›› 2013, Vol. 34 ›› Issue (8): 2385-2392.

• 数值分析 • 上一篇    下一篇

基于SEM的可变形块体离散元法研究

张青波,李世海,冯 春,王 杰   

  1. 中国科学院力学研究所,北京 100190
  • 收稿日期:2012-06-06 出版日期:2013-08-12 发布日期:2013-08-13
  • 通讯作者: 李世海,男,1958年生,博士,研究员,主要从事非连续介质力学及其应用方面的研究。E-mail:shli@imech.ac.cn E-mail:zhangqingbo@imech.ac.cn
  • 作者简介:张青波,男,1986年生,博士研究生,主要从事地震作用下边坡的破坏机理及数值模拟方面的研究。
  • 基金资助:

    国家重点基础研究发展计划(973)项目资助(No. 2010CB731506);国家自然科学基金资助(No. 11002146)。

Study of deformable block discrete element method based on SEM

ZHANG Qing-bo, LI Shi-hai, FENG Chun, WANG Jie   

  1. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2012-06-06 Online:2013-08-12 Published:2013-08-13

摘要: 针对边坡工程中岩土体连续-非连续渐进破坏的特点,提出一种新的变形体离散元方法(DEM)。与传统有限单元法(FEM)不同,弹簧元法(SEM)通过构建一组广义弹簧系统描述单元的力学行为。弹簧元法中的一个广义弹簧可以具有多个方向的刚度系数,确定广义弹簧系统的构造形式及其各刚度系数表达式是弹簧元法的核心。以三角形单元为例,介绍平面弹簧元的基本理论。对任何二维正交广义弹簧系统,通过定义广义弹簧变形与单元应变之间的关系,直接对比单元的应变能与弹簧系统的弹性势能即可得到广义弹簧刚度系数的表达形式。定义泊松刚度系数和纯剪刚度系数两个系统参数,描述正交广义弹簧之间的联系。对任意泊松比的材料,该方法都可准确地描述泊松效应的影响,计算结果与传统有限元法一致。该方法不需要求得有限元单元刚度矩阵的具体形式,具有直接方便、物理意义明确的优点,应用该方法给出任意4节点单元弹簧系统的构造形式及其各刚度系数的表达式。基于SEM的可变形块体离散元法,用弹簧元中的广义弹簧求解块体变形,用离散元中的接触弹簧计算块体间作用力,在单元节点的控制方程中实现弹簧元-离散元耦合计算,通过接触弹簧的状态实现材料由连续到非连续的破坏过程。在基于连续介质离散元法(CDEM)程序的基础上实现弹簧元-离散元耦合程序,应用耦合程序计算均质土坡在重力作用下的弹塑性变形和基覆边坡在重力作用下的破坏,初步证明该方法用于边坡变形渐进破坏分析的可行性。

关键词: 弹簧元法, 离散元法, 弹簧刚度, 边坡工程

Abstract: Aiming at the continuous-discontinuous failure process of rock and soil materials in slope engineering, a novel deformable block discrete element method which combined spring element method(SEM) and discrete element method(DEM) together is presented. Compared with the accustomed element in traditional finite element method(FEM), the element in SEM is described as a spring system that contained some orthogonal generalized springs. This generalized springs are defined in 3D space, which means that each spring can has two or three spring stiffness. How to determine the generalized spring stiffness for continuous material is the difficult and most important in SEM. With the triangle element as an example, the basic theory of SEM is introduced in detail. Assuming the relationship between the generalized spring deformation and the element strain, the generalized spring stiffness can be obtained directly by comparing the elastic strain energy of the element and the elastic potential energy of the spring system. The Poisson and shear stiffness coefficients were defined as system parameters to describe the relationship between different generalized springs. The SEM can consider the Poisson effect accurately for any Poisson’s ratio material; and the result using SEM are the same with using traditional FEM. This method does not need to know the expression of the element-stiffness-matrix. It can be used in 4-node element; and the stiffness expressions of springs are given clearly. With the SEM used to compute the block deformation and the contact-spring used to calculate the interaction between blocks, the combined SEM/DEM program can be used to simulate the failure process of rock and soil material from continuous to discontinuous. The SEM and DEM are combined in the motion equation of each node in each element. The contact-spring in DEM satisfied specific strength criterion. When the contact-spring force exceeded its limit, the material became discontinuous from continuous. The combined SEM/DEM program is implemented easily in the continuum-based discrete element method(CDEM) program. The simulation of a homogeneous soil slope under gravity shows that the SEM is performed as good as FEM when using line elastic constitutive and reasonable when using Mohr-Coulomb strength criterion. The simulation of a bedrock and overburden layer slope shows that the combined program is suitable to simulate the slope failure process.

Key words: spring element method(SEM), discrete element method(DEM), spring stiffness, slope engineering

中图分类号: 

  • TU 473
[1] 闫国强, 殷跃平, 黄波林, 张枝华, 代贞伟, . 三峡库区巫山金鸡岭滑坡成因机制与变形特征[J]. 岩土力学, 2019, 40(S1): 329-340.
[2] 王伟, 陈国庆, 郑水全, 张广泽, 王栋, . 考虑张拉-剪切渐进破坏的边坡矢量和法研究[J]. 岩土力学, 2019, 40(S1): 468-476.
[3] 蒋泽锋, 张戈, 朱大勇, 王军, . 锚固力作用下的边坡临界滑动场法研究与应用[J]. 岩土力学, 2019, 40(7): 2799-2806.
[4] 王蕴嘉, 宋二祥. 堆石料颗粒形状对堆积密度及强度影响的 离散元分析[J]. 岩土力学, 2019, 40(6): 2416-2426.
[5] 申海萌, 李 琦, 李霞颖, 马建力, . 川南龙马溪组页岩不同应力条件下脆性破坏特征室内实验与数值模拟研究[J]. 岩土力学, 2018, 39(S2): 254-262.
[6] 胡唯哲,谢凌志,岑望来,殷 实,罗云川,赵 鹏,. 基于细观试验和离散元法的盐岩力学特性[J]. , 2018, 39(6): 2073-2081.
[7] 刘 洋,李 爽. 散粒介质临界状态细观力学结构特征的数值模拟与分析[J]. , 2018, 39(6): 2237-248.
[8] 崔芳鹏,许 强,殷跃平,胡瑞林,陈紫娟,刘 伟,. 基于带状震源破裂机制的斜坡动力响应[J]. , 2018, 39(1): 320-330.
[9] 张科芬,张 升,滕继东,盛岱超, . 颗粒破碎的三维离散元模拟研究[J]. , 2017, 38(7): 2119-2127.
[10] 王 超,张社荣,张峰华,杜成波. 基于实时更新数值模型的高陡边坡动态仿真分析方法及应用[J]. , 2016, 37(8): 2383-2390.
[11] 易 颖,周 伟,马 刚,杨利福,常晓林, . 基于精确缩尺的颗粒材料流变研究[J]. , 2016, 37(6): 1799-1808.
[12] 陈静瑜 ,赵炼恒 ,李 亮 ,谭捍华,. 基于Excel数据表和极限分析法的滑坡抗剪强度参数反演分析[J]. , 2016, 37(3): 827-834.
[13] 沈华章,郭明伟,王水林,葛修润. 基于离散元的边坡矢量和稳定分析方法研究[J]. , 2016, 37(2): 592-600.
[14] 严成增 ,郑 宏 ,孙冠华 ,葛修润,. 基于FDEM-Flow研究地应力对水力压裂的影响[J]. , 2016, 37(1): 237-246.
[15] 蒋明镜 ,金树楼 ,刘 蔚 ,刘 俊 , . 粒间胶结接触力学特性的三维试验研究[J]. , 2015, 36(S1): 9-13.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 梁桂兰,徐卫亚,谈小龙. 基于熵权的可拓理论在岩体质量评价中的应用[J]. , 2010, 31(2): 535 -540 .
[2] 马文涛. 基于灰色最小二乘支持向量机的边坡位移预测[J]. , 2010, 31(5): 1670 -1674 .
[3] 于琳琳,徐学燕,邱明国,闫自利,李鹏飞. 冻融作用对饱和粉质黏土抗剪性能的影响[J]. , 2010, 31(8): 2448 -2452 .
[4] 王 伟,刘必灯,周正华,王玉石,赵纪生. 刚度和阻尼频率相关的等效线性化方法[J]. , 2010, 31(12): 3928 -3933 .
[5] 王海波,徐 明,宋二祥. 基于硬化土模型的小应变本构模型研究[J]. , 2011, 32(1): 39 -43 .
[6] 曹光栩,宋二祥,徐 明. 山区机场高填方地基工后沉降变形简化算法[J]. , 2011, 32(S1): 1 -5 .
[7] 刘华丽 ,朱大勇 ,钱七虎 ,李宏伟. 边坡三维端部效应分析[J]. , 2011, 32(6): 1905 -1909 .
[8] 刘年平 ,王宏图 ,袁志刚 ,刘竟成. 砂土液化预测的Fisher判别模型及应用[J]. , 2012, 33(2): 554 -557 .
[9] 王卫东 ,李永辉 ,吴江斌 . 超长灌注桩桩-土界面剪切模型及其有限元模拟[J]. , 2012, 33(12): 3818 -3824 .
[10] 卫振海 ,王梦恕 ,张顶立 . 土结构强度模型研究[J]. , 2013, 34(1): 40 -46 .