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Measurement and 2D Axisymmetric Modeling of Mining Blast-Induced Ground Vibrations

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Abstract

Blast-induced ground vibrations are considered as an undesirable phenomenon resulting from productivity explosions in the extractive industries. Moreover, they are considered as a high potential cause for the damage of the surrounding structures. In this paper, the ground vibration data were recorded using a seismograph device at different distances from the detonation point in the quarry site of “Sococim Cement Factory,” which is located on Senegal. Thereafter, 2D axisymmetric numerical model has been established to simulate the propagation of the mechanical shock wave in the considered medium. The numerical modeling was developed under AUTODYN software, which is an explicit FEM code. First of all, the numerical model has been validated against the experimental measurements, by comparing the numerical and experimental longitudinal (\(V_{{\rm l}}\)) and vertical (\(V_{\mathrm{v}}\)) velocity signal at different gauges, for different equivalent explosive charges per delay (\(m_{\mathrm{eq(TNT)}}\)). A calibration was carried out only on the elastic properties of the rock to achieve this purpose. The adjusted values of K and G allowed to reproduce the numerical PPVs, in order to be in a good agreement with the measured PPVs. The energy dissipation due to the RHT model and the phenomenon of vibration’s damping as a function of time at the gauges locations is well reproduced by the numerical model. It is noted that the plasticity and damage near the borehole have no effect on the propagation celerity of the shock wave, which remains the same in the elastic medium. Furthermore, the damaged zone nearby the detonation point has been assessed and described by identifying the transition of limestone properties from the elastic–plastic to plastic-damage state. The characterization of the damaged zone, near the borehole for different explosive charges per delay, helps to calculate the face burden side and to enhance the blasting design.

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Abbreviations

C :

Porous sound speed (m/s)

\(C_{\mathrm{L}}\), \(C_{\mathrm{T}}\) :

Longitudinal and transversal celerities (m/s)

\(C_{\mathrm{s}}\) :

Bulk sound speed (m/s)

e :

Internal energy (J)

\(ef_{\mathrm{min}}\) :

Minimum strain to failure

E :

Young modulus (kPa)

\(\mathbf {f}\) :

Vector of external force (N)

\(f_{\mathrm{c,el}}\) :

Elastic compressive strength (MPa)

\(f_{\mathrm{t,el}}\) :

Elastic tensile strength (MPa)

\(f_{\mathrm{c}}\) :

Uniaxial compressive strength (MPa)

\(f_{\mathrm{s}}\) :

Shear strength (MPa)

\(f_{\mathrm{t}}\) :

Uniaxial tensile strength (MPa)

G :

Elastic shear modulus (kPa)

I :

Identity tensor

K :

Elastic bulk modulus (kPa)

L :

Length (m)

\(L_{\mathrm{TNT}}\) :

Length of TNT (m)

\(m_{\mathrm{eq(TNT)}}\) :

Equivalent mass of TNT (kg)

N :

Compaction exponent

p :

Pressure (Pa)

\(p_{\mathrm{comp}}\) :

Solid compaction pressure (Pa)

\(p_{\mathrm{el}}\) :

Initial compaction pressure (Pa)

t :

Time (s)

\(U_{x}\), \(U_{y}\) :

Mechanical displacements (m)

\(\mathbf {v}\) :

Velocity vector (m/s)

\(V_{{\rm l}}\), \(V_{\mathrm{v}}\) :

Longitudinal and vertical velocities (m/s)

\(Y_{\mathrm{elastic}}\) :

Yield surface

\(Y_{\mathrm{fail}}\) :

Failure surface

\(Y_{\mathrm{fric}}\) :

Residual friction resistance surface

\(\gamma\) :

Ratio of specific heats

\(\mu\) :

Dynamic viscosity (Pa.s)

\(\nu\) :

Poisson coefficient

\(\rho\) :

Density (kg/cm\(^{3}\))

\(\rho _{0}\) :

Initial density (kg/cm\(^{3}\))

\(\rho _{\mathrm{TMD}}\) :

Theoretical maximal density (kg/cm\(^{3}\))

\(\sigma\) :

Total Cauchy stress tensor (kPa)

\(\alpha\) :

Porosity parameter

\(\alpha _{\mathrm{int}}\) :

Initial porosity

\(\theta\) :

Lode angle

\(\varGamma\) :

Grüneisen parameter

\(\frac{\rho _{\mathrm{matrix}}}{\rho _{\mathrm{porous}}}\) :

Additional state variable

\(\epsilon\) :

Strain rate

BIGVs:

Blast-induced ground vibrations

PPV:

Peak particle velocity

FEM:

Finite element method

RHT:

Riedel, Hiermaier and Thoma

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Acknowledgements

The authors wish to express their gratitude to “Sococim company” for good hospitality and cooperation.

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Authors and Affiliations

  1. Laboratoire d’Etude des Matériaux Avancés et Applications (LEM2A), Ecole Supérieure de Technologie de Meknès, Université Moulay Ismail (UMI), Km 5, route d’Agouray, N6, 50040, Meknes, Morocco

    Imad Kadiri, Younès Tahir, Omar Iken, Maryam Dlimi, Rachid Agounoun & Khalid Sbai

  2. École Supérieure de Technologie de Fès, Université Sidi Mohamed Ben Abdellah (USMBA), Route d’Imouzzer, BP 2427, Fes, Morocco

    Saïf ed-Dîn Fertahi

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  1. Imad Kadiri
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Kadiri, I., Tahir, Y., Fertahi, S.eD. et al. Measurement and 2D Axisymmetric Modeling of Mining Blast-Induced Ground Vibrations. Indian Geotech J 50, 96–116 (2020). https://doi.org/10.1007/s40098-019-00388-0

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