Bill Dershowitz Fracture Aperture Correlations Golder ... · PDF fileSlide 1 Fracture Aperture Correlations Session Chair Interlude for Paper #469 Bill Dershowitz Golder Associates

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Fracture Aperture Correlations Session Chair Interlude for Paper #469

Bill Dershowitz Golder Associates Inc Seattle, WA

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Fracture Aperture, 1979 “Cubic Law”

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Fracture Aperture, 1979 “Cubic Law”

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Aperture Measures, Correlations and Functional Relationships

Measures Mechanical Aperture eM (Apparent, Roughness, Max/Min) Hydraulic Aperture eh (Flow Capacity, Transmissivity, Permeability) Storage Aperture es (Storativity, Fracture Porosity) Transport Aperture et (Volume or Water Residence Time Aperture)

Correlations and Functional Relationships Fracture Size Fracture Roughness (JRC) In Situ Stress (Depth) Induced Shear and Normal Displacements

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Aperture Measures (Tsang, 1992; Doe, 2010)

Cubic Law “Hydraulic” Aperture

Transport Aperture (“Mass Balance Aperture”)

Storage Aperture (Doe)

Frictional Loss Aperture SKB R-09-28 (2009)

gCkh

gCTe

ηρηρ==s

eL

et

eH

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Another View of Hydraulic Aperture

EXTREME #1: Fracture as Confined Aquifer (e.g. filled with sand of hydraulic conductivity K) T = K e - T = a e1

IN BETWEEN: Fracture as Rough, Channelized, Mineralized, Partially Filled T = a e b - T = a e2

EXTREME #2: Fracture as Smooth Parallel Plate T = ( ρ g / 12 μ ) e3 - T = a e3

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Fracture Size (“Length” or “Radius”) and Aperture

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Fracture Size (“Length” or “Radius”) and Aperture

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y = 5E-10x1.3861

R2 = 0.68

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1 10 100 1000 10000

Dimension (m)

Tran

smis

sivi

ty (m

2/s)

Task 5TRUE BSTRUE BGAllPower (All)

Fracture Transmissivity and Size

Dershowitz et al (2003)

T = 5x10-10 x L1.36

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Transport Aperture and Transmissivity

SKB R-09-28 (2009)

et = 0.327 T 0.306

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Transport Aperture and Storativity

SKB R-09-28 (2009)

et = 11.4 x S0.550

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Transmissivity (Aperture ?) and Depth (Stress ?)

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Power-law Transmissivity-Size Relationship

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Roughness, Stress, and Hydraulic Aperture

T = 1991 x em6.73

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Aperture and Critical Stress Concepts