采动地表下沉时间序列的曲线拟合研究
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摘要
基于煤层开采地表下沉的时间过程为先加速后减速的变速运动的特征,提出了一种适合采动地表下沉时间序列曲线的拟合函数,分析了该函数中的拟合参数b和c对曲线形态、下沉速度和加速度的影响规律。用1stOpt 1.5软件编制计算程序,拟合了实测的煤层开采引起的地表下沉时间序列曲线,并与其他3种类型的拟合函数进行了对比分析。研究结果表明:提出的拟合函数的数学公式简单、参数数量适中,从下沉曲线形态,下沉速度和加速度3个方面均符合煤层开采地表下沉的动态过程。该拟合函数对实测曲线的拟合精度高,拟合的相关系数为0.996 8,用该拟合函数预测的最大下沉量468.7 mm、计算出的最大下沉速度为0.325 mm/d,对应的时间594.3 d,均与实测值接近。
A fitting function suitable for surface subsidence time series curve is proposed based on the characteristics of the variable speed of the surface subsidence after coal seam mining. The influence of fitting parameters b and c on curve shape,subsidence velocity and acceleration are analyzed. The calculation program was compiled with 1stOpt 1.5 Software,and a time series curve of surface subsidence caused by coal seam mining was measured and compared with other three types of fitting functions. The research results show that the proposed mathematical formula of the fitting function is simple and the number of parameters is moderate. From the aspects of sinking curve shape,sinking speed and sinking acceleration,it is consistent with the dynamic process of surface subsidence in coal seam mining. The fitting function has high fitting precision to the measured curves,and the correlation coefficient of the fitting is 0.9968. The maximum sinking amount predicted by the fitting function is 468.7 mm,and the calculated maximum sinking speed is 0.325 mm/d,and the corresponding time is 594.3 d,which are all close to the measured value.
A fitting function suitable for surface subsidence time series curve is proposed based on the characteristics of the variable speed of the surface subsidence after coal seam mining. The influence of fitting parameters b and c on curve shape,subsidence velocity and acceleration are analyzed. The calculation program was compiled with 1stOpt 1.5 Software,and a time series curve of surface subsidence caused by coal seam mining was measured and compared with other three types of fitting functions. The research results show that the proposed mathematical formula of the fitting function is simple and the number of parameters is moderate. From the aspects of sinking curve shape,sinking speed and sinking acceleration,it is consistent with the dynamic process of surface subsidence in coal seam mining. The fitting function has high fitting precision to the measured curves,and the correlation coefficient of the fitting is 0.9968. The maximum sinking amount predicted by the fitting function is 468.7 mm,and the calculated maximum sinking speed is 0.325 mm/d,and the corresponding time is 594.3 d,which are all close to the measured value.
引文
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[15]王正帅,邓喀中.采动区地表动态沉降预测的Richards模型[J].岩土力学,2011,32(6):1664-1668.WANG Zhengshuai,DENG Kazhong.Richards Model of surface dynamic subsidence prediction in mining area[J].Rock and Soil Mechanics,2011,32(6):1664-1668.
[16]张兵,崔希民.开采沉陷动态预计的分段Knothe时间函数模型优化[J].岩土力学,2017,38(2):541-548.ZHANG Bing,CUI Ximin.Optimization of segmented Knothe Time Function model for dynamic prediction of mining subsidence[J].Rock and Soil Mechanics,2017,38(2):541-548.
[17]常占强,王金庄.关于地表点下沉时间函数的研究:改进的克诺特时间函数[J].岩石力学与工程学报,2003,22(9):1496-1499.CHANG Zhanqiang,WANG Jinzhuang.Study on time function of subsidence:the improved Knothe Time Function[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(9):1496-1499.
[18]尤明庆.试验结果的数学拟合与力学模型[J].岩石力学与工程学报,2008,27(2):251-256YOU Mingqing.Discussion on mathematical fitness and mechanical model of experimental results[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(2):251-256
[19]朱珉仁.Morgan-Mercer-Flodin模型和Weibull模型的拟合[J].数学的实践与认识,2003,33(1):1-4.Zhu Minren.Fitting on Morgan-Mercer-Flodin Model and Weibull Model[J].Mathematics in Practice and Theory,2003,33(1):1-4
[20]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.
[2]袁亮.煤炭精准开采科学构想[J].煤炭学报,2017,42(1):1-7.Yuan Liang.Scientific conception of precision coal mining[J].Journal of China Coal Society,2017,42(1):1-7
[3]钱鸣高,许家林,王家臣.再论煤炭的科学开采[J].煤炭学报,2018,43(1):1-13.QIAN Minggao,XU Jialin,WANG Jiachen.Further on the sustainable mining of coal[J].Journal of China Coal Society,2018,43(1):1-13
[4]刘见中,申宝宏,姜鹏飞,等.提高我国煤炭科学产能的技术对策[J].煤炭科学技术,2013,41(1):21-55.LIU Jianzhong,SHEN Baohong,JIANG Pengfei,et al.Technical countermeasures of improving china coal production capacity[J].Coal Science and Technology,2013,41(1):21-55.
[5]李绪国.我国煤炭资源安全高效绿色开发现状与思路[J].煤炭科学技术,2013,41(8):53-57.LI Xuguo.Status and idea on safety and high efficient and green development of china coal resources[J].Coal Science and Technology,2013,41(8):53-57
[6]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.
[7]左建平,孙运江,文金浩,等.岩层移动理论与力学模型及其展望[J].煤炭科学技术,2018,46(1):1-11,87.ZUO Jianping,SUN Yunjiang,WEN Jinhao,et al.Theoretical and mechanical models of rock strata movement and their prospects[J].Coal Science and Technology,2018,46(1):1-11,87.
[8]李德海,许国胜,余华中.厚松散层煤层开采地表动态移动变形特征研究[J].煤炭科学技术,2014,42(7):103-106.,LI Dehai,XU Guosheng,YU Huazhong.Study on features of surface dynamic movement and deformation caused by coal mining under thick alluvium[J].Coal Science and Technology,2014,42(7):103-106.
[9]侯得峰,李德海,许国胜,等.厚松散层下采高对地表动态沉降特征的影响[J].煤炭科学技术,2016,44(12):191-196.HOU Defeng,LI Dehai,XU Guosheng,,et al.Impact of mining thickness on dynamic subsidence characteristics in condition of mining under thick unconsolidated layers[J].Coal Science and Technology,2016,44(12):191-196
[10]何国清,杨伦,凌赓娣,等.矿山开采沉陷学[M].徐州:中国矿业大学出版社,1991.
[11]沈光寒,李白英,吴戈,等.矿井特殊开采的理论与实践[M].北京:煤炭工业出版社,1992.
[12]刘玉成,曹树刚,刘延保.可描述地表沉陷动态过程的时间函数模型探讨[J].岩土力学,2010,31(3):925-930.LIU Yucheng,CAO Shugang,LIU Yanbao.Discussion on some time functions for describing dynamic course of surface subsidence due to mining[J].Rock and Soil Mechanics,2010,31(3):925-930.
[13]刘玉成.基于Weibull时间序列的动态沉陷曲线模型[J].岩土力学,2013,34(8):2409-2413.LIU Yucheng.Dynamic surface subsidence curve model based on Weibull time function[J].Rock and Soil Mechanics,2013,34(8):2409-2413.
[14]刘玉成.煤层开采地表移动过程的FLAC3D模拟研究[J].煤炭科学技术,2012,40(5):93-95.LIU Yucheng.Study on FLAC3Dsimulation of surface ground movement process for underground seam mining[J].Coal Science and Technology,2012,40(5):93-95.
[15]王正帅,邓喀中.采动区地表动态沉降预测的Richards模型[J].岩土力学,2011,32(6):1664-1668.WANG Zhengshuai,DENG Kazhong.Richards Model of surface dynamic subsidence prediction in mining area[J].Rock and Soil Mechanics,2011,32(6):1664-1668.
[16]张兵,崔希民.开采沉陷动态预计的分段Knothe时间函数模型优化[J].岩土力学,2017,38(2):541-548.ZHANG Bing,CUI Ximin.Optimization of segmented Knothe Time Function model for dynamic prediction of mining subsidence[J].Rock and Soil Mechanics,2017,38(2):541-548.
[17]常占强,王金庄.关于地表点下沉时间函数的研究:改进的克诺特时间函数[J].岩石力学与工程学报,2003,22(9):1496-1499.CHANG Zhanqiang,WANG Jinzhuang.Study on time function of subsidence:the improved Knothe Time Function[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(9):1496-1499.
[18]尤明庆.试验结果的数学拟合与力学模型[J].岩石力学与工程学报,2008,27(2):251-256YOU Mingqing.Discussion on mathematical fitness and mechanical model of experimental results[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(2):251-256
[19]朱珉仁.Morgan-Mercer-Flodin模型和Weibull模型的拟合[J].数学的实践与认识,2003,33(1):1-4.Zhu Minren.Fitting on Morgan-Mercer-Flodin Model and Weibull Model[J].Mathematics in Practice and Theory,2003,33(1):1-4
[20]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.