Analytic Hierarchy Process-Fuzzy Comprehensive Evaluation Method-based Depletion Assessment Study of Xinshan Iron Ore Mine

: Taking the Xinshan iron ore mine as an example, this paper, based on collecting and analyzing the actual production data and similar simulation test data of this iron ore mine, analyses various factors affecting ore depletion by bottomless column segmental chipping method by using hierarchical analysis method (AHP) and fuzzy comprehensive evaluation method (FCE), and establishes an evaluation system for comprehensively assessing the depletion of the ores. The results show that structural parameters, blasting parameters, loading parameters, and geological conditions are the main factors affecting ore depletion. The structural parameters are the most important factors, accounting for 35%. With the increase of the released amount, the released grade gradually decreases, the depletion rate gradually increases, and the comprehensive evaluation value gradually decreases. The released body is an approximate ellipsoidal block with a wide upper and narrower lower part. The end wall plays an obstructive role in the flow of the bulk body, which makes the end of the released grade higher and the middle of the released body higher. At the same time, due to the influence of blasting and shovel loading, the particles in the release body show some sorting phenomena. This paper provides a scientific basis and reference for predicting and controlling ore depletion in the bottomless column segmental chipping method.


RESUMEN
Con la mina de hierro de Xinshan como un ejemplo y con el fin de recolectar y analizar la producción de información y los datos de prueba de simulaciones similares en esta mina, este trabajo analiza varios factores que afectan el agotamiento de la mena a través del método de astillado segmentario de pilar sin base por el Proceso de Análisis Jerárquico (del ingles AHP, Analytic Hierarchy Process) y por la Evaluación Integral Difusa (del inglés FCE, Fuzzy Evaluation Method, y establece un sistema de evaluación para medir ampliamente el agotamiento del recurso.Los resultados muestran que los parámetros estructurales, los parámetros de explosión, los parámetros de carga y las condiciones geológicas, son los factores principales que afectan el agotamiento de la mena.Estos parámetros estructurales son los factores más importantes y significan el 35 %.Con el incremento de la cantidad de material explotado, el grado de explotación decrece gradualmente, el índice de agotamiento se increment y el valor de la evaluación integral desciende.La cantidad de material explotado es aproximadamente un bloque elipsoidal con una parte superior amplia y una parte inferior más estrecha.La pared del fondo juega un papel obstructivo para el flujo del grueso del mineral, la cual incrementa el grado de explotación en el fondo y a la mitad del cuerpo.Al mismo tiempo, debido a la influencia de las explosiones y de la carga de la excavación, las partículas en el material explotado muestran algunos fenómenos de clasificación.Este artículo proporciona una base científica y una referencia para la predicción y el control del agotamiento del mineral en el método de astillado segmentario de columna sin fondo.

Introduction
Bottomless pillar segmental chipping is a mining method that uses selfweight to sink the overburden rock, chipping the ore body and releasing it through the discharge holes to the surface or underground storage (Wang et al., 1988).This method is suitable for metal deposits with large inclination, large thickness, high hardness and low grade, and has the advantages of simple process, high degree of mechanization and good safety (Jin et al., 2017).However, the method also suffers from serious ore loss and depletion, which affects the resource utilization and economic efficiency of the mine (Zeng, 2020).Ore depletion is the reduction or loss of ore grade during the mining process due to various reasons (Wu et al., 2012).Ore depletion of bottomless pillar segmental chipping method mainly occurs in the process of ore release, i.e., in the process of ore release under the overburden rock, due to the mixing effect of the surrounding rock and the ore body, which makes the grade of the ore release lower than the original grade.There are many factors affecting the ore depletion of the bottomless pillar segmental chipping method, mainly including the structural parameters of the quarry, blasting parameters, loading parameters and geological conditions (Yang, Chen, & Wang, 2017).
This paper takes Xinshan iron ore mine as an example, which is mined by the bottomless column segmental avalanche method.Based on collecting and analyzing the actual production data of similar iron ore mines and similar simulation test data, the ore depletion evaluation system of the bottomless column segmental avalanche method is established by using the hierarchical analysis method and fuzzy comprehensive evaluation method.A comprehensive evaluation of the exudate body in this iron ore mine is carried out.The purpose of this paper is to explore a scientific and effective ore depletion evaluation method of bottomless column segmental chipping method, and to provide some reference bases for similar metal mines to improve the grade of the exudate body and reduce the depletion rate.

Experimental analysis methods
The analytical methods in this paper is twofold: firstly, the hierarchical analysis method (AHP), which is used to determine the weights of the factors affecting ore depletion in the bottomless column segmental disintegration method; and secondly, the Fuzzy Comprehensive Evaluation (FCE), which is used to carry out a comprehensive evaluation of the releasing body based on the weights of the factors and the evaluation indexes.

Experimental step
The principle and methodology of the similarity simulation tests were referred to the literature (Zhang, 2023), and the main steps are as follows: 1. Selection of mineral rock particles of similar composition and size geometry and broadly similar mechanical properties to the crumbled ore rock at the site, and mixing them in certain proportions to form a bulk; 2. Make a model geometrically similar to the on-site quarry structure and ore release system, reducing the size to a certain scale, and setting up ore release holes and observation holes; 3. Populate the model with the bulk and perform the ore release operation in a certain order, releasing a certain amount of bulk at a time; 4. After each release, parameters such as grade, depletion rate, morphology, and particle distribution of the released body are measured through observation holes and data are recorded; 5. Repeat the above steps until all the bulk is released.There are two main sources of data for this paper: the actual production data from this iron ore mine and the similar simulation test data from this iron ore mine.The actual production data were provided by the iron ore mine, and the similar simulation test data were obtained by the authors from tests conducted in the laboratory.

Modelling the hierarchy
The principles and steps of hierarchical analysis method and fuzzy comprehensive evaluation method were referred to the literature ( [26] , and firstly, the hierarchical structure model of ore depletion evaluation by bottomless column segmental disintegration method was established.

Constructing a judgement matrix
As shown in Figure 3, the expert scoring method was used to make the determination of the degree of two-by-two matrix comparison, and the fuzzy linguistic variables from 1 to 9 were used to indicate the relative importance between the factors, as shown in Table 6, and the scoring resulted in Table 5;

Solve for the vector of evaluation indicator weights
Calculate the maximum eigenvalue and eigenvector of the judgement matrix, get the weights of each factor, and carry out the consistency test to ensure the reasonableness of the judgement matrix; since the judgement matrix is composed of fuzzy numbers, it is necessary to calculate the maximum eigenvalue and eigenvector using the algorithm in fuzzy mathematics, and use fuzzy consistency ratio to test the consistency; 1. Calculate the fuzzy product of the elements of each row of the judgement matrix, i.e., multiply the elements of each row by columns to obtain: Where a i1 ,a i2 ,a i3 ,a i4 denote the four elements of row i of the judgement matrix and -denotes the multiplication operation of fuzzy numbers, i.e..

, , (
) • , , ) = , ( 2. Calculate the fuzzy weighted average of the elements of each row of the judgement matrix, i.e., obtained by dividing the elements of each row by the median of their fuzzy product: 2, 3, 4   Where m i denotes the intermediate value of A i , i.e., m i = (A i ) 2 and / denotes the division operation of fuzzy numbers, i.e..

Conducting consistency tests
The specific steps and formulas for calculating the fuzzy consistency ratio to test consistency are as follows: 1. Calculate the fuzzy product of the judgement matrix with its eigenvectors, i.e., multiply each row element with its corresponding weight and sum the results by rows to obtain: 2, 3, 4   where n denotes the order of the judgement matrix.2. Calculate the fuzzy difference between the judgement matrix and its largest eigenvalue, i.e., subtract each row element from its corresponding largest eigenvalue and take the absolute value to obtain: where l denotes taking the absolute value sign and -denotes the subtraction operation of fuzzy numbers, i.e.. 3. Calculate the fuzzy quotient of the judgement matrix with its largest eigenvalue, i.e., divide each row element with its corresponding largest eigenvalue and take the reciprocal to obtain: = 1, 2, 3, 4   Continuing to calculate the fuzzy quotient of the judgement matrix with its largest eigenvalue yields.
Calculate the fuzzy consistency index of the judgement matrix, i.e., the fuzzy difference of the elements of each row is added to its corresponding fuzzy quotient and the minimum value is obtained: Calculate the fuzzy consistency ratio of the judgement matrix, i.e., divide the fuzzy consistency index of each row element with its corresponding random consistency index and take the minimum value to obtain: where RI denotes the random consistency index, when n = 4.RI=0.9,CR= , catch: CR= 0.0925 < 0.10 ,adopted by consensus.

Identification of evaluation indicators
The experimental data from the second segment was used to calculate the depletion because the second segment had good ore release.Based on the parameters such as grade, depletion rate, morphology and particle distribution of the releases, the releases are classified into four grades, namely, excellent, good, moderate and poor, and the definitions and ranges of the grades are given, as shown in Table 9.According to the evaluation indexes and the actual data of the releasing body, the affiliation function is established, and the fuzzy number is used to express the affiliation degree of the releasing body to each grade.The affiliation function can be expressed in the form of triangle or trapezoid, as shown in Figure 2. Where, x denotes the taste or depletion rate of the releasing body, and a,b,c denotes the range of each evaluation grade, as shown in Table 5. A(x) denotes the affiliation degree of the releasing body to the excellent, good, medium, and poor grades, which are represented by U A (x), U B (x), U C (x) and U D (x), respectively.For example, for a release volume of 1000 t with a taste of 1.2%, a depletion rate of 20%, an excellent morphology (set to class 3) and a good particle distribution (set to class 2), the degree of affiliation to each class can be calculated using the following steps: 1.The affiliation function can be calculated using the following formula where A(x) denotes the affiliation of the putative body to the excellent, good, moderate and poor grades.2. Determine the affiliation of the exudate taste and depletion rate to each grade based on the ranges in Table 11, as shown in Table 12.

Figure 1 .
Figure 1.Flow chart of Xinshan iron ore release simulation experiment

Figure 3 .
Figure 3. Front and side view of mine release model the maximum eigenvalues and eigenvectors of the judgement matrix, i.e., sum the elements of each column and normalise them to obtain:⎝ ⎠Where ∑ denotes the summation symbol and + denotes the addition operation of fuzzy numbers, i.e..As if:

Figure 5 .Figure 6 .Figure 7 .Figure 8 .
Figure 5.The relationship between different crumbling steps and the amount of waste rock released

Figure 9 .
Figure 9. Evaluation level and range of the emitter 2.3.2Creating an affiliation function

Table 1 .
Particle size volume parameter

Table 3 .
Classification of importance of indicators

Table 5 .
Judgment matrix after scoring

Table 6 .
Random consistency index RI

Table 7 .
Calculation of the amount of ore released at different crumbling steps in the second section

Table 8 .
Statistics of waste rock release at the cut-off release grade of each approach

Table 9 .
Evaluation levels of emitters and their definitions and ranges