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Anisotropy is Everywhere, to See, to Measure, and to Model

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Abstract

Anisotropy is everywhere. Isotropy is rare. Round stones are collectors’ items, and any almost cubic blocks are photographed, as they are the exception. The reasons for rock masses to frequently exhibit impressive degrees of anisotropy, with properties varying with direction of observation and measurement, are clearly their varied geological origins. Origins may provide distinctive bedding cycles in sedimentary rocks, distinctive flows and flow-tops in basalts, foliation in gneisses, schistosity in schists and cleavage in slates, and faults through all the above. We can add igneous dykes, sills, weathered horizons, and dominant joint sets. Each of the above are rich potential or inevitable sources of velocity, modulus, strength and permeability anisotropy—and inhomogeneity. The historic and present-day stress anisotropy provides a wealth of effects concerning the preferentially oriented jointing, with its reduced roughness and greater continuity. High stress may also have induced oriented micro-cracks. All the above reinforce disbelief in the elastic-isotropic-continuum or intact-medium-based assumptions promoted by commercial software companies and used by so many for modelling rock masses. RQD and Q are frequently anisotropic as well, and Q is anisotropic not just because of RQD. The authors, therefore, question whether the a priori assumption of homogeneous-isotropic-elastic behaviour has any significant place in the scientific practice of realistic rock mechanics.

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Abbreviations

BB:

Barton-Bandis constitutive model for rock joints

E mass :

Static modulus of deformation

E :

Average physical aperture of a joint

e :

Hydraulic aperture of a joint

EDZ:

Excavation disturbed zone

J a :

Rating for joint alteration, discontinuity filling

JCS:

Joint wall compression strength

J n :

Rating for number of joint sets

J r :

Rating for joint surface roughness

JRC:

Joint roughness coefficient

J w :

Rating for water softening, inflow and pressure effects

K :

Permeability (units m/s)

K n :

Normal stiffness of a joint

K s :

Shear stiffness of a joint

K int :

Intermediate principal permeability

K max :

Maximum principal permeability

K min :

Minimum principal permeability

k o :

Ratio of σ h/σ v

NGI:

Norwegian Geotechnical Institute

Q :

Rock mass quality rating (range 10−3 to 103)

Q c :

Rock mass quality rating (Q, or Q o normalized by σ c/100)

Q o :

Q calculated with RQDo oriented in the loading or measurement direction

Q seis :

Seismic quality factor—the inverse of attenuation (used by geophysicists, normally with the P- and S-wave components ‘Q p’ and ‘Q s’)

RQD:

Rock quality designation (% of core-pieces ≥10 cm in length)

RQDo :

RQD oriented in the loading or measurement direction (in the QTBM model it is in the tunnelling direction)

σ c :

Uniaxial strength

σ v :

Vertical (principal) stress

σ h :

Horizontal (principal) stress

σ θ :

Tangential stress (surrounding an excavation, borehole)

UDEC:

Universal distinct element code, for modelling a two-dimensional, 1 m thick slice of the rock mass

V p :

P-wave seismic velocity (km/s)

V s :

S-wave seismic velocity (km/s)

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Authors and Affiliations

  1. NB&A, Fjordveien 65c, Høvik, 1363, Oslo, Norway

    Nick Barton

  2. BGTech, Rua Miguel de Almeida Prado 20, Butantá, SP, Brazil

    Eda Quadros

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  1. Nick Barton
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Barton, N., Quadros, E. Anisotropy is Everywhere, to See, to Measure, and to Model. Rock Mech Rock Eng 48, 1323–1339 (2015). https://doi.org/10.1007/s00603-014-0632-7

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  • DOI: https://doi.org/10.1007/s00603-014-0632-7

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