第36卷第12期 北京科技大学学报 Vol.36 No.12 2014年12月 Journal of University of Science and Technology Beijing Dec.2014 Bandis经验公式修正及其应用 祁建东”，金爱兵，王贺”，高艳华”，于咏妍” 1)北京科技大学土木与环境工程学院，北京1000832)北京矿治研究总院，北京100070 ☒通信作者，E-mail:jinaibing@vip.sina.com 摘要针对三维离散元程序中刚度参数合理选取方法及其应用开展研究.通过理论分析，给出了结构面剪切刚度及法向刚 度的理论公式：结合室内剪切试验研究和数值分析，得到了符合工程实际的剪切刚度修正Bnds经验公式及法向刚度参数经 验公式，从而明确提出了一种结构面刚度参数的选取方法：通过实际工程边坡稳定性分析，探究了基于上述方法选取的参数 对实际工程模拟的适用性.研究表明，岩体结构面刚度参数是应力的函数，修正Bdis经验公式能够较为完善地表征剪切破 坏前结构面的剪切刚度变化规律：利用编制FSH程序使刚度参数随应力变化而改变的方法，使3DEC软件对工程岩体变形特 征的模拟更加符合实际，从而验证了该方法的合理性. 关键词岩体：刚度；经验公式：剪切试验；数值分析：边坡稳定性 分类号TU452 Correction and application of the Bandis empirical formula QI Jian-dong",JIN Ai-bing,WANG He2,GAO Yan-hua,YU Yong-yan 1)School of Civil and Environmental Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)Beijing General Research Institute of Mining and Metallurgy,Beijing 100070,China Corresponding author,E-mail:jinaibing@vip.sina.com ABSTRACT A reasonable method was discussed for choosing and applying stiffness parameters in a 3D distinct element code.The formulas of pre-peak shear stiffness and normal stiffness of the fracture were derived through theoretical analysis.In combination with data from indoor shearing experiment,a corrected Bandis empirical formula of shear stiffness and a normal stiffness empirical formula were developed,which were proved to be logical by numerical analytical study.At last,a reality engineering of slope slide was discussed as a further evidence to describe the applicability of stiffness parameters chosen by the method mentioned above.It is obvious that the stiffness parameters of the fracture are a function of stress whether shear stiffness or normal stiffness.The corrected Bandis empirical formula can reflect the behavior of shear stiffness in the pre-peak range well.It is practicable to make the stiffness of the frac- ture changed with stress by developing a FISH program (in 3DEC),and therefore,the simulation can more in line with the practical engineering.In conclusion,the method mentioned above is proved to be reasonable KEY WORDS rock mass:stiffness:empirical formulas;shear test:numerical analysis:slope stability 岩体结构面为岩体内具有一定方向、延展较大键因素之一.Nassir等同通过理论分析给出了节理 且厚度较小的面状地质界面口.在高陡岩质边坡 岩体刚度参数的表征公式：肖卫国等0利用经典弹 中，岩体的变形破坏主要受岩体内结构面尤其是软塑性理论提出了充填节理岩体增量型应力与位移的 弱结构面的空间组合关系和结构面的力学性质控 本构模型：陈卫忠等固和王芝银等分别提出了基 制回.合理的工程岩体参数是工程稳定性评价的关 于力学实验的结构面刚度参数确定方法 收稿日期：2013-10-10 基金项目：中央直属高校基本科研业务费资助项目(FRF-SD-12O02A) DOI:10.13374/j.issn1001-053x.2014.12.002:http://journals.ustb.edu.cn第 36 卷 第 12 期 2014 年 12 月 北京科技大学学报 Journal of University of Science and Technology Beijing Vol． 36 No． 12 Dec． 2014 Bandis 经验公式修正及其应用 祁建东1) ，金爱兵1) ，王 贺2) ，高艳华1) ，于咏妍1) 1) 北京科技大学土木与环境工程学院，北京 100083 2) 北京矿冶研究总院，北京 100070  通信作者，E-mail: jinaibing@ vip． sina． com 摘 要 针对三维离散元程序中刚度参数合理选取方法及其应用开展研究． 通过理论分析，给出了结构面剪切刚度及法向刚 度的理论公式; 结合室内剪切试验研究和数值分析，得到了符合工程实际的剪切刚度修正 Bandis 经验公式及法向刚度参数经 验公式，从而明确提出了一种结构面刚度参数的选取方法; 通过实际工程边坡稳定性分析，探究了基于上述方法选取的参数 对实际工程模拟的适用性． 研究表明，岩体结构面刚度参数是应力的函数，修正 Bandis 经验公式能够较为完善地表征剪切破 坏前结构面的剪切刚度变化规律; 利用编制 FISH 程序使刚度参数随应力变化而改变的方法，使 3DEC 软件对工程岩体变形特 征的模拟更加符合实际，从而验证了该方法的合理性． 关键词 岩体; 刚度; 经验公式; 剪切试验; 数值分析; 边坡稳定性 分类号 TU452 Correction and application of the Bandis empirical formula QI Jian-dong1) ，JIN Ai-bing1)  ，WANG He2) ，GAO Yan-hua1) ，YU Yong-yan1) 1) School of Civil and Environmental Engineering，University of Science and Technology Beijing，Beijing 100083，China 2) Beijing General Ｒesearch Institute of Mining and Metallurgy，Beijing 100070，China  Corresponding author，E-mail: jinaibing@ vip． sina． com ABSTＲACT A reasonable method was discussed for choosing and applying stiffness parameters in a 3D distinct element code． The formulas of pre-peak shear stiffness and normal stiffness of the fracture were derived through theoretical analysis． In combination with data from indoor shearing experiment，a corrected Bandis empirical formula of shear stiffness and a normal stiffness empirical formula were developed，which were proved to be logical by numerical analytical study． At last，a reality engineering of slope slide was discussed as a further evidence to describe the applicability of stiffness parameters chosen by the method mentioned above． It is obvious that the stiffness parameters of the fracture are a function of stress whether shear stiffness or normal stiffness． The corrected Bandis empirical formula can reflect the behavior of shear stiffness in the pre-peak range well． It is practicable to make the stiffness of the frac￾ture changed with stress by developing a FISH program ( in 3DEC) ，and therefore，the simulation can more in line with the practical engineering． In conclusion，the method mentioned above is proved to be reasonable． KEY WOＲDS rock mass; stiffness; empirical formulas; shear test; numerical analysis; slope stability 收稿日期: 2013--10--10 基金项目: 中央直属高校基本科研业务费资助项目( FＲF--SD--12--002A) DOI: 10． 13374 /j． issn1001--053x． 2014． 12． 002; http: / /journals． ustb． edu． cn 岩体结构面为岩体内具有一定方向、延展较大 且厚度较小的面状地质界面［1］． 在高陡岩质边坡 中，岩体的变形破坏主要受岩体内结构面尤其是软 弱结构面的空间组合关系和结构面的力学性质控 制［2］． 合理的工程岩体参数是工程稳定性评价的关 键因素之一． Nassir 等［3］通过理论分析给出了节理 岩体刚度参数的表征公式; 肖卫国等［4］利用经典弹 塑性理论提出了充填节理岩体增量型应力与位移的 本构模型; 陈卫忠等［5］和王芝银等［6］分别提出了基 于力学实验的结构面刚度参数确定方法．