1 Introduction

As far as Indian mining scenario is concerned, the employment of drilling and blasting is immense in the extraction of mineral deposits including 90% of coal deposits and almost 100% for metalliferous deposits [1]. Despite being the primary excavation method, only 20-30% of the explosive energy is effectively used for rock fragmentation, and the rest of the energy is dissipated in various forms [2]. The dissipation of the wasted energy is primarily in the forms of blast-induced ground vibration, air blast, fly rocks, undesirable noises, and back-breaks. The propagated ground vibration on encountering a structure induces high levels of structural oscillations causing significant degrees of damages and failure [3]. The intensity of blast-induced ground vibration is dependent on parameters including the geological formation and the design criteria of the blasts that are grouped into controllable and uncontrollable parameters [4].

The levels of blast-induced vibration are quantified in terms of PPV or the vibration amplitude, the frequency of vibration and the duration of vibration. PPV is simply the excitation velocity at which the ground particles move when a blast wave travels through them. The contribution of the dominant frequency and the relative amplitude of vertical and horizontal components is also significant. To minimize the ill effects of possible structural damage, the prediction of vibration levels is necessary. This study employs PPV as a measure to quantify ground vibration for relating the strain induced in the ground in response to the passage of ground waves through it [5, 6].

Through advancement in recent times, several developments are evident towards establishment of predictor equations for blast-induced ground vibration and various models have been proposed by researchers throughout the globe by considering the maximum explosive charge per delay and the distance of monitoring station from the blasting site. However, it is still a major challenge to incorporate the anisotropic nature of the rocks and the varied local geology of the formation into the predictor equations, hence, it is quite difficult to formulate a generalized equation for the prediction of PPV. The work, first of its kind, involving the monitoring of blast-induced ground vibration to assess the possible damages on structures was carried out by Rockwell [7]. Over the years, various researchers have established several predictor equations from the data obtained from different mines all across the globe [8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Most of the existing predictor equations have been formulated from the site-specific data obtained as the results of numerous blasting operations carried out to predict and control the effects of blasting. A summary of such predictor equations formulated in the works of several researchers from the literature have been presented in Table 1. Most of these equations consider the PPV to be the required output using the scaled-distance concept.

Table 1 Summary of existing empirical models for the prediction of blast-induced ground vibration as proposed by different researchers.
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Most of the existing studies have considered one or two influencing variables for ground vibration prediction (e.g., D and Qmax). Rarely do we find any study which has incorporated or tested multiple influencing parameters such as, B, S, Φ, n, Qt, Lc and, L, for blast-induced ground vibration prediction model development. Thus, the present study aimed to experiment with a different statistical approach (e.g., linear, multiple, polynomial, and logarithmic regression-based models) involving multiple influencing variables for predicting blast-induced ground vibration.

2 Study location

The Sukinda chromite mining region of Odisha (Indian state) was chosen for this study, depicted in Figure 1. The region accounts for more than 97% of the country’s chromite deposit. The study area is characterized by low grade metamorphism and deformation. The Sukinda chromite deposits are localized in the Sukinda thrust occurring as stratified cumulative bands having been intruded into the Pre-Cambrian North Odisha Singbhum Craton. The chromiferous bands exhibit distinct granular texture due to gravitative settling hosted by dunite-peridotite ultramafic suite. Majority of the ultramafic rocks have been altered to serpentinites. The regional trend of the ore body is ENE-WSW dipping sharply towards north-west. The ore bands are localized between Daitari and Mahagiri Hills and hence known as the Sukinda valley deposit.

Figure 1
figure 1

Location map of the study area, the chromite mining region (Sukinda valley) in the Indian state of Odisha.

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3 Materials and method

The study broadly involves the selection of a critical site for conducting the study, followed by in-situ data collection, field experimentations, model development, ground vibration prediction, and validation-comparison of the developed model. The workflow of the present study is provided in Figure 2. A few key steps of the present study are discussed in further subsections.

Figure 2
figure 2

Workflow of the study.

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3.1 In-situ data collection

Multiple field campaigns were conducted for acquiring the blast related in-situ data from the Sukinda chromite mining region during the period between October, 2022 and January, 2023. Two active open cast chromite mines were chosen for conducting the blasting events for acquiring the field data. The blasts were conducted at various benches throughout the mines, including the overburden benches, as well as floor blasts on the ore body having no free faces. Altogether 39 numbers of production blasts were conducted during the study, where 30 were bench blasts and 9 were floor blasts. Individual blasts were monitored for blast-induced ground vibration using three numbers of seismographs (Make: Instantel©). Using the three seismographs, a total number of 86 observations of PPV were recorded from a total of 39 blasting events. In all the blasting events, site-mixed slurry explosive (SME) was used for charging the blast holes as it was deemed appropriate for providing adequate detonation energy required for fragmentation depending upon the stratum condition. Approximately, 30–50 kgs of explosive was charged in each hole depending on the hole depth and the required column of explosive charge in holes contributing to a total explosive charge of 3-6 tons in a round of blasting. For some of the blasting patches, deck blasting was adopted with a decking length of 0.5 m. Decking was employed to prevent the formation of large boulders and for effective utilization of explosives and thereby, limiting the powder factor. Emulsion boosters were lowered into each hole prior to charging them with explosive. Boosters used weighed 150 gm, one in number when the quantity of explosive charge in a hole remained less than 60 kg; otherwise, two numbers of boosters were used. Non-electric system of detonators was used for the initiation of the charged holes involving down-the-hole delay detonator (DTH), trunk line delay detonator (TLD) and detonating fuse (DF). The blast-induced ground vibration data was recorded with the help of seismographs by tactically placing them at the required distances covering the statutory monitoring points in and around the mine lease area. The primary data obtained from the seismographs were the levels of blast-induced ground vibration, the frequency of the ground vibration waves and the blast-induced air-overpressure. Similarly, the output from a blasting event was recorded in terms of blast vibration or PPV, noise or air-overpressure, occurrences, and extent of flyrock ejection, the throw and profile of the blasted muck pile, rock fragmentation, etc.

The other crucial details of individual blasting events that were collected from the site included the hole diameter, quantity of explosives charged per hole, total quantity of explosives used in individual blasting rounds, length of the stemming column in individual blast holes, length of explosive charge column in individual holes, total explosive charge length in individual blasting rounds. powder factor, maximum explosive charge per delay in blasting rounds and, volume of the rock blasted. All the above-mentioned parameters were collected in-situ before the occurrence of a blasting event and were subsequently used in the development of a predictive model for blast-induced ground vibration. The statistical overview of the data acquired during field monitoring of the blasting events, including the design parameters as well as the outputs from the monitored blasts are represented in Table 2.

Table 2 Statistical overview of the in-situ recorded data during the field monitoring of blasting events
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3.2 Method

The methodology for the study involved all the necessary actions and processes for the development of a predictive model for blast-induced ground vibration involving field experimentations, model development and validation, comparison with existing models and in-situ observations. Some key steps of the methodology are described in further subsections.

3.2a Pre-requisite to statistical model development for ground vibration prediction: In the present study linear regressions with logarithmic transformations were used for the development of ground vibration prediction model. Development of such models require extensive field experimentations for generating ample number of datasets. The datasets used for model development should be such that they influence the outcome of the operation which also serves as the output of the regression-based model. Blast-induced ground vibrations are dependent on several factors which can be classified as controllable or uncontrollable. The characteristic properties of the rock mass blasted which includes the strength of the rock, its modulus of elasticity, Poisson’s ratio, etc., are uncontrollable in nature. Further, suppose the local geology of the rock formations is considered including the presence of geological formations like faults, joints and discontinuities or the presence of surface water bodies—these factors are again uncontrollable in nature. However, the blast design factors including the number of holes, hole diameter, depth of hole, column length of explosive charge, total explosive charge and maximum explosive charge per delay in a blasting round, initiation system of the blast—are controllable in nature. These controllable factors can be parameterized in individual rounds of blasts by the design engineer which can be optimized to match the legislative levels of blast-induced ground vibrations.

The entire dataset consisting of 86 observations acquired from field monitoring, represented in Table 2, was initially considered for the development of a predictive model for PPV by correlating it with the blast design parameters, using linear regression analysis. However, a valid model could not be established considering all the data points, due to the presence of outliers which degraded the fit of the model and subsequently reducing the obtained R2. Therefore, all the outliers in the dataset were identified using visual inspection with the help of scatterplot and were eliminated from the consideration of statistical model development. Thus, after eliminating the outliers, a total of 39 observations corresponding to 39 blasting events were finally considered for model development. The dependency of PPV (dependent variable) on the individual influencing parameters were checked and the best predictive parameters were decided based on the R2. The extent of dependency of the independent variables and their subsequent rejection is done by the p-value approach (p < 0.05). Furthermore, the best correlated parameters at 95% significance level were considered for developing ground vibration prediction model based on multiple regression analysis. Before performing the multiple regression analysis, all the variables (dependent and independent) were converted to logarithmic scale to improve the fit of the model. The probability of individual parameters influencing the dependent variable to an equal extent seldom exists and therefore, using logarithmic transformations becomes convenient means to transfer highly skewed variables to a more normalized dataset. This is in response to producing the smallest error possible in predicting a given output while also preventing the overfitting the model. Another reason for using a log-log linear regression model is to obtain a better representative form of the relation between the dependent and the independent variables by eliminating the logarithmic transform of the individual covariates such that directly and inversely related parameters are better understood from the equation. This process also enables easy optimization of various independent parameters. The generalized form of a log-log linear regression model is represented in the equation 1 below.

$$ \log Y = A + B \cdot logX_{1} + C \cdot logX_{2} + D \cdot logX_{3} + \cdots $$
(1)

where, Y = Dependent variable; X1, X2, X3, …….. = Independent variables; A = Coefficient of the intercept; B, C, D, ….. = Coefficients of the individual independent parameters respectively.

3.2b Site-specific United States Bureau of Mines (USBM) predictor equation: USBM equation is a universally accepted equation for the prediction of blast-induced ground vibration. The equation is site-specific and empirical in nature relating the PPV with D and Qmax (scaled-distance concept). It is characterized by the two constant terms in it, known as the site constants. These constants are obtained from regression analysis of the blasting data. To carry out statistical analysis, the blasting data obtained from the production blasts were grouped together and the prediction equation was established and is presented along with its correlation coefficient in equation (2).

$$ PPV = 446.14 \times \left( {\frac{D}{{\sqrt {Q_{{{\text{max}}}} } }}} \right)^{ - 1.533} ;\quad R^{2} = 0.66 $$
(2)

where, PPV = Peak particle velocity (mms-1); D = Radial distance between the initiation point of the blasting patch and the monitoring station (m); Qmax = Maximum explosive charge per delay in a blasting round (kg).

4 Results and discussion

4.1 Statistical model development and prediction of ground vibration

Initially, multivariate linear regression analysis with logarithmic transformations was performed against PPV by correlating it with n, B, S, Lc, D, Qt, and Qmax. The correlation coefficient for this multivariate regression as shown in Table 3 is 0.73. The output of the regression from Table 3 shows that p-value for number of holes is 0.7, which signifies the fact that 70 times in every 100 numbers of cases the dependency of number of holes on the PPV is null. Hence, number of holes has not been used as an independent parameter in the subsequent steps of regression and has been eliminated. Subsequently, all the parameters having p-value greater than 0.1 have been eliminated and multivariate logarithmic regression has been performed. Finally, it has been observed that PPV when considered as a function of B, S, Qmax and D, the p-value falls within the desired cut-off limits, using which the final predictive model for PPV has been developed. The summary of this regression-based model is presented in Table 4, having R2 of 0.83.

Table 3 Output of multivariate log–log regression for PPV estimation using n, B, S, Lc, D, Qt, and Qmax as independent parameters.
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Table 4 Output of multivariate log-log regression for the prediction of PPV using B, S, Qmax and D as independent parameters.
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The standard form of the equation as obtained from the result of the regression in Table 4 is represented in equation (3):

$$ Log PPV = - 4.27 + 10.24 \cdot Log B + 7.28 \cdot Log S - 0.64. Log Q_{max} - 1.31 \cdot Log D $$
(3)

Equation (3) has been further modified by eliminating the log in individual terms and reformulated as a relatable mathematical relation involving the dependent and independent parameters of the model and represented in equation (4). The reformulated equation could be effectively used to convey the direct correlation between B and S with PPV while an inverse correlation between Qmax and D with the PPV. The correlation coefficient for the developed equation is 0.83 .

$$ PPV = \frac{{5.3 \times 10^{ - 5} \cdot B^{10.24} \cdot S^{7.25} }}{{Q_{max}^{0.64} \cdot D^{1.31} }};\quad R^{2} = 0.83, \quad p < 0.01 $$
(4)

where, PPV = Peak particle velocity (mm/s); B = Burden in m; S = Spacing in m; Qmax = Maximum explosive charge per delay in kg; D = Distance of monitoring point from the blasting site in m.

4.2 Model validation and evaluation

Overall, this study has employed three distinct sets of data individually, for the development of a statistically formulated predictive model, followed by its validation and comparison, respectively. An illustrative representation of the involvement of datasets used in the process of model validation and comparison is shown in Figure 3.

Figure 3
figure 3

Workflow for validation and comparison of the proposed model predicted PPV and USBM predicted PPV using the in-situ recorded PPV data.

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The values of PPV obtained using equation (4) were validated against the in-situ recorded PPV values using R2, RMSE, MAE and MAPE as statistical tools for evaluating the efficiency of the developed model. Thereafter, the results of the universally employed USBM model were validated against the experimentally acquired in-situ PPV data using the same statistical tools. Finally, the results of the developed model and the USBM model were compared with the in-situ recorded PPV data to justify the enhanced performance efficiency of the proposed model over the USBM model in predicting blast-induced ground vibration.

The R2 measures the wellness of fit of a statistical model for predicting the required outcome and RMSE signifies the standard deviations of the prediction errors representing the concentration of data points around the line of best fit. In other words, it can be used to verify experimental results in regression analysis. MAE is the average of all the absolute errors in the experimental and prediction data groups. The ratio of the sum of all absolute errors in individual observation cases to the number of observation points gives the mean absolute error for that experimental and prediction data group. MAPE refers to the mean of all percentage errors between the predicted values and observed values. MAPE is similar to that of MAE, however it goes a step further by adding the actual value in division to convert the error into a percentage. The return of errors as percentages in MAPE facilitates easy understanding of the errors and enables better comparison across different datasets and models. The mathematical expressions for R2, RMSE, MAE and MAPE have been showcased in equations (5), (6), (7) and (8), respectively.

$$ R^{2} = 1 - \frac{{\mathop \sum \nolimits_{i = 0}^{N} \left( {Actual\;values - Forecasted\; values} \right)^{2} }}{{\mathop \sum \nolimits_{i = 0}^{N} \left( {Actual\; values - Average\; value} \right)^{2} }} $$
(5)
$$ RMSE = \sqrt {\frac{1}{N}\mathop \sum \limits_{i = 0}^{N} \left( {Actual\;values - Forecasted\; values} \right)^{2} } $$
(6)
$$ MAE = \frac{1}{N}\mathop \sum \limits_{i = 0}^{N} \left| {Actual\;values - Forecasted\;values} \right| $$
(7)
$$ MAPE = \frac{100\% }{N}\mathop \sum \limits_{i = 0}^{N} \left| {\frac{Actual\;values - Forecasted\;values}{{Actual\;values}}} \right| $$
(8)

where, R2 = Coefficient of determination; RMSE = Root Mean Square Error; MAE = Mean Absolute Error; MAPE = Mean Absolute Percentage Error; N = Number of observations in the dataset; Absolute values = Experimentally obtained data; Forecasted values = Model predicted data.

The combined correlation plots between the outputs of the statistically proposed predictive model and USBM predictor model with the in-situ recorded PPV data is shown in Figure 4. The plot shows an R2 value of 0.8 between the statistically predicted and in-situ recorded PPV values which signifies the fact that nearly 80% of the variations in the outcome are successfully explained by the covariates included in the model. The value of R2 could be further increased by inclusion of more variables in the model. However, the extent of dependency of the variables are identified from the p-value using t-test approach followed by subsequent elimination of variables having p < 0.05. The RMSE between the same has been found to be 2.85 which provides an estimation of the degree of accuracy of the developed predictive model. An RMSE value of 2.85 is likely to be good provided that the average of the observed in-situ data is 5.6. Similarly, MAE is estimated as 1.92 which is also likely to be good being considerably a smaller quantity as compared to the average of the observed values (i.e., 5.6). The MAPE is found to be 0.5 or 50% representing a satisfactory fit of the developed model in comparison with the field recorded values.

Figure 4
figure 4

Combined correlation plot justifying the wellness of fit of the proposed model over the USBM model.

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Similarly, Figure 4 also shows the correlation plot between the in-situ recorded PPV values and the USBM model predicted PPV values shows an R2 of 0.28, thereby predicting around 28% of the outcomes successfully using the covariates used in the USBM model. In this correlation, a significant reduction in the R2 value has been observed due to the involvement of fewer covariates in the USBM model. Similarly, the RMSE for this correlation is 8.13 indicating larger deviations in the predictive errors and exceeding the average of the observed values (i.e., 5.6). The estimated values of MAE and MAPE between the same has been estimated as 4.72 and 0.68, respectively. The obtained MAE is close to the average of the observed values (i.e., 5.6) and the MAPE is around 68% indicating significant estimation errors in the values predicted by the USBM predictor model on comparison with the field recorded data. Thereby, justifying the performance efficiency and prediction accuracy of the developed model for blast-induced ground vibration prediction in the opencast chromite mines of the study area.

Lastly, the PPV outputs from the proposed PPV prediction model and the USBM predictor model were compared with the in-situ recorded PPV data for all the 39 datapoints corresponding to the 39 blasting events and is represented in Figure 5. The sole purpose of this plot is to interpret the enhanced performance efficiency of the proposed predictive PPV model over the USBM predictor model and to present an overview of the overall performance of the proposed model.

Figure 5
figure 5

Comparison plot showing the PPV output variations in individual observations among in-situ recorded PPV data, statistically predicted PPV values and the USBM model predicted PPV values.

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The enhanced performance efficiency of the proposed predictive PPV model over the USBM predictor model can be better explained by the standardized residual plots of both the individual predictor models with due consideration to the in-situ recorded PPV data. The combined standardized residual plots of the proposed model (equation (4)) and the formulated USBM predictor model (equation (2)) are represented in Figure 6, obtained by plotting the standardized predicted values along the abscissa and the standardized residuals along the ordinate. The mathematical expressions for residuals, standardized residuals, and standardized predicted values are shown in equations (9), (10), and (11), respectively.

$$ \varepsilon_{i} = Y_{i} - \widehat{{Y_{i} }} $$
(9)
$$ \left( {\varepsilon_{z} } \right)_{i} = \frac{{\varepsilon_{i} }}{Standard\;deviation \;of\;residuals} $$
(10)
$$ \left( {\hat{Y}_{z} } \right)_{i} = \frac{{Y_{i} }}{Standard \;deviation\; of\;predicted \;values} $$
(11)
Figure 6
figure 6

Combined standardized residual plots of the proposed model and the USBM model.

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where, \({\varepsilon }_{i}\) = Residual for the ith observation; \({Y}_{i}\) = Observed value for the ith data point; \({\widehat{Y}}_{i}\) = Predicted value for the ith data point; \({\left({\varepsilon }_{z}\right)}_{i}\) = Standardized residual of the ith observation; \({\left(\widehat{{Y}_{z}}\right)}_{i}\) = Standardized predicted value for the ith observation.

A horizontal trendline \((Y=0)\) signifies no definitive pattern in the standardized residual plot, signifying the alignment with the model’s assumptions and ensuring the validity of the statistical tests. Therefore, a closer inclination of the trendline towards \(Y=0\) line signifies homoscedasticity, generally suggesting a constant levels of variations in the residuals. The plot in Figure 6 exhibits a homoscedastic nature of the residuals for the proposed model with the trendline being more inclined towards the line \(Y=0\). Similarly, the trendline for the USBM model is comparatively more inclined away from the \(Y=0\) line. Outliers are evident in both the models; however, the better homoscedastic nature of the proposed model (equation (4)) justifies its better performance efficiency over the USBM model (equation (2)). Further, a better fit of the proposed model can be ensured by incorporating additional predictor variables in the model forming the scope of future study.

5 Discussion

Globalization along with increasing demands for the manufacturing industries has catapulted opencast mine workings to the forefront in meeting industry demands, which in turn has challenged the production capacities of the opencast mines. Blasting remains the primary production operation in any major opencast mine and thus requires significant management and attention towards its undesirable outcomes that are observed primarily in the form of blast-induced ground vibrations causing structural damages and ejection of flyrocks or environmental impacts due to ejection of dusts and air blasts. Consequently, these impacts have been observed, among others [22,23,24,25,26,27,28,29,30]. These outcomes are of major concerns over areas where opencast mining is a dominant economic activity and requires the implementations of safe practices to be undertaken by the local regulatory bodies as well as the mining organizations. This study however focuses on the aspects of blast-induced ground vibration concerning its prediction to minimize the ill effects.

Absence of a comprehensive blast design system and an efficient model for the prediction of PPV are of serious concerns over the Sukinda chromite mining region. This study devised a site-specific model for PPV prediction and justified its efficiency for predicting the same by comparing its outcome with that of the USBM model for ground vibration prediction, [1, 31, 32]. Employing multivariate statistical analysis for the prediction of blast-induced ground vibration has been a proven approach provided that the variations in the covariates used as input data are significant in individual monitoring events. This study has also tried and successfully incorporated the dimensional parameters of a blasting patch (spacing and burden) into the PPV prediction model which is integral from the point of view of achieving the required size of rock fragments obtained after blasting, [33,34,35,36,37,38]. As opposed to the statistical approach, noteworthy works have also been conducted by several researchers involving machine learning algorithms for predicting the same, among others [23, 39,40,41,42,43,44,45,46,47,48,49,50,51]. In this regard, to overcome the negative impacts of opencast mining activities, particularly blast-induced ground vibration, the Regulatory Agency under the Ministry of Labour and Employment, Government of India catering to the requisites of occupational safety, health and welfare of persons employed in the mines (coal, metalliferous mines and oil-wells) has prescribed legislative limits that ensures that blasting activities in opencast mines are carried out judiciously, and that regular monitoring of blast-induced ground vibration is an integral part of mining process.

However, several challenges remain till date to limit the levels of blast-induced ground vibration either due to the lack of any scientific approach in achieving the same or due to the improper implementation of regulatory framework within organizations which requires the mining companies to frequently carry out studies for monitoring the aftermath. This has resulted in many mining companies avoiding their responsibilities and minimizing the costs of optimization. Therefore, with scientific approach and regular monitoring guided by proper regulations, it is possible to curtail the effects of blast-induced ground vibration. With emerging trends and development of new technologies, the monitoring and regulatory processes become easy, efficient, and effective using new computational tools and modifications in the in-situ blast design parameters.

6 Optimization of the blast design parameters for the study conducted using USBM model

A site-specific predictive model for blast-induced ground vibration has been developed by statistical modelling using multivariate logarithmic regression (Table 4). The model correlates the PPV with B, S, Qmax and D (equation (4)). The design parameter chosen for optimization is the Qmax at different distances as required for a PPV threshold of 10 mms−1. The proposed model incorporated the spacing and burden in it which are varied in individual blasting events depending upon the fragmentation requirements and the geological setting of the strata. The south side of the lease area is inhabited by a settlement consisting of structures not belonging to the owner. The average distances to it from the nearest blasting patches are within 75 m, the least being 50 m. Production bench blasting carried out in the vicinity of the settlement are characterized by limited variations in the spacing and burden values. Therefore, Qmax for blasts at those benches have been optimized using the developed predictive model (equation (4)), represented in Table 5 for different combinations of spacing and burden values. Thereafter, for day-to-day production blasts covering the entire mine lease area where the choices of spacing and burden values are not limited, the developed site-specific USBM predictor equation (equation (2)) is used for the optimization of Qmax in a blasting round at different distances for a PPV threshold of 10 mms−1, depicted in Table 6. Standards of permissible ground vibration have been obtained from the guidelines as per the Directorate General of Mine Safety (DGMS) circular no. 7 of 1997 as presented in Table 7. These standards are formulated based on the frequency of the blast-induced ground vibration. To obtain the threshold limits of ground vibration in the study conducted, the recorded peak dominant frequency was plotted against the monitoring distance as shown in Figure 7.

Table 5 Recommended blast design parameters for the structures not belonging to the owner in the vicinity of the lease area.
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Table 6 Recommended blast design parameters for day-to-day blasting.
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Table 7 Legislative standards of blast-induced ground vibrations as per DGMS Circular No. 7 of 1997 [52].
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Figure 7
figure 7

Plot showing the distribution of the maximum dominant frequency over the range of monitoring distances.

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The plot in Figure 7 reveals that majority of the recorded blast vibrations (~51% of 39 observations) lie between maximum dominant frequency range of 8–25 Hz, hence the threshold limits was restricted to 10 mm/s for PPV for surface structures not belonging to the owner. Henceforth, the threshold limits of blast-induced ground vibration levels were used to optimize the blast design to restrict the levels of blast vibration.

The selection of distances in Table 6 were as per the locations of statutory monitoring points (surface structures) not belonging to the owner.

7 Conclusion

Till date, blasting remains the most sought-after method for displacing significant volume of earth as overburden in the case of open cast mining operations and for the extraction of ores. The major concern associated with blasting activities is ground vibration that are induced on the ground only after a surface blasting event is conducted causing significant degrees of damages to the structures. Hence, predicting the levels of ground vibrations induced beforehand with the help of a site-specific model forms the key in the work and is a major concern for the design engineers such that the design parameters can be effectively optimized keeping in mind the production standards. Statistical analysis using multivariate regression is an effective predictive measure to correlate the PPV generated after a blast with the blast design parameters. A similar multivariate regression analysis has been performed in this study to establish a predictive model for blast-induced ground vibration at opencast chromite mines in the Sukinda valley of the Indian state of Odisha. Based on the present study, following conclusive remarks are drawn:

  1. i.

    The chromite mining region of the Sukinda valley is devoid of any such predictive model for PPV prediction which has been developed successfully considering varied blast design parameters on a local scale by conducting the study in two active open cast chromite mines in the region. The predictive capabilities of the developed model are solely governed by the prevailing geology, and is therefore site-specific in nature.

  2. ii.

    There has been reported cases of significant damages to surface structures caused by blast induced ground vibrations and hence with their known distances from the blasting patch, blast-induced ground vibration can be predicted beforehand with the designated blast design parameters.

  3. iii.

    The incorporation of blasting patch dimensions such as burden and spacing into the predictive model benefits the fragmentation requirements over a particular rock stratum considering its geological setting along with the prediction of ground vibration induced in it due to blasting activity.

  4. iv.

    The comparison of the performances of the developed model with that of the universally employed USBM model establishes the superiority of the developed site-specific model for PPV prediction, particularly because the model incorporates more predicting variables into it for the same. Also, the validation of the developed model against the universally applicable USBM model, with the field recorded data exhibits higher R2 and lower RMSE, MAE and, MAPE values for the developed model and vice-versa for the USBM model. Thereby, establishing a higher performance efficiency of the proposed site-specific predictive model.

  5. v.

    The performance of the proposed model can be further improved by including additional independent parameters for the prediction of PPV, which requires conducting blasting events by varying the design parameters in individual blasts. The proposed model may have performed well in comparison with the USBM model; however, the model cannot be generalized. To develop a comprehensive predictive model, further studies are required that may involve the incorporation of machine learning algorithms with nature inspired optimization techniques for implementation on a global scale.

  6. vi.

    The outcomes of the present study shall help the regional policy and decision makers, legislative and regulatory bodies, stakeholders and mining authorities towards the formulation of an efficient blast design system considering its undesirable effects (blast-induced ground vibration) with respect to the designated legislative limits for the safety and protection of structures above the ground (inclusive of both human dwellings and industrial structures) in the chromite mining belt of Sukinda valley, India.