Line integral method for predicting surface subsidence in irregular working face mining
-
摘要: 沉陷预计方法对于预判煤层开采诱发的负面影响十分重要。概率积分法是开采沉陷预计的重要方法,但对于不规则工作面开采,其预计精度有待提高。本文针对这一问题,利用格林公式(Green formula)对概率积分法公式进行积分转换,将对工作面的积分转换为对采区边界的线积分;将边界简化分割为多条直线段,分别对各直线段作积分计算;通过叠加计算完成地表任意点及地表沉陷盆地移动变形预计;最后基于某实例进行了应用研究,验证了本文方法的有效性,相比概率积分法,本文提出的线积分法预计精度提高了23 %。Abstract: The subsidence prediction method is very important for predicting the negative impact induced by coal mining.Probability integral method is an important method for mining subsidence prediction, but for irregular working face mining, its prediction accuracy needs to be improved.Aiming at this problem, the Green formula was used in this paper to transform the formula of the probability integration method, and convert the integration of the working face to the line integration of the boundary of the mining area; the boundary of working face was simplified and divided into multiple straight line segments, and each straight line segment was integrated separately; the prediction of the movement and deformation of any point on the surface and the surface subsidence basin was completed through superposition calculation; finally, an application study was carried out based on a certain example, which verified effectiveness of the method in this paper.Compared with the result of the probability integration method, the prediction accuracy of the line integral proposed in this paper was improved by 23 %.
-
表 1 预计与实测结果对比
Table 1. Comparison between expected and measured results
观测站名 X/m Y/m WM/mm WL/mm WP/mm EL/mm KL/% EP/mm KP/% Z24 21 407.759 12 806.044 712 775 1053 63 9 342 48 Z23 21 398.671 12 820.932 762 730 1044 33 4 281 37 Z22 21 412.550 12 812.203 730 767 1044 37 5 314 43 Z21 21 444.825 12 833.500 785 749 984 36 5 200 25 Z20 21 458.626 12 854.431 825 753 918 72 9 94 11 Z19 21 485.023 12 868.538 824 751 852 73 9 28 3 Z18 21 511.239 12 887.827 815 706 773 109 13 42 5 Z17 21 546.331 12 894.322 787 690 728 97 12 59 8 Z16 21 565.749 12 877.906 801 714 759 87 11 42 5 Z15 21 602.747 12 890.826 755 661 676 94 12 79 10 Z14 21 630.499 12 907.033 673 567 583 106 16 90 13 Z13 21 659.265 12 909.485 622 526 532 96 15 91 15 Z12 21 687.566 12 923.365 572 437 437 135 24 135 24 Z11 21 714.213 12 916.019 524 409 406 115 22 118 23 Z10 21 727.008 12 925.877 445 357 353 88 20 92 21 Z09 21 761.254 12 929.839 375 278 273 97 26 102 27 Z08 21 772.381 12 952.902 331 213 208 118 36 122 37 Z07 21 797.187 12 978.393 265 135 132 129 49 133 50 Z06 21 838.361 13 012.708 221 60 58 161 73 163 74 Z05 21 862.588 13 018.361 194 42 40 152 78 154 79 Z04 21 893.285 13 027.978 183 24 23 159 87 160 87 Z03 21 928.004 13 025.148 151 14 14 137 90 138 91 Z02 21 966.312 13 013.130 181 8 8 172 95 173 96 Z01 21 987.028 13 021.893 130 5 5 125 96 125 96 注:X、Y为观测站坐标;WM、WL、WP分别为地表下沉实测值、线积分法预计值和概率积分法预计值;EL、EP表示利用线积分法和概率积分法计算时,地表下沉预计值与实测值的绝对偏差;KL、KP表示利用线积分法和概率积分法计算时,地表下沉预计值与实测值的相对偏差。 表 2 精度评定
Table 2. Assessment of accuracy
误差种类 E平均/mm K平均/% M绝对/mm M相对/% RMSE/mm 线积分法 104 34 33 30 111 概率积分法 136 39 81 32 158 注:E平均、K平均分别为两方法预计结果与实际观测值的绝对偏差、相对偏差的平均值;M绝对、M相对分别为绝对偏差和相对偏差的中误差;RMSE为均方根误差。 -
[1] 邓喀中. 变形监测及沉陷工程学[M]. 徐州: 中国矿业大学出版社, 2014: 10-12. [2] 崔希民, 邓喀中. 煤矿开采沉陷预计理论与方法研究评述[J]. 煤炭科学技术, 2017, 45(1): 160-169.Cui Ximin, Deng Kazhong. Research review of predicting theory and method for coal mining subsidence[J]. Coal Science and Technology, 2017, 45(1): 160-169. [3] 郭增长, 殷作如, 王金庄. 随机介质碎块体移动概率与地表下沉[J]. 煤炭学报, 2000, 25(3): 264-267. doi: 10.3321/j.issn:0253-9993.2000.03.010Guo Zengzhang, Yin Zuoru, Wang Jinzhuang. Random medium shiver movement probability and surface subsidence[J]. Journal of China Coal Society, 2000, 25(3): 264-267. doi: 10.3321/j.issn:0253-9993.2000.03.010 [4] Wang Zijian, Li Guangjie, You Bing, et al. Application of probability integral method in ground deformation prediction[J]. Global Geology, 2012, 15(3): 237-240. http://sjdz.jlu.edu.cn/Jweb_sjdz_en/CN/article/downloadArticleFile.do?attachType=PDF&id=8481 [5] 张华兴. 开采沉陷预测的标准化[J]. 煤矿开采, 2014, 19(1): 1-2, 20. https://www.cnki.com.cn/Article/CJFDTOTAL-MKKC201401002.htmZhang Huaxing. Standardization of mining subsidence prediction[J]. Coal Mining Technology, 2014, 19(1): 1-2, 20. https://www.cnki.com.cn/Article/CJFDTOTAL-MKKC201401002.htm [6] 刘欣, 吴昊, 贾勇帅, 等. 基于概率积分法的矿区地表沉陷预计分析[J]. 北京测绘, 2017(1): 123-126. doi: 10.3969/j.issn.1007-3000.2017.01.031Liu Xin, Wu Hao, Jia Yongshuai, et al. Surface mining subsidence predicting and analysis based on probability integral method[J]. Beijing Surveying and Mapping, 2017(1): 123-126. doi: 10.3969/j.issn.1007-3000.2017.01.031 [7] 张豪杰, 查剑锋, 李怀展. 概率积分法参数影响因素分析与研究展望[J]. 煤炭技术, 2015, 34(4): 18-21. https://www.cnki.com.cn/Article/CJFDTOTAL-MTJS201504007.htmZhang Haojie, Zha Jianfeng, Li Huaizhan. Analysis and prospect of influencing factors to parameters of probability integral method[J]. Coal Technology, 2015, 34(4): 18-21. https://www.cnki.com.cn/Article/CJFDTOTAL-MTJS201504007.htm [8] 李培现, 万昊明, 许月, 等. 基于地表移动矢量的概率积分法参数反演方法[J]. 岩土工程学报, 2018, 40(4): 767-776.Li Peixian, Wan Haoming, Xu Yue, et al. Parameter inversion of probability integration method using surface movement vector[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(4): 767-776. [9] 周棒, 康建荣, 胡晋山, 等. 基于改进果蝇算法的概率积分法预计参数反演[J]. 中国矿业, 2018, 27(11): 169-173, 180.Zhou Bang, Kang Jianrong, Hu Jinshan, et al. Prediction parameters inversion of the probability integral method based on the improved fruit flies algorithm[J]. China Mining Magazine, 2018, 27(11): 169-173, 180. [10] 贾艳昌, 谢谟文, 昌圣翔, 等. 基于概率积分法和自四归模型的开采沉陷算法[J]. 科学技术与工程, 2017, 17(7): 148-152. doi: 10.3969/j.issn.1671-1815.2017.07.026Jia Yanchang, Xie Mowen, Chang Shengxiang, et al. The subsidence prediction of goaf based on probability integral method and auto regressive moving average model[J]. Science Technology and Engineering, 2017, 17(7): 148-152. doi: 10.3969/j.issn.1671-1815.2017.07.026 [11] 张华兴, 焦传武. 地表移动精确预计法: 线积分运算[J]. 矿山测量, 1988(4): 21-29.Zhang Huaxing, Jiao Chuanwu. Precise prediction method of surface movement line integral operation[J]. Mine Surveying, 1988(4): 21-29. [12] 周万茂, 张华兴, 何瑞华. 任意形状工作面拐点移动距求取方法[J]. 煤矿开采, 2000, 5(4): 13-14, 16. doi: 10.3969/j.issn.1006-6225.2000.04.004Zhou Wanmao, Zhang Huaxing, He Ruihua. A method for determining the displacement distance of the inflection point of the mining faces with arbitrary shapes[J]. Coal Mining Technology, 2000, 5(4): 13-14, 16. doi: 10.3969/j.issn.1006-6225.2000.04.004 [13] 吴侃, 周鸣. 矿区沉陷预测预报系统[M]. 徐州: 中国矿业大学出版社, 1999. [14] 蔡音飞, 李晓静. 基于Mathematica的任意形状工作面离散化和沉陷预测[J]. 煤炭技术, 2017, 36(11): 148-150.Cai Yinfei, Li Xiaojing. Subsidence prediction and discretization of arbitrary-shape working face based on Mathematica[J]. Coal Technology, 2017, 36(11): 148-150. [15] 许冬, 王临清, 吴侃. 任意形状工作面沉陷预计计算方法[J]. 金属矿山, 2014(5): 55-59. https://www.cnki.com.cn/Article/CJFDTOTAL-JSKS201405014.htmXu Dong, Wang Linqing, Wu Kan. Mining subsidence prediction calculation methods of random shape working face[J]. Metal Mine, 2014(5): 55-59. https://www.cnki.com.cn/Article/CJFDTOTAL-JSKS201405014.htm [16] 赵晓东, 陈阳, 蒋建. 任意形状工作面沉陷预测的概率积分法及其应用[J]. 岩土力学, 2016, 37(12): 3387-3392, 3400. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201612006.htmZhao Xiaodong, Chen Yang, Jiang Jian. Probability integral method of arbitrary shape face to predict mining subsidence and its application[J]. Rock and Soil Mechanics, 2016, 37(12): 3387-3392, 3400. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201612006.htm [17] 李永树, 韩丽萍. 非规则采矿工作面积分区间确定方法[J]. 测绘学报, 2000, 29(2): 166-171. doi: 10.3321/j.issn:1001-1595.2000.02.013Li Yongshu, Han Liping. Method for defining integral region of any shape of mining face[J]. Acta Geodaetica et Cartographic Sinica, 2000, 29(2): 166-171. doi: 10.3321/j.issn:1001-1595.2000.02.013 [18] 张兵, 崔希民. 任意开采工作面积分区间的划分与实现[J]. 地矿测绘, 2009, 25(3): 7-9, 13. doi: 10.3969/j.issn.1007-9394.2009.03.003Zhang Bing, Cui Ximin. Establishment and realization of integral region for any shape of mining face[J]. Surveying and Mapping of Geology and Mineral Resources, 2009, 25(3): 7-9, 13. doi: 10.3969/j.issn.1007-9394.2009.03.003 [19] 周棒, 康建荣, 胡晋山, 等. 基于VC++的任意形状工作面计算坐标系的自动确定[J]. 矿业研究与开发, 2018, 38(9): 54-58.Zhou Bang, Kang Jianrong, Hu Jinshan, et al. Automatic determination of calculating coordinate system for arbitrary shape working face based on VC++ programming language[J]. Mining Research and Development, 2018, 38(9): 54-58. [20] 景慧丽, 刘华. 基于"以学为中心"理念的格林公式的探究式教学[J]. 首都师范大学学报: 自然科学版, 2020, 41(6): 76-79.Jing Huili, Liu Hua. Inquiry teaching of Green's formula based on "learning-centered"[J]. Journal of Capital Normal University: Natural Science Edition, 2020, 41(6): 76-79. [21] 熊菊霞, 黄勇, 靳庆庚, 等. 线面积分的类比教学法[J]. 教育教学论坛, 2019(10): 178-180.Xiong Juxia, Huang Yong, Jin Qinggeng, et al. The analogy method of teaching surface integration and curvilinear integration[J]. Education Teaching Forum, 2019(10): 178-180. [22] 阎跃观, 代文晨, 牛永泽, 等. 矿区非线性沉降的GM(1, 1)预计残差改进模型及应用[J]. 矿业科学学报, 2020, 5(5): 475-481. doi: 10.19606/j.cnki.jmst.2020.05.001Yan Yueguan, Dai Wenchen, Niu Yongze, et al. Improved GM(1, 1)model based on predicted residual in mining area with non-linear subsidence and its application[J]. Journal of Mining Science and Technology, 2020, 5(5): 475-481. doi: 10.19606/j.cnki.jmst.2020.05.001 [23] 郝登程, 王国瑞, 李培现, 等. 开采沉陷监测数据处理的分段卡尔曼滤波模型[J]. 矿业科学学报, 2021, 6(4): 371-378. doi: 10.19606/j.cnki.jmst.2021.04.001Hao Dengcheng, Wang Guorui, Li Peixian, et al. Subsection Kalman filter model for mining subsidence monitoring data processing[J]. Journal of Mining Science and Technology, 2021, 6(4): 371-378. doi: 10.19606/j.cnki.jmst.2021.04.001