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Slide 1
Fracture Aperture Correlations Session Chair Interlude for Paper #469
Bill Dershowitz Golder Associates Inc Seattle, WA
Slide 2
Fracture Aperture, 1979 “Cubic Law”
Slide 3
Fracture Aperture, 1979 “Cubic Law”
Slide 4
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
Slide 5
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
Slide 6
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
Slide 7
Fracture Size (“Length” or “Radius”) and Aperture
Slide 8
Fracture Size (“Length” or “Radius”) and Aperture
Slide 9
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
Slide 10
Transport Aperture and Transmissivity
SKB R-09-28 (2009)
et = 0.327 T 0.306
Slide 11
Transport Aperture and Storativity
SKB R-09-28 (2009)
et = 11.4 x S0.550
Slide 12
Transmissivity (Aperture ?) and Depth (Stress ?)
Slide 13
Power-law Transmissivity-Size Relationship
Slide 14
Roughness, Stress, and Hydraulic Aperture
T = 1991 x em6.73
Slide 17
Aperture and Critical Stress Concepts
