Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 724619, 11 pages

http://dx.doi.org/10.1155/2015/724619

## Rock Mass Blastability Classification Using Fuzzy Pattern Recognition and the Combination Weight Method

State Key Laboratory of Coal Resources and Safe Mining, School of Mines, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Received 27 January 2015; Accepted 27 May 2015

Academic Editor: Rama S. R. Gorla

Copyright © 2015 Shuangshuang Xiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Rock mass blastability classification provides a theoretical basis for rock mass blasting design, which is used to select blasting explosives, to estimate the unit explosive consumption, and to determine blasting design parameters. The primary factors that affect rock mass blastability were analyzed by selecting five indexes for rock mass blastability classification, that is, the rock Protodyakonov coefficient, rock tensile strength, rock density, rock wave impedance, and integrity coefficient of rock mass, and by identifying standards for the rock mass blastability classification and a method for testing the blasting classification indexes. The index weights were calculated using the combination weight method, which is based on game theory. A model for rock mass blastability classification was developed in combination with a fuzzy pattern recognition method. This classification method was applied to a Heidaigou open-pit coal mine, where mudstone, fine sandstone, medium sandstone, and coarse sandstone were determined to have a blastability degree of II, which corresponds to a blastability characterization of “easy,” and the unit explosive consumption of mudstone, fine sandstone, medium sandstone, and coarse sandstone was determined to be 0.44, 0.42, 0.40, and 0.36 kg/m^{3}, respectively. These results were used to develop a loose blasting design that was effective for loose blasting.

#### 1. Introduction

Rock mass blastability is a measure of the resistance of a rock mass to blasting and crushing. The physical and mechanical properties and structural characteristics of rocks synchronize to various extents and in different ways to impede blasting and crushing under blasting loading [1]. Thus, the rock mass blastability is also a comprehensive indicator of several inherent properties of a rock mass under dynamic loading. The rock mass blastability reflects the degree of difficulty in rock blasting [2]. An understanding of rock mass blastability and systematic rock mass blastability classifications form the theoretical basis of blasting optimization design [3]. The rock mass blastability can be used to select suitable explosives, estimate the explosive unit consumption, and determine reasonable blasting parameters, which can reduce blasting costs and improve labor productivity by ensuring predictable blasting characteristics.

Foreign and Chinese scholars have conducted numerous research studies on rock mass blastability classification using different methods from various perspectives and have developed a variety of indexes and methods for rock mass blastability classification [4]. There are currently two methods for rock mass blastability classification. In the first method, the analysis and calculation involve one or more parameters, and a numerical value, such as a blastability index or the crushing energy, is chosen as a measure of the blastability of the rock mass [5]. In the second method, various parameters are chosen to describe the rock mass, and the rock mass blastability classification is performed using statistical mathematics, fuzzy mathematics, or other mathematical methods. The characteristics and internal mechanisms that affect rock mass blastability can be identified more accurately using several indexes to systematically evaluate the rock mass blastability. Therefore, many classification schemes and evaluation algorithms have been applied to rock mass blastability classification, including neural networks [6–8], projection pursuit [9], genetic algorithms [10], fuzzy set theory [11–13], cluster analysis [14], and attribute recognition [15]. Each algorithm has its advantages and disadvantages. For example, a neural network has considerable fault-tolerance ability and a rapid evaluation speed but requires a representative learning sample. In addition, the learning parameters and number of hidden layers are difficult to identify, and the number of hidden layers affects the convergence rate, the convergence properties of the network, and its applicability to nonlinear problems. The index weights do not need to be identified when the rock mass blastability is classified using the projection pursuit algorithm, thereby ensuring that the classification is objective. However, when optimizing the projection direction, this scheme can easily converge to a local optimum, which results in early maturing or early convergence, among other problems. Genetic algorithms can be used to accurately classify the respective categories but has additional parameter requirements, such as gene variables and genetic generations. The challenge encountered in using cluster analysis and attribute recognition is to determine reasonable index weights.

There are three essential requirements for developing a rock mass blastability classification model. First, the most representative characteristic must be chosen as the classification index, and classification standards must be developed. Second, each index should be assigned a reasonable weight. Finally, a suitable evaluating algorithm should be chosen. The rock blasting mechanism and the factors affecting rock mass blastability for the aforementioned research scenario were used to identify the classification indexes and classification standards for rock mass blastability. The blastability of a rock mass was described using the following values: “easy,” “moderate,” “difficult,” and other fuzzy values, depending on practical production requirements. The indices of two rock samples typically have similar values but are characterized by different rating categories by observation. This result is not reasonable. Thus, rock blastability can be characterized using transitional values that lie in between different levels; that is, the values are fuzzy. There is no distinct boundary between different levels. The same rock mass could be assigned to different classifications by different people or based on different situations. Thus, it is more suitable to use fuzzy mathematics to classify rock mass blastability. Rock mass classification can then be based on this developed rock mass rating and the rock characteristics; that is, rock mass blastability classification is a pattern recognition problem. Therefore, fuzzy pattern recognition was used to develop a rock mass blastability classification model. However, the weights of the indexes are not considered in pattern recognition, which prevents the application of this method to cases with unequal index weights. The combination weight method was used to identify the index weights to reduce the effects of subjective factors and avoid irrelevant factors.

#### 2. Indexes and Standards for the Classification of Rock Mass Blastability

##### 2.1. Selection of Classification Index

Explosive blasting can fracture a rock mass in two ways. First, the cohesive force between rock granules can be overcome, thereby rupturing the internal rock structure and producing a new fracture surface. Second, primary and secondary fractures can be exacerbated via further expansion. Therefore, the primary influential factors of rock mass blastability are the physical and mechanical properties of the rock and the structural characteristics of the rock mass [16]. Typical indexes for classifying rock mass blastability include the rock density, rock wave impedance, rock tensile strength, integrity coefficient of the rock mass, and the mean crack interval of the rock mass. These indexes reflect different aspects of rock mass blastability. However, to simplify rock mass blastability classification and enable its practical application, all of the indexes are not used. The characteristics of a rock mass must be considered when choosing indexes for rock mass blastability classification. Minor representative indexes can comprehensively reflect different aspects of the rock mass blastability. There should be little or no correlation between the indexes. The chosen indexes should be easy to obtain using various methods, such as experiments and field measurements. The aforementioned considerations were used to select the following final indexes for when considering rock mass blastability.

###### 2.1.1. Protodyakonov Coefficient and Tensile Strength of Rock

The shock wave and detonation gas produced by explosive blasting can typically rupture a rock mass through pulling and pressing. Therefore, the Protodyakonov coefficient and tensile strength of the rock are important parameters in rock mass blastability. During blasting, the rock is subject to temporary impact loading, for which the rock dynamic loading strength is clearly higher than the rock static loading strength. Therefore, the rock mass blastability can be accurately measured by indexes for the dynamic loading strength that are affected by the triaxial effect of the rock. However, the dynamic loading strength of rock is difficult to measure and exhibits a strong linear correlation with the uniaxial static loading compression strength and tensile strength [17]. Thus, the static loading strength is chosen as one of the indexes for rock mass blastability classification. The Protodyakonov coefficient of the rock, which is determined from the uniaxial compressive strength of the rock (1), is an objective measure of rock fastness that is widely applied in China. Therefore, the Protodyakonov coefficient and compressive strength of the rock are chosen as indexes for rock mass blastability classification:

In the equation above, is the Protodyakonov coefficient of the rock; is the rock’s uniaxial compressive strength in MPa; and is a constant equal to 10 MPa.

###### 2.1.2. Rock Density

The energy produced from rock blasting is transferred into kinetic energy in the rock block, which can result in the displacement or thrusting of the rock block. A higher rock density causes more of the energy produced in rock blasting to be consumed by the displacement and thrusting of the rock. Therefore, the amount of energy consumed is indicative of the difficulty of the rock blast; that is, the rock mass blastability decreases with increasing rock density. Therefore, the rock density is generally used as an index for rock mass blastability classification.

###### 2.1.3. Rock Wave Impedance

The dynamic Poisson’s ratio, dynamic elastic modulus, bulk modulus, and Lamé parameter for rock can be derived from the P- and S-wave velocities of the rock. All of the physical property indexes of rocks such as the mineral composition, porosity, water-bearing, and weathering degree are captured in the P-wave velocity of the rock. The P-wave velocity of the rock can be easily measured. The rock wave impedance can be obtained by multiplying the P-wave velocity of the rock by the rock density (2). The impedance is a measure of the force of the disturbance required to produce a unit speed of a moving rock particle during the transmission of a stress wave in the rock and is a measure of the resistance of the rock to momentum transfer. Therefore, the rock wave impedance is chosen as one of the indexes for the rock mass blastability classification:

In the equation above, denotes the rock wave impedance (10^{6} kg/m^{3} × m/s), denotes the rock density (kg/m^{3}), and denotes the P-wave velocity of the rock (m/s).

###### 2.1.4. Integrity Coefficient of Rock Mass

The geological properties of a rock mass, such as the integrity, fissure, and degree of development of a joint fissure, are captured in the P-wave velocity of the rock mass. A fast wave propagation velocity in a rock mass typically corresponds to mild rock densification, hardness, integrity, and weathering. In contrast, a slow wave propagation velocity corresponds to severe rock porosity, weakness, fragmentation, structural development, and weathering. The integrity coefficient of a rock mass is given by the square of the ratio of the P-wave velocity of a rock mass to the P-wave velocity of the rock (3), which reflects the extent of fracturing for a geological discontinuity, such as a joint fissure. A rock mass with a small integrity coefficient is susceptible to a large amount of rock mass crushing, and the rock mass can be easily blasted. Therefore, the integrity coefficient of the rock mass is chosen as one of the indexes for the rock mass blastability classification:

In the equation above, denotes the integrity coefficient of the rock mass, denotes the P-wave velocity of the rock mass (m/s), and denotes the P-wave velocity of the rock (m/s).

In conclusion, five indexes were chosen for the rock mass blastability classification: the Protodyakonov coefficient and tensile strength of the rock, rock density, rock wave impedance, and the integrity coefficient of the rock mass. Among these indexes, the Protodyakonov coefficient and tensile strength of the rock are mechanical property indexes of the rock, the rock density and rock wave impedance are physical property indexes of the rock; and the integrity coefficient of the rock mass is a measure of the geological properties of the rock mass. These five indexes primarily reflect the relevant physical and mechanical properties and characteristics of the geological structure of a rock mass and blasting and can be easily obtained by field measurements and experiments.

##### 2.2. Determination of the Standards for Rock Mass Blastability Classification

The value selection and designation of classification standards play an important role in the development of models for rock mass blastability classification. In the literature, the standards for classification indexes are determined using five ranks for rock mass blastability: very easy, easy, moderate, difficult, and very difficult. These classification standards for rock mass blastability are shown in Table 1 [18].