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Analysis of ground vibration risk on mine infrastructures: integrating fuzzy slack-based measure model and failure effects analysis

  • E. BakhtavarEmail author
  • S. Yousefi
Original Paper

Abstract

Blasting operation is the main unit of ore production in open-pit mining cycle. Detonation energy is mostly released as ground vibration using Rayleigh waves that extensively damage nearby infrastructures within or outside of a mining area. This work introduces a new hybrid approach based on the integration of fuzzy failure mode and effects analysis with the fuzzy slack-based measure model form of data envelopment analysis; this approach prioritizes and analyzes ground vibration risks on open-pit infrastructures. The approach uses a special risk prioritization algorithm by failure mode and effects analysis and data envelopment analysis under fuzzy conditions. In the fuzzy slack-based measure part of the approach, α-level cut method is used to prepare the necessary data. An open-pit copper mine is exemplified to present the approach in detail and analyze ground vibration risk. Potential failure modes, consist of infrastructures and blasting sources, are specified on the map on the mine area. Results indicate that blasting at the point of 3 imposes the highest ground vibration risk on the industrial site located within the final pit limits. The failure modes of water treatment site, crusher, gas station, explosive storage, switchgear, thickener site, power station, and processing plant have other priorities.

Keywords

Blast-induced ground vibration Fuzzy data envelopment analysis Fuzzy failure mode and effects analysis Risk analysis Slack-based measure model 

Introduction

Advances in technology and growth of residential areas increased the demand for mineral resources in terms of raw and processed materials (Bakhtavar et al. 2017a). The extensive need for the mineral resources resulted in large-scale mining and decreased the distance between infrastructures (human-made buildings) and mines (Segarra et al. 2010). Surface and underground methods are applied to mining above and below the ground surface, respectively, to extract ore deposits. Ore deposits above or near ground surface are usually mined by using surface mining methods; those placed at high depths are ideal for mining using underground methods from the beginning. Open pit, which is a well-known applicable surface method, has more benefits than underground methods, especially in production capacity, recovery, ore loss, dilution, grade control, operational costs, mechanization, and safety. However, underground mining methods are more acceptable than open pit from the environment and social viewpoints (Bakhtavar et al. 2012).

In the meantime, according to the technological advancement of open-pit mining and the equipment, use of blasting operation has become the most common technique of rock fragmentation (Jimeno et al. 1995). During blasting operation, drill holes are charged with explosives, which are detonated in sequence. The released energy due to detonation is transmitted in all directions from the blasting source in three main waves: shear, compression, and Rayleigh (Gad et al. 2005). Most of the detonation energy can be received by Rayleigh waves that usually significantly damage mine infrastructures and cause undesirable environmental impacts through ground vibration, flyrock, and air blast (Jimeno et al. 1995; Gad et al. 2005; Bakhtavar et al. 2017b), as well as high quantity of toxic gases and dust pollutants (Abdollahisharif et al. 2016). Ground vibration and its impacts on nearby infrastructures should be analyzed to avoid casualties and economic losses in mining projects (Bakhtavar et al. 2017a). In spite of the undesirable environmental impacts of blasting operations, most of the detonation energy should break rocks if the best possible blasting plan is designed and implemented (Segarra et al. 2010; Bakhtavar et al. 2017a). In this case, an ideal rock fragmentation can be achieved by consuming low detonation energy, which can decrease the operational costs of other sub-systems (Bakhtavar et al. 2015). Figure 1 shows some of the undesirable impacts of blasting operations (Jimeno et al. 1995; Elevli and Arpaz 2010).
Fig. 1

Undesirable impacts of blasting operation (based on Elevli and Arpaz 2010)

Given the importance of the analysis of ground vibration, some researchers have assessed the impacts of blast-induced ground vibration (BIGV) and the related risks on human-made structures and infrastructures in general and with mining applications. Some of these researchers have considered the concept of peak particle velocity (PPV) to predict BIGV (Ozer et al. 2008; Görgülü et al. 2013). Gad et al. (2005) investigated BIGV results based on PPV monitored during a one-year period in a building near a coal mine. Richards and Moore (2007) investigated the impacts of blasting operations, in the form of ground vibration in surface coal mines, on nearby infrastructures, such as underground workings, power transmission towers, electrical substations, conveyors, bridges, pipelines, and public access roads. Jordan et al. (2009) monitored the effects of blast-induced ground waves and vibrations on several buildings. Moreover, they analyzed the frequency of waves received by one building and numerically modeled the effects of the waves generated by an artificial blast on the building.

In the following, Dogan et al. (2013) implemented an experimental plan and recorded surface and underground blast parameters accordingly to assess the impacts of BIGV on the General Directorate of Security in Ankara, Turkey. Consequently, an empirical relationship was developed among PPV, the distance between blasting source and structure, and explosive quantity. Karadogan et al. (2014) introduced a risk analysis-based criterion norm for the damage imposed by BIGV on the adjacent structures after recording massive vibration-based data from various rock units. Yugo and Shin (2015) implemented a monitoring plan on the rockbolts employed in numerous drifts at Yukon Zinc’s Wolverine mine in Canada to investigate failures in the drifts caused by blasting-induced seismic waves. Kabwe and Wang (2016) utilized two calibrated seismographs to monitor the impacts of ground vibration and airblast levels induced by the Chimiwungo Open-Pit Mine blasts on nearby communities. Avellan et al. (2017) investigated the vibrations induced by the blasts operated near the Olympic Stadium tower in Finland. Koçaslan et al. (2017) developed an adaptive neuro-fuzzy inference system to assess the effects of controllable and uncontrollable parameters, such as blast design parameters and rock characteristics, on BIGV in four surface mines.

On the other hand, risk assessment and analysis techniques should be used to identify potential hazards due to BIGV on mine infrastructures and their causalities. Among the various quantitative and qualitative techniques, failure mode and effects analysis (FMEA) is one of the common methods has been used for identifying and analyzing failures and assessing their risks in various scientific fields (Liu et al. 2013). Unlike other techniques, FMEA is a proactive precautionary technique that predicts potential failures and measures their risks. In many studies using FMEA, risks have been identified and prioritized based on traditional risk priority number (RPN) score by multiplying three factors of severity (S), occurrence probability (O), and detection probability (D).

The quantity of failures cannot be certainly considered because they occur in the future and the values of the three factors are considered based on some predictions. Therefore, obtaining certain values for the factors is difficult due to a kind of inherent uncertainty in data (Baghery et al. 2016; Yousefi et al. 2018). Other drawbacks of the conventional FMEA technique are incapability in fully prioritizing (Rezaee et al. 2018), disability in distinguishing failure modes with similar RPNs but dissimilar severities, and breakdown in considering different importance degrees for the triple factors (Zhang and Chu 2011).

Given the shortcomings of the traditional FMEA technique and the importance of studying ground vibration risks on open-pit infrastructures, the objective of this study is to develop a hybrid approach based on fuzzy FMEA and fuzzy slack-based measure (SBM) model for prioritizing and analyzing BIGV risks. The hybrid approach uses fuzzy rating scales updated for the triple risk factors and assigns different weights to these factors using the fuzzy SBM model form of data envelopment analysis (DEA). Therefore, the approach can provide real and stable results based on different opinions by experts. Given that the weights of the triple factors are based on the mathematical programming of the DEA model, the dependency of results to experts’ opinions and the contradiction of the opinions are reduced.

Thus, the main novelty of the present study is the analysis of BIGV risks in open-pit mining on the facilities, infrastructures, and buildings associated with the mine site using map surveying. Another innovation of the study is the new hybrid approach that uses a special risk prioritization algorithm that employs the FMEA method and SBM model under fuzzy conditions. The proposed approach has been exemplified by use of the data of Sungun copper mine, which located in Northwest Iran, in 2017.

The rest of this study is organized as follows: In Sect. 2, the materials and methods include the introduction of the proposed hybrid approach and further explanations of fuzzy DEA models are provided. In Sect. 3, a case study is introduced, and the analysis of results from the implementation of the proposed approach is carried out. Finally, in Sect. 4, the conclusions and corrective solutions to reduce the negative impact of failures which have priority in the studied problem are expressed.

Materials and methods

Algorithm of the methodology

The purpose of this study is to analyze and prioritize the BIGV risk in open-pit mining on the mine infrastructures by using a new hybrid approach based on fuzzy FMEA and fuzzy DEA methods in uncertainty conditions. In the first step of this approach, failure modes (risks) are identified based on FMEA methodology. As mentioned, in conventional FMEA, the RPN rank risks in a system by determining the multiplication of S, O, and D factors. Alternately, the multiplication of the probability degree, injury intensity degree, and disability (out-of-work time) degree is considered to prioritize risks based on the RPN concept (Behraftar et al. 2017).

Based on the present study and in order to consider the uncertainty in the triple factors, an FMEA team expresses the values of the triple risk factors for each event on a fuzzy number base according to organization specifications. Uncertainty conditions are considered using fuzzy numbers to score the three risk factors, which is advantageous as it improves the experiences and judgments of the executive team, which sometimes leads to the inadequate scoring of factors due to mistakes, contradictions, and ambiguities in their judgments. Therefore, the fuzzy FMEA method is used in the first stage of this study. As mentioned before, traditional RPN has some deficiencies in prioritizing the failure modes identified based on the triple factors. Hence, the new score based on fuzzy DEA according to fuzzy FMEA output is presented in the second stage of the methodology, which can quantify the fuzzy factors of each event and consider different importance degrees for these factors.

In the second stage, the fuzzy DEA using the SBM model is applied to reduce dependency on expert ideas and to prioritize failure modes based on the triple fuzzy factors. The fuzzy DEA part of the methodology determines factor weights using mathematical programming and ultimately calculates a score for each failure mode. The triple risk factors are considered as the evaluation criteria in the fuzzy DEA model. Management attempts to eliminate the criticality of failure modes by reducing the values of the triple factors; hence, these factors are considered as model inputs. In the studied problem, a fuzzy DEA model without outputs is used because factors and criteria should not be increased. Based on the score obtained from this model, the failure mode with the least efficiency score is ranked first with the highest priority of consideration. In the fuzzy DEA model without outputs, efficiency score decreases as inputs increase. Thus, a risk becomes more critical as increased inputs decrease efficiency score, and a high priority of consideration is required. Figure 2 shows the hybrid methodology algorithm used in this study.
Fig. 2

Algorithm of the proposed hybrid methodology

Fuzzy DEA

DEA is a nonparametric approach based on the mathematical modeling of objective function subjected to the required constraints, which measures the relative efficiency of decision-making units (DMUs). Charnes et al. (1978) introduced DEA based on the assumption of returning a constant to scale for solving decision-making problems. In inefficient DMUs, the scores of a DMU using the DEA model are less than or equal to one. Considering n DMU, m inputs based on xij (i = 1,, m) are used for each DMUj (j = 1,, n) to generate s outputs based on yrj (r = 1,…, s). The DEA model called CCR by Charnes et al. (1978) evaluates the efficiency of the kth DMU in Eq. (1), and it is known as a fractional programming model.
$$\begin{aligned} & {\text{Max}}\frac{{\sum\nolimits_{r = 1}^{s} {u_{r} y_{rk} } }}{{\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } }} \\ & {\text{s}} . {\text{t:}} \\ & \quad \frac{{\sum\nolimits_{r = 1}^{s} {u_{r} y_{rj} } }}{{\sum\nolimits_{i = 1}^{m} {v_{i} x_{ij} } }} \le 1,\quad \forall j \\ & \quad \quad u_{r} ,v_{i} > 0,\quad \forall i,\;r \\ \end{aligned}$$
(1)
where \(u_{r}\) is the rth output weight; \(v_{i}\) is the ith input; \(k \in \left\{ {1,2, \ldots ,n} \right\}\) is the DMU index; \(y_{rk}\) is the rth output value for the DMU under consideration; \(x_{ik}\) is the ith input for the DMU under consideration.
Tone (2001) developed the DEA in the form of non-radial DEA models based on SBM using auxiliary variables. The results of these models are independent from measuring units. The efficiency value of SBM based on the auxiliary variables in DEA is a non-radial efficiency model that deals with input surplus and output slack and uses a feasible collective model. This non-radial efficiency model provides value in the range [0, 1], which covers all inefficiencies determined by the model. The non-radial DEA model aims to improve efficiency based on auxiliary variables instead of efficiency based on objective functions. The non-radial model is then developed into a fuzzy model that calculates the fuzzy efficiency of each DMU \((\tilde{\delta }_{k} )\) based on the fuzzy inputs and outputs provided in the model shown in Eq. (2).
$$\begin{aligned} & {\text{Min}}\;\tilde{\delta }_{k} = q - \frac{1}{m}\sum\limits_{i = 1}^{m} {{{S_{i}^{ - } } \mathord{\left/ {\vphantom {{S_{i}^{ - } } {\tilde{X}_{ik} }}} \right. \kern-0pt} {\tilde{X}_{ik} }}} \\ & {\text{s}} . {\text{t}} .\\ & \quad 1 = q - \frac{1}{s}\sum\limits_{r = 1}^{s} {{{S_{r}^{ + } } \mathord{\left/ {\vphantom {{S_{r}^{ + } } {\tilde{Y}_{rk} }}} \right. \kern-0pt} {\tilde{Y}_{rk} }}} \\ & \quad q\tilde{X}_{ik} = \sum\limits_{j = 1}^{n} {\tilde{X}_{ik} \lambda_{j}^{{\prime }} + S_{i}^{ - } } \quad i = 1, \ldots ,m \\ & \quad q\tilde{Y}_{rk} = \sum\limits_{j = 1}^{n} {\tilde{Y}_{rk} \lambda_{j}^{{\prime }} + S_{r}^{ + } } \quad r = 1, \ldots ,s \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j}^{{\prime }} } = q \\ & \quad \quad \lambda_{j}^{{\prime }} \ge 0,j = 1, \ldots ,n,\quad S_{i}^{ - } \ge 0,\;\;i = 1, \ldots ,m,\;\;S_{r}^{ + } \ge 0,\;\;r = 1, \ldots ,s,\;\;q > 0. \\ \end{aligned}$$
(2)
In the model given in Eq. (2), \(\tilde{X}_{ji}\) and \(\tilde{Y}_{jr}\) indicate uncertain inputs and output values for the DMUs that can be represented by membership functions \(\mu\) in the form of \(\mu_{{\tilde{X}_{ji} }}\) and \(\mu_{{\tilde{Y}_{jr} }}\) in the convex fuzzy set, respectively. Furthermore, \(S_{i}^{ - }\) and \(S_{r}^{ + }\) indicate the auxiliary variables used in the model constraints for inputs and outputs, respectively. The number of inputs, outputs, variable change, and dual variable per DMU is represented by \(m\), \(s\), \(q\), and \(\lambda_{j}^{{\prime }}\), respectively. The fuzzy set of inputs and outputs is then converted to a certain set by defining membership threshold and using the \(\alpha\)-level cut method. Moreover, \(S(\tilde{X}_{ji} )\) and \(S(\tilde{Y}_{jr} )\) are created to support \(\tilde{X}_{ji}\) and \(\tilde{Y}_{jr}\), which defines support in relation to the element set with the membership functions greater than zero. Finally, \(\tilde{X}_{ji}\) and \(\tilde{Y}_{jr}\) are defined in Eqs. (3) and (4) using \(\alpha\)-level cut method, respectively.
$$(X_{ji} )_{\alpha } = \left\{ {x_{ji} \in S(\tilde{X}_{ji} )|\mu_{{\tilde{X}_{ji} }} (x_{ji} ) \ge \alpha } \right\},\quad \forall j,i$$
(3)
$$(Y_{jr} )_{\alpha } = \left\{ {y_{jr} \in S(\tilde{Y}_{jr} )|\mu_{{\tilde{Y}_{jr} }} (y_{jr} ) \ge \alpha } \right\},\quad \forall j,r$$
(4)
where \(x_{ji}\) and \(y_{jr}\) indicate the input value i and output value r per DMU j, respectively. Moreover, \((X_{ji} )_{\alpha }\) and \((Y_{jr} )_{\alpha }\) are certain sets per input values and uncertain outputs per DMUs with different \(\alpha\) levels, respectively. Therefore, using \(\alpha\)-level cut, input and output values are determined as certain intervals between 0 and 1 per different \(\alpha\) levels instead of fuzzy values. Sets of \(\alpha\) standard levels are given in Eqs. (5) and (6) based on Eqs. (3) and (4).
$$\begin{aligned} (X_{ji} )_{\alpha } & = \left\{ {x_{ji} \in S(\tilde{X}_{ji} )|\mu_{{\tilde{X}_{ji} }} (x_{ji} ) \ge \alpha } \right\} = \left[ {(X_{ji} )_{\alpha }^{L} ,(X_{ji} )_{\alpha }^{U} } \right],\quad \forall j,i \\ & = \left[ {\min_{{x_{ji} }} \left\{ {x_{ji} \in S(\tilde{X}_{ji} )|\mu_{{\tilde{X}_{ji} }} (x_{ji} ) \ge \alpha } \right\},\;\;\max_{{x_{ji} }} \left\{ {x_{ji} \in S(\tilde{X}_{ji} )|\mu_{{\tilde{X}_{ji} }} (x_{ji} ) \ge \alpha } \right\}} \right] \\ \end{aligned}$$
(5)
$$\begin{aligned} (Y_{jr} )_{\alpha } & = \left\{ {y_{jr} \in S(\tilde{Y}_{jr} )|\mu_{{\tilde{Y}_{jr} }} (y_{jr} ) \ge \alpha } \right\},\quad \forall j,r \\ & = \left[ {\min_{{y_{jr} }} \left\{ {y_{jr} \in S(\tilde{Y}_{jr} )|\mu_{{\tilde{Y}_{jr} }} (y_{jr} ) \ge \alpha } \right\},\;\;\max_{{y_{jr} }} \left\{ {y_{jr} \in S(\tilde{Y}_{jr} )|\mu_{{\tilde{Y}_{jr} }} (y_{jr} ) \ge \alpha } \right\}} \right] \\ \end{aligned}$$
(6)
At different \(\alpha\) levels for \(\{ (X_{ji} )_{\alpha } |0 < \alpha \le 1\}\) and \(\{ (Y_{jr} )_{\alpha } |0 < \alpha \le 1\}\), the fuzzy DEA model can be converted to crisp DEA. The efficiency membership function for the jth DMU can be expressed by Eq. (7) (Zimmermann 1975).
$$\mu_{{\tilde{E}_{k} }} (z) = \mathop {\sup }\limits_{x,y} \;\hbox{min} \left\{ {\mu_{{\tilde{X}_{ji} }} (x_{ji} ),\mu_{{\tilde{Y}_{jr} }} (y_{jr} ),\left. {\forall j,r,i} \right|z = E_{k} (x,y)} \right\}$$
(7)
where \(E_{k} (x,y)\) is the efficiency value calculated through the traditional DEA model based on the auxiliary variables under a set of inputs and outputs. According to Eq. (7), the minimum membership degree equals to membership from \(\tilde{E}_{k}\) in point z for each efficient value with the combination of \(x_{ji}\) and \(y_{jr}\) from z. The upper and lower bounds are determined from a cut under \(\mu_{{\tilde{E}_{k} }}\) according to Eqs. (5) to (7). Furthermore, a two-stage mathematical programming model can be converted into a traditional one-stage programming model through the Pareto optimal solution. Therefore, the model given in Eq. (2) can be converted to the models represented in Eqs. (8) and (9) in order to calculate the efficiency limits at different \(\alpha\) levels (Chen et al. 2013).
$$\begin{aligned} & {\text{Min}}\;(\delta_{k} )_{\alpha }^{U} = q - \frac{1}{m}\sum\limits_{i = 1}^{m} {{{(S_{i}^{ - } )^{L} } \mathord{\left/ {\vphantom {{(S_{i}^{ - } )^{L} } {(x_{ik} )_{\alpha }^{L} }}} \right. \kern-0pt} {(x_{ik} )_{\alpha }^{L} }}} \\ & {\text{s}} . {\text{t}} .\\ & \quad 1 = q - \frac{1}{s}\sum\limits_{r = 1}^{s} {{{(S_{r}^{ + } )^{U} } \mathord{\left/ {\vphantom {{(S_{r}^{ + } )^{U} } {(y_{rk} )_{\alpha }^{U} }}} \right. \kern-0pt} {(y_{rk} )_{\alpha }^{U} }}} / \\ & \quad q(x_{ik} )_{\alpha }^{L} = \sum\limits_{j = 1, \ne k}^{n} {(x_{ij} )_{\alpha }^{U} \lambda_{j}^{{\prime }} + (x_{ik} )_{\alpha }^{L} \lambda_{j}^{{\prime }} + (S_{i}^{ - } )^{L} } \quad i = 1, \ldots ,m \\ & \quad q(y_{rk} )_{\alpha }^{U} = \sum\limits_{j = 1, \ne k}^{n} {(y_{rj} )_{\alpha }^{L} \lambda_{j}^{{\prime }} + (y_{rk} )_{\alpha }^{U} \lambda_{j}^{{\prime }} - (S_{r}^{ + } )^{U} } \quad r = 1, \ldots ,s \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j}^{{\prime }} } = q \\ & \quad \quad \lambda_{j}^{{\prime }} \ge 0,\;\;j = 1, \ldots ,n,\;\;(S_{i}^{ - } )^{L} \ge 0,\;\;i = 1, \ldots ,m,\;\;(S_{r}^{ + } )^{U} \ge 0,\;\;r = 1, \ldots ,s,\;\;q > 0 \\ \end{aligned}$$
(8)
$$\begin{aligned} & {\text{Min}}(\delta_{k} )_{\alpha }^{L} = q - \frac{1}{m}\sum\limits_{i = 1}^{m} {{{(S_{i}^{ - } )^{U} } \mathord{\left/ {\vphantom {{(S_{i}^{ - } )^{U} } {(x_{ik} )_{\alpha }^{U} }}} \right. \kern-0pt} {(x_{ik} )_{\alpha }^{U} }}} \\ & {\text{s}} . {\text{t}} .\\ & \quad 1 = q - \frac{1}{s}\sum\limits_{r = 1}^{s} {{{(S_{r}^{ + } )^{L} } \mathord{\left/ {\vphantom {{(S_{r}^{ + } )^{L} } {(y_{rk} )_{\alpha }^{L} }}} \right. \kern-0pt} {(y_{rk} )_{\alpha }^{L} }}} \\ & \quad q(x_{ik} )_{\alpha }^{U} = \sum\limits_{j = 1, \ne k}^{n} {(x_{ij} )_{\alpha }^{L} \lambda_{j}^{{\prime }} + (x_{ik} )_{\alpha }^{U} \lambda_{j}^{{\prime }} + (S_{i}^{ - } )^{U} } \quad i = 1, \ldots ,m \\ & \quad q(y_{rk} )_{\alpha }^{L} = \sum\limits_{j = 1, \ne k}^{n} {(y_{rj} )_{\alpha }^{U} \lambda_{j}^{{\prime }} + (y_{rk} )_{\alpha }^{L} \lambda_{j}^{{\prime }} - (S_{r}^{ + } )^{L} } \quad r = 1, \ldots ,s \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j}^{{\prime }} } = q \\ & \quad \quad \lambda_{j}^{{\prime }} \ge 0,\;\;j = 1, \ldots ,n,\;\;(S_{i}^{ - } )^{U} \ge 0,\;\;i = 1, \ldots ,m,\;\;(S_{r}^{ + } )^{L} \ge 0,\;\;r = 1, \ldots ,s,\;\;q > 0 \\ \end{aligned}$$
(9)
where \((\,\delta_{k} )_{\alpha }^{U}\) and \((\,\delta_{k} )_{\alpha }^{L}\) are the upper and lower bounds of the efficiency of DMU k for \(\alpha\) level, and \((x_{ik} )_{\alpha }^{L}\), \((x_{ik} )_{\alpha }^{U}\), \((y_{rk} )_{\alpha }^{L}\), and \((y_{rk} )_{\alpha }^{U}\) are the upper and lower bounds of inputs and outputs for DMUs k at different \(\alpha\) levels. This study uses the fuzzy DEA model without outputs because the criteria derived from the fuzzy FMEA method are considered, and the management aimed to reduce their amounts. Both factors have an input role in the DEA part of the methodology. DEA without outputs can be used in the case of efficiency evaluation problems wherein DMUs have numerous inputs (Lovell and Pastor 1999). Therefore, in this study, the models given in Eqs. (8) and (9) are used with the assumption of a constant output equal to one due to the fuzzy values of the inputs.
The calculated relative efficiency values differ with the calculated values of the traditional DEA with fuzzy numbers. The problem is how to prioritize DMUs according to the interval values of the efficiency for different α-cut levels. Equation (10) introduced by Chen and Klein (1997) is used to solve this problem.
$$I\left( {\tilde{E}_{{\tilde{k}}} ,R} \right)_{\,m \to \infty } = \frac{{\sum\nolimits_{i = 0}^{m} {\left[ {(E_{k} )_{{\alpha_{i} }}^{U} - c} \right]} }}{{\sum\nolimits_{i = 0}^{m} {\left[ {(E_{k} )_{{\alpha_{i} }}^{U} - c} \right]} - \sum\nolimits_{i = 0}^{m} {\left[ {(E_{k} )_{{\alpha_{i} }}^{L} - d} \right]} }}$$
(10)
where k is the counter for DMUs, i is the counter for different \(\alpha_{i}\) levels (\(i = 0, \ldots ,m\)); \((E_{k} )_{{\alpha_{i} }}^{U}\) and \((E_{k} )_{{\alpha_{i} }}^{L}\) are the upper and lower bounds of the efficiency of DMU k for \(\alpha_{i}\) level; c and d values are equal to \(\min_{i,k} \{ (E_{k} )_{{\alpha_{i} }} \}\) and \(\max_{i,k} \{ (E_{k} )_{{\alpha_{i} }} \}\), respectively; and a high value of \(I(\tilde{E}_{{\tilde{k}}} ,R)\) means that the DMU under evaluation has a high priority. However, in this study, depending on the nature of the problem and the absence of variable outputs in the DEA model, failure modes with high \(1 - I(\tilde{E}_{{\tilde{k}}} ,R)\) scores have critically high priorities.

Results and discussion

In this section, the proposed approach has been applied for analysis of BIGV risks on the infrastructures of Sungun copper mine in Northwest Iran, and the relevant results are presented. The Sungun copper mine consists of approximately 796 million tonnes of geological reserve and 388 million tonnes of the mineable reserve. In this mine, the copper-based ore deposit will be extracted through the bench blasting method on one wall of the mountain between the levels 2362.5 and 1600 m (Bakhtavar et al. 2015). Based on the mine plan, the annual production of the ore varies between 5 and 14 million tonnes over the mine life. The porphyry type of copper ore with a phyllic alteration discontinued by several joint sets is currently extracted at the mine. Based on the mine blasting plan, blast holes are charged with ammonium nitrate with fuel oil as the main charge together with different types of boosters placed in various parts of the blast holes (Abdollahisharif et al. 2016).

Table 1 summarizes the basic information from Sungun copper mine required to evaluate the BIGV risk on surface infrastructures using the introduced methodology. This information is obtained from various processes on the mine area map, as shown in Fig. 3. The figure shows that the potential failure modes associated with the BIGV risk on infrastructures are considered in various parts of Sungun copper mine. The information presented in Table 1 and Fig. 3 can help experts identify the initial parameters in evaluating and analyzing risks easily and reliably. Each failure mode is defined on the mine map by considering infrastructure and related blasting sources at an equal level. At equal levels, the infrastructure can be impacted by ground vibration waves from blasting. As shown in Table 1 and Fig. 3, the main infrastructures of the mine considered for analysis are crusher, thickener site, industrial site, processing plant, switchgear, gas station, water treatment site, power station, and explosive storage.
Table 1

Database from the studied area associated with the BIGV risk on infrastructures

Infrastructure type

Sign

Infrastructure level

Blasting source

Blasting source level

Hole diameter (mm)

Number of holes in the final delay

Distance between blasting and infrastructure (m)

Crusher

Cr

1987

1

1987.5

165

18

375

Thickener site

ThS

2083

2

2087.5

165

7

590

Industrial site

InS

2278

3

2275

165

17

105

Processing plant

PrP

2110

4

2112.5

165

8

980

Switch gear

SwG

2178

5

2175

165

16

645

6

2175

165

16

795

Gas station

GaS

2297.5

7

2300

165

18

200

Water treatment site

WaT

2312.5

8

2312.5

165

13

40

Power station

PoS

2221

9

2225

127

9

770

Explosive storage

ExS

2288

10

2287.5

165

13

395

Fig. 3

Position of blasting sources and related infrastructures under the BIGV risk in Sungun

Results of alpha-level-based fuzzy system

Based on the methodology algorithm and after identifying risks, severity, occurrence probability, and detection probability are the three effective factors for risk analysis using fuzzy FMEA determined for each event based on fuzzy numbers. For this purpose, the fuzzy triangular numbers are utilized based on the pattern presented in Fig. 4 (Wang et al. 2009) and the ranking described in Table 2 to determine the fuzzy numbers of the risk factors for each failure modes identified in Fig. 3 and Table 1. The fuzzy values of risk factors are determined for the BIGV failure modes as given in Table 3. \(\alpha\)-level cut method is used to prepare the data necessary to apply the fuzzy SBM based models provided in Eqs. (8) and (9). In this case, fuzzy values are converted to interval values based on \(\alpha\)-level cut method to play the role of inputs in the models. The results of the interval values for the three risk factors based on the cuts implemented in levels α = 0, α = 0.6, and α = 1 are presented in Table 4. Given that the fuzzy numbers in Table 3 are based on (L, M, U), the values in Table 4 are calculated using L* = α·M + (1 − α)L and U* = α·M + (1 − α)U in the form of (L*, U*). These relationships are employed to calculate the input values for the DEA model at other α levels.
Fig. 4

A standard pattern for fuzzy triangular numbers (Wang et al. 2009)

Table 2

Fuzzy rating scale updated for the three risk factors in BIGV

Mark

Fuzzy number

Occurrence probability (O)

Severity (S)

Detection probability (D)

A

(9, 10, 10)

More than one event per day

Complete destruction of infrastructure

Undetectable

B

(8, 9, 10)

More than one event per week

Serious damage to infrastructure and long work stoppage

Very unexpected detection

C

(7, 8, 9)

An event per week

Serious damage to infrastructure and temporary work stoppage

Unlikely event detection

D

(6, 7, 8)

More than one event per month

Damage to infrastructure and temporary work stoppage

Likely to detect too little

E

(5, 6, 7)

One event per month

Minor damage to infrastructure and temporary work stoppage

Low detection probability

F

(4, 5, 6)

More than one event per 6 months

No damage to infrastructure and temporary work stoppage

Medium detection probability

G

(3, 4, 5)

More than one event per year

No damage and continuing work after major modifications

Almost high detection probability

H

(2, 3, 4)

More than one event per two years

No damage and continuing work after minor modifications

High detection probability

I

(1, 2, 3)

One event over 2– 5 years

No damage and continuing work with the minimum limitations

Very high detection probability

J

(1, 1, 2)

One event in more than 5 years

No impact

It can be definitely detected

Table 3

Fuzzy numbers for the risk factors based on the case study

Failure modes

Severity (S)

Occurrence probability (O)

Detection probability (D)

Cr-1

(7, 8, 9)

(2, 3, 4)

(8, 9, 10)

ThS-2

(2, 3, 4)

(4, 5, 6)

(3, 4, 5)

InS-3

(6, 7, 8)

(3, 4, 5)

(7, 8, 9)

PrP-4

(1, 2, 3)

(1, 2, 3)

(1, 2, 3)

SwG-5

(5, 6, 7)

(2, 3, 4)

(5, 6, 7)

SwG-6

(1, 2, 3)

(2, 3, 4)

(5, 6, 7)

GaS-7

(7, 8, 9)

(2, 3, 4)

(8, 9, 10)

WaT-8

(8, 9, 10)

(2, 3, 4)

(8, 9, 10)

PoS-9

(1, 2, 3)

(3, 4, 5)

(3, 4, 5)

ExS-10

(5, 6, 7)

(2, 3, 4)

(7, 8, 9)

Table 4

Implementation of α-level cut method for the values of the three risk factors

Failure mode

α = 0 (L* = L, U* = U)

α = 0.6

α = 1 (L* = U* = M)

S

O

D

S

O

D

S

O

D

Cr-1

(7, 9)

(8, 10)

(2, 4)

(7.8, 8.2)

(8.8, 9.2)

(2.8, 3.2)

8

9

3

ThS-2

(2, 4)

(3, 5)

(4, 6)

(2.8, 3.2)

(3.8, 4.2)

(4.8, 5.2)

3

4

5

InS-3

(6, 8)

(7, 9)

(3, 5)

(6.8, 7.2)

(7.8, 8.2)

(3.8, 4.2)

7

8

4

PrP-4

(1, 3)

(1, 3)

(1, 3)

(1.8, 2.2)

(1.8, 2.2)

(1.8, 2.2)

2

2

2

SwG-5

(5, 7)

(5, 7)

(2, 4)

(5.8, 6.2)

(5.8, 6.2)

(2.8, 3.2)

6

6

3

SwG-6

(1, 3)

(5, 7)

(2, 4)

(1.8, 2.2)

(5.8, 6.2)

(2.8, 3.2)

2

6

3

GaS-7

(7, 9)

(8, 10)

(2, 4)

(7.8, 8.2)

(8.8, 9.2)

(2.8, 3.2)

8

9

3

WaT-8

(8, 10)

(8, 10)

(2, 4)

(8.8, 9.2)

(8.8, 9.2)

(2.8, 3.2)

9

9

3

PoS-9

(1, 3)

(3, 5)

(3, 5)

(1.8, 2.2)

(3.8, 4.2)

(3.8, 4.2)

2

4

4

ExS-10

(5, 7)

(7, 9)

(2, 4)

(5.8, 6.2)

(7.8, 8.2)

(2.8, 3.2)

6

8

3

Assessing BIGV risk on the basis of fuzzy DEA

After preparing the input values for the fuzzy DEA model, the models given in Eqs. (8) and (9) are run to calculate the upper and lower limits of the efficiency score, respectively. Each model is run by different levels of α. The results of the upper and lower bounds of the efficiency scores per decision-making unit (failure mode) at different levels of α (0, 0.2, 0.4, 0.6, 0.8, and 1) are shown in Table 5. The calculated relative efficiency values differ from the values calculated from the traditional DEA method with fuzzy numbers. Equation (10) is utilized to prioritize the DMUs relative to the efficiency interval values obtained at various levels. Results are presented in Table 6.
Table 5

Upper and lower bounds of the efficiency scores calculated for different risk failure modes

Failure mode

Level cut

α = 0

α = 0.2

α = 0.4

α = 0.6

α = 0.8

α = 1

LB

UB

LB

UB

LB

UB

LB

UB

LB

UB

LB

UB

Cr-1

0.1537

0.5536

0.1664

0.4699

0.1800

0.3975

0.1945

0.3339

0.2100

0.2775

0.2269

0.2269

ThS-2

0.2056

0.8333

0.2285

0.7073

0.2536

0.5983

0.2810

0.5032

0.3111

0.4192

0.3444

0.3444

InS-3

0.1454

0.4762

0.1576

0.4139

0.1706

0.3573

0.1843

0.3056

0.1988

0.2581

0.2143

0.2143

PrP-4

0.3333

1.0000

0.3810

1.0000

0.4359

1.0000

0.5000

1.0000

0.5758

1.0000

0.6667

0.6667

SwG-5

0.1786

0.6667

0.1956

0.5676

0.2138

0.4815

0.2335

0.4057

0.2547

0.3383

0.2778

0.2778

SwG-6

0.2421

1.0000

0.2656

1.0000

0.2915

1.0000

0.3203

0.6140

0.3525

0.4915

0.3889

0.3889

GaS-7

0.1537

0.5536

0.1664

0.4699

0.1800

0.3975

0.1945

0.3339

0.2100

0.2775

0.2269

0.2269

WaT-8

0.1500

0.5417

0.1625

0.4597

0.1759

0.3889

0.1902

0.3268

0.2056

0.2716

0.2222

0.2222

PoS-9

0.2444

1.0000

0.2718

1.0000

0.3021

1.0000

0.3359

0.6435

0.3737

0.5205

0.4167

0.4167

ExS-10

0.1680

0.6095

0.1822

0.5177

0.1974

0.4381

0.2136

0.3681

0.2311

0.3058

0.2500

0.2500

Table 6

Prioritized failure modes based on the fuzzy SBM model

Failure mode

\(\mathop {\hbox{min} }\limits_{i} \left\{ {(E_{k} )_{{\alpha_{i} }} } \right\}\)

\(\mathop {\hbox{max} }\limits_{i} \left\{ {(E_{k} )_{{\alpha_{i} }} } \right\}\)

\(I\left( {\tilde{E}_{{\tilde{k}}} ,R} \right)\)

\(1 - I\left( {\tilde{E}_{{\tilde{k}}} ,R} \right)\)

Priority of being critical

Cr-1

0.1537

0.5536

0.2217

0.7783

3

ThS-2

0.2056

0.8333

0.3667

0.6333

6

InS-3

0.1454

0.4762

0.1896

0.8104

1

PrP-4

0.3333

1.0000

0.6068

0.3932

9

SwG-5

0.1786

0.6667

0.2865

0.7135

5

SwG-6

0.2421

1.0000

0.4667

0.5333

7

GaS-7

0.1537

0.5536

0.2217

0.7783

3

WaT-8

0.1500

0.5417

0.2148

0.7852

2

PoS-9

0.2444

1.0000

0.4777

0.5223

8

ExS-10

0.1680

0.6095

0.2537

0.7463

4

\(c = \mathop {\hbox{min} }\limits_{i,k} \left\{ {(E_{k} )_{{\alpha_{i} }} } \right\}\)

0.1454

\(d = \mathop {\hbox{max} }\limits_{i,k} \left\{ {(E_{k} )_{{\alpha_{i} }} } \right\}\)

1.0000

According to the explanations presented in relation to the methodology, given that the DEA model without outputs is employed in this study, the failure mode with the lowest value of \(I(\tilde{E}_{{\tilde{k}}} ,R)\) has the highest critical priority. Accordingly, failure modes are prioritized based on the values and scores derived from \(1 - I(\tilde{E}_{{\tilde{k}}} ,R)\) given in Table 6. In this manner, the failure mode with the highest value has the utmost critical priority. In this case, the failure mode InS-3 at 0.8104 is the first critical priority. This finding means that the blasting operation at the point of 3 imposes the highest ground vibration risk on the site of the industrial structures (InS). Failure mode InS-3 has the highest risk among all considered failure modes for the following reasons: a number of 17 holes with a diameter of 165 mm blasted in the final delay, a low distance of 107.9 m between the blasting point 3 and the industrial site location, high importance of the structures located at the industrial site, and the industrial site location within the final mine limits. Failure mode WaT-8 at 0.7852 takes the second critical priority. The high risk for failure mode WaT-8, which imposes a high BIGV risk to the water treatment site, is attributed to the particularly low distance of 36.8 m between the blasting point 8 and the treatment site location and its location within the mine final limits. However, this failure mode includes 13 holes in the final delay, and the importance of the treatment site is less than the industrial site. Failure modes Cr-1 and GaS-7 with equal values of 0.7783 take the third critical priority. Failure mode Cr-1 indicates that the blasting point of 1 at 1987.5 m imposes BIGV risk to the mine crusher at the final mine limits. The third rank for mode Cr-1 is caused by the long distance of 376.8 m to the blasting source compared with modes InS-3 and WaT-8. However, mode Cr-1 is an important structure, and 18 holes are blasted in the final delay at the blasting point of 1. Although the distance between the blasting source 7 and gas station site (GaS-7) is 200 m, which is lower than a distance of 376.8 m in the case of Cr-1 mode, the crusher is more important than the gas station in mine management from the viewpoints of investment and mining requirements. However, failure modes Cr-1 and GaS-7 consist of 18 blast holes with the same diameter. Management should consider treatment solutions to reduce the negative impacts of the mentioned blasting sources on the structures. Failure modes ExS-10, SwG-5, ThS-2, SwG-6, PoS-9, and PrP-4 have other priorities. The last score the failure mode PrP-4 is justifiable because the processing plant (PrP) is located in a high distance of 980 m far from the blasting point 4 that includes 8 holes blasted in the final delay.

The distance between the blasting source and structure, the number of holes to be blasted in the final delay of a round, the hole diameter, and the difference between the levels of the blasting source and the structure play major roles in the level of BIGV risk and its impacts on infrastructures. As discussed above, to exploit ore from the mine, some of the structures are placed within or on the mine final limits where blasting operations should be performed. The structures within the mine final limits should be located due to the incomplete exploration data and process, which are insufficient to model the actual dimensions and shape of an ore deposit. Accordingly, mine limits are designed to be smaller than its actuality. When supplementary explorations are implemented, large deposits can usually be explored similar to the case of Sungun copper mine and other open-pit mines in Iran. In this case, as a result of the initial exploration data, the infrastructures located out of the initial mine limits are placed within or on the final mine limits designed and expanded based on the supplementary exploration data. The first-four high-risk failure modes (modes InS-3, WaT-8, Cr-1, and GaS-7) are examples of these conditions. Two solutions are proposed to this problem include “reconstructing the infrastructures out of the final limits” and “remaining a part of the ore deposit placed beneath the infrastructures.” An economic comparison is required to apply one of the solutions. Both solutions can be adopted to decrease the distance between blasting source and infrastructure. Another attempt to reduce the impacts of BIGV is to blast few holes in the final delay that diminishes charge. The diameter of the blast holes can also be decreased to reduce BIGV risks on infrastructures. To further decrease BIGV risks, infrastructures at higher upper levels than the levels of blasting sources should be located.

Conclusion

Blasting operation in surface mines is used to break ore and waste rocks, which are feasibly loaded by shovels and hauled by trucks. Based on an ideal blasting plan, most detonation energy breaks rock with desirable fragmentation sizes in spite of the undesirable environmental impacts of blasting operation in the forms of ground vibration, flyrock, air blast, dust, and toxic gases. Thus, ground vibration and its impacts on the adjacent infrastructures are analyzed to avoid casualties and economic losses of a mining project. During blasting, energy is released and transmitted in the forms of shear, compression, and Rayleigh waves in all directions from the blasting source. Rayleigh waves play a major role in ground vibrations and usually considerably damage mine infrastructures. The new hybrid approach presented in this study, which integrates fuzzy FMEA and fuzzy DEA, has a specific algorithm to prioritize and analyze the BIGV risks on open-pit infrastructures. Based on the algorithm, three factors including severity, occurrence probability, and detection probability are focused on for risk analysis using fuzzy FMEA. Several failure modes of BIGV risks are considered by surveying Sungun copper mine area map. The information related to the failure modes effectively determined the fuzzy values of the three risk factors during the fuzzy FMEA part of the approach. After calculating the upper and lower bounds of the efficiency scores for each risk failure mode using the \(\alpha\)-level cut method, the failure modes as DMUs are prioritized relative to the efficiency interval values using the fuzzy SBM. In conclusion, failure modes InS-3 and WaT-8 at 0.8104 and 0.7852 take the first and second critical priorities, respectively. Failure modes Cr-1 and GaS-7 obtained equal values of 0.7783 and take the third critical priorities, respectively. Failure modes ExS-10, SwG-5, ThS-2, SwG-6, PoS-9, and PrP-4 take other critical priorities. Management should consider treatment solutions to reduce the negative impacts of the failure modes located within or on the final pit limits of infrastructures. Two main solutions are proposed for this problem, including “reconstructing the infrastructures out of the final limits” and “remaining a part of the ore deposit placed beneath the infrastructures.” These solutions should be economically compared before selecting one of them. Moreover, these solutions can be adopted to decrease the distance between blasting source and infrastructure while considering BIGV risk.

Notes

Acknowledgements

The authors would like to thank the Urmia University of Technology for providing suitable support. We would also like to the experts at Sungun copper mine gave us their valuable ideas.

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Copyright information

© Islamic Azad University (IAU) 2018

Authors and Affiliations

  1. 1.Faculty of Mining and Materials EngineeringUrmia University of TechnologyUrmiaIran
  2. 2.Faculty of Industrial EngineeringUrmia University of TechnologyUrmiaIran

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