IDM MODEL OF RED ROT OF SUGERCANE By Md. Kamaruzzaman Shakil
LECTURE : 3 HRS / WEEK Kamaruzzaman Mohamed Dean Office ... · PDF fileLECTURE : 3 HRS / WEEK...
Transcript of LECTURE : 3 HRS / WEEK Kamaruzzaman Mohamed Dean Office ... · PDF fileLECTURE : 3 HRS / WEEK...
LECTURE : 3 HRS / WEEK
Kamaruzzaman Mohamed
Dean Office / T1-A13-15C
Tel : 016-5320264
Rock at depth is subjected to stresses resulting from the
weight of the overlying strata and from locked in stresses of
tectonic origin.
When an opening is excavated in this rock, the stress field
is locally disrupted and a new set of stresses are induced in
the rock surrounding the opening.
Knowledge of the magnitudes and directions of these in situ
and induced stresses is an essential component of
underground excavation design since, in many cases, the
strength of the rock is exceeded and the resulting instability
can have serious consequences on the behaviour of the
excavations.
Introduction
Introduction
Besides basic material properties, equally important is in-
situ stress
In-situ stress is important to define the boundary conditions
for mechanical analysis
Rock engineering is concerned mainly with the effect of
altering the geometry of a pre-stresses material, hence
changing the pre-existing
stress state when extra loads are applied or when rock is
excavated
In-situ stress is important for underground engineering
1.1 Factors influencing the stress state
- Surface topography
- Erosion and temperature
- Non-homogeneity
- Discontinuities
- Time (e.g, postglacial rebound, viscosity)
- Presence of excavations
- Representative volume element (RVE)
1 Initial Stress
World Stress Map
Surface Topography
1.1 Factors influencing the stress state
Higher stress
Lower stress
Higher stress
Lower stress
These effects may influence the
vertical stress to some extent. The
effect of topography on vertical
stresses depends on the height of the
hill or valley in relation to its width.
Topography
1.1 Factors influencing the stress state
Stress conditions often may change
significantly across structures such
as faults, dyke contacts and major
joints. Stiffer geological materials
tend to attract stress, so that stress in
say a dyke may be higher than in a
rock such as quartzite in close
proximity.
These effects may influence the
vertical stress to some extent. The
effect of topography on vertical
stresses depends on the height of the
hill or valley in relation to its width.
Discontinuities
1.1 Factors influencing the stress state
Stiff material
Soft material
Stress of stiff layer
makes higher stress
Erosion
1.1 Factors influencing the stress state
Eroded Height !!!!!
Stress reduces by γ∆H
σ1=γh
(Fresh rock, K = 1),
Presence of excavation
1.1 Factors influencing the stress state
Presence of excavation
1.1 Factors influencing the stress state
Stress vector
Representative volume
element (RVE) or
representative
elemental volume, VH
I << H << L
L
H
I
Macro
Meso
MicroH
I
Real heterogeneous
material in modeled at
the meso-scalled by a
continuum
RVEs in Rock Mass
Rock mass is a multiscale structure
(1) no unique choice of the RVE.
(2) several continuum media can be associated with the rock mass
Scale 2 Micro2 Meso2
Scale 1 Micro1 Meso 1
A A A A A A
H1 H2
A-A
Stresses at microscale
A-A
Stresses at macroscale
A-A
Stresses at mesoscale
x
σ
x
σ
x
σ
H1
H2
Representative Volume Element
1.1 Factors influencing the stress state
A A A A
RVE
A-A
Stresses at microscale
A-A
Stresses at macroscale
x
σ
x
σ
H1
Borehole scale
Regional scale
Engineering
structure scale
Scale Effect in Stress Measurements
Size of the volume element (rock mass volume involved in the test)
A s
tres
s co
mponen
t
RVEs
RVEs
RVEs
Averaging over RVE
Meso
Micro
Macro
Representative Volume Element
1.1 Factors influencing the stress state
Vertical stress & Horizontal stress
1.2 In-situ Stress Measurement
Depth, z
Horizontal stress, σh
Ver
tica
l st
ress
, σ
v
Vertical stress
The stress
acting at a point
below the
ground surface
is due to the
weight of
everything lying
above: rock,
water, and
surface loading.
Horizontal stress
The stresses
acting horizontally
on an element of
rock at a depth z
below the surface
are much more
difficult to
estimate than the
vertical stresses.
Ground level
Measurements of vertical stress at various mining and civil engineering sites around the world confirm that this relationship is valid although, as illustrated above, there is a significant amount of scatter in the measurements
Vertical stress
1.2 In-situ Stress Measurement
Normally, the ratio of the average horizontal
stress to the vertical stress is denoted by the
letter k such that:
Terzaghi and Richart (1952) suggested that,
for a gravitationally loaded rock mass in which
no lateral strain was permitted during
formation of the overlying strata, the value of k
is independent of depth and is given by
where ν is the Poisson's ratio of the rock
mass.
Horizontal stress
1.2 In-situ Stress Measurement
Horizontal stress
1.2 In-situ Stress Measurement
Horizontal stress
1.2 In-situ Stress Measurement
Variation of
horizontal to vertical
stress ratio with depth
below surface
Shorey, 1994
Average deformation modulus
Correlation of ratio σh/σv to depth (z)
1.2 In-situ Stress Measurement
Variation of average
horizontal to vertical
stress ratio with depth
below surface
Brown & Hoek, 1978
1.2 In-situ Stress Measurement
Correlation of mean ratio σh/σv to depth (z)m
inim
um
2.1 Method performed on rock surface
- Flat Jack
- Surface relief method
2.2 Methods performed in borehole
- Hydraulic Fracturing
- Borehole breakout
- Overcoring
2.3 Methods performed using a drill cores
- Acoustic Method
- Core discing
- Strain recovery method
2 Method of Stress Measurement
1.2 Method Performed in Borehole
Hydraulic Fracturing Method
Po
Ps
Pc2
Pc1
2. Measurement1.2 In-situ Stress Measurement
Hydraulic Fracturing : Analysis (Kirsch’s solution)
fractured
borehole
ppAA
1.2 In-situ Stress Measurement
Flat Jack Method
1.2 In-situ Stress Measurement
Flat Jack Method
1.2 In-situ Stress Measurement
Flat Jack Method : Analysis
Pin
se
pa
ratio
n
do
Time Jack pressure
σθ
Overcoring - measure of distortion (strain!).
1.2 In-situ Stress Measurement
(1) advance +76mm main borehole
to measurement depth,
(2) drill +36mm pilot hole and
recover core for appraisal,
(3) lower probe in installation tool
down hole,
(4) probe releases from installation
tool; gauges bonded to pilot-
hole wall under pressure from
the nose cone,
(5) raise installation tool; probe
bonded in place and
(6) overcore the probe and recover
to surface in core barrel.
Overcoring
1.2 In-situ Stress Measurement
Overcoring : Analysis
1.2 In-situ Stress Measurement
CHILE versus DIANE
Continuous
Homogeneous
Isotropic
Linearly
Elastic
Discontinuous
Inhomogeneous
Anisotropic
Non-Linearly
Elastic
Strength Criteria for isotropic rock-failure theory proposed to explain observed rock failure phenomena
Types of strength criterion:
• Peak strength criterion
stress components which will permit the peak strengths developed under various stress combinations to be predicted
• Residual strength criterion
used to predict residual strengths under varying stress conditions
• Yield strength criterion
is a relation between stress components which satisfied at the onset of permanent deformation
3 Theory of Rock Failure
• Mohr-Coulomb’s strength criterion
• Griffith Crack Theory
• Empirical criteria – Hoek and Brown
.
3 Theory of Rock Failure
Methods of Analysis
φ
σ
τ
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
Normal stress
Shear
str
ess
σ
τ
τ = c
Normal stress
Shear
str
ess
c
Coulomb condition
(cohesive material)
Failure occurs when an applied
stress exceeds the intrinsic
bonding strength between sample
grains
Mohr condition
(cohessionless material)
Failure occurs when an applied
stress overcomes internal
resistance on incipient failure
surfaces
φ
σ
τ
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
Normal stress (Mpa)
Shear
str
ess (
Mpa)
Mohr-Coulomb condition
(c & φ material)
Strength characteristics are mobilised both by cohesive and frictional resistance effects
c
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
ROCK CONDITION
Where rock exists in an
undisturbed, intact state the
resultant failure envelope will
exhibit both cohesional and
frictional strength behaviour
Once the rock has been
broken, local cohesional
bonding strength can often be
assumed to be negligible
In badly fragmented condition,
little or no cohesional strength
will exist to impart shear
resistance
φ
σ
τ
Normal stress (Mpa)
Shear
str
ess (
Mpa)
c
φ
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
c
φ
σ3 = 0σ
τ
Intergranular
crushing which
occurs between
grain boundaries
within rock test
specimens under
high confining stress
3 Theory of Rock Failure
σ1 = σcσT
Linear
compressionTension Non-linear
compression
Mohr-Coulomb failure criterion
Actual plot of shear versus normal stress data
NO FAILURE
JUST FAILING
FAILED
c
φ
σ3 σ1(a) σ1(b) σ1(c)
ROCK INSTABILITY DUE TO INCREASING AXIAL STRESS APPLICATION
For a fixed level of confinement, sample failure becomes more likely as the
magnitude of axial- applied stress is increased
σ
τ
When stress circle
contact is made
with the locus it is
assumed that the
rock failure will
take place
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
Circle shrinksc
φ
σ3(a) σ3(b) σ1
ROCK INSTABILITY DUE TO INCREASING CONFINEMENT STRESSWhen confining stress increase, the stress circles reduces in size, and it displace
further, thereby indicating that a position of greater stability can be achieved
σ
τ
This example
therefore
demonstrate the
necessity for
applying support
to rock excavation
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
c
φ
σ3 σ1
ROCK INSTABILITY DUE TO EXISTING OF GROUNDWATERWhere groundwater may exist, it is shown to remain of a fixed size but to be displace
left.
σ
τ
Such
displacement
towards the failure
locus indicated
that the action of
pore water
pressure serves
to destabilise rock
against failure
σ1- uσ3 - u
3 Theory of Rock Failure
Mohr-Coulomb failure criterion
3 Theory of Rock Failure
σ3
σ1
σ1
σ1
σ1
σ3
Uniaxial tension
Uniaxial compression
Triaxial compression
σ3
σ1
compressiontension
HOEK-BROWN
FAILURE LOCUS
Hoek-Brown failure criterion
Major principle stress at failure
Minor principle stress at failure
Unconfined compressive strength of intact rock
Rock constants
3 Theory of Rock Failure
or Using table provided by Hoek
For fresh rock, s = 1
For GSI>25, α = 0.5
Hoek-Brown failure criterion
3 Theory of Rock Failure
Hoek-Brown versus Mohr-Coulomb
3 Theory of Rock Failure
Hoek-Brown failure criterion
Value of mi for
intact rock
(Hoek 2002)
Hoek and Bown (1980) described the peak triaxial
compressive strength of isotropic rock as shown in
the equation given below. The mean value of the
uniaxial compressive strength of the intact sample
(σc) was found to be 35 MPa. Given the Hoek and
Brown (1980) failure criteria is:
σ1/ σc = σ3 / σc + { m σ3 / σc +1}½
Taking the rock material constant m is equal to 15 for
sandstone, tabulate the peak strength of
sandstone(σ1) against the confining pressure (σ3)
when the triaxial test was carried out at the confining
pressure range from 0.2, 0.4, 0.6, 0.8 and 1.0 ,
hence plot the peak strength envelope .
If similar test is to be carried out for granite with the
material constant is twice of sandstone, roughly plot
the graphical peak strength envelope of granite. How
is the different rock type contributed to the peak
strength envelope of rock?
3 Theory of Rock Failure
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8 1
Hoek-Brown failure criterion
3 Theory of Rock Failure
Griffith’s theory of tensile rock failure
3 Theory of Rock Failure
Griffith’s theory of tensile rock failure
σ3
σ1
8ST
ST
3ST
3 Theory of Rock Failure
Griffith’s theory of tensile rock failure
Strength envelope
3 Theory of Rock Failure
Griffith’s theory of tensile rock failure
LIMITATION
Not in the idealised elliptical form suggested such as
natural flaw shapes and their associated fracture
mechanism are much more complex
Many efforts within laboratory environments to
duplicate of simulation the Griffith’s fracture
mechanism, no development of crack growth and
macroscopic sample failure has been able to be
duplicated in the manner suggested by Griffith