Genetic programming and gene expression programming for flyrock assessment due to mine blasting
Introduction
Blasting, which is the controlled use of the explosive material, is considered as a common technique for rock mass removal.[1], [2] Conducting a desired blasting operation may provide several beneficial factors such as overall cost reduction, and improving the efficiency of drilling operation.[1], [3] According to several scholars, more than 85% of blasting energy is dissipated through the ground and can create some undesirable environmental effects on the surrounding areas e.g. ground vibration, air-overpressure, flyrock and back-break.[4], [5], [6], [7], [8], [9], [10] Among them, flyrock is considered to be the main cause of human injuries, fatalities and structural damage.[11], [12] Any unexpected throw or movement of the fragmented rocks due to excessive force of the explosive material is defined as flyrock.[1], [13] In flyrock mechanism, there is an important relationship among mechanical strength of the rock mass, explosive energy distribution, and charge confinement.[14], [15], [16] According to Bajpayee et al.15 and Roy,17 any mismatch between these factors may create flyrock phenomenon. There are three mechanisms for generation of flyrock namely cratering, rifling and face bursting which are described briefly in the following paragraph.[5], [18]
When the ratio of stemming length to diameter of blast-hole is too small, cratering will happen. In this situation, flyrock can be projected in any direction from a crater at the hole collar. If the utilized stemming material is inefficient or is absent, rifling will be occur. During rifling, gases from blast can stream up the blast-hole along the path with the least resistance resulting in stemming ejection and sometimes ejection of the collar rock as harmful flyrock.5 Face bursting happens when explosive material converges major geological structures or when is situated in close closeness of fragile planes. In this circumstance, flyrock can be created on account of the high-weight gasses of the touchy plane along the weaker planes.
Taking into account past examinations, flyrock is affected by controllable and uncontrollable elements. Controllable variables can be changed by the impacting design, while uncontrollable components are normal and cannot be reformed. Insufficient burden and spacing, inaccurate drilling and inadequate stemming are some examples of controllable factors on flyrock.[1], [5], [15] Moreover, uncertain geological and geotechnical conditions in the rock mass are considered as the most effective uncontrollable factors on flyrock.
Several empirical models have been proposed for flyrock prediction.[22], [23], [24], [25] Lundborg et al.22 developed an empirical equation based on hole and rock diameters which are demonstrated below:where D is the hole diameter in inches, Lm is the maximum rock projection in meter, and Tb is the size of the fragmented rock in meter. Another empirical equation was suggested based on stemming length and burden in the study conducted by Gupta24 for flyrock and the predictions are as follows:where d is the distance of thrown rock in meter and L is the ratio of stemming length to burden. In another study, McKenzie26 used density, hole diameter, explosive density, and confinement state to propose two empirical equations for prediction of flyrock and particle (rock) size. A new empirical formula for flyrock estimation was developed by Trivedi et al.27 as follows:where q is specific charge, is linear charge concentration, is unconfined compressive strength, B is burden, ST is stemming length, and RQD is Rock Quality Designation. In another study, Ghasemi et al.5 performed dimensional analysis on some blasting data and then proposed an equation for predicting flyrock distance. The equation is formulated as displayed below:where S is spacing, B is burden, St is stemming, H is hole length, P is powder factor, D is the diameter of the blast-hole, and Q is the mean charge per blast-hole. Two empirical formulas (power functions) based on powder factor and maximum charge per delay for predicting flyrock were suggested by Marto et al.28 Moreover, Jahed Armaghani et al.29 suggested an empirical graph for prediction of flyrock resulting from quarry blasting. They mentioned that maximum charge per delay and powder factor are the two most influential parameters on flyrock distance. As a result, the capacity of performance prediction of the empirical models is generally poor.2 This is may be due to the complex nature of the flyrock problem.30 In addition, prediction of flyrock with a suitable degree of accuracy is an essential task to investigate blast safety area. Therefore, there is a need to propose more accurate models/techniques for predicting flyrock distance compared to the previous developed models.
Apart from empirical models, Monte Carlo (MC) technique has been used to predict the probability of flyrock distance risk (e.g.).[18], [31], [32] In this technique, by assigning a distribution function to each model input (or the most effective factors effecting flyrock), relative probability of flyrock distance can be simulated. Little and Blair18 conducted a research developing a new mechanistic MC model for flyrock simulation. Their flyrock range was in the range of 0–600 m. They concluded that there is only one in a million chance that the flyrock distance will exceed 640 m. In another study of MC, considering a dimensional analysis, Ghasemi et al.5 simulated flyrock results, collected from Sungun copper mine, Iran. A difference of about 9 m between the mean value of measured and the predicted flyrock were obtained by Ghasemi et al.5 (measured, 72.43 m, simulated, 81.44 m). As a result, the main limitation of MC is that does not rely on a historical database to determine input distributions.18
Moreover, many attempts have been made for prediction of flyrock utilizing soft computing techniques. Rezaei et al.30 developed a fuzzy interface system (FIS) model to predict flyrock induced by blasting works in Gol-E-Gohar iron mine, Iran. Ghasemi et al.33 examined and proposed two well-informed systems including artificial neural network (ANN) and FIS to predict flyrock distance. They concluded that both of the proposed systems are applicable for flyrock prediction. Furthermore, three new hybrid models i.e., imperialist competitive algorithm (ICA)-ANN, particle swarm optimization (PSO)-ANN and genetic algorithm (GA)-ANN were introduced by Marto et al.,28 Jahed Armaghani et al.2 and Monjezi et al.,34 respectively, to predict flyrock resulting from blasting operations.
Genetic programing (GP) and gene expression programing (GEP) are the developed versions of GA that is known as an evolutionary computing. These algorithms are based on Darwin's theory of “survival of the fittest”. Utilization of GP and GEP models in the area of rock mechanics and mining sciences has been limited to a few researches. As the first attempt, Shuhua et al.35 utilized the GP methodology for solving problem of surface subsidence produced by mining. They estimated surface subsidence with a relative error of less than 10% that shows a high performance prediction of the GP. Li et al.36 developed the fuzzy genetic programming method (FGPM) for estimation of surface movement caused by the underground mining. A Linear Genetic Programming (LGP) model was developed by Baykasoglu et al.37 for estimation of tensile and compressive strengths of limestone samples. In addition, two attempts for predicting/approximating deformation modulus and strength of rock using GP were conducted by Beiki et al.38 and Asadi et al.,39 respectively. Karakus40 used GP in function finding to estimate intrinsic strength and elastic properties of granitic rocks. The results demonstrated that GP is a powerful tool for identifying the most important variables (terminals). Ghotbi Ravandi et al.41 presented the successful use of GP in predicting rock mass modulus. Shirani Faradonbeh et al.3 developed two models namely GP and Non-Linear Multiple Regression (NLMR) to estimate back-break due to blasting.
In the view of GEP application in the field of rock mechanics, Ozbek et al.42 developed five GEP models with different parameters for prediction of the uniaxial compressive strength (UCS) of various rock types and mentioned that GEP is able to solve their problem. In another research, Ahangari et al.43 introduced two models i.e. adaptive neuro-fuzzy inference system (ANFIS) and GEP in estimating settlement induced by tunneling on the basis of the data obtained from 53 tunnels. They indicated the superiority of GEP model in settlement prediction compared to ANFIS predictive model.
As far as the authors are aware, there is no study developing GP and GEP models for flyrock prediction induced by blasting. Hence, in this study, applications of genetic programming and gene expression programming are utilized to develop new models for prediction of flyrock distance. In order to achieve the aims of this study, sufficient number of blasting operations are investigated at Delkan iron mine, Iran and the related blasting parameters are collected. Eventually, a comparison is made between results of GP and GEP to show applicability of these models in flyrock prediction.
Section snippets
Genetic programming
Genetic programming (GP) which is an extension version of genetic algorithm, is considered as a branch of evolutionary computing (EC) family that first invented by Cramer44 and then developed by Koza.45 In fact, the idea of GP is according to Darwin's theory of ‘survival of the fittest’. The main difference between the GP and GA is related to their individual structure. In GA, individuals are linear coded binary strings of fixed length (chromosomes) but in the GP, individuals are the computer
Case study and data collection
The datasets used in this paper were collected from the Delkan iron mine, which is situated at the north-east of Iran; at latitude of 35°0′21″ N and longitude of 57°47′10″ E. Also, the estimated reserve of this mine is more than 1 Mt. Drilling and blasting is the most commonly-used method for rock breakage in Delkan iron mine. Flyrock is one of the most adverse effects induced by blasting in this mine.
A total number of 97 blasting operations were investigated and their blasting parameters were
Prediction of flyrock by GP
In the literature, most of the studies of flyrock predictions have been done, using soft computing methods such as ANN, FIS, ANFIS and also a hybrid method with optimization algorithms that are mainly based on the black box procedures.[2], [11], [28], [33], [34] Although these models can predict flyrock with a high degree of accuracy, they cannot propose a mathematical equation using inputs to predict flyrock distance. GP and GEP are two applications that can solve this problem and can
Prediction of flyrock by GEP
The process of GEP modeling is presented in the flowchart displayed in Fig. 4. Similar to the GP part, the same training and testing datasets were utilized for GEP design. For this purpose, GeneXproTools 4.0 software that is a powerful tool in function finding, classification and logic synthesis aims, was selected and used.66 The same terminal and function sets used in modeling process of GP, were performed in the GEP models. For determination of appropriate fitness function, several GEP models
Results evaluation
In this study, an attempt has been made to develop practical equations for predicting flyrock distance using GP and GEP techniques. In these techniques, burden, spacing, stemming length, hole depth, and powder factor were considered as predictors. Prior to the process of GP and GEP models, previous related studies were carefully reviewed. Considering previous investigations and using trial-and-error procedures, 5 GP and 5 GEP models were developed to predict flyrock distance. Then, some
Summary and conclusions
In order to develop new practical equations using the GP and GEP techniques for prediction of flyrock distance, Delkan iron mine in Iran was investigated and the most effective parameters on flyrock were recorded. To achieve the aim of this study, ninety-seven datasets comprising of five inputs (i.e. burden, spacing, stemming length, hole depth, and powder factor) and one output (flyrock) were prepared. Then, several GP and GEP models were constructed to estimate flyrock distance.
The
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