Lecture 12Yield Zones

Deep Excavations and Rock Burst Conditions

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

Triaxial (compression) test

increasing

brittle ductile

transition

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.

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).

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

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)

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

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)

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)

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,

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

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

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

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

n c

t

m n 1 0 5.

Hk

c

p

1

M

nm

mc

1 0 25 1

1

0 2

0 5

..

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

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

Rock bursts“A sudden and violent failure of overstressed rock resulting in the instantaneous release of large amounts of accumulated energy.”

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.

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

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

Key Factors• Rock bolt reinforcement too short• Location and orientation of local

faults• High in situ stress• Brittle rock - marble

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

Laerdal Tunnel, Norway 24.5 km long

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w. h

an

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van

well.

web

-log

.nl

Laerdal Tunnel, Norway• Tunnel excavated by conventional drill

and blast methods.• Support comprised galvanised steel

rockbolts (2m to 5m long) and fibre reinforced shotcrete.

• 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.

Seymour-Capilano Tunnels

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alk

.com

Seymour-Capilano Tunnels

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.com

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.

Rock burst in brittle rock under very high stress

E.H

oek

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.

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

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

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.

“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

a

ccc

sm

331

b - Hoek and Brown

F. R

ojat

,V.

Labi

ouse

, P.

K.

Kai

ser

& F

. D

esco

eudr

es,

2009

. B

rittle

Roc

k F

ailu

re in

the

Ste

g La

tera

l Adi

tof

the

Lo¨

tsch

berg

Bas

e T

unne

l. R

ock

Mec

h R

ock

Eng

42:

341–

359

Aft

er M

.S. D

iede

rich

s, P

,K,K

aise

r, E

.Ebe

rhar

dt, 2

004.

Dam

age

init

iati

on a

nd p

ropa

gati

on in

har

d ro

ck

duri

ng tu

nnel

ling

and

the

infl

uenc

e of

nea

r-fa

ce s

tres

s ro

tati

on. I

nt.J

.Roc

k M

ech.

& M

in.S

ci.,

41, p

p.78

5-81

2

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

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.

Influence of discontinuities on rock bursts

Buckling of rock slabs is driven by the release of gravitational and elastic potential energy (A).

A weak discontinuity can dramatically increase the amount of energy released, resulting in a more hazardousrock burst (B).

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.

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

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.

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

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

Assessment of rock burst risks

Palm

strö

m, 1

99

5

Palm

strö

m, 1

99

5

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

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.

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

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

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