## 1 Introduction  
The bench blast has been widely applied in many fields, such as mining engineering and hydraulic tunnel excavation. The effects of the bench blast would directly affect subsequent operations, such as loading, hauling and crushing. Otherwise, the bench blast would also cause some undesirable impacts, such as fly-rock, vibration and back-break, if the blast design is not optimized [1]. To improve and optimize the bench blast design, a comprehensive, valid and convenient for application evaluation method of blast performance is therefore expected by mining engineers.  
As efforts to find more scientific and the reliable methods to evaluate bench blast performance, various research studies were initiated. These works can be divided into three types from different viewpoints: (1) statistical analysis method; (2) harmful effects evaluation method; (3) numerical modeling method.  
The statistical analysis method mainly employed the Artificial Neural Network (ANN) [2; 3; 4; 5; 6; 7]. The ANN is an information processing system that is used for modeling complex relationships between input and output data. An ANN consists of an input layer, hidden layers and an output layer. Once the network has been trained by the previous blasting parameters and results, the results can be predicted by the network according to the new data inputs. However, in hidden layers, all the input parameters are calculated as whole, so this method can only show approximate relationships between parameters and results.  
The numerical simulation method has been widely applied to predict the results of the bench blast, such as the Finite Element Method (FEM) [8; 9; 10], Discrete Element Method (DEM) [11; 12; 13] and Discontinuous Deformation Analysis (DDA) [14; 15; 16]. The feedback from simulated results can provide a direction for design. However, the numerical model needs many parameters, such as geological and construction conditions, and some parameters are unavailable or difficult to be determined. The simulated results always have a significant difference with the results measured on site. Therefore, the numerical modeling method is only considered as a reference for bench blast design.  
The harmful effects evaluation method mainly focuses on predicting the harmful effects induced by bench blasts [17; 18; 19; 20]. For example, the famous Sadovsky equation [21] was employed to predict the peak particle velocity (PPV) for a certain bench blast design, and some empirical formulas were obtained to evaluate the distance of the fragments flying away from the blast source [22]. In this method, the single factor of bench blast performances was analyzed, instead of the comprehensive evaluation of the bench blast. Although they are still widely used due to their simplicity and relatively good reliability of results, these equations have one-sidedness because they only consider the harmful effects of blasting to evaluate the blasting effect.  
To overcome the limitations of the abovementioned methods, a comprehensive evaluation method of bench blast in an open pit mine was proposed in this work. Eleven parameters were determined to evaluate the performance of bench blasts. Then, an evaluation model based on the linear programming and the fuzzy mathematics was proposed. Furthermore, a program code was developed on the platform of VC++. An application case of a bench blast was finally analyzed.