交错断层四面体自适应网格分级细化研究

陈应显; 朱喆; 马慧茹; 富颉鹏

doi:10.13272/j.issn.1671-251x.2024030058

交错断层四面体自适应网格分级细化研究

doi: 10.13272/j.issn.1671-251x.2024030058

辽宁工程技术大学矿业学院，辽宁阜新　123000

基金项目: 国家自然科学基金项目（52374123）；辽宁工程技术大学学科创新团队资助项目（LNTU20TD-01，LNTU20TD-07）。

详细信息

作者简介:
陈应显（1975—），男，四川中江人，副教授，研究方向为露天开采理论与技术、数字矿山， E-mail：lntucyx@163.com

通讯作者:
朱喆（1999—），男，河南周口人，硕士研究生，研究方向为数字矿山，E-mail：zhuzhe19990506@163.com。

中图分类号: TD76/82
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出版历程
- 收稿日期: 2024-03-22
- 修回日期: 2024-07-29
- 网络出版日期: 2024-08-02

Research on tetrahedral adaptive mesh grading refinement for intersecting faults

College of Mining, Liaoning Technical University, Fuxin 123000, China

摘要

摘要: 目前四面体自适应网格细化技术多集中于简单层状地质体的三维重构与表达分析，对结构复杂、数据不连续的含交错断层等地质体进行自适应网格细化时，易出现过度细化，导致断层区域的网格结构受到影响。为了提高含复杂断层四面体网格模型的精度，提出一种适用于交错断层的四面体自适应网格分级细化方法。首先，根据断层影响范围公式，自适应确定断层网格附近的细化范围；其次，构建四面体和四面体边的分级细分公式，确定细化范围内的四面体和四面体边的分级；然后，针对四面体网格细分时出现的多种情况，通过对边的升级处理，将细分的8种类型统一为3种类型；最后，在细化范围内，通过新增加顶点和原顶点重新连接四面体，改变网格的单元尺寸，生成高质量的网格模型。以内蒙古自治区某含交错断层露天煤矿的四面体网格模型为例，使用三维网格质量评估算法及FLAC3D模拟软件分析细化前后的网格模型，结果表明：细化后的网格模型失真值从0.331 7降低到0.306 1，表明网格的质量得到提升；在相同参数下，未细化模型的最大位移为1.16 m，稳定性系数为1.27，分级细化后模型的最大位移为1.29 m，稳定性系数为1.23；细化后模型的位移云图处于断层处，且能够体现断层分布特征和断层对边坡的影响规律，而未细化模型的位移云图的位置偏离断层中心，断层对边坡的影响效果不明显。
- 交错断层 /
- 自适应网格细化 /
- 四面体 /
- 四面体边 /
- 自适应分级细化 /
- 网格建模
Abstract: Current tetrahedral adaptive mesh refinement techniques have primarily focused on the 3D reconstruction and analysis of simple stratified geological bodies. When applying adaptive mesh refinement to complex geological structures, such as those containing intersecting faults with discontinuous data, excessive refinement can easily lead to compromised mesh structures in the fault zones. To improve the accuracy of tetrahedral mesh models for such complex fault systems, this study proposed a tetrahedral adaptive mesh grading refinement method specifically for intersecting faults. Initially, the refinement range around the fault was adaptively determined based on a fault influence formula. Subdivision formulas were then developed for tetrahedrons and tetrahedral edges to grade both the tetrahedrons and their edges within the refinement range. To address the various scenarios that arose during tetrahedral mesh subdivision, the eight types of subdivisions were unified into three types by upgrading the edge treatments. Finally, new vertices were introduced, and existing vertices were reconnected to tetrahedrons within the refined area, adjusting mesh element sizes to generate a high-quality mesh model. A case study was conducted on a tetrahedral mesh model from an open-pit coal mine in Inner Mongolia. The mesh model was analyzed before and after refinement using a 3D mesh quality evaluation algorithm and FLAC3D simulation software. Results showed that the distortion value of the refined mesh model decreased from 0.3317 to 0.3061, indicating an improvement in mesh quality. Under the same parameters, the unrefined model exhibited a maximum displacement of 1.16 m with a stability coefficient of 1.27, while the refined model showed a maximum displacement of 1.29 m and a stability coefficient of 1.23. The displacement cloud map of the refined model was aligned with the fault, accurately reflecting the fault distribution and its impact on the slope. In contrast, the displacement cloud map of the unrefined model was misaligned with the fault center, demonstrating a less pronounced effect of the fault on the slope.
- intersecting faults /
- adaptive mesh refinement /
- tetrahedron /
- tetrahedral edge /
- adaptive grading refinement /
- mesh modeling

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图 1 断层长度与断层影响范围关系曲线

Figure 1. Relationship curves of fault length and fault influence range

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图 2 确定四面体边的分级

Figure 2. Grading for determining tetrahedral edges

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图 3 四面体网格边的升级过程

Figure 3. Upgrade process for tetrahedral mesh edges

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图 4 初始四面体

Figure 4. Initial tetrahedron

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图 5 case①细分结果

Figure 5. Subdivision results for case ①

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图 6 case②细分结果

Figure 6. Subdivision results forcase ②

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图 7 case③细分结果

Figure 7. Subdivision results for case ③

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图 8 四面体网格自适应分级细化方法流程

Figure 8. Adaptive grading refinement method for tetrahedral meshes

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图 9 自适应分级细化示例

Figure 9. Example of adaptive grading refinement meshes

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图 10 矿区断层分布

Figure 10. Fault distribution in mining area

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图 11 含交错断层四面体网格模型

Figure 11. Tetrahedral mesh model with intersecting faults

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图 12 网格模型自适应分级细化结果

Figure 12. Adaptive grading refinement results of the mesh model

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图 13 网格模型自适应分级细化内部情况

Figure 13. Internal state of the mesh model's adaptive grading refinement

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图 14 网格整体失真的评估

Figure 14. Evaluation of overall mesh distortion

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图 15 网格模型FLAC3D模拟

Figure 15. FLAC3D simulations of the mesh model

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表 1 不同四面体类型边的升级情况

Table 1. Upgrades for edges of different tetrahedral types

类型	u	分级大于0的边是否共面	是否改变边的分级	进行升级的边个数	分级大于 0的边个数	细分模式
①	1	是	否	0	1	case①
②	2	是	是	1	3	case②
③	2	否	是	4	6	case③
④	3	是	否	0	3	case②
⑤	3	否	是	3	6	case③
⑥	4	否	是	2	6	case③
⑦	5	否	是	1	6	case③
⑧	6	否	否	0	6	case③

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表 2 不同断层模型算法的计算时间

Table 2. Computation time of the different fault model algorithms

断层模型	顶点数	三角面数	四面体数	细分耗时/s	总耗时/s
初始网格模型	16 570	69 192	46 629	0	0
F1断层	225 620	935 428	630 385	3.5	5.1
F1和F 2断层	457 431	1 896 517	1 278 063	7.3	8.9

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