锦屏大理岩动态劈裂拉伸破坏及能量演化特征分析

缪逢晨; 王志亮; 孙盼; 李松玉; 傅晶晶

doi:10.16030/j.cnki.issn.1000-3665.202211033

锦屏大理岩动态劈裂拉伸破坏及能量演化特征分析

1.
合肥工业大学土木与水利工程学院，安徽合肥　230009

基金项目: 国家自然科学基金项目（U1965101；12272119）

详细信息

作者简介: 缪逢晨（1998—），男，硕士研究生，从事岩石动态损伤机理研究。E-mail：miaofengchen@163.com

通讯作者: 王志亮（1969—），男，博士，教授，主要从事岩石动力学研究。E-mail：cvewzL@hfut.edu.cn

中图分类号: TU45

收稿日期: 2022-11-10

修回日期: 2023-02-27

录用日期: 2023-03-16

刊出日期: 2024-03-15

Analysis of dynamic splitting tensile failure and energy evolution characteristics of Jinping marble

1.
School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei, Anhui　230009，China

More Information

Corresponding author: WANG Zhiliang, cvewzL@hfut.edu.cn

Received Date: 10 November 2022

Revised Date: 27 February 2023

Accepted Date: 16 March 2023

Publish Date: 15 March 2024

摘要

摘要:
劈裂拉伸破坏是隧洞围岩失稳破坏的主要形式之一。现阶段，在动态劈裂条件下岩石裂纹扩展及对应阶段的能量演化机制鲜有涉及。基于此，采用分离式霍普金森压杆对锦屏大理岩试样进行了不同弹速下的劈裂试验，并借助ANSYS/LS-DYNA有限元软件，模拟试样动态劈裂破坏过程。从试验测试和数值计算角度，重点分析大理岩劈裂过程中的裂纹扩展机制以及能量演化特征。结果表明：在应变率为5～35 s⁻¹时，大理岩的动态拉伸强度与应变率呈线性正相关，同其他地区大理岩相比较，锦屏大理岩的应变率敏感性相对较低；随着弹速的增加，系统内能和动能均增大，在试样破坏的瞬间系统内能降至最低；采用标定的Cowper-Symonds本构模型参数进行数值模拟，所得的试样最终破坏形态与试验观察到的现象基本一致。研究结果可为具体工程应用提供指导和参考。
- 大理岩 /
- 应变率 /
- 裂纹扩展 /
- 能量特征 /
- 数值模拟
Abstract:
Splitting tensile failure is one of the main forms of instability failure of tunnel surrounding rock. At present, the mechanisms of rock crack propagation and energy evolution at the corresponding stages under dynamic splitting conditions have been rarely addressed. In this study, the splitting tests were carried out on Jinping marble samples using a split-Hopkinson pressure bar under different striking velocities. The dynamic damage processes of the samples were simulated with the ANSYS/LS-DYNA finite element software. From the perspectives of loboratory tests and numerical calculations, the mechanism of crack propagation and the characteristics of energy evolution during the splitting process of marble were comprehensively analyzed. The results show that the dynamic tensile strength of marble is linearly and positively related to the strain rate in the range of 5 s⁻¹ to 35 s⁻¹. The strain rate sensitivity of the Jinping marble is relatively low compared with the marbles of other regions. With the increase of the striking velocity, both the internal energy and kinetic energy of the system increase. At the moment of sample failure, the internal energy of the system drops to a minimum. Based on the calibrated parameters of Cowper-Symonds constitutive model, the final failure modes of the numerically simulated samples are basically consistent with the observed ones in the experiments. The research results of this study can provide guidance and reference for specific engineering applications.
- marble /
- strain rate /
- crack extension /
- energy characteristics /
- numerical simulation

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图 1 SHPB装置示意图

Figure 1.

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图 2 动态应力均衡图

Figure 2.

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图 3 劈裂强度与应变率关系比较

Figure 3.

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图 4 典型弹速下试样破坏比较

Figure 4.

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图 5 动态模拟中有限元网格划分

Figure 5.

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图 6 Cowper-symonds本构中参数拟合曲线

Figure 6.

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图 7 入射波形对比

Figure 7.

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图 8 不同时刻裂纹的扩展过程（v=5.0 m/s）

Figure 8.

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图 9 不同弹度下裂纹扩展最终形态

Figure 9.

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图 10 系统能量时程曲线

Figure 10.

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图 11 系统内能与动能时程曲线

Figure 11.

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表 1 大理岩基本物理力学参数

Table 1. Basic physical and mechanical parameters of marble

参数	ρ₀/（kg·m⁻³）	E/GPa	G/GPa	μ	f_c/MPa
取值	2 763	33.32	12.43	0.34	120
注：ρ₀为密度；E为弹性模量；G为剪切模量；μ为泊松比；f为抗压强度。

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表 2 试样几何尺寸和对应的子弹速度

Table 2. Sample geometric dimension and corresponding striking velocity

编号	M/g	l/mm	d/mm	ρ₀/（kg·m⁻³）	v/（m·s⁻¹）
C14	134.5	24.99	49.65	2 779.89	5.11
C15	137.6	25.38	49.72	2 793.13	4.93
C21	138.2	25.40	49.70	2 806.09	5.06
C1	136.8	25.10	49.70	2 810.12	6.87
C2	133.9	25.10	49.68	2 753.49	6.64
C18	138.6	25.54	49.77	2 789.81	6.66
C8	136.1	25.60	49.72	2 738.21	8.77
C9	130.0	25.13	49.66	2 671.19	9.30
C11	138.3	25.40	49.72	2 805.13	8.88
注：M为质量；l为高度；d为直径；ρ₀为密度；v为弹速。

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表 3 Cowper-Symonds本构参数

Table 3. Constitutive parameters of the Cowper-Symonds model

参数	ρ₀/（kg·m⁻³）	E/GPa	μ	C	p	β
取值	2 763	33.32	0.34	162.19	1.25	0.1
注：ρ₀为密度；E为弹性模量；μ为泊松比；C、p为应变率常数；β为硬化参数。

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