rock strength (shear strength, compressive strength, tensile strength… · 2011. 3. 28. ·...
Post on 06-Sep-2020
37 Views
Preview:
TRANSCRIPT
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock Strength (Shear strength, Rock Strength (Shear strength, compressive strength, tensile strength, compressive strength, tensile strength,
fracture strength, crushing strength, etcfracture strength, crushing strength, etc……) )
Maurice Dusseault
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Common Symbols in RMCommon Symbols in RM
� E, ν: Young’s modulus, Poisson’s ratio� φ: Porosity (e.g. 0.25, or 25%)� c′, φ′,To: Cohesion, friction ∠, tensile strength� T, p, po: Temperature, pressure, initial pres.� σv, σh: Vertical and horizontal stress� σhmin, σHMAX : Smallest, largest horizontal σ� σ1,σ2,σ3:Major, intermediate, minor stress� ρ, γ: Density, unit weight (γ = ρ × g)� K, C: Bulk modulus, compressibilityThese are the most common symbols we use
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Chalk Fracture ExperimentsChalk Fracture Experiments……
a. Three-point loading 2P
P PTensile stress
Compressive stressSurface of fracture
Fracture location directly under 2P
b. Four-point
loading
P
P P
Tensile stress
Compressive stress Surface of fracture
Fracture location indeterminate, but between
the two vertical loads
Pd. Pure torsion (moment)
c. Pure axial tension
Maximum tensilestress orientation
M M
T T
Surface of fracture
Fracture location indeterminate
? ?
Surface of fracture is a helical shape
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
What is Strength?What is Strength?
� It turns out that the “strength” of a geomaterial is a highly complex subject…
� There still remain issues on which experts are not in full agreement (e.g. scale dependency of tensile strength, “creep failure”…)
� Strength can be a simple measure, such as unconfined compressive strength (UCS)
� It can be complex (shear stress under a full 3-dimensional stress state, under temperature and elevated pore pressure conditions, etc.)
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Yield Modes around a BoreholeYield Modes around a Borehole……
σHMAX Brittle beam bucking under high uniaxial local loads
breakout
Destabilized column is “popping” out
High pw leads to slip of a joint or fault.
Usually occurs only with high MW Slip
plane
Axial extension fractures: tensile failure when pw > σθ
Shear failure in low cohesion rock precedes sloughing of cavings
σHMAX
High MW – Low MW
Crushing in breakout apex
Plus some others…
�Fissile shale sloughing if the borehole
axis is close to parallel to fissility axis
�Swelling, weakening, turning to “mush”
�Borehole surface spalling from high σθ,
perhaps arising from heating, low σʹθ
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock StrengthRock Strength
� Strength is the capacity to sustain (support):�Shear stress (shear strength)
�Compressive normal stress (crushing strength)
�Tensile stress (tensile strength)
�Bending stress (bending or beam strength)
� All of these depend on effective stresses (σ′), thus, we must know the pore pressure (p or po)
� Rock specimenstrength is different than rock massstrength (joints, fissures, fissility…)
� Tests are done on cores, chips, analogues…
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock Mass vs Sample StrengthRock Mass vs Sample Strength
faultsjoints
fracturesgrains
bedding
coresZ
Scale differences and flaws mean that direct extrapolation of test results to the field is difficult in
Petroleum Geomechanics
Field stresses
Sample damage can change properties!
Field scale: grains to kilometers. Lab scale: grains to 100 mm diameter specimen.
100 m
σa
σrσr = σ3
σa = σ1 τmax planesslip
planes
TriaxialTest
Stresses
100 mm
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
How We Measure Rock StrengthHow We Measure Rock Strength……
� Simple measurements (called “index” tests)�Uniaxial Compressive Strength (UCS), σ′3 = 0
�Tensile strength (pure tension, hard for rocks!)
� Indirect tensile test (Brazilian test)
�Point-load, beam-bending, scratch test, needle…
� Direct shear tests of a planar surface�A joint surface, bedding plane, fault plane,
sheared plane, lithologic interface, etc.
�The surface is loaded, then sheared, and the resistance to shear loads is recorded
rock
σ′nτ
slip plane
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Beam Bending TestsBeam Bending Tests
P/2
P/2
Beam-bending
“tensile” testP/2
P/2
X-section
Core testsThe “strength” of a rock in beam bending is strongly dependent on the specimen size and the “quality” of the surface finish!
Prepared specimen tests
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Effect of Flaws on TEffect of Flaws on Too
P/2
P/2ƒ
ToA B C
A: notchedB: roughC: polished
Surface finishThus, To is flaw size dependent
Beam-bending
tensile test
P/2
P/2
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Surface Finish and FlawsSurface Finish and Flaws
� If the strength of rock in beam-bending depends on the surface finish…�Beam-bending is of little value to engineering
design issues
�The strength of rock in tension is dependent on the size of the flaw
� These observations, combined with the fact that rock masses have many discontinuities…�Suggest that tensile strength may be inappropriate
for many rock engineering problems
�Measurements of To are of questionable value
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Cracks and FlawsCracks and Flaws
P/2
P/2 P/2
P/2
Rock
Flaw
The flaw tip concentrates stresses, making brittle
rupture much easier
Stress “trajectories”
Flaws in Rock :•Pores•Grain boundaries•Joints•Fractures•Faults, etc.
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Stress ConcentrationsStress Concentrations
Hoek and Bieniawski 1965, Int J Frac Mech 193) 137-155
www.webpages.uidaho.edu/~simkat/geol542.html
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
““ GriffithGriffith 11”” CracksCracks……
� Flaws serve as local stress concentrators
� The applied stress is far lower than the yield value for the “intact” material…
� Stress concentration at the flaw tip locally overcomes material strength�ƒ(crack length, orientation, sharpness)
� Strength of a “flawed” brittle material is therefore far lower than an “intact” material
� All rocks are flawed! Hence, weak in tension, strong in compression
1 - Griffith AA. 1920. The phenomena of rupture and flow in solids. Phil Tran Roy Soc of London A221:163-198
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
NeverthelessNevertheless…… Tensile StrengthTensile Strength……
� Tensile strength (To) is extremely difficult to measure: it is direction-dependent, flaw-dependent, sample size-dependent, ...
� An indirect method, the Brazilian disk test, is used
� For a large reservoir, To may be assumed to be zero because of joints, bedding planes, etc.
A
To = F/APrepared
rock specimen
Pure tension test:extremely rare
F
F
Brazilian indirect tension test, common usage
F
F
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
jack
L
slab
scriberpull
load epoxy
rock
flat
L
round
core
reboundmeasure
mandril
Schmidt Hammer or Sclerometer
Other Index Tests of StrengthOther Index Tests of Strength
� Index tests: strength “indices” only
� Point load tests on core disks or chunks
� Brinnell Hardness test, or penetration test
� Scratch test on slabbed core sections
� Sclerometer or steel bar rebound tests
� All these use correla-tion charts for strength estimates
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
RecommendationRecommendation
� Include a strength index test program in all your core analyses (good for drilling…)
� Service companies can provide this systematically upon request
� The data bank can be linked to compaction potential, drillability, other factors…
� It may help identify particularly troublesome zones that could cause troubles
� Any systematically collected data will prove useful for correlations and engineering
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Cautions!Cautions!
� However, index values are estimates only!
� Scale is a problem!�What is the scale of interest to the problem?
� Is testing a drill chip a test of sufficient scale?
� Is it possible to index test fractured reservoirs?
� Geometry is an issue!�How is strength affected by a 2 mm thick shale
lamination in an otherwise intact sandstone?
� Is strength anisotropic?
�What is orientation w.r.t. the anisotropy?
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Core Core ##2 ~275002 ~27500′′ below sea levelbelow sea level
0
1000
2000
3000
4000
5000
6000
7000
8000
Cor
rela
tion
to U
CS
(ps
i)
~ 1 foot (300 mm) length
Scratch test results
Red line is output from the load cellBlue line is a moving average value of the force
This core section is quite homogeneous throughout
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
0
1000
2000
3000
4000
5000
6000
27264.0 27264.1 27264.2 27264.3 27264.4 27264.5 27264.6 27264.7 27264.8 27264.9 27265.0
Depth (ft)
UC
S (
psi)
Cor
rela
tion
to U
CS
(ps
i)
~ 1′ (300 mm)
Scratch test results
Red line is output from the load cell. Blue line is an averaged value of the force
Core Core ##1 ~280001 ~28000′′ below sea levelbelow sea level
Heterogeneous and damaged core
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
27348.0 27348.1 27348.2 27348.3 27348.4 27348.5 27348.6 27348.7 27348.8 27348.9 27349.0
Depth (ft)
UC
S (
psi)
Epoxy Spike
Cor
rela
tion
to U
CS
(ps
i)
~ 1 foot (300 mm) length
Scratch test results
Core Core ##2 ~275002 ~27500′′ below sea levelbelow sea level
Heterogeneous, damaged core
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock StrengthRock Strength-- Shear StrengthShear Strength
� Shear strength: a vital geomechanics measure, used for design
� Shearing is associated with:•Borehole instabilities, breakouts, failure•Reservoir shear and induced seismicity•Casing shear and well collapse•Reactivation of old faults, creation of new ones•Hydraulic fracture in soft, weak reservoirs•Loss of cohesion and sand production•Bit penetration, particularly PCD bits
rock
σ′n
τslip planeσ′n is normal effective stress
τ is the shear stress,║to slip plane
σ′ 3
σ′1
σ′σ′σ′σ′n
ττττ
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
How We Measure Rock StrengthHow We Measure Rock Strength……
� Direct measurements with confinement (σ′3)�Compressive Strength: Triaxial Testing Machine
�Encase the core in an impermeable sleeve
�Confining stress is applied σ3 first�σa is then increased while…
�Pore pressure constant
�Record ∆σa, εa, εr, ∆V
� More exotic tests…�∆T, ∆p, even ∆chemistry
�Creep tests (constant σ, measure ε)
�Hollow cylinders…
TriaxialTest
Stresses
Strain rate
σ′r = σ′3
σ′a = σ′1 σ′n
τf
shear planes
•
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
High Confining Pressure FrameHigh Confining Pressure Frame
Core Lab Inc.
σ′a
σ′r
Press
Cel
l
Frame
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
The Triaxial CellThe Triaxial Cell
load platen
p control, ∆Vp
εa, εr
impermeable membrane
σr ap
plie
d th
roug
h oi
l pre
ssur
e
strain gauges
σa
σa
seals
thin porous stainless steel
cap for drainage
CS
IRO
-Aus
tral
ia
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Triaxial Test ApparatusTriaxial Test Apparatus
� A confining stress σ′3 is applied (membrane)
� The pore pressure is zero, or constant
� The axial stress is increased slowly until well past peak strength
� Deformation behavior is measured during test
� T, po… can be varied in sophisticated systems
Sing06.049
Triaxial test cell. ( a) Cell components including spherical seats A, end caps B, specimen C,fluid port D, Strain Gauges E (optional), and polyurethane rubber sleeve F. (b) Insertion ofsleeve. ( c) End cap removed to clean accumulated rock fragments. ( d) Triaxial test with cellin position, showing four-column load frame, 200-t hydraulic jack load cell and pressuretransducer connected to cell for automatic plotting of stress path. (Franklin and Hoek, 1970.)
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
φφφφ = 30% in situ, 35% in the core labdamage
Some Issues in TestingSome Issues in Testing
� Sample disturbance
� Sample homogeneity
� Representativeness
� Specimen preparation
� Lateral ε data? ∆V?
� ∆p response (shales)?
� Testing must be done by a commercial lab with good QC
� Even then, results are critically examined
Shaley zone, sheared
Oil sand, intact
σ′a
σ′r
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Shear Failure of SandstoneShear Failure of Sandstone
σa
σr = σ3
σa = σ1
� High quality cylinder
� L = 2D
� Flat ends
� High angle shear plane
� Zone of dilation and crushing
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
A A σ′σ′ -- εε Curve for a Rock SpecimenCurve for a Rock Specimenst
ress
diff
eren
ceσ1 - σ3
axial strain
εa
Y - peakstrength
sudden stress drop (brittle)
massive damage, shear plane develops
continued damage
ultimate orresidualstrength
cohesionbreaking
damage starts
“elastic” part of σ′-ε curve
seating, microcrack closure
σ´3 = σ´r
σ′r = σ′3
σ′a = σ′1 σ′n
τf
shear planes
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Yield and StrainYield and Strain--WeakeningWeakening……
� At one σ′3 value…� YP: peak shear strength
� YR: residual strength
� Red curve is at a high confining stress –σ′3
� Blue curve, low σ′3� E.g.: high pore pressure
= low σ′3, low strength, brittle behavior!
� Low po… higher strength, ductile
Str
ess
–σσ σσ a
-σσ σσ r
Axial strain - εεεεa
strain-weakening
σ’ – ε behavior
YP
YR
brittle rupture
YP
YR
ductile yield
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Measurement of Measurement of ∆∆(Pore Volume)(Pore Volume)
� The specimen is isolated from all liquids in the cell
� The pore space is liquid-saturated (water or oil)
� As the axial stress is increased, ∆V measured
� This gives an estimate of the dilation of the rock as it shears
load platen
impermeable membrane
σr
= σ
3
σa
σa
seals
thin porous stainless steel
cap for drainage
σr
= σ
3
∆V
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Dilatancy During Rock ShearingDilatancy During Rock Shearing
� When rocks shear under low σ′3, they dilate (+V)
� Dilation = +∆V increase in pore V, microcracks
� Rock is weakened, but with higher φ, k values
� For reservoirs and high p, σ′3 is low; dilation enhances permeability, an important factor in heavy oils…
Str
ess
–σ a
-σ r
σ’ – ε behavior
+∆V
-∆V
compression
dilation = +∆V
Axial strain - εa
Axial strain - εa
Y
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Behavioral Model RepresentationBehavioral Model Representation
Strain (%)
Dev
iato
ric s
tres
s∆∆ ∆∆V
(D
evia
toric
co
mpo
nent
)
+ve
-ve
E
E
C, D AB
Constitutive models:A: Linear elastic, no deviatoric dilation
B: Perfect plasticity, no deviatoric dilation
C: Instantaneously strain-weakening, post failure dilation angle
D: Gradual weakening, post failure dilation
E: General response, simulated with more complex models…
σ−ε curves
A
B
C D
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Full Triaxial Data Set ExampleFull Triaxial Data Set Example
σ a-
σ r (
MP
a)
Strain- %0
1%
10
20
30
40
UCS, σ´3 = 0
σ´3 = 2.0 MPa
σ´3 = 14.0 MPa
Strain- %+∆V-∆V
Volume change measurement (dilation)
σ−ε curves
σ´3 = 7.0 MPa
1.0
-1.0
σ′r = σ′3
σ′a = σ′1 σ′n
τf
shear planes
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock Strength: the MRock Strength: the M--C PlotC Plot
� To plot a yield criterion from triaxial tests, on equally scaled τ, σ′ axes, plot σ′1 and σ′3 at fail-ure, join with a semicircle, then the tangent = Y
σ′3 σ′1To
σ′n
τ
cohesion
c
Different σ′3 values
4 triaxial tests are plotted here, plus the tensile strength from other tests
Y
Normal stress
Shear stress
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Standard Approximation for YStandard Approximation for Y
To σ′n - normal stress
τ - shear stress
Rocks are weak in tension!!
Y = M-C Yield Criterion:τf = c′ + σ′n·tanφ′ for σ′n ≥ To
τf = 0 for σ′n < To
real Y
Known as the Mohr-Coulomb (M-C) failure criterion
cohesion
Y - linearapproximation
φ′
c′
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Geomaterial Failure ModesGeomaterial Failure Modes
Shear rupture•Bifurcation plane•Some general damage•Localization effects•Plasticity theory
with shearing
Low confinement
General damage•No bifurcation•Distributed
general damage•Continuum damage
mechanics best
High confinement
Tensile rupture•Single plane•Minimal general
damage•Fracture
mechanics
-ve confinement (i.e. tension)
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock Failure Modes and Rock Failure Modes and σσ′′33
van der Pluijm and Marshak, 1997
Davis and Reynolds, 1996
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Use a Reasonable Use a Reasonable YY ApproximationApproximation
To σ′n - normal stress
τ - shear stress
cohesion
c′
standardapproximation
real Y
Mohr-Coulomb failure (or yield) criterion
φ′
This is a better approximation for cases of low confining stress
Rocks are weak in tension: can
we assume that To = 0 for large
scale problems?
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Different Methods to Present Different Methods to Present YY
� In the literature, there are > five different methods to plot rock yield (failure) criteria
� The next slides show other examples of M-C yield criterion plots
� I prefer the Standard Mohr plot…�Simple, clear, easy circle construction for σ
� There are also many yield criteria: Lade, Druker-Prager, Modified Von Mises…
� I suggest: stick with the M-C criterion, it is robust, well understood, direct…
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
σσ′′11 ×× σσ′′33 Plotting MethodPlotting Method
� Plot σ′1, σ′3 values at peak strength on axes
� Fit a curve or a straight line to the data points
� y-intercept is Co or UCS
� (Note that circles to solve for stresses can only be used on a conventional M-C plot, not on this one!)
σσσσ′′′′1 - σσσσ′′′′3 ·tan2αααα - Co = 0
σ′1
σ′3
Uniaxialcompressivestrength, Co
(not same as To)
tan2α
Curved orlinear fit
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
pp ×× qq Plotting MethodPlotting Method
� p = (σ′1 + σ′2)/2� q = (σ′1 - σ′2)/2� p is mean σ′n� q is shear stress
� This method is most common in soil mechanics
� Sometimes used in petroleum rock mechanics
p
q
α
q = Co/2 + p·tanα
actual curve
straight line assumption
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Why Approximations for Why Approximations for YY??
� Linear approximations of Y are easy to understand: cohesion plus friction effects
� When yield (failure) criteria are plotted from real lab data, there is a lot of scatter
� Numerical modeling is the only way to use the full curvilinear Y envelopes…
� Thus, a linear approximation allows:�Quick calculations and estimates
�A clearer picture of the physics
�But! Use the right stress range to improve results of simple calculations
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Still the Best (in my view)!Still the Best (in my view)!
σ’1To ~ 0.12·UCS
σ′n - normal stress
cohesion
c’
φ’
Y
Mohr-Coulomb yield criterionτ - shear stress- σ1 – σ22
UCSσ’3
σ′r = σ′3
σ′a = σ′1 σ′n
τf
shear planes
σ′n
τf
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
What is What is ““ FailureFailure”” ??
� Be very careful!! Failure is a loss of function. Rock yield is a loss of strength.
� Don’t confuse them!!
� For example:� Most boreholes have
“yielded” zones
� But, the hole has not collapsed! …or “failed”!
� It still fulfills its function (allowing drill advance)
σMAX
σmin
Breakouts
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock Strength Rock Strength –– Sophisticated TestsSophisticated Tests
� More sophisticated rock tests are also possible and useful in some circumstances:
� Hollow cylinders, cavity tests…
� Creep tests for salt and soft shales
� Thermal effects tests
� Shale properties with different geochemistry
� Drillability tests… etc.
Radial section
Axial section
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Shear of Weak SandShear of Weak Sand
Cou
rtes
t Nor
weg
ian
Geo
tech
nica
l Ins
titut
e
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Geomaterial CharacteristicsGeomaterial Characteristics
� Strain-weakening (peak strength & residual strength, YP, YR, are different)� failure strain, εf = ƒ(σ′3 ): εf ↑ as σ′3↑�YP, YR = ƒ(σ′3 ): YP and YR ↑ as σ′3 ↑�YP/YR = ƒ(σ′3 ): YP/YR ↓ as σ′3 ↑
� Dilatancy �+∆V ↑ with increasing σ1 - σ3
�dilatancy suppressed as σ′3 ↑� Thus we must link stresses, strains and failure
behavior in our rock testing
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
List of Tests* from Core Lab Ltd.List of Tests* from Core Lab Ltd.-- AA
� Triaxial and uniaxial testing for E, ν, UCS � Sonic velocity testing for dynamic Young's
Modulus and Poisson's Ratio (ED, νD)� Mohr-Coulomb envelope analysis and
construction � Sonic velocity & acoustic impedance under σ′
� Sonic velocity in crude oils and brines � Seismic velocity testing at 10Hz � Hydrostatic and uniaxial pore volume
compressibility � Calibration of sonic and dipole log
*Downloaded list from their website
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
List of Tests from Core Lab Ltd. List of Tests from Core Lab Ltd. -- BB
� Fracture azimuth and max stress azimuth (sonic velocity anisotropy)
� Evaluation of natural fracture conductivity � Thick wall cylinder test (sand production onset)� Fracture toughness analysis � Brinell hardness test for closure stress analysis � Proppant embedment testing vs. closure stress � Brazilian indirect tensile strength � Point load tensile test for wellbore stability
analysis www.corelab .com/PetroleumServices/Advanced/RockMech.asp
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Strain and Shear Slip (Displacement)Strain and Shear Slip (Displacement)
� As σa increased, εa took place as well
� However, when yield took place, deformation only along slip plane!
� We cannot speak about strain any more, only slip or deformation
� Also, there is elastic strain and plastic strain…
σa = σ1
σa = σ1
σr=
σ3
σr=
σ3
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Diagenesis and StrengthDiagenesis and Strength
shear stress
normalstress
chemical cementation
densification(more interlock)
originalsediment
diageneticstrengthincrease
σ′1σ′3
cohesion
diagenesiseffects on the
Mohr-Coulomb strength envelope
σa
σrσr = σ′3
σa = σ′1 τmax planesslip
planes
TriaxialTest
Stresses
c′
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Extreme Diagenesis CaseExtreme Diagenesis Case……
Xal overgrowths, interpenetrative structure!
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Rock Strength Rock Strength –– Shear Box TestsShear Box Tests
� Strength of joints or faults require shear box tests
� Specimen must be available and aligned properly in a shear box
� Different stress values (N) are used
N - normal force
S - shearforceN
S Shear box
Area - A
SA
NA
Linear “fit”
Curvilinear “fit”
data point
cohesionc
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Shearbox ApparatusShearbox Apparatus
� Normal load (stress)
� Reaction frame with high stiffness
� Split box for rock specimens to be tested � Different sizes can be
mounted in the device
� Shear displacement on lower half of “box”
� Rails allow continuous “self-centering”
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Yield Criterion in Shearbox TestsYield Criterion in Shearbox Tests
� Also a Mohr-Coulomb plot
•The points representing normal load and shear load are plotted on axes of equal
•As with triaxial test data, a straight line fit is often used
•This Y is for the joint surface only, not for the entire rock mass…
SA
NA
Linear “fit”
Curvilinear “fit”data point
cohesionc
= τ
= σ′n
Y
rock
N
Sslip plane
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Cohesion and FrictionCohesion and Friction……
� Bonded grains
� Crystal strength
� Interlocking grains
� Cohesive strength builds up rapidly with strain
� But! Permanently lost with fabric damage and debonding of grains
stre
ss d
iffer
ence
σ1 - σ3
εa
complete σ-ε curve
cohesion mobilization
frictionmobilization
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
FrictionFriction
� Frictional resistance to slip between surfaces
� Must have movement (ε) to mobilize it
� Slip of microfissures can contribute
� Slip of grains at their contacts develops
� Friction is not destroyed by strain and damage
� Friction is affected by normal effective stress
� Friction builds up more slowly with strain
τmob = cohesion + friction τf = c′ + µσ′nThis is merely the M-C curve
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Estimating Rock StrengthEstimating Rock Strength
� Laboratory tests OK in some cases (salt, clay), and are useful as indicators in all cases
� Problems of fissures and discontinuities
� Problems of anisotropy (eg: fissility planes)
� Often, a reasonable guess, tempered with data, is adequate, but not always
� Size of the structure (eg: well or reservoir) is a factor, particularly in jointed strata - scale
� Strength is a vital factor, but often it is difficult to choose the “right” strength value
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Strength AnisotropyStrength Anisotropy
Vertical core
Bedding inclination
θθ
0° 30° 60° 90°
UCS
θ
UCS
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Crushing StrengthCrushing Strength
� Some materials (North Sea Chalk, coal, diatomite, high porosity UCSS*) can crush
� Crushing is collapse of pores, crushing of grains, under isotropic stress (minimal τ)
� Tests involve increasing all-around effective stress (σ′) equally, measuring ∆V/∆σ′
� Tests can involve reducing p in a highly stresses specimen (ie: σ’ increases as p drops)
*UCSS = unconsolidated sandstone
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
HighHigh--Porosity ChalkPorosity Chalk
Hollow, weak grains (coccoliths)
Weak, cleavable grain mineral (CaCO3)
Weak cementation (dog-tooth calcite)
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Cracks, Grain Contacts, StrengthCracks, Grain Contacts, Strength
� Point-to-point contacts are much weaker than long (diagenetic) contacts , lower Y
� Large open microfissures also lead to lower strength (cracks = stress concentrators)
� Oriented contacts or microfissures give rise to anisotropy of rock strength as well
� Rocks with anisotropic fabric or exposed to differential stress fields over geological time develop strength anisotropy as well
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Particle Contacts & StrengthParticle Contacts & Strength
� In granular media, contact forces(fn, fs) govern strength
� fs]f = c′ + µ⋅fn
� Again, the Mohr-Coulomb frictional concept…
fs = shear force
fn = normal force
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
A NonA Non--Crushing RockCrushing Rock
� 25% porosity SiO2sandstone (99.5% Q)
� Contacts are diagenetic in nature…
� This gives a very high stiffness, even though…
� The rock is totally devoid of cohesion!
� Athabasca oil sands, Faja del Orinoco sands, are “similar” to this
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Crushing StrengthCrushing Strength
� Apply p, σ (σ > p), allow to equilibrate (σ′ = σ - p)
� Increase σ′ by increasing σ or dropping p
∆σ′ = ∆σ - ∆p
� Record ∆V/V, plot versus effective stress
� The curve is the crushing behavior with +∆σ′
σ
σ
σ
σ
p
∆V
LE
crushingmaterial
σ′
∆V
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
σ′nnormal stress
cohesion
c’
Mohr-Coulomb yield criterionτ - shear stress- σ1 – σ22
σ′r = σ′3
σ′a = σ′1 σ′n
τf shear planes
Initial state
σ′1σ′3
shear yield, th
en collapseFabric collapse
Collapsing in a ChalkCollapsing in a Chalk
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
cohesion
c’
Mohr-Coulomb yield criterionτ - shear stress- σ1 – σ22
σ′r = σ′3
σ′a = σ′1 σ′n
τf shear planes
Initial state
shear yield, th
en collapseFabric collapse
σ′nnormal stress
Increased effective stress leading to pore collapse
Increased pore pressure leading to shear, then collapse
Stress Changes Leading to CollapseStress Changes Leading to Collapse
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Griffith Flaw TheoryGriffith Flaw Theory
� Rock is a “flawed” material
� Flaws are stressed (τ) by deviatoric loads
� Tensile σθ develops at tips
� Rock is weak in tension
� Tensile cracks form easily
� They propagate ⊥ to σ3
� As L↑, acceleration
� Sudden rupture ensues
initial flaw
induced tensile fracture
deviatoric loading
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Low Confining Stress (Low Low Confining Stress (Low σ′σ′33))
� Low σ′3: brittle rupture
� Fractures develop parallel to σ′1
� Specimen may separate into several “columns”
� When column L/w ratio becomes large, buckling or crushing
� Rupture is sudden
� ε energy is released
Axial fractures
Edgechipping
Surface spalls
σ′1
σ′3
w
L
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
θ
θ
Microfissurefabric at yield
Intercrystalline forces at yield
Stress-induced anisotropy
At high stress, general damage occurs; much microfissuring, then coalescence takes place (“bifurcation”)
High σ3
Crystal debonding
Yield at Higher Yield at Higher σσ′′33
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Low Low σσ33, Jointing Dominates, Jointing Dominates
σ1
σ1
σ3
σ3
fractures
blocksloosened
initial jointing
This becomes important in fractured shale drilling, in reservoir mechanics of jointed weak limestones…
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
How Do We How Do We ““ TestTest”” This Rock Mass?This Rock Mass?
� Joints and fractures can be at scales of mm to several meters
� Large φ core: 115 mm
� Core plugs: 20-35 mm
� If joints dominate, small-scale core tests are “indicators” only
� This issue of “scale”enters into all Petroleum Geomechanics analyses
1 m
A large core specimenA core “plug”
Machu Picchu, Peru, Inca Stonecraft
©MBDCI©MBDCI
1-F
Roc
k S
tren
gth
Lessons LearnedLessons Learned
� Strength is a complex issue
� We develop behavior “models” to understand strength and to apply it in practice
� Rock mass vs. rock specimen strength problem
� Problems of scale, heterogeneity…
� Nevertheless, rock strength can be measured and used to predict slip, crushing, triggering of fault movement, and so on.
� Combination of field and lab data is best…
top related