Lecture9A(TunnelingGoverningMechanism)

8/13/2019 Lecture9A(TunnelingGoverningMechanism)

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Lecture 9

Governing Mechanism of Tunneling


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Stresses Around a Circular Excavation in an

Elastic Infinite Medium

( ) ( ){ }

( )

( )k3p270and90sidewalltheatand

13kp

180floortheatand

0rooftheatthen

cos2k12k1p

0and

aropening,theAt

z

00

z

0

0

z

rr

=

==

=

=

+=

=

=Klee, Rummel and Williams (1999)

Kirsch (1898)


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( ) ( ){ }

z

z

z

rr

p2sidewalltheatand

p2floorandrooftheatthen1kFor

cos2k12k1p

0and

aropening,theAt

=

==

+=

=

=

MPa60

MPa30x2

=

=

0 r =

Uniaxial Compressive Strength (Granite, Granodiorities

and Tuffs in Table 11 of Geoguide 1)

10 - 150III

100 - 200II

150 - 350I

UCS

MPa

Decomposition

Grade

Initiation of Failure NOT

stress control


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Muirwood [22] andAdyan et al. [23]

Hoek and Brown [13]

For GSI = 50 ( )

1.0150

15

depthm500MPa15

c

1

1

==

=

i

( )

2.0150

30

depthm1000MPa30

c

1

1

==

=

i

( )

15.012.050

6

depthm200MPa6

c

1

1


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5


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For Stress Controlled Problem

Deep Tunnel

1. Create Mesh. Determineextent of boundary.

2. Input material properties.

3. Determine boundary

conditions (degree of

freedom)

4. Turn on gravity or assign

horizontal and vertical

stresses

5. Assign all materials to

have elastic properties

and then delete elementsinside the tunnel


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1. Read out the nodal forces

around the tunnel

boundary

2. Repeat Step 5 by

assigning the true

properties (elasto-plastic

behavior and correct

cohesion and phi) to all

elements AND apply

equal and oppositedirection of nodal forces

obtained from Step 6 to

the tunnel boundary

3. Reduce the nodal forces

proportionally until

inequilibrium is reached

Sh ll T l


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Shallow Tunnel

A 12 m span tunnel is to be

excavated by top heading

and bench methods at a

depth of about 15 m below

the surface. The parallel

highway is to be placed on a

cut, the toe of which isabout 38 m from the tunnel

boundary.

Processes involved in

excavation of the highway cutand the subsequent tunnel

excavation, a simple model is

constructed with no support

in the tunnel.


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Slope stable after cutting


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Surface subsidence and

caving in after top bench is

cut.

Tunnel Face Instability


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Tunnel Face Instability

The advancing tunnel is represented by a

horizontal slot. The 12 m tunnel is driven with 3 m advances

and tractions are applied to represent the

installed support.

The vertical stress due to 15 m of cover is

approximately 0.4 MPa.

With the addition of steel sets, the support

pressure from 6 to 9 m is assumed to be 0.3

MPa. Finally, embedding these sets in

shotcrete gives the support pressure of 0.4 MPaat 9 m behind the face.

3-6m

No support

pressure0-3m6-9m>9mSupport

pressure is0.4 MPa,

representing

steel sets +

shotcrete

Support

pressure is

0.3 MPa,

representing

steel sets

Support

pressure is

0.2 MPa,

representing

shotcrete


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Face stability needs

to be considered

with different

supporting methods.

One method is to use

forepoling.


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A crude equivalent model is used in this analysis

Weighted averages can be used to estimate the strength and deformation of the zone of reinforcedrock

The strength is estimated by multiplying the strength of each component (rock, steel and grout) by

the cross-sectional area of each component and then dividing the sum of these products by the total

area. The tunnel roof required to install the forepoles are approximately 0.6 m deep and hence we

will consider a rock beam 1 m wide and 0.6 m deep.

The resulting rock mass strength for this composite beam is 1.57/0.62 = 2.5 MPa.

After supportingBefore supporting


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The forepoles are installed over the crown of the

excavation.

Deformation modulus is reduced 50% to represent the factthat the face has already reached this point before the

forepoles are installed.

Excavation of the top heading and removing the bench to

create the complete tunnel profile.

Caving has been controlled but large up heave stilloccurs at the invert

Supplemented with the provision of a 30 cm thick shotcrete

temporary invert for the top heading.

The displacements of the top heading invert havebeen halved.

Objective is to investigate a number of alternatives


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The effects of excavation sequence:

The slope is cut first and then tunnel excavated. The tunnel is excavated first, then slope is cut.

Typical Modeling Capability


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yp g p y

Excavation

Staged Excavation

Staged 1 Staged 3

Excavation supported by Bolts and Lining


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pp y g

Effects of Single Joint to Excavation


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For Structural Controlled Problem


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Tunnels excavated in jointed rock masses at relatively shallow depth:

common types of failure are those involving wedges falling from the roof or

sliding out of the sidewalls of the openings.

These wedges are formed by intersecting structural features, such as bedding

planes and joints, which separate the rock mass into discrete but interlocked

pieces.

Sliding wedgeFalling wedge


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Unstable Wedge formed inside Tunnel

Top View Perspective View


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1. Determine the average dip and dip direction of significant discontinuity sets.

2. Identify any potential wedges which can slide or fall from the back or walls.

3. Calculate the factor of safety of these wedges, depending upon the mode of failure.

4. Calculate the amount of reinforcement required to bring the factor of safety up to an

acceptable level.

Use of UNWEDGE Program

= 30 and c=0

Tunnel axisplunges at 15Trend of the axis is 025


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The program determines the location and dimensions of the largest wedges

which can be formed in the roof, floor and sidewalls of the excavation as shown


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Assumes that the discontinuities are ubiquitous, they can occur anywhere in

the rock mass.

Structural features are assumed to be planar and continuous.

Find the largest possible wedges which can form

Very little movement occurs in the rock mass before failure of the wedge.

Factors of safety of 1.5 to 2.0.

Bolts should be inclined so that the angle is between 15 and 30 whichwill induce the highest shear resistance along the sliding surfaces.

FOS (F) for a block or a wedge reinforced


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FOS (F) for a block or a wedge reinforced

against sliding on a single plane:

( )Fsintancos

cAtancosFsinWT+

=

( )TsinWsin

tanTcosWcoscAF++= or

where,

W = weight of wedge or block

T = load in bolts or cables

A = base area of sliding surface

= dip of sliding surface = angle between plunge of bolts or cables and the normal to the sliding surface

c = cohesive strength of sliding surface

= friction angle of sliding surface

Tunneling in Heavily JointedRock Mass


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Relative size of the opening to

the jointing system

Transition from isotropic intact

rock specimen to highly

anisotropic rock mass (controlled

by joints) to isotropic heavily

jointed rock mass


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Hoek-Brown failure criterion - assumes isotropic rock and rock massbehaviour

When the structure being analysed is large and the block size small

in comparison, the rock mass can be treated as a Hoek-Brownmaterial.

Where the block size is of the same order as that of the structure

being analysed or when one of the discontinuity sets is significantly

weaker than the others, the Hoek-Brown criterion should not be used.

In these cases, the stability of the structure should be analysed by

considering failure mechanisms involving the sliding or rotation of

blocks and wedges defined by intersecting structural features.


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Hoek, Kaiser and Bawden (1995)


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Tunnel face coincident

with measuring point astunnel advances

Tunnel face progressed

beyond measuring point

Assume no support

except rock ahead of face

Hoek, Kaiser and

Bawden (1995)

Deformation of Tunnel Driven in Elastic Medium: The Axisymmetric Case


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Assumptions: circular tunnel of Radius

R in homogeneous isotropic medium

Isotropic Stress = 0

Excavation

Face

Radial Displacement = uR

For No Support far behind the

face

Shear Modulus of ground = G

( ) ( ) ( )= RR uxxu

At any distance x from

the face:

1and0between

Initial measuring distance from face = x0

Panet (1993)



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Approximation of Measured Convergence C (based on

observed extent of plastic zone)

( ) ( )

( )assumed0.84RXwhere

xXX1CxC

2

=

+=

Panet (1993)

( )== CC,2Xxat

Assumed Distribution

( )

+

+=2

xX

X10.720.28x



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x < -2Rx =

Assume the same

can be applied to thechange in stress:

( ) 0R x =

Considered the 3-D problem is

an equivalent Plane Strain

Problem



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0

2

2

R1

=Radial Stress

Tangential Stress0

2

2

R1

+=

Distribution of Radial Stress and Tangential Stress in an

Elastic Axisymmetric Case, Panet (1993)



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R

2G

u

20

=Radial Displacement as function of :

2G

Ru

0

R=Radial Displacement at the tunnel

wall where = R:

Convergence-Confinement

Curve, Panet (1993)

Support installed at a distance d from the

face (d=unsupported span)

Stiffness of Support = Kc

Pressure on the Support = ps

Radial Displacement of the Support = uSR

= uR(x)-uR(d)

( )[ ] 0c

cs d1

2GK

Kp

+=

2G

R0

cK2G

cKd2G

Ru

+

+=

At EquilibriumAt Equilibrium

P0 = Pi


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Assumption in this case:

P0 = h = v

Rock mass behavior is not

time-dependent

Step 3

Step 1

Step 4

Step 5

Step 2

ui0

Steel sets support Opening support by

tunnel faceP0 = 0

Complicated ground-reaction interaction simplified by approximate solution


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Basic Assumption:

Stress induced deformation

No time-dependent behaviour

P0 =h =v

Rock mass (original, unbroken)

is linear elastic with strengthcriterion as:

In the elastic region, strain is

governed by E and . At failure,rock will dilate and strain iscalculated using associated flow

rule in the plasticity theory

Rock mass (broken in the plastic

zone is perfectly plastic with

strength criterion as:

Weight of broken rock is added

after stress analysis to simplify

procedure

( )21

2

c3c31 sm ++=

( )21

2

cr3cr31 sm ++=

Based on differential equation for equilibrium:


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Based on differential equation for equilibrium:

( )0r

dr

d rr

=

+and boundary conditions:

0r

rere

P,rat

,rrat

==

==

Stresses in the ELASTIC region:

( )2

e

re00r r

rPP

=

( )2

ere00

r

rPP

+=

Stresses in the BROKEN rock:

( ) i21

2

cricr

i

2

i

4

m

r PsPmr

rln

r

rln cr ++

+

=

Stresses at the Plastic and Elastic Zone Boundary:


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( )re0ree P2 +=

8

ms

Pm

4

m

2

1M

where

MP

2

1

c

02

c0re

+

+

=

=

Radius of the Plastic Zone:

( )

+

=2

12cricr

cr

sPmm

2N

ie err

where

( )2

12

cr

2

cr0crcr MmsPmm

2

N +=

At the elastic boundary, the Radial

Displacement u is given by:Analysis of Deformation


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( )( ) ere0e rPE

1u

+=

+

=

R

111

r

r

r

r

r

u2

e2

i

e

2

i

e

e

e

av

i

e

i

e

rr2DlnR,3

rrrockbrokenthinFor =

2

1

c

re s

m4m

mD

++

=

At the opening, the Radial Displacement

ui is given by:

+

=2

1

avi0i

A1

e11ru

2

i

eav

e

e

r

re

r

u2A

where

=

Displacement ue is given by:y

The average plastic volumetric strain in the

BROKEN zone is given by Ladanyi (1974) as:

re=radius of plastic zone

c0re MP =Ground Convergence Curve


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c0icr MPP =

( )

+=

>>

i0i0i

icri0

PPE

1ruthen

PPPifElasticMassRock

+=

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