lecture notes/Week 4-Part 2 MC.pdf
Moon Hill, China
RSE3010
MINE GEOTECHNICAL ENGINEERING
WEEK 4 THEORIES OF DEFORMATION AND
FAILURE OF ROCKS: PART 2
• Uniaxial and Triaxial Compressive Behaviou
• Mohr-Coulomb Criterion
• Hoek-Brown Criterion
• Griffith Theory
• von Mises Criterion
• Combined Failure Criteria
3
MONASH
CIVIL
ENGINEERING
STRENGTH/FAILURE CRITERIA
▪ The behaviour law of a material
– defined as the relationship between the stress components that
indicate the state of strain that the material undergoes. It is a
oader concept than that of strength or failure criterion since it
efers to the relationship between the stresses throughout the
whole process of deformation of rock.
▪ Diagram of general failure criterion in 2D
– Ki: other influencing factors
▪ such as temperature, velocity
– “Impossible” state of stress
– Possible state of stress
4
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
▪ Mohr-Coulomb Criterion
– The Mohr–Coulomb theory is
named in honour of Charles-
Augustin de Coulomb and
Christian Otto Mohr.
– The criterion assumes that a shear
failure plane at angle to the
minor principal stress is developed
in the
ittle material
– Coulomb’s shear strength () is
made up of two parts, a constant
cohesion (c), and the angle of
internal friction ()
= c + n tan
n
c,
‘Grandfather of Soil Mechanics’
Concepts of active and passive earth pressure
Concept of friction
Coined the term “Cohesion”
1
3
n
5
MONASH
CIVIL
ENGINEERING
▪ Stresses by Mohr’s Circle
MOHR-COULOMB CRITERION
3 1
n
1. We start the Mohr’s diagram by constructing a 2D coordinate
system where the horizontal axis is the normal stress, σn, and the
vertical axis is the shear stress, .
2. Then we mark the magnitude of the minimum and the maximum
principal stresses σ3 and σ1, respectively, on the σn-axis.
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MONASH
CIVIL
ENGINEERING
▪ Stresses by Mohr’s Circle
MOHR-COULOMB CRITERION
3 1
n
3. Then we draw a circle (or,
more commonly, a semicircle)
through σ3 and σ1, so that the
circle/semicircle has a diameter
equal to σ1 – σ3.
7
MONASH
CIVIL
ENGINEERING
▪ Stresses by Mohr’s Circle
MOHR-COULOMB CRITERION
4. We can use this diagram to
obtain the values of the normal
stress σn and the shear stress
on any crustal plane of interest.
Each plane is marked by a point
P on the circle/semicircle.
5. The point P is
connected to the centre
of the circle C through a
line that makes an angle
of 2θ with the positive
(right) part of the σn -axis.
3 1
n
2
½ (1 + 3)
P
C
8
MONASH
CIVIL
ENGINEERING
▪ Stresses by Mohr’s Circle
MOHR-COULOMB CRITERION
3 1
n
(n, )
2
½ (1 + 3)
n
180-2
6. The coordinates of P are then
σn and . Thus, the circle consists
of an infinite number of points that
show the stresses on planes with
all possible values of θ.
7. The distance of the
centre C from the origin
equals (σ1 + σ3)/2. The
adius of the circle PC
equals to (σ1 – σ3)/2,
which is also the
maximum shear stress
when the shear stress
eaches it maximum on
planes oriented at θ = 45◦.
P
C
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MONASH
CIVIL
ENGINEERING
▪ Stresses by Mohr’s Circle
MOHR-COULOMB CRITERION
3 1
n
c
(n, )
½ (1 + 3)
n
= ½ (1 – 3) sin(180–2)
n = ½ (1 + 3) – ½ (1 – 3) cos(180–2)
= ½ (1 – 3) sin2
n = ½ (1 + 3) + ½ (1 – 3) cos2
180-2 2
P
C
The tangent point of the
Mohr circle with the straight
line represent:
(1) the stresses conditions
on the shear plane, and
(2) the inclination of the
shear plane, where the
shear failure occurs.
= c + n tan
0
1
3
n
10
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
▪ Failure Condition
– = c + n tan is a
straight line strength
envelope
– In the diagram, when the
Mohr circle touches the
strength envelope, on the
touching point, the stress
condition on the shear
plane meets the criterion.
– Failure occurs along the
shear plane when
stresses (n, ) meet
shear strength condition.
11
MONASH
CIVIL
ENGINEERING
▪ Failure Condition
– Failure does not occur if the
Mohr circle (black) does not
touch the failure envelope.
– Four ways to make Mohr
circle touching the failure
envelope:
▪ Increasing 1 (blue);
▪ Decreasing 3 (red);
▪ Decreasing 1 and 3 at the
same time (green);
▪ Combination of the above
three.
MOHR-COULOMB CRITERION
3 1
n
12
MONASH
CIVIL
ENGINEERING
▪ Orientation of Shear Failure Plane
– From the Mohr circle, the strength envelope is perpendicular to
the line defined by 2, where
2 = /2 + , then, = ¼ + ½
– which is the angle of failure plane to the minor principal stress 3.
MOHR-COULOMB CRITERION
1
3
n
13
MONASH
CIVIL
ENGINEERING
▪ Compressive and Tensile Strengths
– Replacing = ¼ + ½ in the equation of 1, it gives
– when 3=0, 1 is uniaxial compressive strength c
– when 1=0, 3 is tensile strength t
MOHR-COULOMB CRITERION
c
nt c0
13
c (1 – sin)
t = (1 + sin)
2
2c cos
c = 1 - sin
2c cos
t = 1 + sin
14
MONASH
CIVIL
ENGINEERING
▪ Tensile Cut-Off
– Tensile strengths given
y Mohr-Coulomb
Criterion is much higher
than the actual ones.
– A tensile cut-off can be
applied at around
t’ = 1/10 c.
– Mohr-Coulomb Criterion
used for rock mechanics
is a straight line at
compression with tensile
cut-off
MOHR-COULOMB CRITERION
c
nt c
0
t′
Gives t = 1/3 c
for = 30°
Actual t ≈ 1/8 1/15 c
2c cos
t = 1 + sin
15
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
▪ RocData Software
– Levenberg–Marquardt: non-linear least squares curve fitting
– or Linear Regression
= c + n tan
3 (MPa) 1 (MPa)
0 75
3 99
10 120
14 139
21 146
46 206
70 265
100 330
16
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
▪ RocData Software
– Wombeyan Ma
le
– Update the Custom with Sigmax = 100 MPa
▪ Cohesion: 29.94 MPa
▪ Friction angle: 24.6°
3 (MPa) 1 (MPa)
0 75
3 99
10 120
14 139
21 146
46 206
100 330
17
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
= c + n tan
c
▪ RocData Software
– Linear Regression
Wombeyan Ma
le
Melbourne MudstoneBlackingstone Granite
18
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
▪ Mohr-Coulomb Criterion in 1 – 3 plots
▪ The 1 – 3 plots for Mohr-Coulomb
Criterion are straight lines.
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MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
▪ Mohr-Coulomb Criterion in 1 – 3 plots
3 (MPa) 1 (MPa)
0 75
3 99
10 120
14 139
21 146
46 206
100 330
Wombeyan Ma
le
c=93.3 MPa
=67.6°
=
20
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
2. c=75 MPa
1. Hoek-Brown
4. t= -14 MPa
▪ Mohr-Coulomb Criterion in 1 – 3 plots
21
MONASH
CIVIL
ENGINEERING
MOHR-COULOMB CRITERION
▪ Comments on the Mohr-Coulomb Criterion
– It is suitable for estimating compressive strengths at low confining
stresses. It much overestimates tensile strengths. It also
overestimates compressive strengths at high confining stresses.
– Most of the rock engineering activities are at shallow depths and
low confining stresses, so the criterion gives reasonable
estimations for rock material strengths
c
nt c0
13
2
__MACOSX/lecture notes/._Week 4-Part 2 MC.pdf
lecture notes/Week 2-Part 2 RQD.pdf
Bryce Canyon National Park, Utah
RSE3010
MINE GEOTECHNICAL ENGINEERING
WEEK 2 ROCK MASS CLASSIFICATIONS: PART 2
• Intact Soil & Rock Classification
• Rock Quality Designation (RQD)
• Rock Tunnel Quality Q-System
• Rock Mass Rating (RMR)
• Geological Strength Index (GSI)
• Rock Load Facto
• Rock Structure Rating (RSR)
• Rock Mass index (RMi)
3
MONASH
CIVIL
ENGINEERING
MELBOURNE METRO ALIGNMENT MAP
▪ The Melbourne Metro Tunnel (MMT) presents many unique
challenges: construction of the 9km twin tunnels and 5 underground
stations involve TBMs, mined caverns and open cut excavations.
4
MONASH
CIVIL
ENGINEERING
GEOLOGICAL PROFILE ALONG THE PROPOSED ALIGNMENT
The Silurian bedrock in the area of the Melbourne Metro project is the Melbourne
Formation, which consists of mudstone, sandstone and siltstone that has been
folded, faulted and intruded with igneous rocks. These rocks have been
weathered to varying depths, with fresh (unweathered) rock sometimes existing
within the shallow profile.
What is the geologic period of Silurian rock?
5
MONASH
CIVIL
ENGINEERING
AHD (Australian Height Datum)
GEOLOGICAL PROFILE ALONG THE PROPOSED ALIGNMENT
Quaternary
Tertiary Silurian
Older Volcanic basalts
6
MONASH
CIVIL
ENGINEERING
UNDERGROUND STATION: CBD NORTH, NOW STATE LIBRARY
▪ EES: Environmental Effects Statement (under the
Environment Effects Act 1978)
▪ Plan View of selected station
▪ What does ‘GA15-BH169’ stand for?
7
MONASH
CIVIL
ENGINEERING
UNDERGROUND STATION: CBD NORTH, NOW STATE LIBRARY
▪ Section Alignment
▪ Segment 11: TBM (Tunnel Boring Machine) Tunnel
▪ Segment 12: State Li
ary Station, Underground Mine,
Tri-arch Cavern including central cavern and two platform
caverns https:
metrotunnel.vic.gov.au/construction/cbd
uilding-cbd-stations
https:
metrotunnel.vic.gov.au/construction/cbd
uilding-cbd-stations
8
MONASH
CIVIL
ENGINEERING
SOIL AND ROCK BOREHOLE LOGS
▪ Drilling Method, NMLC: Diamond Core - 52 mm
9
MONASH
CIVIL
ENGINEERING
REPORT OF SOIL AND ROCK BOREHOLE
10
MONASH
CIVIL
ENGINEERING
ABBREVIATIONS AND TERMS
▪ TCR = Total Core Recovery (%)
– TRC(%)=(Length of core recovered)/(Length of core run)×100
▪ SCR = Solid Core Recovery (%)
– SCR(%)=( Length of cylindrical core recovered)/(Length of core run)×100
▪ RQD = Rock Quality Designation (%)
– RQD(%)=( Axial lengths of core >100 mm)/(Length of core run)×100
11
MONASH
CIVIL
ENGINEERING
ROCK QUALITY DESIGNATION (RQD)
10 cm <10 cm <10 cm core loss
X X XX X
L1 L2 L3 L4 L5 LnLi
L
▪ Rock Quality Designation (RQD)
– RQD was proposed by Deere XXXXXXXXXXas a measure of the quality
of borehole core.
– RQD is defined as the percentage of rock cores that have length
equal or greater than 10 cm over the total drill length.
RQD = Li / L x 100%, Li > 10 cm
RQD = (L1 + L2 + … + Ln) / L x 100%
12
MONASH
CIVIL
ENGINEERING
ROCK QUALITY DESIGNATION (RQD)
XXXXXXXXXX
▪ Don U. Deere
– 1955, PhD from University of
Illinois
– XXXXXXXXXX, ISRM Board
Members with Charles Fairhurst
– 1964, Rock Quality Designation
(RQD)
– 1972, US National Committee
on Tunnelling Technology
– Member of National Academy of