Biot固结有限元方程组的病态规律分析

›› 2007, Vol. 28 ›› Issue (2): 269-273.

Biot固结有限元方程组的病态规律分析

丁洲祥¹，龚晓南²，朱合华¹ ，蔡永昌¹，李天柱³，唐亚江³

1. 同济大学地下建筑与工程系，上海 200092；2. 浙江大学岩土工程研究所，杭州 310027；3．宁夏公路勘察设计研究院，银川 750004

收稿日期:2004-10-14 出版日期:2007-02-10 发布日期:2013-08-28
作者简介:丁洲祥，男，1976年生，博士，讲师，从事隧道与地下工程、土力学与地基处理等方面的研究
基金资助:
国家自然科学基金及二滩水电开发有限责任公司雅砻江水电开发联合研究基金项目（No. 50579093，No. 50578143）

Study on ill-conditioned problems of Biot’s consolidation finite element equations

DING Zhou-xiang¹, GONG Xiao-nan², ZHU he-hua¹, CAI Yong-chang¹, LI Tian-zhu³, TANG Ya-jiang³

1. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China; 2. Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310027, China; 3. Ningxia Highway Survey and Design Institute, Yinchuan 750004, China

Received:2004-10-14 Online:2007-02-10 Published:2013-08-28

摘要/Abstract

摘要： 针对Biot固结有限元方程组的病态问题，采用正交试验和量纲分析法探讨病态性的变化规律及其影响因素。主要考虑单元平均尺寸、时间步长、压缩性和渗透性等4个因素的影响。分别提出2组相互独立的相似准则，在此基础上得到2个新的无量纲量，并将其用于分析Biot固结有限元方程组系数矩阵的条件数的变化规律。结合算例进行参数分析结果表明，对病态程度的敏感性由大到小依次为单元平均尺寸、时间步长、压缩性和渗透性；单元平均尺寸太小会使病态加剧；随着2个无量纲量的增大，病态程度呈现单调增加的趋势。其结果为深化对Biot固结数值分析病态问题的认识提供有益参考。

关键词: Biot固结理论, 有限元法, 病态问题, 正交试验, 量纲分析

Abstract: Aimed at the ill-conditioned problem of Biot’s consolidation finite element method (BCFEM), both orthogonal test and dimensional analysis method are used to study the ill-conditioning regularity and its influencing factors. The influencing factors such as the average size of finite element, the length of timestep, the compressibility of soil and the permeability of soil are taken into account. Two groups of independent similarity criteria are proposed, on the basis of which, two novel dimensionless variables are obtained to analyze the variation of the condition number of BCFEM coefficient matrix. Through the parametric study of an illustrative case, the results show that the average size of finite element, the length of timestep, the compressibility of soil and the permeability of soil are in the order of priority of sensitivity. The smaller the averaged size of finite element, the worse the ill-conditioning situation of BCFEM. With the increase of the presented dimensionless variables, the ill-conditioning number shows a tendency to increasing, etc. The conclusions are helpful to study the ill-conditioned problem of BCFEM.

Key words: Biot’s consolidation theory, finite element method, ill-conditioned problem, orthogonal test, dimensional analysis

中图分类号:

TB 115

丁洲祥，龚晓南，朱合华，蔡永昌，李天柱，唐亚江. Biot固结有限元方程组的病态规律分析[J]. , 2007, 28(2): 269-273.

DING Zhou-xiang, GONG Xiao-nan, ZHU he-hua, CAI Yong-chang, LI Tian-zhu, TANG Ya-jiang. Study on ill-conditioned problems of Biot’s consolidation finite element equations[J]. , 2007, 28(2): 269-273.

参考文献

相关文章 15

[1]	王翔南, 李全明, 于玉贞, 喻葭临, 吕禾, . 基于扩展有限元法对土体滑坡破坏过程的模拟[J]. 岩土力学, 2019, 40(6): 2435-2442.
[2]	付宏渊, 刘杰, 曾铃, 卞汉兵, 史振宁, . 考虑荷载与浸水条件的预崩解炭质泥岩变形与强度试验[J]. 岩土力学, 2019, 40(4): 1273-1280.
[3]	郑安兴, 罗先启, 陈振华, . 基于扩展有限元法的岩体水力劈裂耦合模型[J]. 岩土力学, 2019, 40(2): 799-808.
[4]	郑安兴，罗先启，. 危岩水力劈裂分析的扩展有限元法[J]. , 2018, 39(9): 3461-3468.
[5]	宋佳，古泉，许成顺，杜修力，. 饱和土动力方程全显式有限元法在 OpenSees中的实现与应用[J]. , 2018, 39(9): 3477-3485.
[6]	宋佳，杜修力，许成顺，孙宝印，. 饱和土场地-桩基-地上结构体系的地震响应研究[J]. , 2018, 39(8): 3061-3070.
[7]	张晨，蔡正银，徐光明，黄英豪，. 冻土离心模型试验相似准则分析[J]. , 2018, 39(4): 1236-1244.
[8]	任松，李振元，邓高岭，刘伟，蒲文明，. 多因素作用下石膏岩软化特性[J]. , 2018, 39(3): 789-796.
[9]	李宁，郭双枫，姚显春,. 再论岩质高边坡稳定性分析方法[J]. , 2018, 39(2): 397-406.
[10]	刘金辉，李文枭，刘宇森，刘保国，. 多孔含水岩层的相似材料配比研究[J]. , 2018, 39(2): 657-664.
[11]	罗先启，郑安兴,. 岩体裂隙模拟的扩展有限元法应用研究[J]. , 2018, 39(2): 728-734.
[12]	刘忠玉, 张家超, 郑占垒, 关聪. 考虑Hansbo渗流的二维Biot固结有限元分析[J]. 岩土力学, 2018, 39(12): 4617-4626.
[13]	姚囝，叶义成，王其虎，岳哲，罗斌玉，. 基于量纲分析的缓倾斜空区顶板稳定性的影响规律研究[J]. , 2018, 39(11): 4232-4241.
[14]	刘振平，杜根明，蔡洁，周凡，刘建，卞康，. 基于MeshPy的3DGIS与三维有限元数值计算无缝耦合方法[J]. , 2018, 39(10): 3841-3852.
[15]	岳哲，叶义成，王其虎，姚囝，施耀斌. 基于量纲分析的岩石相似材料抗压强度计算模型[J]. , 2018, 39(1): 216-221.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed