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A New Improved Failure Criterion for Salt Rock Based on Energy Method

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Abstract

A non-linear triple shear energy yield criterion for salt rock is presented in this paper. It is the development of the triple shear energy yield criterion, of which the Mohr–Coulomb criterion can be seen as a special case. The main factors affecting the primary strength of salt rock, such as the mean stress and the Lode angle, are considered in the non-linear triple shear energy yield criterion. The non-linear new criterion provides the non-linear change trend of salt strength both in the I 1–J 2 stress space and in the deviatoric plane. Comparative study between the non-linear criterion predictions and experimental results of salt rock shows that the non-linear triple shear energy yield criterion fits quite well with both conventional triaxial test data and the true triaxial test data. For Maha Sarakham salt, the predictive capability of the non-linear triple shear energy yield criterion is clearly better than that of some other criteria used by Sriapai, such as modified Lade criterion, 3-D Hoek, and Brown criterion, Drucker–Prager criterion et al. The availability of the non-linear triple shear energy yield criterion can also be confirmed by comparative analysis between theoretical values and experimental values for non-salt rocks. So the non-linear triple shear energy yield criterion is a general failure criterion for rocks fractured by shear stress.

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Abbreviations

c :

Cohesion in Mohr–Coulomb criterion

c 1 :

Cohesion in σ 1–σ 3 plane

D 1, D 2, D 3, D 4, D 5 :

Material constants

G :

Shearing modulus of elasticity

I 1 :

First invariant of the stress

J 2 :

Second invariant of deviatoric stress

k :

Limit of the maximal value of shear strain energy on failure plane

K :

Sum of the limit of the maximal value of shear strain energy for an element

N :

Power parameter

w 1, w 2, w 3 :

Maximal value of shear strain energy on the τ 1 plane, on the τ 2 plane, on the τ 3 plane, respectively

α 1, α 2, α 3 :

Angle of the τ 1 plane, the τ 2 plane, the τ 3 plane, respectively

β :

Dimensional constant with the same units as I 1

σ 1, σ 2, σ 3 :

Major, intermediate and minor principal stress, respectively

σ n1, σ n2, σ n3 :

Normal stress acting on the τ 1 plane, on the τ 2 plane, on the τ 3 plane, respectively

σ m :

Mean stress

τ 1 :

Maximum principal shear stress

τ 2 :

Intermediate or minimum principal shear stress

τ 3 :

Intermediate or minimum principal shear stress

θ :

Lode angle

φ 1, φ 2, φ 3 :

Maximal friction angle in σ 1–σ 3 plane, in σ 1–σ 2 plane, in σ 2–σ 3 plane, respectively

φ :

Friction angle in Mohr–Coulomb criterion

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Acknowledgments

This study was financially supported by the National Nature Science Foundation of China (51225404), Shanxi Nature Science Foundation (2014011044-1), and San-Jin scholar support project, which are gratefully acknowledged.

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Authors and Affiliations

  1. College of Mining Engineering, Taiyuan University of Technology, Taiyuan, Shanxi, China

    T. S. Hao & W. G. Liang

  2. Key Lab of In-situ Property-Improving Mining of Ministry of Education, Taiyuan, Shanxi, China

    T. S. Hao & W. G. Liang

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  1. T. S. Hao
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  2. W. G. Liang
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Correspondence to W. G. Liang.

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Hao, T.S., Liang, W.G. A New Improved Failure Criterion for Salt Rock Based on Energy Method. Rock Mech Rock Eng 49, 1721–1731 (2016). https://doi.org/10.1007/s00603-015-0851-6

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