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Strength and dilatancy of jointed rocks with granular fill

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Abstract

It is well recognised that the strength of rock masses depends upon the strain history, extent of discontinuities, orientation of plane of weakness, condition of joints, fill material in closely packed joints and extent of confinement. Several solutions are available for strength of jointed rock mass with a set of discontinuities. There is a great multiplicity in the proposed relationships for the strength of jointed rocks. In the present study, the author conceives the effect of increasing stresses to induce permanent strains. This permanent strain appears as micro crack, macro crack and fracture. A fully developed network of permanent deformations forms joint. The joint may contain deposits of hydraulic and hydrothermal origin commonly known as gouge. The joint factor numerically captures varied engineering possibilities of joints in a rock mass. The joints grow as an effect of loading. The growth of the joints is progressive in nature. It increases the joint factor, which modifies the failure stresses. The dilatancy explains the progressive failure of granular media. Hence, a mutual relationship conjoins effectively the strength of jointed rock and a dilatancy-dependent parameter known as relative dilatancy. This study provides a simple and integral solution for strength of jointed rocks, interpreted in relation to the commonly used soil, and rock parameters, used for a realistic design of structure on rock masses. It has scope for prediction of an equivalent strength for tri-axial and plane strain conditions for unconfined and confined rock masses using a simple technique.

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Abbreviations

ϕcn, ϕpeak :

Angle of critical friction and peak internal friction, respectively (°)

ϕj :

Equivalent friction angle for the jointed rocks (°)

ψ:

Angle of dilatancy (°)

γp, ε p :

Plastic shear and plastic volumetric strain

A :

Empirical constant and has a value of 3 for axe-symmetrical and 5 for plane strain case

C′ and C:

Initial confining pressure-dependant empirical fitting parameters for jointed rocks

c g :

A modification factor for gouge

d a :

Reference depth of joint (=sample diameter in mm)

d j :

Depth of joint in mm

D p :

Dilatancy as a function of plastic shear and volumetric strain

dεv/dε1:

Ratio of changes in volumetric and axial strain

g d :

Correction factor depending upon the density of gouge in joint

I r :

relative dilatancy index

\( J_{{d_{\text{j}} }} \) :

Joint depth parameter

J f :

Joint factor

J fg :

Joint factor corrected for gouge

J n :

Number of joints in the direction of loading (joints per metre length of the sample)

J t :

Gouge thickness parameter

L na :

Reference length (=1 m)

M and B:

Empirical rock constants

n :

Joint orientation parameter depending upon inclination of the joint plane [β (°)] with respect to the direction of loading

p :

Mean confining pressure (kPa)

pa and σa:

Reference pressure (=1 kPa)

p i :

Initial mean confining pressure (kPa)

q :

Shear stress (kPa)

Q j and r j :

Empirical material fitting constants for gouge

r :

Joint strength parameter

RAC:

Ramamurthy–Arora criterion

R D :

Relative density of gouge

t :

Thickness of gouge in the joint (mm)

t a :

Reference thickness of gouge in the joint (=1 mm)

λ:

Empirical coefficient for joint factor

ξ :

Empirical coefficient for dilatancy

α :

Fitting constant

σ1, σ3 :

Major and minor principal stresses, respectively (kPa)

σci, σcj, σcjg :

Uniaxial compressive strength of intact, jointed and jointed rock with gouge respectively (kPa)

σcr :

Strength ratio

S cr :

Strength reduction factor during shear along the gouge

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Acknowledgment

The author is thankful to the Delhi College of Engineering (Faculty of Technology, University of Delhi) for providing ample space for his research studies. The author sincerely compliments the reviewers for their savant inputs, comments and questions, which significantly improved the quality of this paper.

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Technology (FoT), University of Delhi, Delhi College of Engineering Campus, Bawana Road, House No. 8, Type V, Delhi, 110042, India

    Ashutosh Trivedi

  2. Delhi College of Engineering, Faculty of Technology (FoT), University of Delhi, House No. 8, Type V, Delhi College of Engineering, Bawana Road, Delhi, 110042, India

    Ashutosh Trivedi

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Trivedi, A. Strength and dilatancy of jointed rocks with granular fill. Acta Geotech. 5, 15–31 (2010). https://doi.org/10.1007/s11440-009-0095-2

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