providing a measure of confinement.

Copenhagen Metro FE model of groundlining interaction

Behavior of ground mass 3. A lining placed in an excavated opening in an elastic rock mass at the time that 70% of all latent motion has taken place will experience stresses from release of the remaining 30% of displacement.

Lining segments

Segmental lining of Copenhagen Metro

FE Model to simulate the installation of segments

Support pressure

Schematic support vs deformation during excavation and support installation pa

Initial ground stress 1

Ground state at time of temp support installed

2

Ground state at time of temp support to load

3

Ground state at time of perm support installed

4

5

Ground state at time of perm support to load 6

Equilibrium and compatibility

D 0

ua

Radial displacement

Analytical methods Active loads

Proof

Pwall

Lining deformation profile

Pinvert

• • • •

Ground reactions (passive load at interaction zone)

Elastic closed form solutions Beam-spring models Beam-continuum models Empirical techniques

Tunnel Lining Design Model 1

σv=γH H R

σh=Κ0σv

Full overburden spring model

Tunnel Lining Design Model 2

σv

H

σh

R

Two dimensional continuum model

Tunnel Lining Design Model 3

σv σh

H h R

Active ground pressure derived from three dimensional analysis

Tunnel Lining Design Model 4

σv σh

R

Empirical approach

1. 2. 3. 4. 5. 6. 7. 8. 9.

Design for different conditions

Section with the deepest overburden Section with the shallowest overburden Section with the highest groundwater table Section with the lowest groundwater table Section with maximum surcharge Section with eccentric loads Section with future development Soft ground section Mixed ground section

Reservoir

Load factors and loading combinations 1. Particular environment and behavior of underground structure 2. Carefully evaluate design load cases and factors for each tunnel design 3. Rock loads to be derived from rockstructure interaction assessments

Construction methods and stages 1. 2. 3. 4.

Drill and blast method Mechanized method NATM NMT

TBM Tunnels Open TBM for rock

E. P. B. M. for soil

TBM

Slurry TBM for soil

Shielded TBM for weak rock

Shield TBM

Immediate Ground Support Cutterhead chamber

Annular void grouting to control and restrict settlement at surface and to securely block the lining ring in position

TBM shield

Segmental lining with annular grout

Evolution of settlements along a shield Distance d1: settlement caused by the face

d3 : settlement induced by post shied/grout loss d4 settlement induced by lining deflection and long-term settlement

Face

Displacement

d2: settlement caused by the overcut

Cutterhead and shield

Segmental lining with annular grout

Design Steps for TBM tunnels Step 1: Define geometric parameters Alignment, excavation diameter, lining diameter, lining thickness, width of ring, segment system, joint connections Step 2: Determine geotechnical data Shear strength of soil, deformation modulus, earth pressure coefficient Step 3: Select critical sections Influence of overburden, surcharge, groundwater, adjacent structures

Design Steps for TBM tunnels Step 4: Determine mechanical data of TBM Total thrust pressure, number of thrusts, number of pads, pad dimensions, grouting pressure, space for installation Step 5: Define material properties Concrete: strength, elastic modulus Reinforcement: type, strength Gasket: type, dimensions, elasticity Step 6: Design loads Soil pressure, water pressure, construction loads

Design Steps for TBM tunnels Step 7: Design models Empirical model, analytical model, numerical model Step 8: Computational results Response: axial force, moment, shear Deformation: deflection Detailing: reinforcement, joints, groove

Double-O Tunnels

Multi-Circular Face Shield Tunneling

Double-O Tunnels

H&V Shield Tunnel

Assembly of Precast Segments

Assembly of Segments

Perspective View of Tunnel