Lecture9A(TunnelingGoverningMechanism)
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Transcript of 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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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)
Deformation of Tunnel Driven in Elastic Medium: The Axisymmetric Case
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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
Deformation of Tunnel Driven in Elastic Medium: The Axisymmetric Case
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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
Deformation of Tunnel Driven in Elastic Medium: The Axisymmetric Case
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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)
Deformation of Tunnel Driven in Elastic Medium: The Axisymmetric Case
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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
+=