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Determining the Viscosity Coefficient for Viscoelastic Wave Propagation in Rock Bars

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Abstract

Rocks with microdefects exhibit viscoelastic behavior during stress wave propagation. The viscosity coefficient of the wave can be used to characterize the attenuation as the wave propagates in rock. In this study, a long artificial bar with a readily adjustable viscosity coefficient was fabricated to investigate stress wave attenuation. The viscoelastic behavior of the artificial bar under dynamic loading was investigated, and the initial viscoelastic coefficient was obtained based on the amplitude attenuation of the incident harmonic wave. A one-dimensional wave propagation program was compiled to reproduce the time history of the stress wave measured during the experiments, and the program was well fitted to the Kelvin–Voigt model. The attenuation and dispersion of the stress wave in long artificial viscoelastic bars were quantified to accurately determine the viscoelastic coefficient. Finally, the method used to determine the viscoelastic coefficient of a long artificial bar based on the experiments and numerical simulations was extended to determine the viscoelastic coefficient of a short rock bar. This study provides a new method of determining the viscosity coefficient of rock.

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Abbreviations

E :

Elastic modulus of the spring

E 1 :

Elastic modulus of segment I

E 2 :

Elastic modulus of segment II

\({\mathcal{F}}\) :

Application of the Fourier transform

Im:

Imaginary parts of a complex expression

k :

Wave number of a harmonic wave

k 1 :

Wave number of a stress wave

l :

Wave travel distance between two points, P1 and P2

T I–II :

Transmission coefficient as the strain wave propagates from segment I to segment II

T II–I :

Transmission coefficient as the strain wave propagates from segment II to segment I

Re:

Real parts of a complex expression

t :

Time

u 0 :

Amplitude of incident wave displacement

u :

Particle displacement

v :

Particle velocity

x :

Cartesian coordinate along the wave propagation path

α x :

Wave attenuation of the harmonic wave

β :

Attenuation coefficient as the strain wave propagates between point P1 and P2

ε :

Strain of the Kelvin–Voigt model

ε 1 :

Strain wave measured at point P1

ε 2 :

Strain wave measured at point P2

ε L1 :

Amplitude of the strain wave measured at point P1 during the impact test at L-end

ε L2 :

Amplitude of the strain wave measured at point P2 during the impact test at L-end

ε R1 :

Amplitude of the strain wave measured at point P1 during the impact test at R-end

ε R2 :

Amplitude of the strain wave measured at point P2 during the impact test at R-end

ε s :

Simulated strain

ε t :

Experimental strain

η :

Viscoelastic coefficient of the dashpot

ξ :

Relative error

ρ :

Density of the medium material

σ :

Stress of the Kelvin–Voigt model

ω :

Harmonic angular frequency after Fourier transform

ω 1 :

Angular frequency

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Acknowledgements

This work is funded by the National Key Research and Development Program of China (Grant No. 2016YFC0801607), National Science Foundation of China (Grant Nos. 51525402, 51374049, 51574060 and 51534003), and the Fundamental Research Funds for the Central Universities of China (Grant No. N160103005). These sources of support are gratefully acknowledged.

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Authors and Affiliations

  1. Center of Rock Instability and Seismicity Research, School of Resources and Civil Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Leilei Niu, Wancheng Zhu, Shaohua Li & Kai Guan

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  1. Leilei Niu
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  2. Wancheng Zhu
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  3. Shaohua Li
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  4. Kai Guan
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Correspondence to Wancheng Zhu.

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Niu, L., Zhu, W., Li, S. et al. Determining the Viscosity Coefficient for Viscoelastic Wave Propagation in Rock Bars. Rock Mech Rock Eng 51, 1347–1359 (2018). https://doi.org/10.1007/s00603-018-1407-3

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  • DOI: https://doi.org/10.1007/s00603-018-1407-3

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