ISSI Seminar 20090504
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Transcript of ISSI Seminar 20090504
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Hands On Mining
The Earth, Its Crust, and Mining
Induced Crustal Instability
Matthew Handley
19th ISSI Seminar
Stellenbosch, 4 May 2009
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Model Inputs and Results for
Stability
11 12 13 11 12 13 11 12 13
21 22 23 21 22 23 21 22 23
31 32 33 31 32 33 31 32 33
v v v m m m t t t
v v v m m m t t t
v v v m m m t t t
+ =
Stress tensor input and output in modelling:
Input virgin
stress model(usually
inaccurate)
Mining induced
stress tensor as accurate and
precise as
modeller desires
Total stress
stress tensor inaccurate from
input
1, X, or S
2, Y or W
3, Z, or V
Typical
Coordinate System,
which must be defined
along with the stress
tensor components
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Estimating in-situStresses All the remaining components need not be
dependent on depth, and generally their valuesand directions will be determined by thegeological history of the rock mass;
There are three very simple models based onphysical processes used to estimate the normalhorizontal components;
The simplest model for estimating shear
component maxima is the Mohr-Coulomb SlipCriterion, most relevant near rockmassdiscontinuities, but also applicable in solid rock.
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Simple Physical Model No. 1:
Heims Rule
Every rockmass, if left undisturbed, will slowly tend
towards a lithostatic stress state over geological time bycreep processes (this includes brittle rocks);
Halite and potash mines show this phenomenon best;
The full stress tensor is therefore given by:
0, ====== zxyzxyzzyyxx gz
This means that if the first stress invariant I1, given by
gzI zzyyxx 31 ++= ,then the rockmass has experienced tectonic disturbances
within its rheological relaxation time.
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Simple Physical Model No. 2:
Rigid confinement During deposition and burial of a sediment it is assumed that
the material has a well defined Poissons Ratio, which
remains unchanged from deposition through to the end of thelithification stage, and then remaining constant thereafter;
Lateral confinement of every particle in the sediment thenresults in the development of a horizontal stress whosemagnitude is determined by the depth of burial and thePoisson Effect;
This model assumes that there are no active geologicalprocesses in progress during or after sedimentation, and thatthe resulting sedimentary rock preserves the deviatoricstresses produced during sedimentation;
The stress tensor is given by:
0,,1
====
== zxyzxyzzzzyyxx gz
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Simple Physical Model No. 3: Denudation
Model (after Gay, 1975 and Voight, 1966)
The rockmass is buried at a certain depth at which thestress state is determined by crustal conditions at thetime of burial;
Subsequent erosion of the rocks overlying the rockmassresult in a relaxation of the vertical stress componentproportional to the thickness of the overlying strata
removed; A similar reduction, also linearly related to the thickness
of overlying strata removed, is manifest in the horizontalstress components, but this reduction does not takeplace at the same rate as the vertical stress reduction;
Non-zero horizontal stresses can exist at surface,whereas this is not possible for the vertical stresscomponent.
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The equations for the erosion model are given
below (after Voight, 1966 and Gay, 1975):
))(027.0( dzahdhyyxx +===
))(027.0( dzvdvzz +==
))(027.0(
))(027.0(
dz
dzak
vd
hd
v
h
+
+==
0=== zxyzxy
d is a specified depth, say 4000 m where hd and vdare defined, while 0 a 1
Simple Physical Model No. 3: Denudation Model
(after Gay, 1975 and Voight, 1966), contd.
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Simple Hard Rock Tabular Mine
Model
Maximum principal stress vertical, and defined
by:
Minimum principal stresses horizontal and
equal, and given by:
1 gz =
2 3 1, 0.4 0.8k k = = =
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Comparison of Models with Measurements
preamble to Graphic Comparisons
In an attempt to obtain consistent stress data from 526crustal stress measurement records made in Southern
Africa, collected into a database, and reported by Staceyand Wesseloo (1998), the following was done:
332 records deleted because full stress tensor notreported (results from hydrofracture, earthquakes, etc.)
From remaining 294 records further 17 deleted becauseof non-orthogonality of principal stress components (2criterion applied)
A further 110 records eliminated because the third stressinvariant IIII for the principal stresses and the standard
stress components >5% different Finally, 132 records excluded because ob greater than10% different than 33
The 35 remaining records used as a comparison with themodels
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0
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60 70 80
Stress (MPa)
Depth(m
)
Measured vertical stress 33
Theoretical overburden stress ob
(after Stacey and Wesseloo, 1998)
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0
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60 70 80
Stress (MPa)
Depth(m
)
Measured vertical stress 33
Measured N-S horizontal stress 11
Measured E-W horizontal stress 22
(after Stacey and Wesseloo, 1998)
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0
500
1000
1500
2000
2500
3000
0 1 2 3 4 5
Depth(m
)
Omni-directional k-Ratio
k-Ratio 1h/33
k-Ratio 2h/33
(after Stacey and Wesseloo, 1998)
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Stress Map of Southern Africa
Maximum Horizontal Stress
(after Stacey and Wesseloo, 1998)
Inset:
Wegener Anomaly,
after Bird et al. (2006)
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Hands On Mining0 20 40 60 80 100 0 20 40 60 80 100 120Stress (MPa)
Heims Rule Rigid Confinement
Denudation Hard Rock Tabular Mine
0
500
1000
1500
20002500
3000
3500
4000
0
500
1000
15002000
2500
3000
3500
Depth
(m)
Comparison between Virgin Stress Models
and Measured Data
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Variation of maximum principal stress both
within and between grains
after Handley, (1995)
15 mm
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Proposed New Models from
Geological Events The data plotted earlier is regional, both at large and
small scales
Individual mines may exhibit local stress conditions thatare represented by one or another of the simple models
Crustal stresses are varied from small to large scales,and also in geological time
Geological processes and events may make overridingimprints on the stress state in rockmasses, but onlylocally and temporarily
Variation in rheological rock properties may sustain
deviatoric stresses in time spans from thousands ofyears (halite, potash) to many hundreds of millions ofyears (quartzites, andesitic lavas)
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Four Geological Process Models
for Horizontal Stress Estimation
Thrusting, folding (Hoek-Brown)
Normal faulting, igneous intrusions (Hoek-Brown)
Denudation (Voight, Gay)
Sedimentation with basin subsidence
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Planet Earth
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La27South Section Line
Lo 10 E Lo 20 E Lo 30 E Lo 40 E
La 10 S
La 30 S
La 20 S
La 27 SLa 27 S
Southern Africa
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+100 km
25 2729
3133
3537
39
232119
1715
1311
09
Kosi BayElizabeth Bay
100km
MSL
-100km
-200km
-300km
+100kmMSL
-100km
-200km
-300km
AfricaLa27S
Mantle
Asthenosphere
LithosphereWitwatersrandBasin
West East
Cross-section through Earth at Latitude 27 South
continentalcrust
Vredefort
Astrobleme
Crustal Thicknesses after Mooney et al., (1998)
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Hoek-Brown Limits to Crustal Stress(m = 12, s = 1,
c
= 60 MPa, t
= 0 everywhere, and at all times
0
10000
20000
30000
40000
50000
60000
0 500 1000 1500 2000 2500 3000
Thrustfaulting,mountainbuilding
Norm
alfa
ultin
g,dyke
intrusio
ns
h
=1
v
=3
v
=1
h
=3
Stress (MPa)
Depth(m
)
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Basin Subsidence
r
a
yc
y
yr
r
Karoo Supergroup Subsidence and the effect it had on horizontal stresses
E (Pa) = 40000000000 Loading Constant 1.00E+04
Poisson's Ratio: 0.3 Thickness (m) = 60000
a (m) = 1400000
Plate constant D: 7.91209E+23
Max Deflection yc (m): -3092.954861
Max Moment Mc (Nm) = 4.0425E+15
Max Stress c (MPa) = 6.7375
13.475
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Intrusion after Subsidence sill and dyke
x
x
x
x
x
x
x
x
x
x
x
x
x
x
xx
xxxxxx
xx
x x x x x x x x
x
x
x
xx
0
500
1000
1500
2000
2500
3000
3500
4000
0 20 40 60 80 100 120 140
Stress (MPa)
Depth(m)
h and
v indykeandh in
cou
ntryrockafterintrusion
v incountryrock
beforeintrusion
h
in
country
rock
befo
reintrusion
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Conclusions Stress data is variable at all scales, from granular scales
(of the order of 1 mm, to continental scales (1600 km)
Not one simple model produces any resemblance tomeasured data distributions
Mining operations need to make regularin situstress
measurements across the mining lease as well as at allmining depths in order to draw any inferences about thestate of virgin stress at the mine
All known stress measurement techniques are too
expensive to gain widespread application, and a newinvention is necessary to make stress measurementcheaper and more practical
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ReferencesAnnhaeusser C and Maske S (Eds.) (1986): Mineral Deposits of Southern Africa, Vols I and II. The Geological Societyof South Africa, Johannesburg, 2376p.
Billington EW and Tate A (1981): The Physics of Deformation and Flow. New York: McGraw-Hill International BookCompany, 626p.
Bird P, Ben-Avraham Z, Schubert G, Andreoli M and Viola G (2006): Patterns of stress and strain rate in SouthernAfrica. Journal of Geophysical Research, Vol. 111, B08402, doi:10.1029/2005JB003882, 2006.
Gay NC (1975): In situ stress measurements in Southern Africa. Tectonophysis, Vol 29, pp. 447-459.
Moony WD, Laske G and Masters TG (1998): CRUST 5.1: A global crustal model at 5x5 degrees. Journal ofGeophysical Research, Vol 103 B1, pp 722-747.
Roark RJ and Young WC (1975): Formulas for Stress and Strain. New York: McGraw-Hill Book Company, 624 p.
Stacey TR and Wesseloo J (1998): Evaluation and Upgrading of Records of Stress Measurement Data in the MiningIndustry. SIMRAC Project GAP511b, Department of Minerals and Energy, Johannesburg, June 1998.
Voight B (1966): Beziehung zwischen grossen horizontalen spannungen im gebirge und der tektonik und derabtragung. 1stCongress of the International Society of Rock Mechanics, Lisbon, 1966, Vol 2., pp.51-56.