Prediction of blast‑induced ground vibrations in quarry sites: a comparison of GP, RSM and MARS

https://doi.org/10.1016/j.soildyn.2019.01.011Get rights and content

Highlights

  • GP, RSM, and MARS methods were employed to predict peak particle velocity (PPV) values.

  • A dataset of 200 published data was used (https://doi.org/10.1016/j.dib.2018.04.103).

  • AI-based models showed better performance compared to empirical equations.

  • The sensitivity analysis showed the influence of each D and W parameters on PPV values based on developed models.

  • The parametric studies to investigate the behavior of various developed models were done.

Abstract

Among the side effects caused by the blast, ground vibration (GV) is the most important one and can make serious damages to the surrounding structures. According to many scholars, the peak particle velocity (PPV) is one of the main indicators for determining the extent of blast‑induced GVs. Recently, following the rapid growth of soft computing approaches, researchers have tried to use these new techniques. This paper aims to explore three methods of soft computing including genetic programming (GP), response surface methodology (RSM), and multivariate adaptive regression splines (MARS) to predict the PPV values. For this purpose, a dataset of 200 published data including PPV, distance from the blasting face (D), and charge weight per delay (W) was used. The data have been recorded using blast seismograph, during the blast-induced earthquake triggered at 10 quarry sites in Ibadan and Abeokuta areas, Nigeria (https://doi.org/10.1016/j.dib.2018.04.103). The coefficient of determination for the MARS model as a most accurate model built in this research based on overall data results (R2 = 0.81), compared with the most accurate empirical equations presented in the research literature, namely general predictor model (R2 = 0.78), had a variation equal to 0.02. This variation for the root mean of squared error (RMSE), mean of absolute deviation (MAD), and mean of absolute percent error (MAPE) values were equal to 0.85, 0.25, and 0.38, respectively. In addition, the sensitivity analysis using cosine amplitude method (CAM) showed that the influence of each D and W parameters on PPV values based on developed models by this paper was more similar with the influence of these parameters based on the actual values, compared to empirical models. Finally, the parametric studies to investigate the behavior of various developed models were done to survey the changes to the values of the two variables D and W.

Introduction

Blasting operation is the most economical strategy to break the rocks in mines, tunnels, and construction [1]. Whenever an explosive operation occurs, a large amount of energy is released in the form of gas, heat, pressure, and stress waves. Only about 20–30% of explosive energy is used to break the rock and the residual energy caused the ground vibration (GV), fly rock, and noise [2]. Among the side effects caused by blasting operation, GV has the biggest share. The GV can make serious damage to the structures [3], [4]. According to many scholars [5], [6], [7], GV can be determined based on two parameters: peak particle velocity (PPV) and frequency. PPV as one of the specifications for vibration is considered as a basic parameter to control the damage level in a structure [8]. Mainly, PPV can be determined based on two factors of charge per delay and the distance from the surface of the blast [9].

From the past until now, several empirical models have been proposed by researchers to predict the PPV. The first model created to predict the PPV is done by thef United State Bureau of Mines (USBM) [10]. Afterward, a number of Predictor models of vibration such as Langefors-Kihlstrom [11], General Predictor [12], Ambraseys-Hendron [13], Bureau of Indian Standard [14], and CMRI predictor [15] have been proposed for the estimation of PPV. The empirical methods have two major constraints: lack of generalizability and a limited number of input variables. Some researchers have suggested the theoretical models based on the physics of the blast. For example, Sambuelli [16] proposed a theoretical model to predict the PPV based on blast design and rock specifications. However, due to the complex nature of the blast process and its very nonlinear transactions with the non-homogeneous and non-isotropic land, obtaining a closed-form mathematical model is almost impossible. More recently, following the rapid growth of soft computational methods, including artificial intelligence (AI), researchers have tried to use these newfound techniques [17]. From the past decades until now, AI techniques have been successful in solving the complex problems of mining [2].

Genetic Programming (GP) is a powerful optimization technique based on genetic and natural selections. The main advantage of the GP-based methods is their ability to provide simple expressions without the need to assume a base form [18]. Recently, gene expression programming (GEP), a developed version of the GP and genetic algorithms (GA), has been widely used to solve the engineering problems. Monjezi et al. [19] used GEP to predict GV. To demonstrate the ability of the GEP model to estimate GV, linear multiple regression (LMR) and nonlinear multiple regression techniques (NLMR) were developed using the same data set. The results indicated that the new proposed model was able more accurately to predict GV resulting from blast than other development techniques. In another study, GEP was used by Faradonbeh et al. [20] to predict the PPV. They applied NLMR to check GEP performance and reported GEP is more appropriate to assess the PPV compared with NLMR model.

Response surface method (RSM) algorithm provided by Tandjiria et al. [21] was also proposed in the study of researchers. The main idea of this approach is to match the performance function with an explicit function of random variables and improve the estimation through repetition. This method uses the second order polynomial with squared terms [22]. Lü [23] used the RSM method and analytical solutions to show the applications of the method of reliability for exploring underground rocks. Babu et al. [24] studied RSM method and its benefits in the analysis of geotechnical systems and concluded that one of the benefits of this method is providing comparable results and its effectiveness in the identification of sensitive parameters in control systems.

Another method that has recently been of interest to researchers is the multivariate adaptive regression spline (MARS) method. MARS is a non-linear and non-parametric regression procedure that models the nonlinear responses between inputs and outputs of a system with a series of piecewise linear segments, the closed linear parts (splines), and various gradients. There is no specific hypothesis about the functional relationship between the input and output variables. The endpoint of segments is called nodes. The MARS model is built over the course of a two-stage process. The forward phase adds the acquirer of the potential nodes to improve the performance and the back phase is effective in the modification of the minimum conditions [25]. Samui developed the MARS model to determine the elastic modulus of the jointed rock mass. The results of the MARS model were compared with artificial neural network (ANN) values using the mean absolute error (MAE) criterion and found that the MARS model is a powerful model to determine the elastic modulus of jointed rock mass [26]. In another paper by Samui et al. [27], the ANFIS and MARS were used for prediction of spatial variability of a reduced level of rock depth in Bangalore. A comparison between MARS and adaptive neuro-fuzzy inference system (ANFIS) models revealed that the MARS model outperforms the ANFIS.

Table 1 is an overview of recent research literature for PPV prediction using different methods of soft computing. The table includes the number of data, the input parameters, the type of technique used, and the coefficient of determination (R2) for each of them. As can be seen in Table 1, in relation to the build of the predictor models for PPV, almost the number of studies in which different methods of AI-based are compared together has been low. Also, up until now, the most research has been done by using the artificial neural network method (ANN) and with a large number of input variables. Hence, in the present research, a comparison between methods of GP, RSM, and MARS will be made in order to build the PPV prediction models based on two variables of distance from blasting the face (D) and charge weight (W) using PPV data for monitored blast-induced earthquakes in quarry sites from the research literature.

Section snippets

Standard genetic programming theory

GP is a population-based learning approach established on evolutionary computing approach [59]. The process of genetic programming can generally be divided into four steps: (1) an initial population of solutions for the problem is produced. (2) the solutions are all in comparison to the training data to determine "fitness" by using a predefined error metrics; (3) the best solutions to minimize the error are proposed and the most severe solutions are discarded; (4) new solutions are created

Dataset

The used dataset in recent paper has been recorded using blast seismograph, during the blast induced earthquake triggered at 10 quarry sites in Ibadan and Abeokuta areas, Nigeria (https://doi.org/10.1016/j.dib.2018.04.103) as it was shown in Fig. 2 [65]. The data include peak particle velocity, distance from the blasting face (D) and charge weight per delay (W). The patterns and protocols applied by the quarry blasters during the shots have been followed in obtaining these data. For blasting

GP model

In this study, GPTIPS MATLAB toolbox version 1.0 was used to develop an equation for PPV prediction. In GP algorithm, there are some important parameters like the rate of genetic operators, number of population, tournament size, and number of genes where they do not follow a certain pattern to assign their rates [66]. So, according to several scholars (e.g. [19], [66], [67]), it is required to achieve an optimum combination of GP parameters based on the trial-and-error procedure to develop a

Conclusions

This paper aims to explore three methods of soft computing including genetic programming (GP), response surface methodology (RSM), and multivariate adaptive regression splines (MARS) to predict the PPV values. For this purpose, a dataset of 200 published data including PPV, distance from the blasting face (D), and charge weight per delay (W) was used. The data have been recorded using blast seismograph, during the blast-induced earthquake triggered at 10 quarry sites in Ibadan and Abeokuta

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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