A Numerical Study on the Screening of Blast-Induced Waves for Reducing Ground Vibration

Abstract

Blasting is often a necessary part of mining and construction operations, and is the most cost-effective way to break rock, but blasting generates both noise and ground vibration. In urban areas, noise and vibration have an environmental impact, and cause structural damage to nearby structures. Various wave-screening methods have been used for many years to reduce blast-induced ground vibration. However, these methods have not been quantitatively studied for their reduction effect of ground vibration. The present study focused on the quantitative assessment of the effectiveness in vibration reduction of line-drilling as a screening method using a numerical method. Two numerical methods were used to analyze the reduction effect toward ground vibration, namely, the “distinct element method” and the “non-linear hydrocode.” The distinct element method, by particle flow code in two dimensions (PFC 2D), was used for two-dimensional parametric analyses, and some cases of two-dimensional analyses were analyzed three-dimensionally using AUTODYN 3D, the program of the non-linear hydrocode. To analyze the screening effectiveness of line-drilling, parametric analyses were carried out under various conditions, with the spacing, diameter of drill holes, distance between the blasthole and line-drilling, and the number of rows of drill holes, including their arrangement, used as parameters. The screening effectiveness was assessed via a comparison of the vibration amplitude between cases both with and without screening. Also, the frequency distribution of ground motion of the two cases was investigated through fast Fourier transform (FFT), with the differences also examined. From our study, it was concluded that line-drilling as a screening method of blast-induced waves was considerably effective under certain design conditions. The design details for field application have also been proposed.

Appendix: RHT Model Equations

The equation of state (EOS) of the fully compacted material:

$$ P = A_{1} \mu + A_{2} \mu ^{2} + A_{3} \mu ^{3} + {\left( {B_{0} + B_{1} \mu } \right)}\rho _{0} e \quad {\text{with}}\;\mu = \frac{\rho } {{\rho _{0} }} - 1 \geq 0 $$

(10)

$$ P = T_{1} \mu + T_{2} \mu ^{2} + B_{0} \rho _{0} e \quad {\text{with}}\;\mu = \frac{\rho } {{\rho _{0} }} - 1 < 0 $$

(11)

where P is the pressure, A ₁, A ₂, A ₃, B ₀, B ₁, T ₁, and T ₂ constants, ρ the density, ρ ₀ the initial density, and e is the specific internal energy.

The EOS of the porous material:

$$ P = f{\left( {\rho \alpha ,\;e} \right)}\quad {\text{with}}\;\alpha = 1 + {\left( {\alpha _{{{\text{init}}}} - 1} \right)}{\left[ {\frac{{P_{{{\text{lock}}}} - P}} {{P_{{{\text{lock}}}} - P_{{{\text{crush}}}} }}} \right]}^{n} $$

(12)

where α is the porosity, α _init the initial porosity, P _lock the initial compaction pressure, P _crush the solid compaction pressure, and n is the compaction exponent.

The failure surface:

$$ Y_{{{\text{fail}}}} = Y_{{{\text{TXC}}}} {\left( P \right)}F_{{{\text{Rate}}}} {\left( {\ifmmode\expandafter\dot\else\expandafter\.\fi{\varepsilon }} \right)}R_{3} {\left( \theta \right)} $$

(13)

$$ Y_{{{\text{TXC}}}} {\left( P \right)} = f_{{\text{c}}} A{\left[ {P^{ * } - {\left( {P^{ * }_{{{\text{spall}}}} F_{{{\text{Rate}}}} } \right)}} \right]}^{N} $$

(14)

$$ F_{\text{Rate}} (\dot{\varepsilon }) = \left( {\frac{{\dot{\varepsilon }}}{{\dot{\varepsilon }_{0} }}} \right)^{\alpha} {\text{with }}P > \frac{{f_{c} }}{3}{\text{ and }}\acute{\varepsilon}_{0} = 30 \times 10^{ - 6} {\text{s}}^{ - 1} $$

(15)

$$ F_{\text{Rate}} (\dot{\varepsilon }) = \left( {\frac{{\dot{\varepsilon }}}{{\dot{\varepsilon }_{0} }}} \right)^{\delta } {\text{ with }}P < \frac{{f_{c} }}{3}\,{\text{and }}\,\acute{\varepsilon}_{0} = 3 \times 10^{ - 6} {\text{s}}^{ - 1} $$

(16)

$$ R_{3} {\left( \theta \right)} = \frac{{2{\left( {1 - Q^{2} } \right)}\cos \theta + {\left( {2Q - 1} \right)}{\left[ {4{\left( {1 - Q^{2} } \right)}\cos ^{2} \theta + 5Q^{2} - 4Q} \right]}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }} {{4{\left( {1 - Q^{2} } \right)}\cos ^{2} \theta + {\left( {1 - 2Q^{2} } \right)}^{2} }} $$

(17)

where Y _fail is the failure surface, Y _TXC(P) the compression meridian, έ the strain rate, F _Rate(έ) the strain rate function, α and δ the material constants, R ₃(θ) a function of an angle rotating around the hydrostatic axis and meridian ratio Q, f _c the compressive strength, A the failure surface constant, N the failure surface exponent, P* the pressure normalized by f _c, and P*_spall = P* (f _t/f _c).

The elastic limit surface:

$$ Y_{{{\text{elastic}}}} = Y_{{{\text{fail}}}} F_{{{\text{elastic}}}} F_{{{\text{CAP}}}} {\left( P \right)} $$

(18)

where F _elastic is the ratio of the elastic strength to failure surface strength and F _CAP(P) is a function that limits the elastic deviatoric stresses under hydrostatic compression.

The residual failure surface:

$$ Y_{{{\text{residual}}}} = B{\left( {P^{ * } } \right)}^{M} $$

(19)

where B is the residual failure surface constant and M is the residual failure surface exponent.

The damage model:

$$ D = {\sum {\frac{{\Updelta \varepsilon _{{{\text{pl}}}} }} {{\varepsilon ^{{{\text{failure}}}}_{{\text{p}}} }}} } $$

(20)

$$ \varepsilon ^{{{\text{failure}}}}_{{\text{p}}} = D_{1} {\left( {P^{ * } - P^{ * }_{{{\text{spall}}}} } \right)}^{{D_{2} }} $$

(21)

$$ G_{{{\text{fracture}}}} = {\left( {1 - D} \right)}G_{{{\text{initial}}}} + DG_{{{\text{residual}}}} $$

(22)

where D, D ₁, and D ₂ are damage constants, Δε _pl the accumulated plastic strain, ε ^failure _p the failure strain, and G _initial, G _residual, and G _fracture are the shear moduli of the initial, residual, and post-damage, respectively.