利用初流量法分析有自由面渗流问题之改进

潘树来; 王全凤; 俞 缙

利用初流量法分析有自由面渗流问题之改进 English Version

1. 华侨大学土木工程学院，福建厦门 361021; 2. 中国矿业大学深部岩土力学与地下工程国家重点实验室，江苏徐州 221008

基金项目: 国家自然科学基金项目（ 51109084 ）；高等学校博士学科点专项科研基金项目（ 200803850001 ）；福建省自然科学基金项目（ 2011J01317 ）；中国矿业大学深部岩土力学与地下工程国家重点实验室开放基金项目（ SKLGDUEK1012 ）；泉州市科技计划项目（ 2010Z81 ）

详细信息

作者简介:
潘树来 (1967 – ) ，男，澳门人，博士研究生，从事计算方法和岩土工程研究。

中图分类号: TV139.11
计量
- 文章访问数: 01167
- HTML全文浏览量: 0
- PDF下载量: 0723
出版历程
- 收稿日期: 2010-11-08
- 发布日期: 2012-02-19

Improvement of analysis of free surface seepage problem by using initial flow method

1. College of Civil Engineering, Huaqiao University, Xiamen 361021, China; 2. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221008, China

摘要

摘要: 在利用初流量法分析带有自由面的渗流问题时，常因采用高斯积分点作为结点初流量计算判断依据所带来的误差而令解出现振荡。为了减低这一因素的影响及提高计算的效率，针对常用的 4 结点平面单元和 8 结点 6 平面三维单元的自由面方程进行分析，提出采用坐标变换和等参变换等技术来改造结点初流量的计算，并建议按自由面穿越单元之状况引用分部积分，使其积分上、下限符合高斯积分法的格式化要求，从而可利用高斯积分法求出精确的结点初流量，而精确的结点初流量则有助于改善解的振荡及提高计算结果的精度。通过一矩形均质坝实例分析，表明该方法的稳定性和收敛性良好。
- 初流量法 /
- 有自由面渗流 /
- 高斯积分法 /
- 固定网格
Abstract: When the initial flow method is applied in solving problems of free surface seepage, we often find an oscillating solution determined due to the error caused by taking the Gaussian integration points as the assumed nodes based on calculation of nodal initial flow. In order to reduce the impact of this factor and to improve the efficiency of computation , an analysis is made with the free surface equation commonly used by 4-node plane elements and 8-node 6-plane three-dimensional elements , a technique of transformation of coordinates as well as isoparameters is proposed to improve the calculation of the nodal initial flow, and an introduction of partial integration is also suggested according to the state of free surface penetrating elements, making the integration upper limit and lower limit in consistence with the formatting of the Gaussian requirements. Accordingly, an exact nodal initial flow integration will be obtained by using the Gaussian method , and this accurate nodal initial flow will then benefit the itself improvement of the oscillating solution and increase the precision of the calculation . Through the analysis of a homogeneous rectangular case, it is shown that a fair state of stability and convergence has been achieved by using the proposed improved method.
- initial flow method /
- unconfined seepage /
- Gaussian integration method /
- fixed mesh

HTML全文

参考文献(9)

[1]	DESAI C S. Finite element residual shemes for unconfined flow[J]. International Journal for Numerical Methods in Engineering, 1976, 10 (6): 1415 – 1418.
[2]	BATHE K J, KHOSHGOFTAAR M R. Finite element free surface seepage analysis without mesh iteration[J]. International Journal of Numerical Analytical Methods in Geomechanics, 1979, 3 (1): 13 – 22.
[3]	张有天 , 陈平 , 王镭 . 有自由面渗流分析的初流量法 [J]. 水利学报 , 1988(8) : 18 – 26 . (ZHANG You-tian, CHEN Ping, WANG Lei. Initial flow method for seepage analysis with free surface[J]. Journal of Hydraulic Engineering, 1988(8): 18 – 26. (in Chinese))
[4]	速宝玉 , 朱岳明 . 不变网格确定渗流自由面的节点虚流量法 [J]. 河海大学学报 , 1991, 19 (5) : 113 – 117 . (SU Bao-yu, ZHU Yue-ming. Procedure of nodal virtual flux for seepage free surface with fixed mesh[J]. Journal of Hohai University, 1991, 19 (5): 113 – 117. (in Chinese))
[5]	凌道盛 . 有自由面渗流分析的虚节点法 [J]. 浙江大学学报 ( 工学版 ) , 2002, 36 (3) : 243-246, 326 . ( LING Dao-sheng . Virtual node method for seepage with free surface problem [J]. Journal of Zhejiang University ( Engineering Science) , 2002 , 36 (3): 2 43 -2 46 , 3 26 . (in Chinese))
[6]	崔皓东 , 朱岳明 . 有自由面渗流分析的改进节点虚流量全域迭代法 [J]. 武汉理工大学学报 ( 交通科学与工程版 ) , 2009, 33 (2) : 238 – 241 . ( CUI Hao-dong , ZHU Yue-ming . I mproved procedure of nodal virtual flux of global iteration to solve seepage free surface [J]. Journal of Wuhan University of Technology (Transportation Science & Engineering) , 2009 , 33 ( 2 ): 238 – 24 1. (in Chinese))
[7]	朱伯芳 . 有限单元法原理与应用 [M]. 第 2 版 . 北京 : 中国水利水电出版社 , 1998 : 254 – 255 . (ZHU Bo-fang. The finite element method theory and applications[M]. 2nd ed. Beijing: China WaterPower Press, 1998: 254 – 255. (in Chinese))
[8]	王媛 . 求解有自由面渗流问题的初流量法的改进 [J]. 水利学报 , 1998(3) : 68 – 73 . (WANG Yuan. The modified initial flow method for 3-D unconfined seepage computation [J]. Journal of Hydraulic Engineering , 1998(3) : 68 – 73 . (in Chinese))
[9]	李新强 . 无压渗流有限元分析的改进初流量法 [J]. 水利学报 , 2007, 38 (8) : 961 – 965 . (LI Xin-qiang. Modified initial flow method for FEM analysis of unconfined seepage[J]. Journal of Hydraulic Engineering, 2007, 38 (8) : 961 – 965. (in Chinese))