基于拉格朗日反分析法的砂岩动态力学特性

张子健; 陈骏; 朱锐; 余浩然; 李冉鑫; 张渊通

doi:10.11883/bzycj-2024-0152

基于拉格朗日反分析法的砂岩动态力学特性

doi: 10.11883/bzycj-2024-0152

1.
中国矿业大学（北京）力学与土木工程学院，北京 100083
2.
北京科技大学土木与资源工程学院，北京 100083

基金项目: 国家自然科学基金项目（51934001）；国家重点研发计划项目（2021YFB3401501）

详细信息

作者简介:
张子健（2001－　），男，硕士研究生，1264928116@qq.com

通讯作者:
陈　骏（1990－　），男，博士，副研究员，cj0354@cumtb.edu.cn

中图分类号: O347.3
计量
- 文章访问数: 50
- HTML全文浏览量: 3
- PDF下载量: 32
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-23
- 修回日期: 2024-06-21
- 网络出版日期: 2024-06-24

Experiment on dynamic mechanical properties of sandstone based on Lagrangian analysis method

1.
School of Mechanics and Civil Engineering, China University of Mining and Technology-Beijing, Beijing, 100083, China
2.
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China

摘要

摘要: 为深入研究深部地层中砂岩在冲击荷载作用下的动态力学特性，建立了一种改进的霍普金森压杆实验系统，对灰砂岩长杆试件开展了不同加载速率的动态压缩实验，并结合高速数字相关技术（DIC）监测试件表面位移场和应变场的演化过程，探讨了灰砂岩在近场冲击加载下的拉伸破坏的规律。从 DIC 分析得到的位移场中提取出不同质点位移时程曲线，进行了拉格朗日反分析算法计算，获得了灰砂岩材料的全场应力应变规律。结果表明：灰砂岩长杆试件以拉伸破坏为主，且出现了近加载端破碎、远离加载端层裂的现象；灰砂岩长杆试件的动态抗压强度因子随应变率增大而增大，有明显的应变率效应；随着加载速率升高，各测点应力峰值与应变峰值均呈增大趋势；在同一加载速率下，灰砂岩长杆的应力-应变曲线呈现出近端测点曲线包络远端测点曲线的现象。
- 动态力学特性 /
- 数字图像相关法 /
- 拉格朗日反分析 /
- 砂岩 /
- 动态强度增强因子
Abstract: To investigate the dynamic mechanical properties of sandstone in deep strata under impact loads, an improved Hopkinson pressure bar experimental system was established. The traditional Hopkinson pressure bar's transmission rod was replaced with a long rod specimen made of gray sandstone to better simulate deep geological conditions. Point spalling treatment was applied to the specimen, and strain gauges were meticulously affixed at critical measurement points.Dynamic compression experiments were meticulously conducted on the gray sandstone long rod specimen at various loading rates (9.57 m/s, 14.78 m/s, 19.32 m/s, and 27.60 m/s). Utilizing high-speed digital image correlation (DIC) technology, the evolution of displacement and strain fields on the surface of the specimen throughout each test was closely monitored. This advanced technique enabled a detailed exploration of how the gray sandstone responded to near-field impact loading, particularly focusing on its tensile failure characteristics.Employing the Lagrangian analysis method, displacement-time curves for different mass points derived from the DIC analysis of displacement fields were extracted. These curves provided critical data to compute the stress-strain behavior of the gray sandstone material under dynamic loading conditions. The study reveals several key findings: the gray sandstone long rod specimen predominantly exhibits tensile failure, with distinct patterns of fragmentation near the loading end and layer cracking away from it. Moreover, the dynamic compressive strength factor of the gray sandstone long rod specimen shows a notable increase with higher strain rates, indicating a significant strain rate effect. Correspondingly, both stress and strain peaks observe an upward trend at various measurement points with increasing loading rates.Remarkably, under identical loading rates, stress-strain curves of the gray sandstone long rod specimen exhibit a unique phenomenon where curves from measurement points closer to the loading end envelop those from points farther away. This observation underscores the complex nature of dynamic loading responses in geological materials.Overall, this comprehensive investigation provides essential theoretical insights and methodological references for understanding the dynamic behavior of sandstone within deep geological formations under impact loads. The findings offer valuable contributions to engineering practices concerned with the stability and resilience of underground structures subjected to dynamic loading conditions.
- dynamic mechanical properties /
- digital image correlation (DIC) /
- Lagrangian inverse analysis /
- sandstone /
- dynamic increase factor(DIF)

HTML全文

图 1 DIC方法基本原理

Figure 1. Basic principle of DIC method

下载: 全尺寸图片幻灯片

图 2 路径线法示意

Figure 2. Schematic of path line method

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图 3 灰砂岩长杆试件冲击实验装置

Figure 3. Impact test device of gray sandstone long rod specimen

下载: 全尺寸图片幻灯片

图 4 不同冲击气压下灰砂岩宏观破坏形态

Figure 4. Macroscopic damage pattern of gray sandstone under different impact pressures

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图 5 DIC计算应变与电测应变曲线对比

Figure 5. Comparison of strain curves by DIC calculation and electrical measurement

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图 6 不同冲击速度下应变的DIC计算云图

Figure 6. Strain cloud diagram by DIC calculation under different impact velocities

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图 7 拉氏反分析法计算得到的位移场和速度场

Figure 7. The Displacement field and Velocity field calculated by Lagrangian analysis

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图 8 拉氏反分析法计算得到的应变场和应力场

Figure 8. The Strain field and Stress field calculated by Lagrangian analysis

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图 9 冲击载荷下灰砂岩中的应变时程曲线

Figure 9. Strain time history curve in gray sandstone under impact load

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图 10 两种方法峰值应变的对比

Figure 10. Comparison of peak strain between the two methods

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图 11 冲击载荷下灰砂岩中的应力时程曲线

Figure 11. The stress time history curve in gray sandstone under impact load

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图 12 不同应变率下灰砂岩试样的DIF值

Figure 12. DIF value of gray sandstone samples under different strain rates

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图 13 冲击载荷下灰砂岩中的应力应变曲线

Figure 13. Stress-strain curve in gray sandstone under impact load

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表 1 灰砂岩的物理参数

Table 1. physical parameters of gray sandstone

密度/(kg·m⁻³) 泊松比抗压强度/MPa 抗拉强度/MPa 弹性模量/GPa

2680 0.19 36.38 3.29 4.43

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表 2 DIF计算参数

Table 2. The calculated parameters of the DIF

冲击速度/m·s⁻¹ 动态抗压强度/MPa DIF 应变率/s⁻¹

9.57 17.3 0.4755 38.9
14.78 26.9 0.7394 85.5
19.32 31.2 0.8576 257.9
27.60 74.2 2.0396 271.2

下载: 导出CSV

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