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
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.
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.
Fig.1Boundary discrete element in scaled boundary finite element method
Fig.2Schematic diagram of cross-scale mesh transition method
Fig.3Schematic diagram of cantilever beam structure
Fig.4Simplified schematic diagram of cantilever beam structure
Fig.5Basic mesh diagram of cantilever beam structure
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
—
Tab.1Node connection relation matrix A
Fig.6Relationship diagram of node connection
节点编号
1
2
3
4
5
6
7
8
连接数目
2
2
1
2
1
1
1
0
Tab.2Number of node connections vector
Fig.7Identification method and process of unit generation
Fig.8Cross-scale mesh of cantilever beam structure of final identification
Fig.9Sketch of material distribution and load steps of embankment
Fig.10Schematic diagram of force on anti-seepage system
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
Tab.3Static parameters of dam body and foundation
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
Tab.4Static parameters of wall and bedrock
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
Tab.5Static parameters of contact surface
Fig.11Diagram of local elements of wall and soil
Fig.12Coupling SBFEM-FEM mesh after mesh recognition
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
Tab.6Information of node and unit
Fig.13Element number of dam and wall for three conditions
Fig.14Distribution of dam displacement after impoundment
Fig.15Horizontal displacement of wall after impoundment
Fig.16Maximum and minimum principal stress distribution of wall in upstream after impoundment
Fig.17Maximum and minimum principal stress distribution of wall in downstream after impoundment
Fig.18Maximum and minimum principal stress distribution of embankment in downstream after impoundment
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
—
Tab.7Principal stress of wall for three conditions
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