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.