lecture 12 yield zones deep excavations and rock burst conditions
TRANSCRIPT
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Lecture 12Yield Zones
Deep Excavations and Rock Burst Conditions
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Triaxial (Compression) Test
O ILO IL
Sp e c im e n
C e ll
Rub b e r sle e ve
2 = 3
1
Hoek Triaxial Cell
specimenRubber sleeve
cell
1
2= 3
ww
w.e
le.o
rg.u
k/M
td/c
at11
/rm
70.p
df
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Triaxial (compression) test
increasing
brittle ductile
transition
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Deformation mechanisms
Deformation
Mechanism
Cataclastic
Crystal-plastic
Localisation
yes no
cataclasticfaulting
plastic shearzone
cataclasticflow
homogeneousplastic flow
inc
inc
inc P & Tinc , inc u
dec , dec u
Aft
er R
utte
r, 1
993.
The
Mec
hani
cs o
f N
atur
al r
ock
Def
orm
atio
n. I
n C
ompr
ehen
sive
Roc
k E
ngin
eerin
g,
Per
gam
on P
ress
. V
ol.1
, pp
.63-
92.
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Figure 7.13 G round-support reaction curves
Roc
k su
ppo
rt p
ress
ure
Pre
ssur
e r
equ
ired
tolim
it d
efo
rmat
ion
Pre
ssur
e a
vaila
ble
fo
r su
ppo
rt
In situ stress prior to excavation
Linear elastic deformation
Start of fa ilure of rock surrounding tunnel
Load deformation curve
Support reaction curves
1
2
3
Radial deformation
A
Rock-support interaction analysis
1
0
2
1
1 rR
GP
r)(
)(
Where n is the gradient of the 3 versus 1 plot (poisson’s ratio).
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Yield Zone
Pi
pb
= Radial Stress to Initiate Failure
pb2 0 - p
b
Assumed Distributionof Tangential Stress,
aR
r
Limit of DestressingObserved Distribution of before and after Destressing (dashed)
Elastic Zone
BrokenZone
r
2 0 - pb
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Yield zone width
Zone Yield criterion
Elastic 1 = C0 + b3
Fractured 1 = d3
C0
Elastic
Fractured
For the hydrostatic case the radial and circumferential stresses are given by:
2
2
0 1r
ar
2
2
0 1r
a
(1)
(2)
(3) (4)
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Since the problem is axisymmetric, there is one differential equation of equilibrium:
0d2
sin2dddd
d rrr
r
drrr
rr
(5)
d
d2
d2
r
r+dr r r
dd
Arc length = ( + ) r dr dArc length = rd
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This simplifies to:
rdr
d rr
From (2) we can see that:
(6)
r d (7)
substituting (7) in (6) gives:
rdr
d rr 1d (8)
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Integrating this expression and introducing the boundary condition, r = Pi when r = a, yields the stress distribution relations:
1d
i aP
rr
1d
i adP
r(9) (10)
Equations (9) and (10) are satisfied throughout the fractured domain and on its boundaries. At the outer limit of the yield zone, fractured rock is in equilibrium with the intact, elastic rock. If P is the equilibrium radial stress at the outer boundary, R:
1d
i a
RP
P
1d/1
iPa
R
Por(11) (12)
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Simple superposition indicates that the stress distribution in the elastic zone is defined by:
(13)
and,
(14)
2
2
2
2
0
RR1
rP
r
2
2
2
2
0
RR1
rP
rr
Therefore, at the inner boundary of the elastic zone (r = R), the state of stress is given by:
P 02 Pr (15) (16)and,
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This state of stress must represent the limiting state for intact rock. Substituting in (1) gives:
(17)
and,
(18)
00 Cb2 PP
substituting in (12) gives:
(19)
b1
C2 00
P
1d/1
i
00
b1
C2
a
R
P
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Alternative models# Elastic Fractured R/a
1
2
3
1 3 c pk
1 3 c pk
1 3 c pk
1 3 c pk
1 3kp
1 3 cr pk
2 1
1 1
0
1
1
k
p k k
p c
i p c p
kp
2
10
1
1
c
i p
k
p k
p
21
1
11
0
1
1
c
cr p
p
icr
p
p
kk
k
pk
k
p
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Alternative models# Elastic Fractured R/a
4
5
1 3 c pk
1 3
0 5
12 1 1
c c
cm
nm
.
1 3 B cb
1 3 c pk
exp
2
1
1
0
1
1
c
p
b
ib
kp
B b
0
1
1
H m
p Hc
i
kp
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where,= triaxial stress factor
c = Unconfined compressive strength
cr= Residual strength of broken rock
t = tensile strength
a = Radius of excavationR = Radius of yield zone perimeterpi = Support pressure
B, b define the curvature of the failure envelope for broken rock
kp
1
1
sin
sin
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n c
t
m n 1 0 5.
Hk
c
p
1
M
nm
mc
1 0 25 1
1
0 2
0 5
..
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Rock A c=30 MN m-2, kp=4, t=10 MN m-2, B=4.82, b=0.709
Rock B c=10 MN m-2
kp=2.5, t=1 MN m-2, B=4.07, b=0.74
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Volumetric closureIt is possible to estimate the extent of excavation closure by measuring the volumetric expansion of laboratory specimens at a confining stress representative of the average level in the yield zone = 0.250.
= estimated bulking factor
u a R ar 1 2 21
2
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Rock bursts“A sudden and violent failure of overstressed rock resulting in the instantaneous release of large amounts of accumulated energy.”
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Rock bursts in tunnelling• Although originally identified in deep mines in
South Africa, India, Canada and USA, problems associated with rock burst conditions are becoming increasingly common in civil engineering projects.
• Tunnels through mountain ranges are often at depths of 1000 m to 2000 m below ground level and there rock bursts pose a significant risk.
• Rock bursts have occurred in civil engineering tunnels in Chile, China, Norway, Canada and the Andes.
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Olmos trans-Andean tunnel A 5.3 m-dia. Robbins
unshielded main beam TBM. 13.8 km-long tunnel through the Andes.
Complex geology consisting of quartz porphyry, andesite, and tuff from 60 to 225 MPa UCS.
One of the deepest tunnelling projects in the world with 1,931 metres of overburden at its deepest point.
http://www.youtube.com/watch?v=RtzNhss2h4w
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The Jinping II Hydropower Station
After C. Zhang, X. Feng, H. Zhou, S. Qiu & W. Wu, 2012. Case Histories of Four Extremely Intense Rockbursts in Deep Tunnels. Rock Mech. Rock Eng. Pub.online
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Key Factors• Rock bolt reinforcement too short• Location and orientation of local
faults• High in situ stress• Brittle rock - marble
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After C. Zhang, X. Feng, H. Zhou, S. Qiu & W. Wu, 2011. A Top Pilot Tunnel Preconditioning Method for the Prevention of Extremely Intense Rockbursts in Deep Tunnels Excavated by TBMs. Rock Mech. Rock Eng. Pub. online
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Laerdal Tunnel, Norway 24.5 km long
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an
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van
well.
web
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.nl
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Laerdal Tunnel, Norway• Tunnel excavated by conventional drill
and blast methods.• Support comprised galvanised steel
rockbolts (2m to 5m long) and fibre reinforced shotcrete.
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• The Laerdal tunnel excavated through with Pre-Cambrian gneiss at depths of up to 1400 metres below surface.
• Rock burst conditions were present due to the high in situ rock stresses. ht
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Seymour-Capilano Tunnels, Vancouver• TBM’s excavating the Seymour-Capilano
twin tunnels in Vancouver were stopped in January 2008 due to concerns regarding tunnel safety.
• At a depth of approximately 550m below ground level the TBM’s encountered weak rock which fell from the tunnel crown.
• Although the failure was not of an explosive nature there was evidence of stress relief.
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Seymour-Capilano Tunnels
ww
w.t
un
nelt
alk
.com
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Seymour-Capilano Tunnels
ww
w.t
un
nelt
alk
.com
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Rock burst Conditions• Generally found in deep excavations in
brittle rocks.• Much research into rock bursts has been
carried out in South Africa in the deep gold mines, where the development tunnels are excavated in very strong, brittle quartzite.
• Large in situ rock stress either through depth or large horizontal stresses.
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Rock burst in brittle rock under very high stress
E.H
oek
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Cause of rock bursts• Failures known as spalling, popping or
rock burst are caused by overstressing of brittle, massive rocks at depth.
• These failures can also be induced at shallower depth where high horizontal stresses or strongly anisotropic stresses are acting.
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Microcrack development
• Compare Griffith theory
• In tunnels, results from removal of confining stress and increased tangential stress. Cracks extend parallel to the excavation wall.
2
2
1
1
P
P
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3-D crack growth in uniaxial compression
Aft
er A
. V
. D
yski
n, E
Sah
oury
eh,
L. N
. G
erm
anov
ich
cross-section plan
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Unconfined Compression Test
1 1
1v
100%
~80%
~36%
max. stress
rupture
unstablefracturepropagation
stablefracturepropagation
recoverableelastic deformation
microcrack and poreclosure
line ofelastic
compaction
onset of
dilatancy
compaction
expansion
f
1
Crack growth typically starts around 0.3–0.5 sc &increases until macroscopic failure takes place.
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“Around an underground opening, this behaviour is significantly modified. Instead of a simple monotonic loading path, the rock mass in the field undergoes a specific stress–strain history, which causes the stress level for crack coalescence to drop to a much lower value. Typically, in massive and moderately jointed hard rock masses, brittle failure occurs around 0.3–0.5 sc, i.e. near or slightly above the stress level required for damage initiation.”F. Rojat,V. Labiouse, P. K. Kaiser & F. Descoeudres, 2009. Brittle Rock Failure in the Steg Lateral Aditof the Lo¨tschberg Base Tunnel. Rock Mech Rock Eng 42:341–359
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a
ccc
sm
331
b - Hoek and Brown
F. R
ojat
,V.
Labi
ouse
, P.
K.
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. D
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. B
rittle
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ailu
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the
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tof
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Lo¨
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berg
Bas
e T
unne
l. R
ock
Mec
h R
ock
Eng
42:
341–
359
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Aft
er M
.S. D
iede
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,K,K
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Dam
age
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nea
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nt.J
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41, p
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2
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Relationship between depth of failure, stress level and Barton’s stress reduction factor (SRF)
Kai
ser
PK
, D
iede
richs
MS
, M
artin
CD
, S
harp
J,
Ste
iner
W (
2000
) U
nder
grou
nd w
orks
in h
ard
rock
tunn
ellin
g an
d m
inin
g. I
n: K
eyno
te le
ctur
e at
Geo
Eng
2000
, M
elbo
urne
, Aus
tral
ia T
echn
omic
Pub
lishi
ng C
o.,
Mel
bour
ne, A
ustr
alia
, p
841–
926
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Overstressed weaker rocks• Squeezing can occur both in massive
(weak and deformable) rocks and in highly jointed rock masses as a result of overstressing.
• It is characterized by yielding under the redistributed state of stress during and after excavation.
• The squeezing can be very large; deformations as much as l7% of the tunnel diameter have been reported in India.
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Influence of discontinuities on rock bursts
Buckling of rock slabs is driven by the release of gravitational and elastic potential energy (A).
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A weak discontinuity can dramatically increase the amount of energy released, resulting in a more hazardousrock burst (B).
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Assessment of rock burst risks• Various attempts have been made to
quantify the likelihood of rock bursts occurring.
• Hoek and Brown produce a simple relationship between the uniaxial compressive strength of the rock and the vertical applied load
• This work was largely based on tunnels of square cross section in brittle quartzites.
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Assessment of rock burst risks• Vertical applied stress = pz
• Uniaxial compressive strength = sc
• pz /sc = 0.1 stable unsupported tunnel
• pz /sc = 0.2 minor sidewall spalling
• pz /sc = 0.3 severe sidewall spalling
• pz /sc = 0.4 heavy support required
• pz /sc = 0.5 possible rock burst conditions
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Assessment of rock burst risks• The Rock Mass index (RMi)
characterises the strength of rock masses and can be applied directly in stability analyses.
• The competency factor (Cg) expressed as the ratio between rock mass strength and the tangential stress (sq) around the opening (Cg = RMi/ sq) is applied to indicate whether the ground is overstressed or not.
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Assessment of rock burst risks• The rock mass index is given as
RMi = sc .JP where JP, the jointing parameter, is a measure for the intensity of jointing (given as block size) and the joint characteristics (Palmström).
• In massive rock where the jointing parameters JP = 1, the rock mass index is RMi = fs. sc and
Cg = RMi/ s q = fs. sc/sq
• fs is the scale effect for the compressive strength given as f s = (50/d) 0.2
(d is the block diameter measured in mm).• In highly jointed and crushed rock masses Cg = sc .JP /s q
Cg = RMi/ sq
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Rock burst risk based on tangential stress and point load strength
A. P
alm
strö
m, 1
995.
Cha
ract
eriz
ing
Roc
k B
urst
and
Squ
eezi
ng b
y th
e R
ock
Mas
s In
dex.
Des
ign
& C
onst
ruct
ion
of U
nder
grou
nd S
truc
ture
s, N
ew D
ehli.
pp.1
0.
Po
int
Lo
ad S
tren
gth
, I
(M
pa)
12
8
4
0 20 60 80 10040
Tangential Stress, (MPa) t
No ro
ck b
urst a
ctiv
ity
Low
Moderate
High rock burst activity
s
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Assessment of rock burst risks
Palm
strö
m, 1
99
5
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Palm
strö
m, 1
99
5
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Empirical criterion4
3
2
1
0 2 4 6 8 10 12 14
0.6 - 1.0 2 - 3 3 - 4 >4
/ q’cmass
Moderate slabbingwith noise (rock burst)
Mild squeezing
Mode
rate
sque
ezin
g Highsqueezing
Joint Alteration Number (Ja)
Join
t R
ou
ghn
ess
Nu
mbe
r (J
r) 16.0cmass
θ
q
5.0a
r J
J
Aft
er K
umar
, 20
02.
Rep
orte
d in
B.S
ingh
& R
.K.G
oel,
2006
. Tu
nnel
ling
in W
eak
Roc
ks.E
lsev
ier.
P.4
89
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Overstressing in weak rocks• In weaker materials high in situ stresses cause
squeezing of the tunnel perimeter.• The squeezing can occur not only in the roof
and walls, but also in the floor of the tunnel.• Squeezing is related to time-dependent
shearing i.e. shear creep. • A general opinion is that squeezing is
associated with volumetric expansion (dilation), as the radial inward displacement of the tunnel surface develops.
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Modes of squeezing failure
Aydan Ö., Akagi T. andKawamoto T. 1993. The squeezing potential of rocks around tunnels;theory and prediction . Rock Mech. Rock Engn, No. 26, pp.137-163. quoted in Palmstrom 1995
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Estimating squeezing potential
Ayd
an Ö
., A
kagi
T. a
ndK
awam
oto
T. 1
993.
The
squ
eezi
ng p
oten
tial
of r
ocks
aro
und
tunn
els;
theo
ry a
nd p
redi
ctio
n.
Roc
k M
ech.
Roc
k E
ngn,
No.
26,
pp.
137-
163.
quo
ted
in P
alm
stro
m 1
995
For straight line fits:NS = no squeezeLS = light squeezeFS = fair squeezeHS = high squeeze
25/1/ Hc35/1/25/1 Hc50/1/35/1 Hc
Hc /50/1
0 1 2 3 4 5 6 7 80
100
200
300
400
OV
ER
BU
RD
EN
H
(m
)
c (MPa)
NS
LS
FS
HS
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Avoiding rock bursts• ‘Perfect support’• Reduce rate of advance – rock absorb strain
energy through creep.• Destressing by inducing yield zone around
opening with radius >b.• Support system should be slow and ductile.• Support pressure: MPa
)(2.0
r
31
roof fJ
Qp
1800/)320(1 Hf
m 1430 ,Overburden Hf = correction factor for HQ = post-construction rock mass quality
Aft
er K
umar
, 20
02.
Rep
orte
d in
B.S
ingh
& R
.K.G
oel,
2006
. Tu
nnel
ling
in W
eak
Roc
ks.E
lsev
ier.
P.4
89