Prediction of fly-rock during boulder blasting on infrastructure slopes using CART technique

Abstract Boulder blasting is a different process from conventional bench blasting. Fly-rock produced in boulder blasting is a major safety concern due to the presence of 360° free-face which may result into excessive throw of the fragments radially up to 900 m distance causing accidents. Many researchers have attempted to predict the fly-rock using empirical and soft computing tools in bench blasting. But, there is paucity of literature to predict the extent of fly-rock in boulder blasting. Machine learning techniques are frequently used in bench blasting to predict ground vibrations, air overpressure, fly-rocks, but it has been rarely used in boulder blasting. In this study, an attempt has been made to use Classification and Regression Trees (CART) technique to predict the fly-rock distance in boulder blasting. Multiple linear regression (MLR) technique has been used to compare the results obtained by the CART technique. Sixty-one boulder blasting events were monitored while excavating the accident-prone slope areas of Konkan Railways. The performance of the developed models using both the techniques has been evaluated using the coefficients of determination (R 2) and root-mean-square error (RSME) values. The results indicate that CART model (R 2 = 0.9555 and RMSE = 1.141) provides better output than MLR model. This paper suggests the use of CART technique in boulder blasting, which will be useful in execution at sensitive locations to predict and control the fly-rock distance.


Introduction
reported that a cut-slope created 20-30 years back should be stabilized considering poor construction practices and continuous degradation due to weathering. Rockfall or landslide along railways or highways in the hilly terrain is a frequent phenomenon. In one of the scientific study, Mignelli et al. (2014) reported that the rock slopes situated aside many kilometres of roads are prone to rockfalls and need proper mitigation Similar rockfall problems are also frequently observed along hundreds of kilometres of slopes aside railways and roadways in India which have caused several accidents and traffic delays (Mid Day News 2014; Ansari et al. 2015;Deccan Chronicle News 2019). Also, lots of rock excavations are in progress for upgrading infrastructures in the vicinity of existing railways and roadways. The rock excavation especially where isolated boulders are found in the slope mass need, safe removal considering the safety of railway tracks, overhead electric lines, signal posts, roadways and residential structures.
Available techniques such as mechanical breaking (rock-breaker, impact hammer, drop ball, high-pressure water-jet), chemical breaking and blasting with explosives (pop shooting, plaster shooting) are being used to fragment oversized boulders (Dick et al. 1983;Kristin and Maras 1994;Murray et al. 1994;Jimeno et al. 1995). In mechanical breaking technique, the transportation of rock-breaker in remote locations are not feasible. Further, it is also difficult to use machineries with limited manoeuvrable space thereby creating chances of dislodgement of the unstable slope. In chemical breaking technique, the use of chemicals for fragmentation of boulders in a large scale is very difficult. The untimely dislodgment of fragments towards the tracks, roads, etc. may also cause accidents. However, blasting with explosives to break the boulders is often used in hilly terrain where the use of other techniques are not feasible (Sawmliana et al. 2018; Deccan Chronicle News 2019; Bhagat et al. 2020b).
During the process of boulder breaking by explosives and blasting, the possibility of uncontrolled fly-rocks is very high due to the presence of multiple free faces. A layout of the bench and boulder blasting is illustrated in Figure 1. Factors affecting the generation of fly-rock in bench blasting are broadly categorized into controllable and uncontrollable groups (Bhandari, 1997;Bajpayee et al. 2004;Khandelwal and Monjezi 2013). In controllable group, some influencing parameters are borehole diameter and depth, sub-grade drilling, inclination of a borehole, burden, spacing, number of rows, explosive quantity per hole and per delay, liner charge concentration, deck-charging, specific charge, total charge, delay in between holes and explosive properties (strength, density, detonation velocity, wrapped or unwrapped form) (Bhandari, 1997;Khandelwal and Monjezi 2013;Trivedi et al. 2014;Armaghani et al. 2020). The uncontrollable parameters group consist of rock mass strength (compressive and tensile strength, density of rockmass) and geological properties (dip, strike, joint-spacing, soft layer in intermixed strata, rock quality designation, rock mass rating and weathering grade) (Fletcher and D'Andrea 1986;Bajpayee et al. 2004;Han et al. 2020). Parameters affecting the generation of fly-rock in boulder blasting are mainly controllable except the strength and density of rock mass.
The mechanics of fly-rock generation can be explained by mainly three theories (i.e. face burst, cratering and rifling) (Bhandari, 1997;Zhou et al. 2019). Inadequate burden and soft geological formation lead to face burst (Little and Blair 2010; whereas, low stemming to burden or hole diameter ratio and incompetent stemming material are responsible for cratering and rifling respectively (Lundborg et al. 1975;Hasanipanah et al. 2018). Further, cratering and rifling can generate fly-rock in any direction whereas, face burst can generate in free face direction only ). In the case of boulder blasting, the direction of face burst is undefined due to uneven burden and multiple free faces.  Empirical formulae primarily developed for bench blasting to predict fly-rock distance are given in Table 1 and some of them may be implemented in boulder blasting as well. Lundborg (1981) developed a formula based on hole diameter and specific charge to predict fly-rock and throw (Table 1). This formula requires a specific charge of more than 0.2 kg/m 3 for prediction, whereas in boulder blasting, the specific charge is normally lower than this threshold value. Formula developed by Gupta et al. (1988) uses stemming to burden ratio only (Table 1). Richard and Moore (2005) have also developed formulae for estimation of fly-rock due to the face burst, cratering and stemming ejection using 102 mm borehole diameter (Table 1). The aforesaid formulae use limited parameters and their predictions are also not so significant. Other formulae shown in Table 1 cannot be used in boulder blasting as they need at least one parameter which is not related to boulder blasting.
The review of blasting parameters influencing fly-rock generation reveals that the controllable parameters like sub-grade drilling, spacing, number of rows, delay between holes and row, maximum charge per delay and uncontrollable geological parameters do not play any major role in boulder blasting. Further, in many cases of boulder blasting, single or multiple holes blasting is conducted instantaneously. Hence, empirical formulae and soft computing tools developed for predicting fly-rock in bench blasting cannot be used directly in boulder blasting. Borehole diameter, density of rock, volume of the boulder, hole depth, burden, specific drilling density, number of holes, charge per hole, stemming length, total charge and specific charge are the major parameters which affect fly-rock generation in boulder blasting. It is also clear from the literature review that the large hole diameters are having higher probability of fly-rock to a greater distance (Mishra and Rout 2012;Mohamad et al. 2012;Koopialipoor et al. 2019). Due to the occurrence of frequent accidents in Indian mines, the Directorate General of Mine Safety (DGMS) have prohibited the use of large hole diameters in boulder blasting to prevent the chances of accidents (Kumar 2020). DGMS have recommended only 32 mm hole diameter with small quantity of explosive (DGMS (Tech) Circular No. 14 of 2020). The quantification of explosive for proper boulder breakage is a significant factor to avoid any fly-rock and hence; it needs careful attention while designing boulder blasting. Mishra and Rout (2012) reported an accident due to fly-rocks at 550 m distance while blasting a boulder having the dimension of 3 m Â 1.5 m Â 1.6 m. Two holes of 45 mm diameter and depths of 1.5 m each were drilled in the boulder and charged with 1.56 kg of explosive per hole. The specific charge used for breaking the boulder was 0.43 kg/m 3 . Various studies suggest that a specific charge of 0.08-0.15 kg/m 3 is required for breaking the open lying boulders whereas for a partially buried boulder, 0.15-0.2 kg/m 3 is optimum (Jimeno et al. 1995;Heinio 1999). Jimeno et al. (1995) also added that the specific charge of 0.2 kg/m 3 or more will be required to get any throw during the bench blasting. Bhagat et al. (2020a) also reported that the specific charge values of 0.04-0.1 kg/m 3 was sufficient to break the rock in small blast geometry without causing throw. The possibility and extent of fly-rock with these specific charges are not revealed in the above studies.
Many researchers have used different soft computing tools in their research work to predict the fly-rock distance in bench blasting. But, in case of boulder blasting, not

Combination of Fuzzy Delphi Method and ANN-based Models
For bench blasting only much studies have been conducted by the researchers throughout the globe. However, Mohamad et al. (2012) have conducted a study of sixteen boulder blasting in mines using soft computing tool. They developed an ANN model using eight input parameters (specific charge, charge length, stemming, hole diameter, hole depth, burden, hole angle and explosive per hole) and found that specific charge, charge length, stemming are the most significant and relevant parameters. The coefficient of correlation in ANN method was 0.92. In the study diameter of drill holes were 89 mm whereas the distance of predicted fly-rock ranged between 160 and 240 m. A brief summary with selected input parameters, soft computing tools and limitations have been presented in Table 2 which reveals that there is no readily available tool that can limit the extent of fly-rock within 20 m in bench or boulder blasting. Further, there is a lack of research works which have utilized the empirical models and softcomputing techniques for predicting the fly-rock during boulder blasting with higher level of accuracy.  presented prediction of fly-rock in bench blasting at Ulu Tiram quarry Malaysia using regression tree method and compared the results with multiple linear regression (MLR) ( Table 2). They suggested that the regression tree is a simple method compared to a complicated technique like ANN in terms of classification, recognition, and estimation. They also displayed that regression tree can forecast better than ANN and conventional statistical methods. Rana et al. (2020) reported that the decision tree-based Classification and Regression Trees (CART) model can be effectively used to control blasting nuisance such as ground vibration. Further, Murlidhar et al. (2021) defined decision tree as a 'white box' technique that develop direct graphical structures to explain the relationship between variables more easily than other machine learning methods. They recommended the use of decision tree technique for the problems having numerous variables acting reciprocally and in a nonlinear manner. Further, MLR has also been used by many researchers for the prediction of blasting nuisances in rock blasting Hudaverdi and Akyildiz 2019). Both the techniques are very powerful and have wide applicability with versatility.
In this paper, an attempt has been made to predict fly-rock distance in boulder blasting using the decision tree-based CART technique which is easy to implement in field by practicing engineers. The input parameters were varied in multiple steps to identify the most influencing parameters to predict the fly-rock distance using statistical tests and sensitivity analysis. Three models of MLR (consisting of three different sets of inputs) have been developed and their performance indicators have been compared with the corresponding three CART models. The performance indices of three CART models have been ranked and their sensitivity analysis has also been carried out to select the best CART model. Sixty-one experiments were carried out at infrastructure slope sites of the Konkan Railway Corporation (KRC) in India to develop the models. The outcome of this study has provided a handy and practical tool to predict the fly-rock distance in many similar cases of unstable slope conditions. The developed model can also be used to resolve similar problems of fly-rock at mining and civil construction sites as well as for delineating the safety distances while conducting boulder blasting.

Site descriptions
The 741 km long KRC route passing through the Western Ghats of India (from Roha near Mumbai, Maharashtra to Thokur, Karnataka) is divided into two sections (Ratnagiri and Karwar). The tracks of KRC were laid in between 1993 and 1997 by excavating the upland region of Deccan Volcanic Provinces, which is considered a vulnerable region for landslide and rockfall. There are 564 rock and soil-mixed boulder cuttings (cumulative length À226.71 km) along the railway route. The dimension after excavating the rock mass of cuttings varies from 10 to 50 m in height, and 50-1000 m in length with slope angles varying between sub-verticals to verticals. The slope mass of cuttings mainly consists of Basalt, Breccia overlaid by lateritic soil or soil-mixed boulders in the Ratnagiri section. Two sets of vertical joints striking NW-SE, NE-SW and horizontal joints are commonly found. In addition to the above, random joints as well as natural and blast-induced fractures are also visible in most cuttings. A red bole soft layer (300-1000 mm thick) is sandwiched between two basaltic formations throughout the cuttings at Ratnagiri section, thereby allowing water percolation during the Indian monsoon. This soft layer is also known as a potential spot for slope failure or rockfall. Granite and Granitoide rocks are common in the Karwar section. Kinematic analysis of geological discontinuities of the slope under investigation before flattening revealed the higher probability of wedge, planar and toppling failures (Bhagat et al. 2020a). KRC observed more than 949 cases of rockfall and soil slippage including few train accidents between 1998 and 2011 (Garg et al. 2013). The heavy precipitation during southwest monsoon (more than 3000 mm annual precipitation), differential weathering due to soft and hard strata are some of the main cause for rockfall and slope failures.
Different sensitive structures (railway track, optical fibre cable, high tension transmission line and signal posts) were located within 2-5 m distance of slopes and in some cases, public residential structures were also located within 50 m distance. Bhandari (1997) has explained the methodology of boulder blasting. He stated that the depth of hole to break the boulder should be in the range of 0.25-0.5 times the thickness of the boulder. He also suggested that hole should be stemmed properly and burden should not be too low in any direction otherwise results would be poor breakage. Further, in case of large sized boulders, spacing of holes should be 0.5-0.9 times the thickness of the boulder with drilling density in the range of 0.2-1.0 m/m 3 and specific charge varying between 0.1 and 0.3 kg/m 3 . The detailed review of different parameters influencing boulder blasting clearly indicated that the geological aspects and blast design parameters for boulder blasting are completely different from bench blasting. In bench blasting, the geological parameters, delay between the holes, scattering in delays, undercut and misfire plays important role apart from the established blast design parameters. However, in boulder blasting, no delay is required between the holes. The geological parameters also do not play much role in boulder blasting except for the strength of rock and its density. The density of the rockmass plays a significant role in flying of fragments. The lighter fragments may travel a long distance due to attainment of momentum during blasting operations (Lundborg 1981). Based on the review of research works (Table 1)

Methodology used in data collection
Boreholes were drilled in the centre of boulders and depths of borehole were kept between 1 = 4 and 3 = 4 of the height of boulder. The directions of blast-holes were kept vertical for restricting the fly-rock and extent of throw. The emulsion cartridge explosives of 25 mm diameter were used to charge the 34 mm diameter boreholes. The velocity of detonation of explosive was 4000 ± 200 m/s and density was 1150 ± 50 kg/m 3 . Detonating cord (D-cord, 10 g/m of PETN) and electric detonators were used to initiate the explosives within borehole. Drill cuttings were used as stemming material. The different input parameters of boulder blasting were carefully recorded during the trial blasts. The estimation of boulder's size was carried out using levelling staff and measuring tape. Fly-rock distances in vertical and horizontal directions were measured using a high-speed camera (250 frames per second). The recorded videos were further analyzed with Kinovea-0.8.15 software to estimate the distance of fragments thrown (fragment size > 5 cm) by pre-calibrating the boulder size in software ( Figure  2). The fly-rock distances were also measured and verified manually using a measuring tape. The extent of fragments thrown and cracks developed during the experiment are shown in Figure 3. Flow-chart elaborating the study and model development is depicted in Figure 4.

Statistical analysis of compiled dataset
Statistical analysis is a process to draw inferences from the collected data samples. Prior to application of any advanced method for data analysis, mainly two types of statistical analysis viz. descriptive and inference are carried out to understand the data, identify the trends, locate the anomalies and visualize the raw data. Descriptive statistics delivers a data summary in the form of minimum, maximum, mean, median, mode, standard deviations and other information of a data sample. Hence, it enables us to present the data in a more logically with simplicity. Whereas, inferential statistics is carried out to study the data even further by making a hypothesis leading to rational decisions about the reality of the effects observed. Ghasemi and Zahediasl (2012) reported that in general any advanced analysis methods like correlation, multiple regression, t-tests and analysis of variance (namely parametric tests) are carried out by considering, data following normal distribution. They further reported that if the sample size is greater than 30 or 40, the violation of normality assumption will not cause any major problem. With this assumption, we can use parametric procedures even if data are not normal. Moreover, for visual inspection of data distribution to judge the distribution readily, researchers are often using boxplot, frequency distribution, probability-probability plot and quantile-quantile plot to check the normality and locate outliers. To display boxplots of sixty-one dataset consisting of eleven input and one output parameters, XLSTAT (Version- 2021.2.1) software has been used ( Figure 5). The boxplots revealed that some parameters are having outliers which are atypical events but they were used in the analysis. Further, the correlation matrix of all the 61 datasets has been established between the inputs and output (Table 3). The established correlation coefficients clearly indicates that there is negative correlation of fly-rock distance with rock density (À0.41) and burden (À0.27). However, the correlation is positive (>0.27) with specific charge, total charge, charge per hole, specific drilling density, number of holes and volume of rock. Rest other parameters such as hole depth, stemming to burden ratio and stemming length are having lower correlation coefficient values (< ±0.17).

Prediction of fly-rock distance
Two types of predictive models, i.e. MLR and CART, have been developed to predict fly-rock distance. As discussed in the previous sections, eleven input parameters have been used to estimate the fly-rock distance. Forty-nine datasets (80% of total datasets) have been randomly selected to train the models whereas the remaining 12 datasets (20%) were selected to test the model's performance and ability ).

MLR
The MLR model has been widely used by many researchers in mining for predicting the blasting-induced nuisances (Tables 1 and 2). The dependent variable and one or more independent variables can be correlated using MLR. This technique is based on minimizing the end differences between predicted and measured output values. An MLR model, in terms of the independent variables, can be represented as: where 'Y' is the predicted variable, 'a 0 ' is intercept, 'a i ' (i ¼ 1, 2, … , n) are the coefficients up to ith input parameter, 'x i ' (i ¼ 1, 2, … , n) are input parameters up to ith term and 'e' is the error associated with the prediction. To develop the MLR model with highly influencing inputs, the different combinations of eleven inputs were examined in multiple steps ) considering the results of boxplots and correlation. For testing the significance of models analysis of variance, F-test, Shapiro-Wilk test, R 2 , root-mean-square error (RSME) have been considered (Table 4). The significance value of calculated F-test of each model is lower than 0.05, indicating null hypothesis of no linear relationship amongst selected inputs and output, is rejected (Hudaverdi and Akyildiz 2019). Further, normality test of the residuals of a MLR models using Shapiro-Wilk test as suggested by Ghasemi and Zahediasl (2012) has also been performed. The computed p-value lower than the significance level ¼ 0.05 is taken to reject the null hypothesis (i.e. the residuals follow a normal distribution) and vice versa to accept the alternative hypothesis. The computed P-value obtained from Shapiro-Wilk test of developed MLR models is greater than significance value of 0.05, thus, indicating that one cannot reject the Null hypothesis for the developed models. Hence, all the three sets of inputs of developed MLR models follow normal distribution and can be used to predict the fly-rock distance. A higher value of R 2 of each model which is more than 90% for training dataset indicates higher predicting probability . Therefore, all the three developed models with varying sets of inputs can be further used for the development of predictive models for MLR and CART tools.
Based on the statistical information depicted in Table 4, model 2 exhibited overall higher performance indices compared to other MLR models. Hence, model 2 has been selected as predictive model. Statistical information of training and testing dataset of selected model are given in Table 5. The more statistical details such as regression coefficients, standard error, t-value and p-value of inputs of developed model 2 are given in where D in kg/m 3 , B, ST in m, SD, in m/m 3 , CPH in kg and SC in kg/m 3 , respectively. The relationship between predicted and actual fly-rock distance for training and testing dataset using the predictive MLR model 2 on 1:1 slope line is shown in Figure  6. Here, the R 2 for training and testing dataset are 0.9114 and 0.7938 as well as RMSE for training and testing dataset are 1.7932 and 4.4868 respectively.

CART technique
The most common technique of classification and prediction is the decision tree. The technique of CART was initially proposed by Breiman et al. (1984) and is one of the   Figure 6. Relationship between measured and predicted fly-rock distance for MLR model 2.
most preferred decision tree algorithms. The decision tree is an inverted graphical tree representing the regression results (Figure 7). The most influencing parameter is placed on the top 'root node' with it's probable values. The root node further branches into interior nodes using specific tests. Further, the data split into leaf nodes according to the tests. The 'test' compares the predicted value to a predefined constant using 'if and then' condition for splitting. A stopping criterion is used for terminating tree development. The value of the dependent variable can be forecasted using a single node or with a combination of nodes. Nevertheless, the data can be classified simultaneously by analysing the superiority of nodes. The XLSTAT software (version 2021.2.1) has been used to develop the CART model to predict fly-rock distance. The same forty-nine training dataset and sets of inputs, used for developing the three MLR models have been used again to develop three CART models. Each set of inputs have been used to calibrate the CART model and the same twelve dataset has been used to test the performance capability of the model. Three main parameters that needed to be tuned are minimum parent size, minimum son size, and maximum tree depth. The minimum parent size and maximum tree depth were varied between 2 to 30 whereas, a minimum number of son size was fixed at 2 for obtaining at least two instances representing the fly-rock distance at the leaf node. The complexity parameter was fixed at 0.0001. A grid search method was performed by varying the minimum parent size and maximum tree depth to get the optimal tree. A mean-square-error statistical index has been used to enable the performance of each grown tree. Three different CART models have been developed with different tree depths and parent size from each set ( Table 7). The performance indices of training and testing dataset of developed CART models 2 and 3 exhibit higher accuracy level with equal overall ranking. Hence, both models can be used as predictive model. However, application of CART model 2 seems to have   better option as it uses an additional parameter, i.e. ST/B ratio. This ratio is vital in predicting the fly-rock distance as reported by Gupta et al. (1988). Figure 8 depicts the best CART model's tree structure obtained from Model 2 of which 'if and then' rule is constructed. The 'if and then' rule obtained from the said decision tree is given in Table 8. Further, Table 8 reveal that nodes 3 , 8, 11, 20, 21 and 36-39 are leaf nodes and there is no additional information left to create new nodes. The application of this developed CART model is easy to predict the fly-rock distance of boulder subjected to blast. For example, at node 39, the predicted fly-rock distance is 0.9 m in 6.1% of cases if, a charge per hole is greater than 0.056 kg, specific charge is varying between 0.03 and 0.056 kg/m 3 and density of rock is greater than 2632.5 kg/m 3 . The relevant outcomes of the CART model are discussed in results and discussion section.

Sensitivity analysis of the proposed CART model
Sensitivity analysis has been carried out to know each input parameter's relative influences, on the prediction of fly-rock results obtained by the CART model. This analysis helped in finding each input parameter contribution in the CART modelling process. For this purpose, a relevancy factor (RF) has been calculated for each of five input parameters using Equation (3) (Murlidhar et al. 2021).  where I i,k and I k represent, the ith and mean values of the kth input variable for n data samples respectively and P i and P show the ith and mean values of the predicted FD for n data samples respectively. Higher RF value shows that the input has higher impact on the prediction of the output value. The RF values for the inputs of the CART models 2 and 3 are shown in Figure 9. From the figure it is clear that the most influential parameters for fly-rock distance assessment is the specific charge for model 2. This result is in agreement with the previous researches carried out by various researchers (Mohamad et al. 2012;Armaghani et al. 2014). The effect of rock density on fly-rock is negative which implies that the denser rock would cover less distance (Lundborg 1981). Further, specific drill density is rarely used in prediction of fly-rock in bench blasting but has a significant role in boulder blasting. It is also reported by Bhandari (1997). The charge per hole is having greater influences on flyrock distance and an increase in the explosive quantity per hole would create more fly-rocks (Mishra and Rout 2012). The stemming to burden ratio is established fact which greatly influences the fly-rocks scattering (Gupta et al. 1988). Aforesaid facts have also been experienced by the authors during the trail blasts.

Results and discussion
Empirical formulae developed for mostly predicting fly-rock in bench blasting, are not applicable for boulder blasting (Table 1). Further, review of past research also indicates that there is lack of proper soft computing techniques which can be directly used in the fly-rock assessment in boulder blasting (Table 2). It is also difficult to trace which model would be the best for considering the field applicability. In several instances, various soft computing tools have been successfully used in solving mining and geotechnical problems. Therefore, the benefits of the prevailing soft computing techniques such as CART and MLR have been used in this study for prediction of fly-rocks in boulder blasting. The different blast design parameters of sixty-one boulder blasting were collected and analyzed statistically. The dataset for training and testing have been selected randomly and divided into 80 and 20% ratio respectively Initially, boxplots, analysis of variances, F-test, Shapiro-Wilk test and multiple regressions have been used to decide the group of most influencing inputs to develop models. The best MLR model 2 was developed using five inputs (D, SD, ST/B, CPH and SC) having high performance indices (R 2 ¼ 0.9114 for training and R 2 ¼ 0.7938 for testing). Hence, Equation (2) can be used as handy formula to predict fly-rock in boulder blasting. The same training and testing dataset of three MLR models have also been used to develop the three CART model. The best CART model from each group of data has been obtained through varying the parent size and maximum tree depth. The R 2 and RMSE have been used to evaluate the performance of the best model. The performance indices of CART model 2 and model 3 gave higher accuracy and their overall ranking are also equal (Table 7). This shows that any of models, either 2 or 3, can be used as predictive model. Further, model 2 is having an addition input parameter, i.e. ST/B, which is known for its detrimental effect on fly-rock and inclusion of this parameter would strengthen the model. Nevertheless, in relevancy factor analysis of developed CART models 2 and 3, model 2 showed slightly better results apart from additional relevancy factor (0.384) of ST/B ratio (Figure 9). Hence, CART model 2 has been selected as predictive model. The relationship between measured and predicted fly-rock distances for the CART model 2 is shown in Figure 10. The performance indices of testing datasets of superior MLR model 2 (R 2 ¼ 0.7932, RMSE ¼ 4.868) and the best CART Model 2 (R 2 ¼ 0.9555, RMSE ¼ 1.141) clearly indicate that CART model 2 is superior to MLR model for predicting the fly-rock distances. The comparison between measured and predicted fly-rock distances by CART model 2 and MLR model 2 is illustrated in Figure 11. This figure also clearly indicates the prediction by CART model 2 is very closer to the actual fly-rock distance. The results of sensitivity analysis also show that the relevancies of used input parameters in prediction of fly-rock distance are following the established research findings.

Limitations and future scope of work
The prediction of fly-rock distance in boulder blasting is very important to define safety zone for the protection of nearby structures from unwanted incidents. For this, it requires a clear understanding of the subject and complete checks on unforeseen parameters (experience of the blasting crew, inferior quality of explosive and accessories). Incorporation of all these parameters in any predictive model is not feasible; however, an attempt should be made to perform the operation easier with utmost safety. The empirical MLR equation and CART model developed in the study are limited for boulder blasting using a 34 mm diameter borehole. Further, this study does not address dynamic strength property of rockmass as well as fragmentation analysis. Hence, in future to have better results these parameters can be incorporated in the model using hybrid intelligence techniques.

Conclusions
The concern of uncontrolled fly-rock is the foremost hurdle in boulder blasting. Literature reviews on boulder blasting revealed a need for suitable technique to mitigate the problem of boulder handling along railways and roadways situated in hilly areas. The developed technique can be further implemented at open-pit mines and civil construction projects. The paper describes the soft computing approach in the form of CART and MLR models for mitigating fly-rock during boulder blasting. For the accurate and precise prediction of fly-rock distance, sixty-one boulder blasting were conducted along the Indian KRC railway route and associated eleven input parameters were recorded. Statistical analyses have been carried out to evaluate the fitness of dataset. For the development of models using CART and MLR techniques, out of 61 datasets, 49 were used to train the models and 12 for testing the models. Multiple regressions and relevant statistical tests have been carried out to select three sets of input parameters for developing three MLR and three CART models for comparison. Sensitivity analysis has been carried out to find the relevancy of selected Figure 11. Comparison of measured and predicted fly-rock distances by best CART 2 and MLR 2.
inputs in model predictability. The CART model 2 and MLR model 2 were found as the best models, each consisting of five inputs (i.e. rock density, specific drill density, charge per hole, stemming to burden ratio and specific charge). The R 2 and RMSE values of testing dataset of CART model 2 are 0.9555 and 1.141 whereas for the MLR model, they are 0.7938 and 4.868 respectively. Therefore, the CART model 2 is proved to be the better model compared to MLR for predicting fly-rock distance. The relevancy factor analysis of inputs of the best model revealed that the most contributing parameters of boulder blasting in chronological order are specific charge (0.935), specific drill density (0.847), charge per hole (0.583), stemming to burden ratio (0.383) and rock density (À0.243). CART model 2 showed promising results in the study and has great potential to predict the fly-rock for deciding the safety zone, protecting the railways, roadways and other structures situated in the proximity of boulders to be fragmented.