chapter 8. strength of rock and rock masses
TRANSCRIPT
Chapter 8. Strength of rock and rock masses
1. Definitions
(1) Intact rock: - The unfractured blocks which occur between structural discontinuities
in a typical rock mass
- Ranging from a few millimeters to several meters in size
- Generally elastic and isotropic
(2) Joints - A particular type of geological discontinuity
(3) Strength - The maximum stress level which can be carried by a specimen
2. Strength of intact rock
(1) Hoek and Brown’s attempt:
- The failure criterion of good agreement with rock strength values
(50 mm, core orientation discontinuity surface)
- Mathematically simple expression
- Possibly of extension to deal with the failure of jointed rock mass
Hoek and Brown’s attempt:
Compare with Mohr-Coulomb failure criterion?
Compare with Mohr-Coulomb failure criterion?
Shear strength tanc n
c = cohesion
= friction angle
2sin2
1
2cos2
1
2
1
31
3131nStresses acting on the shear surface
tan2cos2
1
2
1c2sin
2
1313131
Therefore,
Solving for 1,
1
3
n
2cos1tan2sin
2cos1tan2sinc2 31
c
2
To3 1
n
tanc n
3
1
qu
To
sin1
sin1
sin1
cosc2
245tanq
tanq
3
2
3u
3u1
2. Strength of intact rock
(2) Hoek and Brown failure criterion
1’: major principal effective stress at failure
3’: minor principal effective stress at failure
c: uniaxial compressive strength of the intact rock (50 mm 100 mmH lab test result)
mi: material constant for the intact rock
For smaller diameter (d in mm) cores,
Ex) For 35 mm, cd = 90 MPa was obtained.
2
1
c
3ic31 1
'm''
18.0
cdc
d
50
MPa 84938.0MPa 90
35
50
MPa 9018.0c
UCS Correction Factor
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60 70 80 90 100
Core Diameter (mm)
UC
S R
atio
(S
igm
a c
/Sig
ma c
d)
18.0
cd
cd/50
18.0
cd
c
d/50
1
Ex) For 35 mm, cd = 90 MPa was obtained. MPa 84938.0MPa 90
35
50
MPa 9018.0c
2. Strength of intact rock
(3) c and mi obtained from the results of triaxial tests
- Conventional triaxial cell
- Hoek cell
Conventional triaxial cell
Conventional triaxial cell
Conventional triaxial cell
2. Strength of intact rock
(4) Tables can be used for c and mi instead of triaxial tests
3. Strength of jointed rock masses
(1) General form of the Hoek-Brown criterion
s, a = constants (characteristics of the rock mass)
1’, 3’: axial and confining effective principal stresses
c: uniaxial compressive strength of intact rock piece
mb: value of the constant m for the rock mass
(2) For most rocks of good to reasonable quality (tightly interlocking angular rock pieces): a = 0.5
(3) For poor quality rock mass (no tensile strength or cohesion): s = 0
(4) Above equations are of no practical value unless mb, s and a can be estimated in some way.
- Hoek & Brown (1988) suggested a method to estimate them from RMR ( 25)
- Not satisfactory for all rock qualities
a
c
3bc31 s
'm''
2
1
c
3ic31 1
'm''
For intact rock,
s'
m''c
3bc31
a
c
3bc31
'm''
a
c
3b
c
3
c
1 s'
m''
3. Strength of jointed rock masses
(5) Geological Strength Index (GSI): ~10 100
For GSI > 25 (undisturbed rock mass),
For GSI < 25 (disturbed rock mass),
0.5a
9
100GSIexps
28
100GSIexp
m
m
i
b
100
GSI65.0a
0s
a
c
3bc31 s
'm''
2
1
c
3ic31 1
'm''
Mohr-Coulomb vs. Hoek-Brown Failure Criterion?
c
2
To3 1
n
3
1
qu
To
tanc n
sin1
sin1
sin1
cosc2
245tanq
tanq
3
2
3u
3u1
Mohr-Coulomb
- space 1 - 3 space
Hoek-Brown
3
1
qu = c
To
a
c
3bc31 s
'm''
c
To3 1
n
???
3. Strength of jointed rock masses
(6) Application to the Mohr-Coulomb failure criterion (Balmer, 1952)
For GSI > 25, a = 0.5
For GSI < 25, s = 0
3131
31
313n
1
s'
m''c
3bc31
31
cb
3
1
2
m1
a
c
3bc31
'm''
1a
c
3a
b
3
1 ma1
A set of (n, ) values n - curve fitted (by linear regression analysis) c and determined from the plot
c
n
Uniaxial compressive strength of rock mass
sin1
cosc2cm
A simple spreadsheet (i.e. Excel) calculation can be carried out.
40
10RMR
m 10E
Linear
regression
analysis
* See a spreadsheet calculation
4. Use of rock mass classification for estimating GSI
(1) Bieniawski’s 1976 RMR classification
max = 90 + 10 (for groundwater condition) min = 8 + 10 = 18
RMR76’ < 18 (Inaccurate)
Bieniawski’s 1989 RMR classification
max = 85 + 15 (for groundwater condition) min = 8 + 15 = 23
RMR89’ < 23 (Inaccurate)
4. Use of rock mass classification for estimating GSI
(1) Bieniawski’s 1976 RMR classification
For RMR76’ > 18, GSI = RMR76’
RMR76’ < 18, Use Q’ value. RMR76’ cannot be used to estimate GSI)
(2) Bieniawski’s 1989 RMR classification
For RMR89’ > 23, GSI = RMR89’ – 5
RMR89’ < 23, Use Q’ value. RMR89’ cannot be used to estimate GSI)
(3) Modified Barton, Lien and Lunde’s Q’ classification
Jw = 1, SRF = 1 (Dry, medium stress condition) (Qmin’ = 0.0208, GSI 9)
a
r
n
w
a
r
n J
J
J
RQD
SRF
J
J
J
J
RQD'Q
44'Qlog9GSI e
5. When to use the Hoek-brown failure criterion
2
1
c
3ic31 1
'm''
a
c
3bc31 s
'm''
Only applicable to homogeneous and isotropic
rock or rock mass (either intact or heavily
Jointed rock mass)
Homogeneous, isotropic