Evaluation of goaf stability based on fuzzy statistical method

doi:10.16265/j.cnki.issn1003-3033.2023.02.0629

Abstract

Abstract:

Aiming at the subjective arbitrariness of weight calculation about goaf stability evaluation index and the fuzzy uncertainty of index classification standard, more than 60 research results about goaf stability evaluation in recent ten years were collected to analyze the frequency of goaf stability evaluation indexes by literature research method, and the goaf stability evaluation index system was established based on index statistical frequency. According to the distribution information characteristics of the relative frequency of the evaluation index about goaf stability, the 1-9 scale method was used to describe the relative relationship of 18 equal length distribution intervals of the relative frequency, and the weight calculation method based on the relative frequency of the index was established to reduce the influence of subjective randomness on the calculation of index weight. The membership function of each grade about goaf stability evaluation index was established based on the statistical analysis of the boundary information of each evaluation index, and the reliability of the membership function was verified by using 30 goaf sample data. The goaf stability evaluation model based on the index relative frequency weight algorithm and the membership function of each grade about the evaluation index was constructed and applied to the stability evaluation analysis of the goaf in Xiaojiahe Phosphate Mine. The results show that the grade of the goaf stability of the phosphate mine is gradeⅠ, and the evaluation results conform with the reality, which verifies the effectiveness of the evaluation model of the goaf stability.

Key words: goaf, stability evaluation, fuzzy statistical method, membership function, index relative frequency

KE Lihua, MENG Yaoyao, YAO Nan, WANG Qihu, TANG Huaqian. Evaluation of goaf stability based on fuzzy statistical method[J]. China Safety Science Journal, 2023, 33(2): 59-67.

Figures/Tables 11

Tab.1

Fig.1

Tab.2

Scale of judgment matrix based on relative frequency method and its meaning

标度值	所属分度区间( $T r k > 1)$	标度值	所属分度区间( $T r k < 1)$
1	$[1,\frac{8+\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9})$	1	$[\frac{8+\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9},1]$
3	$[\frac{7+2\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9},\frac{2+\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{3})$	1/3	$[\frac{2+\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{3},\frac{7+2\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9})$
5	$[\frac{5+4\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9},\frac{4+5\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9})$	1/5	$[\frac{4+5\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9},\frac{5+4\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9})$
7	$[\frac{1+2\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{3},\frac{2+7\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9})$	1/7	$[\frac{2+7\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9},\frac{1+2\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{3})$
9	$[\frac{1+8\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9},\text{max}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right))$	1/9	$[\text{min}\left( \frac{{{D}_{jr}}}{{{D}_{jk}}} \right),\frac{1+8\text{min}\left( \frac{{{\text{D}}_{\text{jr}}}}{{{\text{D}}_{\text{jk}}}} \right)}{9})$
2,4,6,8	介于以上2个相邻判断的中值	1/2、1/4、1/6、1/8	介于以上2个相邻判断的中值

Tab.2

Tab.3

Relative frequency of indicators and construction of judgment matrix

指标相对频次						标准值	$m a x T r k$	$m i n T r k$	判断矩阵 $R 1 - 3$	$W$	C.R. <0.1
指标相对频次						标准值	1.30	0.77	判断矩阵 $R 1 - 3$	$W$
	$X 1$		$X 2$		$X 3$		1、1	[1,1.03)	[0.97,1)	$1 1 / 3 6 319 1 / 6 1 / 9 1$		0.28 0.66 0.06
$X 1$	1.00		0.92		1.19		3、1/3	[1.07,1.10)	[0.92,0.95)
$X 2$	1.09		1.00		1.30		5、1/5	[1.13,1.17)	[0.87,0.90)
$X 3$	0.84		0.77		1.00		7、1/7	[1.20,1.23)	[0.82,0.85)
—							9、1/9	[1.27,1.30]	[0.77,0.80)
指标相对频次							标准值	$m a x T r k$	$m i n T r k$	判断矩阵 $R 11 - 14$	$W$	C.R. <0.1
指标相对频次							标准值	1.83	0.55	判断矩阵 $R 11 - 14$	$W$
	$X 11$	$X 12$		$X 13$		$X 14$	1、1	[1,1.09)	[0.95,1)	$1292 1 / 2 171 1 / 9 1 / 7 1 1 / 7 1 / 2 171$	0.45 0.25 0.04 0.25
$X 11$	1.00	1.16		1.83		1.16	3、1/3	[1.18,1.28)	[0.85,0.90)
$X 12$	0.86	1.00		1.58		1.00	5、1/5	[1.37,1.46)	[0.75,0.80)
$X 13$	0.55	0.63		1.00		0.63	7、1/7	[1.55,1.65)	[0.65,0.70)
$X 14$	0.86	1.00		1.58		1.00	9、1/9	[1.74,1.83]	[0.55,0.60)

Tab.3

Fig.2

Tab.4

Distribution information of grade dividing points of goaf stability evaluation index

等级分界点	$X 11$	$X 12$	$X 13$	$X 14$	$X 21$	$X 22$	$X 23$	$X 24$	$X 25$	$X 31$	$X 32$	$X 33$
$v j Ⅰ - Ⅱ$	100~200	100~800	1~3	0.75~0.9	60~280	60~90	0.75~0.9	0.75~0.9	0.75~0.9	0.75~0.9	0.75~0.9	0.75~0.9
$v j Ⅱ - Ⅲ$	200~500	400~1 500	0.3~0.5	0.5~0.6	30~120	50~75	0.5~0.6	0.5~0.6	0.5~0.6	0.5~0.6	0.5~0.6	0.5~0.6
$v j Ⅲ - Ⅳ$	300~1 000	800~2 400	0.25~0.33	0.25~0.3	20~70	25~50	0.25~0.3	0.25~0.3	0.25~0.3	0.25~0.3	0.25~0.3	0.25~0.3

Tab.4

Tab.5

Goaf index membership function

	稳定性隶属度函数 $x ≤ v j Ⅰ - Ⅱ$	基本稳定性隶属度函数 $v j Ⅰ - Ⅱ ≤ x ≤ v j Ⅱ - Ⅲ$	不稳定性隶属度函数 $v j Ⅱ - Ⅲ ≤ x ≤ v j Ⅲ - Ⅳ$	极不稳定性隶属度函数 $x > v j Ⅲ - Ⅳ$
$X 11$	$1 - Φ x - 137.6 22.49$	$Φ x - 137.6 22.49 - Φ x - 236.4 22.25$	$Φ x - 236.4 22.5 - Φ x - 413.1 22.5$	$Φ x - 413.1 22.8$
$X 12$	$1 - Φ x - 903.8 22.49$	$Φ x - 903.8 22.49 - Φ x - 1 250 24.86$	$Φ x - 1 250 24.86 - Φ x - 2 773 24.86$	$Φ x - 2 773 24.86$
$X 13$	$Φ x - 1.125 0.062$	$Φ x - 0.695 3 0.081 - Φ x - 1.125 0.062$	$Φ x - 0.304 3 0.079 - Φ x - 0.695 3 0.081$	$1 - Φ x - 0.304 3 0.079$
$X 21$	$Φ x - 68.05 3.35$	$Φ x - 55 2.55 - Φ x - 68.05 3.35$	$Φ x - 50.94 9.74 - Φ x - 55 2.55$	$1 - Φ x - 413.1 22.8$
$X 22$	$Φ x - 67.94 3.41$	$Φ x - 58.3 3.35 - Φ x - 67.94 3.41$	$Φ x - 41.77 3.5 - Φ x - 58.3 3.35$	$1 - Φ x - 41.77 3.5$
其他指标	$Φ x - 0.75 0.025$	$Φ x - 0.58 0.033 - Φ x - 0.75 0.025$	$Φ x - 0.28 0.033 - Φ x - 0.58 0.033$	$1 - Φ x - 0.28 0.033$

Tab.5

Fig.3

Tab.6

Fig.4

Tab.7

Stability evaluation index data of goaf in Xiaojiahe Phosphate Mine

指标	$X 11$	$X 12$	$X 13$	$X 14$	$X 21$	$X 22$	$X 23$	$X 24$	$X 25$	$X 31$	$X 32$	$X 33$
指标值	600	316.2	0.38	0.8	76.83	65	0.4	0.8	0.8	0.85	0.9	0.9

Tab.7

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指标名称	频次	指标名称	频次	指标名称	频次	指标名称	频次
水文状况	48	岩石抗压强度	29	采空区高度	21	采空区形成时间	10
采空区埋深	44	采空区高跨比	24	工程布置	21	采矿影响	10
地质状况	40	采空区跨度	24	周边采矿影响	21	岩石抗拉强度	9
采空区顶板暴露面积	38	岩体结构	24	矿体倾角	15	构造应力	8
矿柱留设	38	采空区空间形态	24	顶板特性	13	节理条件	7
采空区联通情况	37	岩石质量指标(Rock Quality Designation, RQD)	23	爆破扰动影响	11	结构面间距	7