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A nonlinear criterion for triaxial strength of inherently anisotropic rocks

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Abstract

Rocks encountered at many underground construction sites are laminated and exhibit direction-dependent strength behavior. It is also a well-established fact that the strength varies in a nonlinear manner with confining pressure. There is a need of strength criterion which could capture the nonlinearity as well as the anisotropy in the triaxial strength behavior of the rocks. It is essential that the criterion should be simple and must involve minimum testing to the extent possible. Further, the parameters of the criterion should have wide acceptability among the geotechnical fraternity. In the present study, a nonlinear strength criterion for transversely isotropic rocks is presented. Critical state concept Barton (Int J Rock Mech Mining Sci Geomech Abstr 13(9):255–279, 1976) has been used to define the curvature of the criterion. With a correctly defined curvature and starting from a reference point (UCS), it is possible to accurately assess the triaxial strength for given confining pressure. An experimental study conducted on triaxial strength behavior of three types of anisotropic rocks namely phyllite, slate and orthoquartzite has been discussed. A data base comprising more than 1140 triaxial tests conducted worldwide on anisotropic rocks has been compiled. Statistical evaluation of goodness of fit of the proposed criterion to the data base has been carried out. Further, the predictive capabilities of the proposed criterion have been evaluated by determining the error in estimation of triaxial strength if only few triaxial test data are available for determining the criterion parameters. The data base has also been back analyzed to assess the critical confining pressure for anisotropic rocks. Statistically, the critical confining pressure for anisotropic rocks can be taken nearly equal to 1.25 times the maximum UCS (obtained by applying load either parallel or perpendicular to planes of anisotropy). It is concluded that reasonable estimates of the triaxial strength of anisotropic rock can be made through the proposed criterion using minimum amount of triaxial test data available.

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Abbreviations

β :

Angle between major principal direction and planes of anisotropy

µ β0 :

Coefficient of internal friction (tan ϕ β0) of the rock with planes of anisotropy oriented at angle β at low confining pressure (σ 3 → 0)

σ 1, σ 3 :

Major and minor principal stresses at failure

σ 1av :

Average of the experimental σ1 values for a triaxial data set

σ 1exp σ 1cal :

Experimental and predicted values of the major principal stress at failure

Ψ 2 :

Coefficient of accordance (COA)

σ cβ :

UCS of anisotropic rock with planes of anisotropy oriented at angle of β from major principal stress direction

σ crt :

Critical confining pressure for the rock

A, B, C:

Constants

A′:

An empirical constant which defines the shape of the strength criterion

AAREP:

Average absolute relative error percentage

c β0, ϕ β0 :

Mohr–Coulomb shear strength parameters obtained by conducting triaxial strength tests on rock specimens at low confining pressure (σ3 → 0)

c, ϕ :

Mohr–Coulomb shear strength parameters

l :

Length of rock specimen

m :

Hoek–Brown criterion parameter

N :

Total number of triaxial data points in the data base

npt:

Number of triaxial data points in addition to the UCS for given orientation

pe:

Percent error for each data point

R 2 :

Regression coefficient

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Acknowledgments

Financial support for some part of this study was received from Department of Science and Technology, New Delhi under NRDMS grant. The authors thank Dr Bhoop Singh, Director DST, New Delhi for his cooperation and support during the study.

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Authors and Affiliations

  1. IIT Roorkee, Roorkee, Uttarakhand, India

    Mahendra Singh, N. K. Samadhiya, Vivek Kumar & Bhawani Singh

  2. G.B. Pant University of Agriculture and Technology, Pantnagar, India

    Ajit Kumar

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  1. Mahendra Singh
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  2. N. K. Samadhiya
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  3. Ajit Kumar
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  4. Vivek Kumar
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  5. Bhawani Singh
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Correspondence to Mahendra Singh.

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Singh, M., Samadhiya, N.K., Kumar, A. et al. A nonlinear criterion for triaxial strength of inherently anisotropic rocks. Rock Mech Rock Eng 48, 1387–1405 (2015). https://doi.org/10.1007/s00603-015-0708-z

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