rock mass strength and scale effects
TRANSCRIPT
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