Abstract：The first time fracturing of the main roof is often analyzed with the fixed boundary conditions at four edges which are difficult to achieve in practice. A mechanical model of elastic thin plate with the elastic boundary foundation condition was established. The influences of the elastic foundation coefficient k，the span L，the main roof thickness h，the elastic modulus E，Poisson?s ratio on the principal moments and initial fracture position of the main roof are calculated with the finite difference method. The first time fracturing of the main roof with the elastic foundation boundary calculated based on the fracture criterion of principal moments occurs in the middle or at the long side ahead of the coal wall. When the ratio of k/E or k/h3 or k/(Eh3) is constant，the fracture position of the main roof is not changed. When the ratio of k/E or k/h3 or k/(Eh3) is small，the middle of the main roof fractures firstly，namely，when the coal seam is soft and the thickness and elastic modulus of the main roof are large，the main roof fractures firstly in the middle. When the ratio of k/E or k/h3 or k/(Eh3) is large，the long side edge ahead of the coal wall fractures firstly，namely，when the coal seam is hard，and the thickness and elastic modulus of the main roof are small，the first fracturing position is at the long side edge ahead of the coal wall. The initial fracturing of the main roof with the elastic foundation boundary is determined by k，L and the stiffness D of the main roof.
何富连，陈冬冬，谢生荣. 弹性基础边界基本顶薄板初次破断的kDL效应[J]. 岩石力学与工程学报, 2017, 36(6): 1384-1399.
HE Fulian，CHEN Dongdong，XIE Shengrong. The kDL effect on the first fracture of main roof with elastic foundation boundary. , 2017, 36(6): 1384-1399.
[1] 杜计平，张先尘，贾维勇，等. 煤矿深井采场矿压显现及其控制特点[J]. 中国矿业大学学报，2000，29(1)：82–84.(DU Jiping，ZHANG Xianchen，JIA Weiyong，et al. Characteristics of strata behaviors and roof control for longwall faces in deep mining[J]. Journal of China University of Mining and Technology，2000，29(1)：82–84.(in Chinese))
[2] 曹胜根，缪协兴. 超长综放工作面采场矿山压力控制[J]. 煤炭学报，2001，26(6)：621–625.(CAO Shenggen，MIAO Xiexing. Ground pressure controlling on super-length fully-mechanized mining face with top-coal caving[J]. Journal of China Coal Society，2001，26(6)：621–625.(in Chinese))
[3] 张春雷，张 勇，李 立，等. 大倾角大采高综采工作面坚硬顶板控制技术[J]. 辽宁工程技术大学学报：自然科学版，2014，33(9)：1 172–1 177.(ZHANG Chunlei，ZHANG Yong，LI Li，et al. Control of hard roof in high inclined seam with large-mining-height full- mechanized workface[J]. Journal of Liaoning Technical University：Natural Science，2014，33(9)：1 172–1 177.(in Chinese))
[4] 钱鸣高，石平五，许家林. 矿山压力与岩层控制[M]. 徐州：中国矿业大学出版社，2003：73–97.(QIAN Minggao，SHI Pingwu，XU Jialin. Mine pressure and controlling of rock stratum[M]. Xuzhou：China University of Mining and Technology Press，2003：73–97.(in Chinese))
[5] 付建新，宋卫东，杜建华，等. 中深孔开采急倾斜薄矿体采场顶板力学模型及围岩扰动规律研究[J]. 岩石力学与工程学报，2014，33(1)：3 277–3 283.( FU Jianxin，SONG Weidong，DU Jianhua，et al. Study of stope roof mechanical model and wall rock disturbance law of steeply-inclined this orebody mining using medium-deep hole[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(1)：3 277–3 283.(in Chinese))
[6] 黄庆享. 采场老顶初次来压的结构分析[J]. 岩石力学与工程学报，1998，17(5)：521–526.(HUANG Qingxiang. Structural analysis of main roof stability during first weighting in longwall face[J]. Chinese Journal of Rock Mechanics and Engineering，1998，17(5)：521–526. (in Chinese))
[7] 黄庆享，祈万涛，杨春林. 采场老顶初次破断机理与破断形态分析[J]. 西安矿业学院学报，1999，19(3)：193–197.(HUANG Qingxiang，QI Wantao，YANG Chunlin. Analysis on the initial fracture mechanism and the broken form of stope main roof[J]. Journal of Xi?an Mining Institute，1999，19(3)：193–197.(in Chinese))
[8] 何富连，赵计生，姚志昌. 采场岩层控制论[M]. 北京：冶金工业出版，2009：27–33.(HE Fulin，ZHAO Jisheng，YAO Zhichang. Strata control theory[M]. Beijing：Metallurgical Industry Publishing，2009：27–33.(in Chinese))
[9] 潘 岳，王志强，李爱武. 初次断裂期间超前工作面坚硬顶板挠度、弯矩和能量变化的解析解[J]. 岩石力学与工程学报，2012，31(1)：32–41.(PAN Yue，WANG Zhiqiang，LI Aiwu. Analytic solutions of deflection，bending moment and energy change of tight roof of advanced working surface during initial fracturing[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(1)：32–41.(in Chinese))
[10] 蒋金泉，王 普，武泉林，等. 高位硬厚岩层弹性基础边界下破断规律的演化特征[J]. 中国矿业大学学报，2016，45(3)：490–498. (JIANG Jinquan，WANG Pu，WU Quanlin，et al. Evolutionary characteristics of fracture laws of high-position hard thick strata with elastic foundation boundary[J]. Journal of China University of Mining and Technology，2016，45(3)：490–498.(in Chinese))
[11] 马庆云，赵晓东，宋振骐. 采场老顶岩梁的超前破断与矿山压力[J]. 煤炭学报，2001，26(5)：473–477.(MA Qingyun，ZHAO Xiaodong，SONG Zhenqi. Break of main roof ahead of workface and ground pressure[J]. Journal of China Coal Society，2001，26(5)：473–477.(in Chinese))
[12] 王新丰，高明中. 变长工作面采场顶板破断机理的力学模型分析[J].中国矿业大学学报，2015，41(1)：36–45.(WANG Xinfeng，GAO Mingzhong. Mechanical model of fracture mechanism of stope roof for working face with variable length[J]. Journal of China University of Mining and Technology，2015，41(1)：36–45.(in Chinese))
[13] 秦广鹏，蒋金泉，张培鹏，等. 硬厚岩层破断机理薄板分析及控制技术[J]. 采矿与安全工程学报，2014，31(5)：726–732.(QIN Guangpeng，JIANG Jinquan，ZHANG Peipeng，et al. Thin plate analysis of hard thick strata failure mechanism and its control technology[J]. Journal of Mining and Safety Engineering，2014，31(5)：726–732.(in Chinese))
[14] 王新丰，高明中，陈雨雪，等. 基于弹性薄板理论的采场顶板破断特征分析[J]. 金属矿山，2015，468：24–28.(WANG Xinfeng，GAO Mingzhong，CHEN Yuxue，et al. .Analysis of fracturing characteristics of stope roof based on elastic thin plate theory[J]. Metal Mine，2015，468：24–28.(in Chinese))
[15] 刘 俊. 基于板模型的顶板力学分析及应用[硕士学位论文][D]. 北京：中国矿业大学，2008.(LIU Jun. Mechanical analysis and application of roof based on the thin plate model[M. S. Thesis][D]. Beijing：China University of Mining and Technology，2008.(in Chinese))
[16] 王红卫，陈忠辉，杜泽超，等. 弹性薄板理论在地下采场顶板变化规律研究中的应用[J]. 岩石力学与工程学报，2006，25(增2)：3 769– 3 774.(WANG Hongwei，CHEN Zhonghui，DU Zechao，et al. Application of elastic thin plate theory to change rule of roof in underground stope[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(Supp.2)：3 769–3 774.(in Chinese))
[17] 浦 海，黄耀光，陈荣华. 采场顶板“X—O”型断裂形态力学分析[J]. 中国矿业大学学报，2011，40(6)：835–840.(PU Hai，HUANG Yaoguang，CHEN Ronghua，et al. Mechanical analysis for “X-O”type fracture morphology of stope roof[J]. Journal of China University of Mining and Technology，2011，40(6)：835–840.(in Chinese))
[18] 张益东，程敬义，王晓溪，等. 大倾角仰(俯)采采场顶板破断的薄板模型分析[J]. 采矿与安全工程学报，2010，27(4)：487–493. (ZHANG Yidong，CHENG Jingyi，WANG Xiaoxi，et al. Thin plate model analysis on roof break of up-dip or down-dip mining stope[J]. Journal of Mining and Safety Engineering，2010，27(4)：487–493.(in Chinese))
[19] 朱德仁. 长壁工作面老顶的破断规律及其应用[博士学位论文][D]. 徐州：中国矿业大学，1987.(ZHU Deren. Breaking rules of long wall working face and its application[Ph. D. Thesis][D]. Xuzhou：China University of Mining and Technology，1987.(in Chinese))
[20] 谢生荣，陈冬冬，孙颜顶，等. 基本顶弹性基础边界薄板模型分析(I)——初次破断[J]. 煤炭学报，2016，41(6)：1 360–1 368.(XIE Shengrong，CHEN Dongdong，SUN Yanding，et al. Analysis on thin plate model of basic roof at elastic foundation boundary(I)：First breaking[J]. Journal of China Coal Society，2016，41(6)：1 360–1 368. (in Chinese))
[21] 徐芝纶. 弹性力学[M]. 北京：高等教育出版社，2006：48–53.(XU Zhilun. Elastic mechanics[M]. Beijing：Higher Education Press，2016：48–53.(in Chinese))
[22] 喻文健. 数值分析与算法[M]. 北京：清华大学出版社，2012：265–269.(YU Wenjian. Numerical analysis and algorithm[M]. Beijing：Tsinghua University Press，2012：265–269.(in Chinese))
[23] 张文生. 微分方程数值解：有限差分理论方法与数值计算[M]. 北京：科学出版社，2015：118–124.(ZHANG Wensheng. Numerical solution of differential equation-Finite difference method and numerical calculation[M]. Beijing：Science Press，2015：118–124.(in Chinese))
[24] 艾冬梅，李艳晴，张丽静，等. MATLAB与数学实验[M]. 北京：机械工业出版社，2016：88–89.(AI Dongmei，LI Yanjing，ZHANG Lijing，et al. MATLAB and mathematical experiment of MATLAB[M]. Beijing：Machinery Industry Press，2016：88–89.(in Chinese))
2017, Vol. 36 
