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New Data Processing Protocols to Isolate Fracture Deformations to Measure Normal and Shear Joint Stiffness

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Abstract

The importance of discontinuity geomechanical properties is increasing as the use of numerical models with explicit or discrete rock mass structure becomes the state of practice. Joint normal stiffness and joint shear stiffness are two parameters that characterize the deformation behaviour of discontinuities. This paper presents practical guidelines to correct direct shear testing data for machine influences with regard to normal and shear joint stiffness using a method originally employed by Goodman (Methods of geological engineering in discontinuous rocks. West Publishing Company, St. Paul, 1976) to correct the normal deformation of a direct shear test. This method of correcting the normal deformation has been extended to the shear deformation to account for machine influence during the shear loading stage. The normal stiffness of 23 rough fracture specimens and 10 smooth ground specimens were measured on discontinuities in granitic specimens from NQ and NQ3 sized core using a power law (Swan in Rock Mech Rock Eng 16:19–38, 1983), a hyperbolic law (Bandis et al. in Int J Rock Mech Min Sci Geomech Abstr 20:249–268, 1983), and two semi-logarithmic laws (Bandis et al. 1983; Evans et al. in Geotherm Resour Counc Davis Calif USA 16:449–456, 1992). Measurements from direct shear tests completed at varying maximum applied normal stress show a positive correlation between normal stiffness and normal stress. In addition, the shear stiffness was measured on 19 rough fracture specimens and 4 smooth ground specimens. The compilation of results from these measurements has a range of measured shear stiffness due to varying joint topology and roughness showed a positive correlation between shear stiffness and maximum applied normal stress. As the majority of the joints exhibited non-linear behaviour under normal loading conditions and linear behaviour under shear loading conditions, it is recommended that a stress-dependent normal stiffness model and a linear shear stiffness model be used for numerical modelling purposes.

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Abbreviations

A :

Specimen area

A SC :

Stiffness characteristic

CNL*:

Constant normal stress

CNS:

Constant normal stiffness

E :

Young’s modulus

k n :

Normal stiffness

k ni :

Initial normal stiffness

k nComposite :

Composite normal stiffness

k nFrac :

Fracture normal stiffness

k nSystem :

System normal stiffness

KNM:

Machine normal stiffness

k s :

Shear stiffness

L :

Rock mass joint spacing

p :

Bandis et al. (1983) semi-log parameter

q :

Bandis et al. (1983) semi-log parameter

UCS:

Unconfined compressive strength

V m :

Maximum joint closure

α :

Swan (1983) power law parameter

β :

Swan (1983) power law parameter

ν :

Poisson’s ratio

\(\sigma_{{\text{n}}}\) :

Normal stress

\(\sigma_{{\text{n}}}^{{{\text{Ref}}}}\) :

Reference normal stress

\(\sigma_{{{\text{nT}}}}\) :

Transition normal stress

τ :

Shear stress

\(\tau_{{\text{T}}}\) :

Transition shear stress

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Acknowledgements

The Natural Sciences and Engineering Research Council of Canada through CRD grants held by Dr. Mark S. Diederichs, P.Eng., FEIC and a Post-graduate Scholarship (NSERC-PGS D3 535289-2019) held by Timothy R. Packulak, P.Eng., P.Geo. and the Nuclear Waste Management Organization of Canada have financially supported this research. Thank you to Manitoba Hydro for supplying the rock core samples.

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  1. Department of Geological Sciences and Geological Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Timothy R. M. Packulak, Jennifer J. Day, Mariem T. Ahmed Labeid & Mark S. Diederichs

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  1. Timothy R. M. Packulak
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Correspondence to Timothy R. M. Packulak.

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Packulak, T.R.M., Day, J.J., Ahmed Labeid, M.T. et al. New Data Processing Protocols to Isolate Fracture Deformations to Measure Normal and Shear Joint Stiffness. Rock Mech Rock Eng 55, 2631–2650 (2022). https://doi.org/10.1007/s00603-021-02632-7

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