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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (10): 2116-2125    DOI: 10.3785/j.issn.1008-973X.2023.10.020
土木工程     
跨尺度网格识别方法及在防渗墙分析中的应用
余翔1,2(),赖远平2,王钰轲2,*(),屈永倩3,郑浩然2
1. 中国地球物理学会工程物探检测重点实验室，湖北 武汉 430000
2. 郑州大学 水利与土木工程学院，河南 郑州 450001
3. 大连理工大学 水利工程学院，辽宁 大连 116024
Identification method of cross-scale mesh and application in analysis of cutoff wall
Xiang YU1,2(),Yuan-ping LAI2,Yu-ke WANG2,*(),Yong-qian QU3,Hao-ran ZHENG2
1. Key Laboratory of Engineering Geophysical Prospecting and Detection of Chinese Geophysical Society, Wuhan 430000, China
2. School of Water Conservancy and Civil Engineering, Zhengzhou University, Zhengzhou 450001, China
3. School of Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China
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摘要：

为了高效地生成二维比例边界有限元-有限元（SBFEM-FEM）跨尺度耦合网格，提出跨尺度网格识别方法. 该方法结合CAD人为可控的特点，对图形线段进行识别、裁剪、整理，生成有效节点与线段；根据节点与线段的拓扑关系以及封闭域的构造，生成合理的多边形比例边界单元或有限单元；最后组装节点与单元信息，输出可以用于数值分析的二维SBFEM-FEM跨尺度耦合网格. 为了验证生成SBFEM-FEM跨尺度耦合网格的有效性及计算精度，依托某堤坝工程，对比分析了防渗墙不同网格剖分方法获得的墙体应力变形分布规律及峰值. 结果表明，采用常规大尺度有限元网格模拟获得的主应力误差可以超过48%，基于所提跨尺度精细数值网格获得的结果误差不能超过5%，且其网格单元量大幅度降低. 跨尺度网格识别方法可以为堤坝工程防渗结构提供有力的支持.
关键词： SBFEM-FEM耦合;  跨尺度网格生成;  精细模拟;  堤坝防渗墙;  可控性    
Abstract:

A cross-scale mesh identification method was presented to efficiently create two-dimensional scaled boundary finite element method-finite element method (SBFEM-FEM) cross-scale coupled meshes. The method combined the artificially controllable characteristics of CAD to identify, cut, and organize graphic line segments generating effective nodes and line segments. A reasonable polygonal-scaled boundary element or finite element was generated based on the topological relationship between the nodes and the line segments and the construction of the closed domain. The nodes and element information were assembled. The two-dimensional SBFEM-FEM cross-scale coupled mesh suitable for numerical analysis was produced. The stress and deformation distribution law and peak value of the wall obtained by different mesh generating methods were compared and studied to verify the validity and calculation accuracy of the generated SBFEM-FEM cross-scale coupling mesh based on a dam project. Results showed that the error of the principal stress obtained by the conventional large-scale finite element mesh simulation could exceed 48%, the error of the results obtained based on the proposed cross-scale fine numerical mesh could not exceed 5%, and the number of mesh elements was greatly reduced. The cross-scale mesh identification method can provide strong support for the anti-seepage structures in dam engineering.
Key words: coupled scaled boundary finite element method-finite element method    generation of cross-scale mesh    refined simulation    cutoff wall of embankment    controllability
收稿日期: 2022-11-30 出版日期: 2023-10-18
CLC:  TV 39  
基金资助: 中国地球物理学会工程物探检测重点实验室开放研究基金资助项目（CJ2021D05）；国家自然科学基金资助项目（52192670, 52109151, 51809034）；中国博士后科学基金资助项目（2021M692938）；河南省省重点研发与推广专项资助项目（222102320098）；云南省重大科技专项计划资助项目（202102AF08002）
通讯作者: 王钰轲     E-mail: xiangyu@zzu.edu.cn;ykewang@163.com
作者简介: 余翔（1988—），男，副教授，从事数值仿真方法开发与应用研究. orcid.org/0000-0002-7488-3550. E-mail： xiangyu@zzu.edu.cn
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引用本文:

余翔,赖远平,王钰轲,屈永倩,郑浩然. 跨尺度网格识别方法及在防渗墙分析中的应用[J]. 浙江大学学报(工学版), 2023, 57(10): 2116-2125.

Xiang YU,Yuan-ping LAI,Yu-ke WANG,Yong-qian QU,Hao-ran ZHENG. Identification method of cross-scale mesh and application in analysis of cutoff wall. Journal of ZheJiang University (Engineering Science), 2023, 57(10): 2116-2125.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.10.020    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I10/2116

图 1  比例边界有限元法中的边界离散单元
图 2  跨尺度网格过渡方法的示意图
图 3  悬臂梁结构的示意图
图 4  悬臂梁结构的简化示意图
图 5  悬臂梁结构的基本网格图
节点编号 1 2 3 4 5 6 7 8
1 — 1 — — — 1 — —
2 1 — 1 1 — — — —
3 — 1 — — 1 — — —
4 — 1 — — 1 — 1 —
5 — — 1 1 — — — 1
6 1 — — — — — 1 —
7 — — — 1 — 1 — 1
8 — — — — 1 — 1 —
表 1  节点连接关系矩阵A
图 6  节点连接的关系图谱
节点编号 1 2 3 4 5 6 7 8
连接数目 2 2 1 2 1 1 1 0
表 2  节点连接的数目
图 7  单元生成的判别方法及流程
图 8  最终识别出的悬臂梁结构的跨尺度网格
图 9  堤坝的材料分布及荷载步的示意图
图 10  堤坝防渗系统受力示意图
材料 $ {\gamma _{\text{d}}} $/(kg·m?3) $ {\gamma _{\text{f}}} $/(kg·m?3) $ k $ $ {k_{{\text{ur}}}} $ $ \;\beta $ $ {n_{{\text{ur}}}} $
坝体 16.3 982 300 360 0.34 0.34
坝基 16.5 982 320 390 0.30 0.30
材料 $ {R_{\text{f}}} $ $ {k_{\text{b}}} $ $ q $ $ c $/kPa $ \varphi $/(°) $ \Delta \varphi $/(°)
坝体 0.95 200 0.30 22.2 11.3 0
坝基 0.95 215 0.30 21.6 11.8 0
表 3  坝体和坝基的静力参数
材料 $\; \rho$/(kg·m?3) $ E/{\text{MPa}} $ $ \nu $
混凝土防渗墙 2 400 30 000 0.167
基岩 2 400 200 0.350
表 4  墙、基岩的静力参数
位置 $ K $ $ j $ $ \delta /(^\circ ) $ $ {R_{\text{f}}} $ $ c/{\text{kPa}} $
墙与坝体 757 0.8 11.0 0.89 10.5
墙与坝基 757 0.8 11.0 0.89 10.5
表 5  接触面的静力参数
图 11  墙体与土体局部单元示意图
图 12  耦合SBFEM-FEM网格识别后的单元分布
M N* N n* H1/m H2/m
1 14 906 14 560 144 0.500 0.125
2 15 381 14 968 552 0.125 0.125
3 48 075 47 634 552 0.125 0.125
表 6  节点、单元的信息
图 13  3种模型下堤坝单元和墙体的单元数量
图 14  蓄水后堤体的位移分布图
图 15  蓄水后墙体的水平位移示意图
图 16  蓄水后墙体上游面的最大、最小的主应力分布图
图 17  蓄水后墙体下游面的最大、最小主应力分布图
图 18  蓄水后堤坝的最大、最小主应力分布图
模型 上游 $ {\sigma _1} $ 上游 $ {\sigma _3} $ 下游 $ {\sigma _1} $ 下游 $ {\sigma _3} $
F/MPa D/% F/MPa D/% F/MPa D/% F/MPa D/%
1 3.76 19.7 ?0.16 48.80 0.26 29.50 ?3.37 20.88
2 4.63 1.11 ?0.29 4.43 0.36 3.74 ?4.20 1.43
3 4.69 — ?3.04 — 0.38 — ?4.26 —
表 7  3种模型下墙体的主应力
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