工程科学学报，第38卷，第2期：291-298,2016年2月 Chinese Journal of Engineering,Vol.38,No.2:291-298,February 2016 DOI:10.13374/j.issn2095-9389.2016.02.020:http://journals.ustb.edu.cn 基于复变函数理论和D-P屈服准则的并行隧道合理 间距 宋伟超》，高永涛2)，吴顺川2)，严琼2，吴庆良2》 1)北京科技大学土木与环境工程学院，北京1000832)北京科技大学金属矿山高效开采与安全教有部重点实验室，北京100083 ☒通信作者，E-mail:wushunchuan@usth.cdu.cn 摘要综合利用复变函数理论、解析延拓法和Schwarz交替法揭示相邻水平并行隧道的应力分布特征.在此基础上，结合 考虑了中间主应力效应的DP屈服准则建立相邻水平并行隧道力学模型.提出并行隧道塑性区贯穿半径的概念，建立求解 方程，并通过数值模拟证明其正确性.采用隧道间塑性区临界贯穿状态下的间距作为隧道合理间距，与数值模拟软件FLAC 计算得到的围岩位移量和沉降量随间距变化至基本不发生变化时所对应的隧道间距有较高的吻合性，从而表明其作为相邻 水平并行隧道合理间距的可行性. 关键词隧道工程：间距：复变函数理论；屈服准则：力学模型 分类号U451 Reasonable spacing of parallel tunnels based on the complex function theory and D-P yield criterion SONG Wei-chao,GAO Yong-tao,WU Shun-chuan,YAN Qiong,WU Qing-iang 1)School of Civil and Environmental Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)Key Laboratory of the Ministry of Education for High Efficient Mining and Safety of Metal Mines,University of Science and Technology Beijing,Bei- jing 100083,China Corresponding author,E-mail:wushunchuan@ustb.edu.cn ABSTRACT The stress distribution characteristics of adjacent horizontal parallel tunnels are revealed by comprehensively utilizing the complex function theory,analytic continuation method and Schwarz alternating method.Then a mechanical model of adjacent hori- zontal parallel tunnels is constructed in combination with the D-P yield criterion which considers the effect of intermediate principal stress.The concept of connected radius of the tunnel plastic zone is proposed,the solving equation is established and its correctness is verified by numerical simulation.The critical distance of the plastic zone connected between tunnels is considered as a reasonable spacing,which has a better agreement with the spacing of tunnels when the displacement and settlement of surrounding rock do not basically change with the spacing of tunnels calculated by numerical simulation software FLAC,thus demonstrating its feasibility as the reasonable spacing of adjacent horizontal parallel tunnels. KEY WORDS tunneling:spacing:complex function theory:yield criteria:mechanical models 近年来，受地质、地形条件以及线路和环保要求等 许多学者使用数值模拟和模型试验的方法，对相 因素的制约，为有效利用地下深部资源和空间，隧道开 邻并行隧道的合理间距进行了大量的研究.Barla和 挖的实际埋深越来越大，相邻并行隧道建设十分常见. Ottoviani采用有限元数值模拟的方法对并行隧道的 收稿日期：2014-11-25 收稿日期：基于颗粒元理论的散体矿岩放矿运移机理及可视化研究资助项目(51374032)工程科学学报，第 38 卷，第 2 期: 291--298，2016 年 2 月 Chinese Journal of Engineering，Vol． 38，No． 2: 291--298，February 2016 DOI: 10． 13374 /j． issn2095--9389． 2016． 02． 020; http: / /journals． ustb． edu． cn 基于复变函数理论和 D--P 屈服准则的并行隧道合理 间距 宋伟超1，2) ，高永涛1，2) ，吴顺川1，2) ，严 琼1，2) ，吴庆良1，2) 1) 北京科技大学土木与环境工程学院，北京 100083 2) 北京科技大学金属矿山高效开采与安全教育部重点实验室，北京 100083  通信作者，E-mail: wushunchuan@ ustb． edu． cn 摘 要 综合利用复变函数理论、解析延拓法和 Schwarz 交替法揭示相邻水平并行隧道的应力分布特征． 在此基础上，结合 考虑了中间主应力效应的 D--P 屈服准则建立相邻水平并行隧道力学模型． 提出并行隧道塑性区贯穿半径的概念，建立求解 方程，并通过数值模拟证明其正确性． 采用隧道间塑性区临界贯穿状态下的间距作为隧道合理间距，与数值模拟软件 FLAC3D 计算得到的围岩位移量和沉降量随间距变化至基本不发生变化时所对应的隧道间距有较高的吻合性，从而表明其作为相邻 水平并行隧道合理间距的可行性． 关键词 隧道工程; 间距; 复变函数理论; 屈服准则; 力学模型 分类号 U451 Ｒeasonable spacing of parallel tunnels based on the complex function theory and D--P yield criterion SONG Wei-chao1，2) ，GAO Yong-tao1，2) ，WU Shun-chuan1，2)  ，YAN Qiong1，2) ，WU Qing-liang1，2) 1) School of Civil and Environmental Engineering，University of Science and Technology Beijing，Beijing 100083，China 2) Key Laboratory of the Ministry of Education for High Efficient Mining and Safety of Metal Mines，University of Science and Technology Beijing，Bei￾jing 100083，China  Corresponding author，E-mail: wushunchuan@ ustb． edu． cn ABSTＲACT The stress distribution characteristics of adjacent horizontal parallel tunnels are revealed by comprehensively utilizing the complex function theory，analytic continuation method and Schwarz alternating method． Then a mechanical model of adjacent hori￾zontal parallel tunnels is constructed in combination with the D--P yield criterion which considers the effect of intermediate principal stress． The concept of connected radius of the tunnel plastic zone is proposed，the solving equation is established and its correctness is verified by numerical simulation． The critical distance of the plastic zone connected between tunnels is considered as a reasonable spacing，which has a better agreement with the spacing of tunnels when the displacement and settlement of surrounding rock do not basically change with the spacing of tunnels calculated by numerical simulation software FLAC3D，thus demonstrating its feasibility as the reasonable spacing of adjacent horizontal parallel tunnels． KEY WOＲDS tunneling; spacing; complex function theory; yield criteria; mechanical models 收稿日期: 2014--11--25 收稿日期: 基于颗粒元理论的散体矿岩放矿运移机理及可视化研究资助项目( 51374032) 近年来，受地质、地形条件以及线路和环保要求等 因素的制约，为有效利用地下深部资源和空间，隧道开 挖的实际埋深越来越大，相邻并行隧道建设十分常见． 许多学者使用数值模拟和模型试验的方法，对相 邻并行隧道的合理间距进行了大量的研究． Barla 和 Ottoviani［1］采用有限元数值模拟的方法对并行隧道的