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Prediction of Mechanical Properties of Igneous Rocks Under Combined Compression and Shear Loading Through Statistical Analysis

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Abstract

Mechanical responses of rocks to combined compression and shear have attracted increasing attention but still lack comprehensive understanding. Sixty-eight laboratory tests are conducted on basalt and granite specimens sourced from different origins to generalize the effects of specimen inclination on the mechanical properties of igneous rocks. A novel regression model is established to predict peak strength and elastic moduli of igneous specimens at various inclination angles. The model mechanically considers both the individual effect and the combined effect of independent factors. It is found that specimen inclination has nearly the same effects on the failure patterns, strength, and elastic moduli of all the experimented igneous rocks regardless of origins. Igneous rocks tend to fail in shear under combined compression and shear loading. Both their strength and elastic moduli decline approximately linearly as specimen inclination increases. The reductions of both the strength and the elastic modulus as specimen inclination increases are closely associated with the UCS (θ = 0°) and the Young’s modulus (θ = 0°), respectively. The ratio of the peak strength to the elastic modulus is an inherent property of the igneous specimen, independent of the specimen strength and inclination.

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Abbreviations

a, b, c :

Regression coefficients (–)

E :

The elastic modulus of the igneous specimen under uniaxial compression (GPa)

E θ :

The elastic modulus of the igneous specimen at a given inclination angle (GPa)

N :

The number of samples (–)

R 2 :

The coefficient of determination (–)

w :

The water content (–)

x1, x2 :

The independent factors (–)

y :

The dependent factor (–)

y i :

The observed value (–)

y * i :

The predicted value (–)

σ c :

Peak strength of the igneous specimen under uniaxial compression (MPa)

σ θ :

Peak strength of the igneous specimen at a given inclination angle (MPa)

θ :

Specimen inclination angle (°)

Δσ :

The strength reduction due to specimen inclination (–)

C-CAST:

Combined compression and shear test

FG:

Fujian granite

MR:

Modulus ratio

MTS:

Material Testing System

NB:

New South Wales basalt

NSW:

New South Wales

RMSE:

Root-mean-square error

SG:

Shandong granite

SHPB:

Split Hopkinson Pressure Bar

UCS:

Uniaxial compressive strength

VAF:

Variance account for

var:

Variation

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Acknowledgements

The work of this paper is financially supported by the Jiangsu Province Science Foundation for Youths (Grant Number: BK20180658), State Key Laboratory of Water Resource Protection and Utilization in Coal Mining (Grant Number: SHJT-17-42.11), State Key Laboratory of Coal Resources and Safe Mining (Grant Number: SKLCRSM18X009), and China Postdoctoral Science Foundation (Grant Number: 2018M632422). The authors would like to acknowledge Professor Fidelis Suorineni for his contribution to developing the C-CAST system and the postgraduate students at China University of Mining and Technology for their involvement in the laboratory experiments.

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Authors and Affiliations

  1. State Key Laboratory of Coal Resources and Safe Mining, School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

    Qingyuan He & Jinhai Xu

  2. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Yingchun Li

  3. School of Minerals and Energy Resources Engineering, UNSW Sydney, Sydney, 2052, Australia

    Qingyuan He & Chengguo Zhang

  4. State Key Laboratory of Water Resource Protection and Utilization in Coal Mining, Beijing, 100011, China

    Qingyuan He

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He, Q., Li, Y., Xu, J. et al. Prediction of Mechanical Properties of Igneous Rocks Under Combined Compression and Shear Loading Through Statistical Analysis. Rock Mech Rock Eng 53, 841–859 (2020). https://doi.org/10.1007/s00603-019-01948-9

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