Abstract
Peak particle velocity generated by cylindrically-charged blastholes fired at different delay detonators in surface blasting can be predicted with reasonable degree of certainty by an equivalent spherical charge conversion (ESCC) approach wherein the cylindrical charges are replaced by equivalent spherical charges. The validity of this conversion model has been tested through different predictive equations using experimental data of two opencast mines viz. Bhelatand Amalgamated Colliery and Joribahal Iron Ore Mine. In deriving these equations both maximum charge per delay and total charge fired in the round were considered separately. The results show that ESCC approach can be used as a reliable vibration prediction tool in surface blasting.
Keywords
Introduction
The application of cratering theory to blasting and mining commonly known as Livingston cratering theory (1956) is usefully translated into blast design parameters and used to understand the fundamentals of rock failure in geometries involving cylindrical rather than spherical charges. It has also opened up a new avenue for better understanding of the phenomenon of rock blasting and the characterization of the explosives (Jimeno et al. 1995). Likewise, in surface blasting cylindrical charges in different blastholes fired at different delay intervals can be converted into equivalent spherical charges scattered within the blasting zone at different depths laying at the centre of the cylindrical charges. Such equivalent spherical charges fired at different delay intervals can be modelled empirically to predict ground vibration induced by blasting.
It is a known fact that the charge concentration (i.e. full column, line, point, spherical and decked charges etc.) affects the vibration intensity. Vibrations are generally quantified by means of particle velocities at particular ground locations (Hosseini & Baghikhani 2013). For shallow cover above or in front of charges, the energy gets less obstruction in dissipating to the atmosphere and subsequently a significant amount of flyrock is created and gas released with less vibration being generated. When decoupling is done, less energy is transferred to the surrounding rock mass and as a result, vibration intensity is affected. However, if rock is not properly fragmented, it generates more vibration as majority of the energy is transformed into waste energy (Blasters’ Handbook 2011).
Prominent changes in rock geologic parameters and topography influence the movement of seismic waves in different directions from a source. It has been observed by different researchers that the spatial distribution of the explosive charge affects the frequency and intensity of ground vibration. Geometrical spreading of explosive energy reduces impacts of vibration during propagation of seismic waves.
The present equivalent spherical charge conversion (ESCC) approach for prediction of ground vibration due to blasting is based on the normalizing factor defined as radial distance divided by charge radius. Another approach could be the weight of the spherical charge instead of the radius of the normalized charge.
Mathematical derivations
The conversion of equivalent spherical charge is based on the premise that all explosives loaded in different blastholes are assumed to be spherically distributed, which upon detonation generate strain waves that propagate through the surrounding medium causing geometrical spreading and inelastic attenuation.
The reduction in amplitude (A) of ground vibration due to geometrical spreading is expressed in the following form of a powered-law (Hustrulid 1999, Chapter 15, p. 537).
Where, R = distance travelled, n = 0 (planar), n = ½ (cylindrical), n = 1 (spherical) and A0 is the initial amplitude of the vibratory motion.
The decrease in amplitude of vibration with distance is due to the changing area (geometry) of the wave front and is termed as ‘geometrical spreading’. Because of this, the intensity of all wave motions attenuates with distance and ultimately dies down at the boundary of the undisturbed zone or the seismic zone. Detailed explanations of such factors are available in Pal Roy (1993).
Wave energy
Hustrulid (1999) explained that not only the cube root of charge weight but the cube root charge volume or the radius of the sphere of equivalent explosive charge can be used to determine the impacts of blasting. In such case, scaling distance to the charge radius is expressed as a dimensionless parameter. This method of scaling means that distances are measured in terms of the spherical charge radius and therefore a scaled distance of 1 implies the boundary of the charge.
The strain waves generated by the spherical charge carry wave energy through radial and tangential wave components. Fogelson et al. (1959) showed that except at distances very close to the source, the contribution of the tangential component is small compared to the radial component.
ESCC approach
The ESCC technique is based on the fact that all explosives loaded in different blastholes are assumed to be spherically distributed, which upon detonation generate strain waves which emanate spherically and move through the propagating medium (Figure 1). Such strain waves carry the energy through radial and tangential wave components which ultimately reach the surface and damage the surface structures. The charges firing within 8 ms time interval are considered to be accumulated together forming an equivalent spherical charge. The normalizing factor is determined by dividing the radial distance by the equivalent charge radius. Figure 2 shows various representations like full column, line, point, spherical and decked charges generally used in blasting operations. The proposed ESCC approach considers column and decked charges for conversion into equivalent spherical charges (Figure 2(e) and (f)).
Three dimensional overview of ESCC model.
Model representations of in-hole explosive charge.
To understand the mechanism of ESCC and its usefulness, the data sets of two recently conducted blasting studies at Bhelatand Amalgamated Colliery (BAC) of Tata Steel Limited in Jharkhand state and Joribahal Iron Ore Mine (JIOM) of Patnaik Minerals Private Limited in Orissa state of India were analyzed thoroughly (CSIR-CIMFR 2011, 2012). The results thus obtained were then compared with those of the conventional scaled distance approach involving charge weight per delay and total charge in a round of blast in order to validate the conversion approach.
Field investigations
BAC falls under Jharia coalfield, located in Dhanbad district of Jharkhand state. To recover locked-up coal in fire-prone area of developed underground pillars beneath the opencast mines, deep-hole surface blasting was carried out. The developed coal pillars left in underground mines are often extracted by opencast method if the depth of cover is less, economically exploitable and no surface features are present. The total coal recovery of developed coal pillars can be achieved by opencast mining whereas by underground mining, only 70–80% can be extracted. With the development of safe blasting practices in hot strata, the developed coal pillars as well as any remnant coal left in underground mines can be fully recovered by opencast method.
Investigations were carried out for optimization of blasting parameters beyond 100 m of the public structures for controlling of ground vibrations.
During field investigations, six experimental blasts were conducted using site-mixed emulsion explosive (SME) of M/s IEL-Orica with varying design parameters and explosive charging patterns (Figure 3). The density of explosive was 1175 kg/m3. All the experimental blasts were conducted at 1st overburden sandstone bench in the western side of the mine. The diameter of holes in all the blasts was 110 mm. The depth of holes varied from 5.5 to 8.5 m. Burden and spacing were between 2.5–3.0 m and 3.0–3.5 m, respectively in all the blasts. Top stemming columns ranged between 3.0 and 3.5 m. The total number of holes in a blasting round was between 18 and 65. The number of rows of holes varied from 3 to 7. Thirty-four recorded ground vibration data were analysed for establishing the blast design and charge loading parameters beyond 50 m and within 100 m of public structures.
Charging of holes with SME explosive at Bhelatand Amalgamated Colliery (BAC).
JIOM lies in Keonjhar district of Orissa state. The investigation was carried out for assessing the impacts of blasting in the surrounding environment with the objective of optimising the blasting parameters to minimize the impact on ground vibration, noise/air overpressure, flyrock, etc. Trial blasts were carried out using 102 mm drillhole diameter in iron ore benches (Figure 4). The depth of holes used in the trial blasts varied from 3.0 to 9.5 m. Burden and spacing were 2.0 and 2.5 m, respectively. Top stemming columns were 2.0 and 3.75 m depending upon the depth of holes. The total number of holes in a blasting round varied from 41 to 100. The number of rows varied from 2 to 6. Depending upon blasthole depth, the weight of explosive charge in a hole varied from 21.50 to 45.40 kg. The total explosive weight in the blasting round ranged between 1275.00 and 4400.00 kg and maximum explosive charge weight per delay varied from 50.00 to 181.60 kg.
Charging of holes with SME explosive at Joribahal Iron Ore Mine (JIOM).
Standard error of estimates
The regression line seeks to minimize the sum of the squared errors of prediction. The square root of the average squared error of prediction is used as a measure of the accuracy of prediction. This measure is called the standard error of the estimate and is designated as standard error of estimates (SEE), which becomes smaller when the data points are closer to the regression line. For multiple independent variables (k), the SEE can be calculated using Equation (2). In case of single independent variable k becomes 1 which makes the denominator (n – 2). The two parameters i.e. the slope and the intercept were estimated in order to evaluate the sum of squares-
where,
y i = each observed value of y in the data;
y
i
n = number of data points;
k = number of independent variables.
The square root of the sum of squared residuals divided by the factor (n – k – 1) represents the average distance that the observed values fall from the regression line. Therefore, it reflects how wrong the regression model on average using the units of the response variable. Smaller values are of course better because it indicates that the observations are closer to the fitted line. For example, SEE value equals to 2.58 means that the average distance of the data points from the fitted line is about 2.58% of the predicted vibration.
Unlike R2, the standard error of estimate or SEE assesses the precision of the predictions. Approximately 95% of the observations should fall within ±2 × SEE, which is also a quick approximation of a 95% prediction interval. However, SEE must be ≤ 2.5 to produce a sufficiently narrow 95% prediction interval (Pal Roy 2005; Weiers 2008).
Results and analyses
During analyses of vibration data, following parameters were considered for developing different predictive models of ground vibration due to blasting.
Qt = Total explosive charge fired in a round (kg)
Qd = Maximum explosive charge per delay (kg)
ρ = Density of explosive (kg/m3); [ρ = 1175 kg/m3 (BAC), 1100 kg/m3 (JIOM)]
D = Distance of the measuring point from the blasting source (m)
at = [3 Qt/(4π ρ)]1/3 = Radius of equivalent spherical charge taking total charge fired in the round together (m)
ad = [3 Qd/(4π ρ)]1/3 = Radius of equivalent spherical charge taking maximum charge per delay together (m)
PPV (V) = Peak particle velocity, mm/s.
The experimental results are depicted in the Figures 5–16 wherein the y-axis denotes the ground vibrations measured in Peak Particle Velocity or PPV (mm/s) while the x-axis represents the scaled distance in different formats. In Figures 5 and 11, x = D/at; in Figures 6 and 12, x = D/ad; in Figures 7 and 13, x = D/Qt1/2; in Figures 8 and 14, x = D/Qd1/2; in Figures 9 and 15, x = D/Qt1/3 and in Figures 10 and 16, x = D/Qd1/3. Explicit presentations of data analyses comparing traditional and equivalent charges are shown in Tables 1 and 2 for BAC and JIOM, respectively.
PPV vs. scaled distance in ESCC (total charge): BAC.
PPV vs. scaled distance in ESCC (max. charge/delay): BAC.
PPV vs. conventional square root scaled distance (total charge): BAC.
PPV vs. conventional square root scaled distance (max. charge/delay): BAC.
PPV vs. cube root scaled distance (total charge): BAC.
PPV vs. conventional cube root scaled distance (max. charge/delay): BAC.
PPV vs. scaled distance in ESCC (total charge): JIOM.
PPV vs. scaled distance in ESCC (max. charge/delay): JIOM.
PPV vs. conventional square root scaled distance (total charge): JIOM.
PPV vs. conventional square root scaled distance (max. charge/delay): JIOM.
PPV vs. conventional cube root scaled distance (total charge): JIOM.
PPV vs. conventional cube root scaled distance (max. charge/delay): JIOM.
Comparison of traditional charges with equivalent charges for BAC.
Comparison of traditional charges with equivalent charges for JIOM.
It is apparent from Figures 5 and 6 of BAC and Figures 11 and 12 of JIOM that better correlation is exhibited between peak particle velocity and scaled distance in the ESCC approach in comparison to conventional scaled distance models i.e. the ratio of distance to square root or cube root charge quantity. The results as depicted in Figures 5–16 suggest that the prediction of ground vibration through ESCC approach is better with cube root scaled distance than with square root scaled distance. This could be due to the spherical symmetry of propagating waves in both cube root scaled distance and ESCC approach.
Conclusions and recommendations
In ESCC approach, the cylindrical charges are converted into a number of spherical charges of varying diameters lying at the central locations of the respective charges firing either at different delay intervals (usually 8 ms time gap) or instantaneously. These charges are assumed to be spherically distributed in the blasting zone and on detonation generate strain waves which emanate spherically leading to geometrical spreading of explosive energy and inelastic attenuation till they subside at the boundary of the undamaged rock zone i.e. the zone through which the seismic pulse propagates and ultimately reaches the surface structures.
The predictor equations thus proposed on the concept of ESCC approach are found to be quite suitable for the prediction of ground vibration induced by blasting with reasonable degree of certainty. This approach is conceptually simple and can be used as an effective tool in predicting ground vibrations due to blasting. Further research in this direction can be tried to make this approach more suitable and refined.
Footnotes
Acknowledgements
The author is grateful to the Director, CSIR-CIMFR for giving his permission to publish this paper. Thanks are also due to Dr. Chhangte Sawmliana, Principal Scientist, CSIR-CIMFR and Sri Ajoy Kuchlyan, Technical Assistant, CSIR-CMERI for field experiments and drawings. A technical note on the same model was delivered in the National Seminar on ‘Recent Practices and Innovations in Mining Industry (RPIMI)’, 19th and 20th February, 2016 at National Institute of Technology, Raipur, India. Opinions made herein are of the author and not of CSIR-CIMFR.
Disclosure statement
No potential conflict of interest was reported by the author.