rock mass strength and scale effects

Rock Mass Strengthand Scale Effects

School of Civil & Environmental EngineeringThe University of New South Wales

Sydney, Australia

Rock Mass Strength

DO NOT USE IT!Unless you have

investigated all possible structurally controlled

mechanisms first

From an international journal:

“Different methods can be used to assess the stability of rock and/or soil slopes – the selection of a suitable method being primarily a function of the availability of geotechnical data.”

Nattai escarpment failure

Failure is through numerous defects and/or weak intact rockImpossible to determine precise failure path

structure

mass

Consideration of GSI for slopes

Strength of Intact Material

• Intact rock exhibits a scale effect for block sizes up to at least one metre.

Specimen Diameter (mm)2500

1.3

0.7

UCSSAMPLE / UCS50mm

Hoek & Brown (1980)

RQD

• Based on a fixed length of 100mm– relevance for large rock masses??

• Includes all joints in borehole– may not be significant to large scale

behaviour• Is in addition to spacing

Defect Spacing

• Similar problems to RQD• Developed for underground tunnels of the

order of 10 - 20m in span.• Maximum rating for spacing intervals of:

> 3m - RMR76

> 2m - RMR89

Slopes with Equivalent GSI

10m 100m

Spacing = 2m

Joint Condition

• The scale of a problem affects:– persistence (maximum length >20m)– aperture– roughness– infilling– weathering

Very rough

Smooth&

infilled

Very roughSmooth

Q

• Depends on:– RQD– Number of joint sets– Joint roughness– joint alteration

• Similar problems to RMR factors.

a

r

n JJ

JRQDQ ×=

GSI80

50

10

30

Dec

reas

ing

of in

terlo

ckin

g ro

ck p

iece

s

Decreasing surface quality• GSI Table includes structure & surface conditions.

• Scale independent, providing ‘scale of problem’ is used.

• Intact or massive with very good surfaces GSI > 80 (Hoek, 1999)

• Foliated/sheared not included

Hoek & Browna

cc sm

+

′+′=′

σσσσσ 3

31

• Intact Rock– si = 1– ai = 0.5– mi = triaxial tests or function of rock type

• Rock Mass– sb, ab, mb are functions of the Geological Strength

Index, GSI

20 40 60 80 1000

0.5

1.0

0

abmb/mi

sb

GSI

−−

=D

GSImm

i

b

1428100exp

−−

=D

GSIs39100exp ( )32015

61

21 −− −+= eea GSI

Hoek et al (2002)

Issues with Hoek-Brown

• Intact rock:– Assumes a constant ai = 0.5 (c.f. 0.4-0.9)– mi often based on rock type– Discussed in detail GEOENG 2000

• Rockmass:– Maximum ab = 0.62 (GSI = 5 from Table)– Could expect that a weak rock mass should

have an ab approaching unity– Rockfill has an ab of approximately 0.9

Laboratory test database & analysis

• Data from many sources• 3817 test results forming 485 sets• Most commonly adopted criterion is the

Hoek-Brown• Fitted the Hoek-Brown criterion to these

data• Method of fitting extremely important• For many data sets, mi and σc are not

independent, σc → 0 as mi → ∞

Regression of Intact Data

Sigma 3 (MPa)

Sig

ma

1 (M

Pa)

0

50

100

150

200

250

-10 10 30 50 70

UCS miArtificial data 10.012.0Normal eqn & LS14.97.75Extended eqn & LS 8.4615.5Ext eqn & mod LS 10.712.0Fix UCS & LS 10.05.21Excl Sc or St & LS 6.1921.4DS^2 & LS 3.9735.2Log & LS 8.094.12

Not shownExcl St & LS 9.5213.7DS^2 with UCS fixed 10.013.8DS^2 & Least abs sum 9.1815.4Log with excl St 9.6712.2

−≤=

−>

++=

ic

icc

ic

m

mm

σσσσ

σσσσσσσ

331

3

5.0

331

for

for 1

Sigma 3 (MPa)

Sig

ma

1 (M

Pa)

0

10

20

30

40

-2 0 2 4 6

UCS miArtificial data 10.012.0Normal eqn & LS14.97.75Extended eqn & LS 8.4615.5Ext eqn & mod LS 10.712.0Fix UCS & LS 10.05.21Excl Sc or St & LS 6.1921.4DS^2 & LS 3.9735.2Log & LS 8.094.12

Not shownExcl St & LS 9.5213.7DS^2 with UCS fixed 10.013.8DS^2 & Least abs sum 9.1815.4Log with excl St 9.6712.2

Rock Type vs mi

mite

st

0

10

20

30

40

Cla

ysto

nFi

recl

ayG

reen

sto

Mud

ston

eS

erpe

nti

Schi

stS

hale

Cha

lkC

hlor

itiLi

mes

ton

Mar

ble

Silt

ston

Sla

teB

ioca

lca

Dol

omite

Anh

ydrit

Sal

tC

oal

Tuff

Pyr

ocla

sR

hyol

iteA

plite

Bas

alt

Lam

prop

hTr

achi

teA

gg tu

ffG

reyw

ack

Whi

nsto

nA

ndes

iteD

iaba

seD

oler

iteQ

uartz

doS

ands

ton

Gra

nite

1N

orite

Qua

rtzit

Dun

iteE

clog

iteG

abbr

oP

erid

oti

Am

phib

olD

iorit

eQ

uartz

diG

rano

dio

Gne

iss

Gra

nite

Intact Rock Modificationsia

cic m

+

′+′=′ 13

31 σσσσσ

ti

ciim σ

σ≈

+

+≈

7exp1

2.14.0i

i ma

Note that triaxial testing is preferred

Exponent vs mi

mi

Alp

ha

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50

φ0 15 25

35 45 55 65φ0

Rock mass modifications

• New equations are required to account for the transition between a variable ai and miat GSI = 100 and ab min = 0.9 at GSI = “0”

GSI 100 “0”ab ai 0.9mb mi 2.5sb 1 0

Intact rock testing

Rockfill testing

Rock mass modifications

• Parameter ‘m’– Predominantly affects friction angle at low stress– Should reduce with GSI (less interlocking)

• Parameter ‘s’– Predominantly contributes to cohesion– Expect rapid decrease in s with GSI– H-B use exponential drop

• Exponent ‘a’– Needs to drop from ai to amin limit

Data

• Habimana et al (2002) data used– 35 triaxial tests on rock mass for a hydroelectric plant

& tunnel in Swiss Alps– Tests grouped into GSI = 15, 25, 50, 80– Best quality published data known to authors

• Process used by authors:– Data for each GSI was statistically analysed using the

H-B equation to get ab, mb and sb

– Statistical analysis of results to get new equations for ab, mb and sb

– Global analysis of data to check results

Rock Mass Equations( )

−

=1

1585exp

min

GSI

sb

=5.2

100max

GSImm

i

b

( )

−−+=

i

biib m

maaa 3075exp9.0

Min GSIand mbfrom rockfill

Note linear relationship compared to exponential H-B

0

5

10

15

20

25

0 20 40 60 80 100GSI

mb smb

Equation 6

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100GSI

s b authors' eqn for sauthors' eqn for atest data - atest data - s

αbsb

αbsb

sbαbsb

sb

abab

ab

Equation 7

Equation 8

Max GSI for a well interlocked rockmass

Max abfrom rockfill

0

Transition curve from GSI = 100 to GSI = 0 for mi = 40

mb

( )

−−+=

i

biib m

maaa 3075exp9.0

10.9

0.4

0

a

400 10

Intact rock relationship

+

+≈

7exp1

2.14.0i

i ma

mi

Rock mass limit GSI = 0

Intact sample GSI = 100GSI ≈ 25

=5.2

100max

GSImm

i

b

( )

−−+=

i

biib m

maaa 3075exp9.0

Comparison for mi = 405

0 1

GSI = 100

GSI = 10

Hoek, 2002Author

σ′1/σc

σ′3/σc

Comparison for mi = 45

0 1

GSI = 100

GSI = 10

Hoek, 2002Author

σ′1/σc

σ′3/σc

Conclusions

• Rock mass strength should only be used where the geological model shows that it is valid

• Parameters should be considered on the scale of the slope

• New equations have been developed for the Hoek-Brown parameters to address issues

• Further published data on rock mass would help to give more confidence in the equations