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A New Empirical Approach to Assess Wave Velocities and Dynamic Elastic Properties of Several Models of Jointed Rock Before and After Grouting

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Abstract

Wave velocity as a nondestructive test is widely used in various fields such as mining, civil, rock mechanics and rock engineering, and dynamic elastic properties of rocks are also determined by wave velocity. Rock mass contains discontinuities with different orientation angles, numbers of sets and frequencies and the impacts of such discontinuity properties on the wave velocity have not yet been systematically investigated. In this study, 20 groups of jointed cylindrical specimens with a wide range of discontinuity orientation angles (0°, 30°, 45°, 60° and 90°), numbers of sets and frequencies were prepared, and their P-wave velocities were measured. P-wave velocity (VP) significantly increased with increasing orientation angle (θ) and decreasing the discontinuity frequency (F). Several relations were applied to analyze the results. Finally, a new empirical relation was developed to predict VP as a function of θ angle using two parameters of P-wave velocity perpendicular to the discontinuity plane (VP0°) and P-wave velocity along the discontinuity direction (VP90°) or anisotropy degree (ε = (VP90° − VP0°)/VP0°) with a good correlation of determination (R2 = 0.933), low RMSE (RMSE = 200.0 m/s) and low CV (CV = 6.7%). A good correlation between VP and F was also achieved for the test results. The intact rock elements in the complex nature of a rock mass are surrounded by discontinuities like a three dimensional puzzle. Treatment of such a rock mass system using cement grouting is an attractive method to improve its quality for various purposes. All 20 groups of jointed cylindrical specimens were grouted by cement. Wave velocities of the grouted specimens were measured after 2 months. VP significantly increased after grouting for all models of jointed specimens, as wave velocity of jointed specimens improved and approached to the wave velocity of the intact rock for most cases. The discontinuity orientation of the specimens had no significant effect on the wave velocities after grouting. But the results showed that VP and VS increased little with increasing orientation angle for jointed specimens consisting only of one set of discontinuity. After grouting the jointed specimens, orientation angle and frequency of discontinuities had also similar effects on the dynamic Young's modulus (E), Poisson's ratio (ν), shear modulus (μ), bulk modulus (K) and Lamé’s constant (λ). These results also showed that the dynamic elastic properties of jointed specimens significantly improved using cement grouting.

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Abbreviations

V P :

P-wave velocity in m/s

V S :

S-wave velocity in m/s

E :

Dynamic elastic modulus in GPa

μ :

Dynamic shear modulus in GPa

ν :

Dynamic Poisson's ratio

K :

Dynamic bulk modulus in GPa

λ :

Dynamic Lamé's constant in GPa

θ :

Angle between the axis of symmetry (perpendicular to weakness planes) with the wave propagation direction

V P0 ° :

P-wave velocity perpendicular to the discontinuity plane in m/s e

F :

Frequency of discontinuities in (1/cm)

V Pi :

P-wave velocity of intact rock

\(V_{{{\text{P}}90^\circ }}^{{}}\) :

P-wave velocity along the discontinuity direction in m/s

\(V_{{{\text{S}}0^\circ }}^{{}}\) :

S-wave velocity perpendicular to the discontinuity plane in m/s e

\(V_{{{\text{S}}90^\circ }}^{{}}\) :

S-wave velocity along the discontinuity direction in m/s

ε :

Anisotropy parameter that is the percentage change of \(V_{{{\text{P}}90^\circ }}^{{}}\) with respect to \(V_{{{\text{P}}0^\circ }}^{{}}\)

γ :

Anisotropy parameter that is the percentage change of \(V_{{{\text{S}}90^\circ }}^{{}}\) with respect to \(V_{{{\text{S}}0^\circ }}^{{}}\)

δ :

Anellipticity of the P-wave curve

ρ :

Bulk density gr/cm3

K :

A constant coefficient

a :

A constant coefficient

b :

A constant coefficient

VTI:

Transverse isotropic symmetry

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Acknowledgements

The authors of this paper would like to thank Mr M. Moheb Houri technical officer of Rock Mechanics laboratory of Amirkabir University of Technology for his continual assistance in providing facilities for preparation and testing jointed rock specimens.

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Authors and Affiliations

  1. Rock Mechanics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Hussamuddin Moomivand & Parviz Maarefvand

  2. Rock Mechanics, Urmia University, Urmia, Iran

    Hassan Moomivand

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  1. Hussamuddin Moomivand
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Correspondence to Hassan Moomivand.

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Moomivand, H., Maarefvand, P. & Moomivand, H. A New Empirical Approach to Assess Wave Velocities and Dynamic Elastic Properties of Several Models of Jointed Rock Before and After Grouting. Rock Mech Rock Eng 54, 6439–6455 (2021). https://doi.org/10.1007/s00603-021-02625-6

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