基于博弈论G1-EW-TOPSIS法的岩体质量评价和应用

doi:10.11872/j.issn.1005-2518.2022.05.148

Abstract

Abstract:

The reasonable evaluation of rock quality is the basis for engineering design and construction，and it is of great significance to the safe production and economic benefits of mines.In view of the complex conditions and ambiguity of rock quality evaluation，on the basis of comprehensive reference to relevant research literature，five parameters were selected as rock quality evaluation indexes，including core quality index RQD value（X₁），uniaxial compressive strength of rock σ_c（X₂），rock integrity coefficient K_v（X₃），structural surface strength coefficient J（X₄）and unit time water seepage S（X₅），and a rock quality evaluation model of G1-EW-TOPSIS method based on game theory idea was proposed and applied to the rock quality evaluation of the first mining middle section of a silver polymetallic mine in Inner Mongolia.To verify the validity of the model，firstly，a field survey was conducted to determine five measurement points for the structural surface condition and groundwater flow of the rock mass in the first mining middle section of the mine，and then the subjective weight ω₁ and objective weight ω₂ of the indexes of the measurement points were obtained by combining the G1 method and EW method through game theory to obtain the comprehensive weight ω.Finally，TOPSIS was used to calculate the relative closeness of each measurement point under each rock quality class to determine the rock quality class of the measurement point.The results show that the five rock quality grade evaluation indexes selected in this paper can better reflect the state of the rock mass.The method of calculating the com-prehensive weight of the model not only overcomes the shortcomings of the single assignment method，but also reduces the error and improves the ability of the model to deal with multi-objective decision problems.The rock quality in the first middle section of this mine is mainly evaluated as grade Ⅲ and grade Ⅳ，the rock quality is poor，and the support needs to be strengthened for the roadway and the exposed surrounding rock of the quarry where the rock quality is grade Ⅳ.The calculation results of the model completely match with the rock quality of 5 measurement points at the mine engineering site，which provides a new idea for rock quality evaluation.

Key words: rock mass quality evaluation, combination weighting, TOPSIS, game theory, G1 method, entropy weight method

CLC Number:

TD853.3

Xianfeng XU,Pengfei XING,Suihong WANG,Yong WANG. Rock Mass Quality Evaluation and Application Based on Game Theory and G1-EW-TOPSIS Method[J].Gold Science and Technology, 2022, 30(5): 704-712.

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r_l	赋值说明
1.0	评价指标X_l 与评价指标X_l_-1重要程度一样
1.2	评价指标X_l_-1的重要程度与评价指标X_l 相比稍微重要
1.4	评价指标X_l_-1与评价指标X_l 的重要程度介于稍微重要和非常重要之间
1.6	评价指标X_l_-1的重要程度与评价指标X_l 相比非常重要
1.8	评价指标X_l_-1的重要程度与评价指标X_l 相比极度重要

岩石质量等级	X₁/%	X₂/MPa	X₃	X₄	X₅/［L·min^-1·（10 m）^-1］
Ⅰ（稳定）	90~100	120~200	0.75~1.00	0.8~1.0	0~5
Ⅱ（较稳定）	75~90	60~120	0.45~0.75	0.6~0.8	5~10
Ⅲ（基本稳定）	50~75	30~60	0.30~0.45	0.4~0.6	10~25
Ⅳ（不稳定）	25~50	15~30	0.20~0.30	0.2~0.4	25~125
Ⅴ（极不稳定）	0~25	0~15	0~0.20	0~0.2	125~300

测点编号	指标值
测点编号	X₁	X₂	X₃	X₄	X₅
1	105.01	62	0.46	5.8	6.1
2	92.84	55	0.41	4.2	5.4
3	92.84	60	0.44	4.7	6.7
4	105.01	68	0.47	5.3	8.5
5	76.80	83	0.48	6.2	7.9

专家编号	指标排序	r₂	r₃	r₄	r₅
1	X₂>X₃>X₄>X₁>X₅	1.6	1.5	1.4	1.3
2	X₂>X₄>X₁>X₃>X₅	1.7	1.0	1.2	1.1
3	X₂>X₃>X₅>X₄>X₁	1.7	1.2	1.3	1.0
4	X₃>X₂>X₄>X₅>X₁	1.6	1.4	1.2	1.1

指标	专家排序结果				ω₁
指标	专家1	专家2	专家3	专家4	ω₁
X₁	0.243	0.143	0.173	0.225	0.196
X₂	0.389	0.321	0.353	0.359	0.356
X₃	0.089	0.158	0.133	0.122	0.126
X₄	0.116	0.189	0.208	0.160	0.168
X₅	0.162	0.189	0.133	0.134	0.155

Rock Mass Quality Evaluation and Application Based on Game Theory and G1-EW-TOPSIS Method

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指标	ω₂	ω
X₁	0.160	0.178
X₂	0.267	0.313
X₃	0.162	0.144
X₄	0.199	0.183
X₅	0.212	0.183

测点	相对贴进度					本文方法	G1法	EW法	工程实测
测点	Ⅰ	Ⅱ	Ⅲ	Ⅳ	Ⅴ	本文方法	G1法	EW法	工程实测
1	0.5	0.465	0.516	0.497	0.5	Ⅲ	Ⅳ	Ⅲ	Ⅲ
2	0.5	0.478	0.510	0.592	0.5	Ⅳ	Ⅳ	Ⅲ	Ⅳ
3	0.5	0.476	0.497	0.432	0.5	Ⅲ	Ⅲ	Ⅲ	Ⅲ
4	0.5	0.502	0.505	0.468	0.5	Ⅲ	Ⅳ	Ⅲ	Ⅲ
5	0.5	0.512	0.491	0.480	0.5	Ⅲ	Ⅲ	Ⅲ	Ⅲ

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