Development of artificial neural network based mathematical models for predicting small scale quarry powder factor for efficient fragmentation coupled with uniformity index model

Blasting is the primary method for reducing rock size in small-scale mining operations. The primary purpose of blasting is to assist rock mass reduction and transportation from the mine to the processing facility. The explosive charge utilized in this blasting operation has an impact on production output, safety, and profitability. The explosive powder factor is used in mining to calculate the quantity of explosive required per mass of rock fragmented, and this study looks at how different powder factors affect blast fragmentation. A machine learning approach was used in this study to optimize explosive use in small-scale quarries. This study employed data from a small-scale dolomite quarry in Akoko Edo, Nigeria, for artificial neural network (ANN) modeling and uniformity index model creation (10 production blasts and 38 blast record datasets). Powder factors greater than 0.7–0.8 kg/m3 result in a lower uniformity index, according to an analysis of monitored blast results. The results showed that powder factors of 0.7 kg/m3 (between 1.6 and 1.7) had the highest uniformity index. According to the findings, the small-scale optimum blast uniformity index is between 1.33 and 1.68. The proposed ANN model performs well in terms of prediction accuracy, as determined by five error indices with coefficients of correlation (R2) of 0.997 on the training dataset and 0.97 on the testing dataset. Based on the model performance analysis results, the suggested ANN model can be used to improve the small-scale blast powder factor in actual applications.


Introduction
Rock excavation has become more important as the demand for raw materials for production and manufacturing has increased.Making mine raw materials available necessitates breaking down the rock mass in order to liberate valuable mineral grains, which are then processed into industrial material through ore dressing and metallurgical processes (Luukkanen et al. 2022).Blasting is an attempt to convert explosive material into sufficient energy for rock size reduction and displacement of in-situ formation to enhance material loading and transportation for further size reduction and processing (Sanchidrián et al. 2007).Sanchidrián et al. defined explosive as a material used in blasting operations for rock size reduction (Sanchidrián et al. 2007).They described explosive materials as the primary source of energy for rock mass fragmentation in mining, quarrying, and construction.During the industrial use of explosives, micro-cracks are driven from the borehole into the rock, as explained by Olsson et al. (2002).The importance of the rock powder factor in blast efficiency investigations has been identified by many researchers as the major factor behind the quantity of energy used and the determining factor of blasting safety (Adesida 2022;Singh et al. 2019).Olsson et al. explained that the rock fracturing process during blasting begins with shock wave generation and propagation, which is distinguished by the formation of radial cracks around the borehole.The second stage involved the distribution of gases from the detonated explosive charge into cracks, followed by lateral and axial crack expansion (Olsson et al. 2002).These stages depend basically on the amount of explosive material loaded into the rock mass.Given that the efficiency of the entire mining process is heavily dependent on the fragment size distribution result and that the quality of the fragmentation determines how productive and profitable each downstream operation such as loading, transportation, and crushing is, it is therefore critical to investigate the use of explosive charge weight per rock tonnage (Monjezi et al. 2010;Onederra et al. 2010;Mallo 2012).Artisanal and small-scale mining (ASM) is characterized as an illegal mineral extraction action that includes the mining of minerals like coal, gold, and gemstones, among others (Mallo 2012).A small-scale mining operation includes the utilization of simple instruments, for example, hoes, pick axes, chisels, and shovels, combined with work exercises like digging, breaking, panning, arranging, and conveying manually.As noted by Hilson et al., the ASM around the world keeps on developing impressively and as of now utilizes roughly 42 million individuals, of whom 13 million works in sub-Saharan Africa, around 70-80% are casual specialists, and 30-50% is ladies (Hilson et al. 2018;IGF 2017).According to Perks and Schneck, 80% of the world's supply of sapphire, 20% of gold mining, and up to 20% of diamond mining come from artisanal and small-scale mining (Perks and Schneck 2021).Artisanal and small-scale mining are prevalent in underdeveloped nations in Central and South America, Africa, Asia, and Oceania.Although the sector generally has little research focusing on its limitations and challenges due to its informality and overall lack of mechanization, such an operation as blasting is an important activity that must be properly monitored and improved through research findings to guarantee a safe and productive operation.To ensure good productivity and a greater contribution to the national mining sector, the use of explosives in small-scale mines necessitates competent oversight.Jimeno et al. (1995) define the rock blast powder factor as the amount of explosive charge weight in kilograms (Kg) required blasting one ton of rock.Being a controlled metric, this factor can be utilized for a range of purposes, including as an indicator of rock hardness, the cost of required explosives, and guidance for blast design (Prasad et al. 2017).According to Kahriman et al., the powder factor is one of the most crucial elements for defining ideal blasting settings and computing overall blasting costs (Kahriman et al. 2001).A precise forecast of the blast powder factor during blast design facilitates the decrease of blast and the increase of blast production efficiency (Hosseini et al. 2023;Bhandari and Balkema 1997).Despite the availability of advanced technologies for rock blast design, the challenges of explosive utilization and monitoring of blast fragmentation size distribution in small-scale mines receive very little attention (Leighton 1982).Several authors' works on the subject have been published.Prasad et al. examined the influence of the stemming-burden ratio and powder factor on blast-induced rock fragmentation using a case study of a mine in Dhanbad, Jharkhand, India (Prasad et al. 2017).According to the results of their investigation, the average, minimum and maximum fragmentation sizes of mine blasts decrease as the powder factor rises.Due to the fact that most artisanal and small-scale miners have limited knowledge of blasting theory and principles, it is essential to conduct research assessing the effect of powder factor on blast fragmentation size distribution to improve safety and productivity.Similarly, numerous authors in the field of rock excavation have attempted to improve blast fragmentation over the past decade; however, the significance of the uniformity index as a tool for evaluating the fragmentation efficiency of a blast round has been demonstrated in multiple works, including Cunningham's (Lawal 2021;Ouchterlony and Sanchidrián 2019;Rosa 2020;Stewart and Netherton 2019).Cunningham devised a uniformity index function as one of the Kuz-Ram model factors for the prediction of blast percentage passing size in an effort to improve the Kuz-Ram model (Cunningham 2005).Rock fragmentation size is one of the most important economic parameters in any surface mining operation.Since rock fragment size directly affects the costs of drilling, blasting, loading, secondary blasting, and crushing, several attempts have been made to estimate particle distribution using machine learning algorithms.The application of machine learning to the improvement of mining safety and productivity has increased exponentially over time.Kamran (Kamran 2021) have used an art catboost-based T-distributed stochastic neighbor embedding technique on back-break prediction resulting from dewan cement limestone quarry blasting operations.Amoako et al. (Amoako et al. 2022) used an artificial neural network and a support vector regression approach on blast fragmentation prediction with seven input variables, including powder factor, spacing to burden ratio, and rock strength property.Several soft computing approaches, including support vector regression (Amoako et al. 2022), artificial neural networks (Bhatawdekar et al. 2022;Taiwo 2022a), and multivariate regression frameworks, have been utilized to predict blast size distribution with a limitation gap in explosive utilization efficiency prediction.Table 1 presents the recent application of machine learning models to predict blast fragmentation.This study determines the influence of the powder factor on blast fragmentation size distribution and uniformity index.The study also focused on the application of a machine-learning modeling approach with uniformity index and image analysis software to increase blast efficiency.Mean square error (MSE), root mean square error (RMSE), correlation coefficient (R 2 ), and average absolute error (AAE) were utilized to evaluate the model's prediction accuracy.The optimum model was used to achieve a productive boundary limit powder factor for the best fragmentation uniformity.

Significance of the study
Based on primary controllable design characteristics, this study employs a Bayesian-based artificial neural network to estimate the small-scale explosive usage rate at the Akoko Edo dolomite quarry in Nigeria.To the best of the author's knowledge, this is the first study to estimate blast powder consumption rate by incorporating soft computing models into a mathematically driven equation using the machine learning layers of weight and bias.

Literature review
Rock geological features, explosive properties, and blast design parameters like burden, spacing, and stemming length are among the elements that influence rock blast productivity (Ash 1973;Taiwo 2022b;Singh et al. 2016).Singh et al. (2016) classified all of these factors, including the powder factor, as rock mass features and drill-and-blast design parameters.According to Amoako et al. (2022), blast geometry (see Fig. 1) and explosive properties are characterized as controlled variables that are used to improve the fragmentation efficiency of blasting as they can be modified according to site conditions.Such also include but are not limited to blast delay timing, start sequence, charge quantity, and priming processes as controllable parameters (Singh et al. 2016;Mulenga 2020;Ke et al. 2022).In addition to these criteria, the geological and geotechnical features of the rock mass are uncontrollable elements that influence the size distribution of blast fragments (Kahriman et al. 2001).Due to their inherent nature, these variables cannot be altered to modify blasting outcomes (Taiwo 2022b), but they can be contested by altering the various parameters appropriately.
According to Chung and Katsabanis (2000), the blast uniformity index is an essential statistic for determining fragment size in a given explosion.Due to their mining environment, rock properties, and economic strength, the majority of small and medium-sized industrial rock quarries in developing countries use blasting for excavation.Therefore,   analysis shows that while BI and RQD were the most sensitive parameters, cohesive strength was considered the least sensitive input parameter on the ANN model output.

Field study and lab work
To achieve the study focus, as shown in Fig. 2, a field investigation was conducted at a marble quarry in Akoko Edo.
The mine is situated on a private mineral title in Akoko Edo, Edo State, Nigeria, in the state of Edo.The formation of the area consists of white coarse marble, white dolomite, and clay soil overburden.The topographic map of the mine was drawn using SUFA software, as shown in Figs. 3 and 4. The size of the explosion hole ranges between 1.2 and 1.45 m.The mine's rock strength was assessed in accordance with ISRM (2007) of the International Society of Rock Mechanics Commission.Each blast round was drilled in a  2 for the parameter statistics).The 1.5-m-tall experimental mine benches were drilled and blasted with a handheld jackhammer of small diameter and 25 mm of packed emulsion gel explosive backed by ammonium nitrate and fuel oil (ANFO).The powder factor for each blast round was computed in the same sequence using the rule of thumb method.
After the blasting was complete, a 35-cm-diameter object was placed on the muck pile, and photographs of the entire muck pile were captured using an appropriate camera.Using blast data and blasted block-size photographs of the complete muck pile, WipFrag software version 3.3 was utilized to calculate the uniformity index of each blast result and the fragmentation size distribution curve.Ten blast rounds were used to determine the effects of powder factors on the fragmentation size distribution using five different powder factor values (0.55 kg/m 3 , 0.7 kg/m 3 , 0.6 kg/m 3 , 0.9 kg/m 3 , and 1.0 kg/m 3 ), while thirty-eight (38) blast rounds were used to develop the powder factor model using burden (B), spacing (S), stemming length (T), hole length (H), B/S, and charge length.Figure 5 shows the mine blast's diagonal drill hole charge pattern.

Fragment size analysis using WipFrag software
Before blasting the rock on-site, all blast design and explosive characteristics were measured.With an appropriate camera, photos of the complete muck pile with a scaling object  in place were recorded immediately after blasting.Images were imported using WipFrag version 3.3.Each image of a blast was outlined using both automatic and manual editing tools.After sifting the delimited images, the fragmentation distribution curve was derived.Figure 6 illustrates the WipFrag meshing images for the 10 blast outcomes utilized for determining the uniformity index.The fragmentation size distribution curve was utilized to compute the uniformity index (n) for each blast result.To establish the relationship between the two parameters and estimate the optimal powder factor for small-scale dolomite blasting, the uniformity index for each blast round was compared with the computed powder factor.Using the outcomes of ten blast rounds, a fifth-order polynomial model was developed to forecast the uniformity index.The model-derived optimal powder factor was tested using a fresh field blasting operation, and the fragmentation size distribution curves and uniformity index were compared to the field result.

Application of artificial neural network approach in predicting blast fragmentation
The artificial neural network (ANN) modeling technique learns from the data samples presented to the system; as explained by Agatonovic-Kustrin and Beresford, it adopts a user-supplied dataset for the adjustment of its weights in a bit to capture the relationship between the historical set of model inputs and the corresponding outputs (Agatonovic-Kustrin and Beresford 2000).The 38 blast rounds recorded at the mine were used to gather six input variables (burden, spacing, stemming length, drill hole depth, burden-to-spacing ratio, and charge length) and one output variable (powder factor) for this study.Figure 7 shows the developed ANN model flow sheet.

Blast fragmentation analysis result
The blasting experiment was carried out at the mine site for ten blast rounds.The blast result images were taken from three different loading levels and analyzed with the Wip-Frag software.The particle size distribution from each blast round was evaluated and presented in Tables 3 and 4. The effect of powder factor on the blast fragmentation was  3 and 4).
The result presented in Table 2 was used to plot the cumulative size distribution curve for the ten blast rounds as shown in Fig. 8.The primary crushing inlet size (red line) was used as the evaluation base for interpreting the particle size distribution result.According to the results shown in Fig. 8, 40% of the blasting rounds considered have small fragments with sizes ranging from 200 to 400 mm (green line).Figure 9 illustrates the relationship between the powder factor and size distribution using the 50% passing size.According to the study graph, powder factor has a negative correlation (R 2 = 0.886) with blast fragmentation mean size, with a decrease in fragment size as powder factor increases (see Fig. 9).The work of Prasad et al. on large diameter drill blasting (165 mm) revealed that the blast particle size of rock is highly dependent on blast design parameters and explosive parameters (Prasad et al. 2017).The negative

Developed ANN model for the prediction of powder factor
The mathematically motivated models proposed in this work were constructed using MAT-LAB software, with six blast design parameters as inputs and powder factor as the target value.As illustrated in Fig. 10a, the model was created using seven neurons, Bayesian regularization, and random data division to minimize prediction error and overfitting.During model development, the mean square error performance evaluator was used to consider the MFX calculation method.
The model converges after 737 epochs, as illustrated in Fig. 10b. Figure 10c and d exhibit the training and testing regression curves for the model.Figure 10a depicts the architecture of the ANN model, including the number of input, neuron, and output layers utilized in the development of the proposed model.Using the model epoch analysis curve depicted in Fig. 10b, the performance of the model was evaluated during each cycle.It was determined that the best model with a 6:7:1 training architecture had the highest coefficient of determination (R 2 = 0.997).As illustrated in Fig. 11, the model was evaluated using ten new blasting results (B-1 to B-10), and the predicted powder factor was compared to the calculated powder factor at the site.With an R 2 of 97.0%, the model performed well in terms of prediction accuracy.In the next section, the prediction error of the model was computed using three model error analysis indices.As shown in Table 5, the optimal model was created with 42 input layer weights.According to Taiwo (2022a) explained approach, the recovered input and output layer weight and parameter bias were to derive the optimal model's mathematical expression.Equations ( 1)-( 8) display the empirical models that have been created.
B burden, S spacing, T stemming length, H drill hole length, B/S burden to spacing ratio (1) PF% = 0.6818 tanh

Model prediction error analysis
Five model prediction analysis techniques were performed: mean square error (MSE), root mean square error (RMSE), and average absolute error (AAE).RMSE is a statistical measurement measures the difference between actual and projected values (Upadhya et al. 2022).The AAE error analysis index computes the absolute similarity between the actual and anticipated values of the proposed model.The three statistical error analysis tools were calculated using RMSE [Eq.( 9)], MSE [Eq.( 10)], AAE [Eq.( 11)], and a-20 index [Eq.( 13)], respectively.In addition, using Eq. ( 12), the value account for (VAF) was computed for all the models to display the difference between the model prediction result and the measured value on-site.
where P and M are the model predicted and measured blast fragmentation efficiency values respectively.m20 represents the datasets with a value of rate original/estimated values between 0.80 and 1.20 as mentioned in Nourian and Moomivand (2020) and n is the number of datasets.The low values of the RSME, AAE, and MSE indices and the high values of a-20 index and VAF (see Table 6) indicate that the predicted result from the proposed ANN model has a close correlation with the measured explosive usage rate.Based on the (7) P 6 = 0.7718tanh (0.3429B + 0.1149S − 0.3268T + 0.0649H + 0.5433B∕S + 0.1128CL + 0.8270) (8) P 7 = − 0.3253tanh (−0.0713B − 0.1291S − 0.3833T − 0.4806H −0.2853B∕S − 0.1002CL + 0.8736) results of the model error analysis, the suggested model is considered good for predicting the small-scale blasting powder factor during the pre-planning stage in order to avoid a trial-and-error optimization strategy and ensure efficient power usage and cost control.

Determination of optimum powder factor using uniformity index
According to Nourian and Moomivand (2020), the uniformity index represents the homogeneity of fragmentation size distribution during a blast.This metric describes the effectiveness of explosive power use and blasting output (Rosa 2020).The Wip-Frag result was used to calculate the uniformity index of ten blast rounds (B-1 to B-10, Table 1).(B-1 to B-10, Table 1).The uniformity index results were compared to the blast powder factor, as illustrated in Fig. 13.The result was utilized to determine the optimal powder factor because, according to Thornton et al. (2002) and Singh et al. (2016), the optimal uniformity index of a blast result is one with a high value.According to the data, a low powder factor results in poor fragmentation that is not uniformly distributed.This study's blast results demonstrated that a powder factor greater than 0.7-0.8kg/m 3 results in a poorer uniformity index.The size distribution curve also corroborated this conclusion, as the blast with a powder factor of 1.0 kg/m 3 generated a greater proportion of larger fragments (see Table 2).According to the results, the 0.7 kg/m 3 powder factor has the highest uniformity index between 1.6 and 1.7.To complement the ANN model applicability, the 4th order polynomial prediction model was developed for the evaluation of the uniformity index (Fig. 14).The model equation is present in Eq. ( 12).
where is the uniformity index, and K is the powder factor in Kg/m 3 .
As depicted in Fig. 15 and Table 7, the developed model was compared to the thirdorder polynomial model utilizing RSME, MSE, VAF, the a-20 index, and AAE model error analysis.Due to the minimal prediction error, the fourth-order polynomial model was deemed more suitable.

Conclusion
The blasting powder factor is an important consideration when planning a drilling and blasting operation because it affects both the total production cost and the efficiency of downstream operations.The following conclusions are drawn from the above study:   1. Powder factors above 0.7-0.8kg/m 3 were shown to result in a lower uniformity index in this study's blast results.It was also shown by the size distribution curve that the blast with powder factor of 1.0 kg/m 3 creates a greater proportion of larger fragments (see Table 2).With a uniformity index between 1.6 and 1.7, the 0.7 kg/m 3 powder factor was found to be the most consistent.2. The plot of powder factor against blast fragmentation mean size demonstrated a negative correlation (R 2 = 0.886) between powder factor and blast fragmentation mean size, with fragment size decreasing as powder factor increases (see Fig. 9).The powder study's negative connection is consistent with the findings of Prasad et al. (2017).The effect of the powder factor on the regularity index of blast fragments was also addressed.3. The results indicate that a powder factor of 0.7-0.9kg/m 3 is the efficiency limit for achieving a satisfactory uniformity index in small-scale dolomite blasting.In addition, it was discovered that the uniformity index (n) increases when the powder factor (kg/m 3 ) rises.A polynomial model of the fourth order was also proposed for the prediction of the uniformity index to make powder factor prediction more flexible and straightforward for practical purposes.Compared to the 3rd-order polynomial model, this model was proven to be more suitable and have a lower prediction error.To increase explosive safety and efficiency in the mine, a MATLAB basic ANN toolbox with a 6-7-1 architecture and a Bayesian regularization training approach were used to develop a suggested ANN model.4. The proposed ANN significantly achieves suitable prediction, with R 2 = 0.997 for the training dataset and 0.97 for the testing and validation datasets.Based on the findings of the RMSE, MSE, VAF, a-20 index, and AAE error analyses, the suggested model has high performance and may be used to improve power utilization and cost control.
The authors' future work will focus on applying numerical modeling techniques such as LS-DYNA, universal discrete element continua (UDEC) and Fast Lagrangian Analysis of Continua (FLAC) in modeling the effect of geological properties and rock chemical composition on explosive efficiency.
(2022) 2022 LMR, NLMR, RES LMR = 0.759, NLMR = 0.801, RES = 0.931 the development of empirical models for the prediction of blast utilized powder factor and fragment uniformity index based on blast controllable parameters is essential in order to minimize explosive usage and improve blast material size distribution during blasting (Hilson 2002; Lahiri-Dutt 2003).Artificial neural networks (ANNs) are regarded as one of the most effective techniques for addressing complicated problems.Several researchers have used the ANN system to predict blast-induced rock fragmentation, rock burst, airblast, and ground vibration as the application of artificial neural networks in mining continues to increase (Dehghani and Ataee-Pour 2011; Trivedi et al. 2014; Al-Bakri and Sazid 2021; Afradi and Ebrahimabadi 2020; Gidiagba et al. 2022; Dey et al. 2022).ANN has also found popularity in the mining and civil engineering industries.Maulenkamp and Grima used a neural network to estimate the UCS from hardness tests on rock samples based on input characteristics including hardness, porosity, density, grain size, and rock type (Meulenkamp and Alvarez Grima 1999).To assess the viability of this method, the network's outputs were compared to predictions derived from conventional statistical relationships.Leu et al. created a Levenberg-Marquardt trained ANN prediction model for uniaxial compressive strength predictions utilizing a dataset of 194 rock sample records, ranging from weak sandstones to extremely strong granodiorites (Leu et al. 2001).The results of the artificial neural network (ANN) model were closer to the actual values.Tawadrous used a backpropagation neural network to predict the burden and spacing of the blast pattern using input parameters such as rock type, stratification, blast hole diameter, bench height, type of explosive, priming position, powder factor, and fragmentation size(Tawadrous 2006).He trained the network using 43 case histories collected from the various literatures and validated it with 16 cases from operational quarries.He found a very high correlation between the prediction of burden and spacing by ANN.Rezaei et al. developed  an ANN model to predict the burden in the blasting operation of the Mouteh gold mine, using the geo-mechanical properties of rocks as input parameters.Blastability index (BI), rock quality designation (RQD), unconfined compressive strength (UCS), density, and cohesive strength were among the input parameters used(Rezaei et al. 2012).It was observed that the ANN's prediction capability is better than that of the MVRA.Further, a sensitivity

Fig
Fig. 2 A flow chart of the study objectives

Fig. 3
Fig. 3 Topographic map of the mine formation

Fig. 5
Fig. 5 General layout of the blast hole section

Fig. 10
Fig. 9 Relationship between powder factor and mean size fragmentation

Fig
Fig. 11 Relationship between the actual calculated powder factor and the predicted

Fig
Fig. 15 Error analysis result of the proposed model as compared with 3rd order polynomial model

Table 1
Application of soft computing models related to this study FIS fuzzy inference system, ANN artificial neural network, ANFIS adaptive neuro-fuzzy inference system, LMR linear multiple regression, ABC artificial bee colony, RES rock engineering system, NLMR non-linear multiple regression, FA firefly algorithm, CSO cat search optimization, SVR support vector regression, XGBoost eXtreme gradient boosting, RF random forest, KNN K-Nearest Neighbors, GEP gene expression programming Rezaei et al. (2012)23di 2020)cial neural networks (ANNs)for predicting backbreak in the blasting operation of the Chadormalu iron mine (Iran)(Monjezi et al. 2013).After trying various hidden layers and neurons, the network with topology 10-7-7-1 was deemed optimal.The ANN model proved superior to the conventional regression analysis using mean square error (MSE), variance account for (VAF), and coefficient of determination (R2) as the means of comparison.Combining artificial neural networks (ANN), support vector machines (SVM), and gene expression programming (GEP) modeling techniques, Afradi and Ebrahimabadi achieved realistic models for predicting the tunnel boring machine penetration rate in Iranian water conveyance tunneling(Afradi and Ebrahimabadi 2020).The study demonstrates that machine learning models can be used to anticipate the TBM penetration rate in the Chamshir tunnel.Armaghani et al. evaluated ground vibration caused by Shi Ban Gou tunnel blasting using two neuro-based metaheuristic approaches (PSO and ICA)(Armaghani et al. 2023).The work of Gidiagba et al. concluded that the ANN model development technique is an appropriate method for resolving the problem of uncertainty in various mining operations(Gidiagba et al. 2022).In addition,Sayadi et al. (2014)andRezaei et al. (2012)revealed that artificial neural network (ANN) techniques are an effective method for tackling mining, geosciences, and engineering challenges.

Table 3
Fragmentation size distribution analysis result from WipFrag for Blast 1-5

Table 5
Optimum model input weights

Table 7
Prediction result from the two developed polynomial models