不同应变率下煤岩破坏特征及其本构模型

郑钰; 施浩然; 刘晓辉; 张文举

doi:10.11883/bzycj-2020-0072

不同应变率下煤岩破坏特征及其本构模型

doi: 10.11883/bzycj-2020-0072

郑钰^1,,
施浩然^{1, 2},
刘晓辉^{1, 2, ,},
张文举³

1.
西华大学能源与动力工程学院，四川成都 610039
2.
西华大学流体与动力机械教育部重点实验室，四川成都 610039
3.
中国市政工程西南设计研究总院有限公司，四川成都 610084

基金项目: 四川省教育厅重点科研基金（18ZA0457）；西华大学重点科研基金（Z17113）；西华大学研究生创新基金（ycjj2020110）；深地科学与工程教育部重点实验室（四川大学）开放基金（DESE202003）

详细信息

作者简介:
郑　钰（1997－　），女，硕士研究生，zhengyu@stu.xhu.edu.cn

通讯作者:
刘晓辉（1977－　），女，博士，副教授，liuxh@mail.xhu.edu.cn

中图分类号: O382.2
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- 被引次数: 0
出版历程
- 收稿日期: 2020-03-19
- 修回日期: 2021-01-15
- 网络出版日期: 2021-04-08
- 刊出日期: 2021-05-05

Failure characteristics and constitutive model of coal rock at different strain rates

ZHENG Yu^1
,,
SHI Haoran^{1, 2},
LIU Xiaohui^{1, 2
, ,},
ZHANG Wenju³

1.
School of Energy and Power Engineering, Xihua University, Chengdu 610039, Sichuan, China
2.
Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu 610039, Sichuan, China
3.
Southwest Municipal Engineering Design and Research Institute of China, Chengdu 610084, Sichuan, China

摘要

摘要: 利用直径50 mm的分离式霍普金森压杆，对煤岩展开20～100 s⁻¹动态应变率下的单轴冲击压缩试验，结合高速摄影分析其变形破坏特征，并建立基于Weibull统计分布和Drucker-Prager破坏准则的煤岩动态强度型统计损伤本构模型。试验结果表明：（1）煤岩动态应力-应变曲线存在明显的非线性特征，随应变率升高，动态抗压强度与弹性模量均呈线性增长且增幅显著，破坏形态由低应变率下的轴向劈裂破坏向高应变率下的压碎破坏过渡；（2）在动态应变率20～100 s⁻¹下，煤岩破坏后碎块具有明显的分形特性，破碎块度分维值为1.9～2.2，且随着应变率的升高，煤岩破碎程度增大，碎块块度减小；（3）基于Weibull分布参数F₀、m和应变率的关系，修正煤岩的本构模型，并与试验结果进行对比，验证该模型的合理性。
- 分离式霍普金森压杆 /
- 动态应变率 /
- 破碎块度 /
- 分形维数 /
- 动态本构模型 /
- 煤岩
Abstract: With the increasing demand for coal resources, safe and efficient coal mining has attracted the attention of all sectors of society. In order to study the dynamic failure characteristics and constitutive relation of coal rock under different strain rates, uniaxial impact compression tests of coal rock were carried out over a strain rate range from 20 s⁻¹ to 100 s⁻¹ under nine air pressures by using a split Hopkinson pressure bar (SHPB) with a diameter of 50 mm, and a high-speed camera was used to monitor the whole process of coal rock failure. Based on the dynamic mechanical properties and fracture fractal dimension characteristics of coal rock under different strain rates, the dynamic failure characteristics of coal rock were deeply analyzed, and a dynamic strength statistical damage constitutive model was established based on Weibull statistical distribution and Drucker-Prager failure criterion. The results show that the dynamic stress-strain curves of coal rock under different strain rates exhibit obvious nonlinear characteristics, which can be roughly divided into linear elastic stage, plastic yield stage, peak stress stage and post-peak softening stage. As strain rate increases, dynamic uniaxial compressive strength and elastic modulus both show a significant linear growth. The failure mode of coal rock changes from axial cleaving failure at low strain rate to crushing failure at high strain rate. Coal rock fragments after dynamic failure are sieved and found to have obvious fractal characteristics. At the strain rates of 20−100 s⁻¹, average fragmentation of coal rock samples is concentrated in 30−40 mm, and fractal dimension ranges from 1.9 to 2.2. With the increase of strain rate, the degree of fragmentation increases and fractal dimension increases, indicating that the proportion of large-scale coal rock fragments to the total mass gradually decreases. Based on the relationship between the Weibull distribution parameters F₀, m and strain rate, the dynamic constitutive model of coal rock is modified. Comparing the model results with test results, it is found that the model can fully reflect the relationship between stress, strain and strain rate, and the rationality of this model is also verified.
- splitHopkinsonpressurebar(SHPB) /
- dynamic strain rate /
- fragmentation /
- fractal dimension /
- dynamic constitutive model /
- coal rock

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图 1 分离式霍普金森压杆装置示意图

Figure 1. Sketch map of a split Hopkinson pressure bar device

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图 2 煤岩动态应力-应变曲线

Figure 2. Dynamic stress-strain curves of coal rock

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图 3 不同应变率下的抗压强度

Figure 3. Compressive strengths under different strain rates

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图 4 不同应变率下的弹性模量

Figure 4. Elastic modulii under different strain rates

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图 5 不同应变率下煤岩的动态破碎特征

Figure 5. Dynamic fracture characteristics of coal rock at dfferent strain rates

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图 6 两个典型煤岩试样动态破坏过程的高速摄影图片

Figure 6. High-speed photographies for the dynamic fracturing process of two typical coal rock specimens

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图 7 煤岩破碎平均块度、分形维数与应变率的关系

Figure 7. Average fragmentation and fractal dimension of coal rock at different strain rates

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图 8 参数F₀随应变率的变化关系

Figure 8. Variation of parameter F₀ with strain rate

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图 9 参数m随应变率的变化关系

Figure 9. Variation of parameter m with strain rate

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图 10 不同应变率下煤岩试验和理论应力-应变曲线

Figure 10. Comparison between experimental and theoretical stress-strain curves of coal rock under different strain rates

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表 1 煤岩基本物理力学参数

Table 1. Basic physical and mechanical parameters of coal rock

气压/MPa	$\dot \varepsilon $/s⁻¹	D/mm	L_s/mm	ρ/（g·cm⁻³）	σ_d/MPa	ε_m/10⁻²	E_d/GPa	变异系数/%
气压/MPa	$\dot \varepsilon $/s⁻¹	D/mm	L_s/mm	ρ/（g·cm⁻³）	σ_d/MPa	ε_m/10⁻²	E_d/GPa	ρ	E_d
0.30	20.22	48.27	51.21	1.372	8.01	0.08	3.78	4.9	17
	22.99	47.61	50.17	1.462	7.19	0.24	2.73
	24.84	47.52	51.19	1.328	8.94	0.42	2.99
0.32	29.12	47.44	51.53	1.521	10.46	0.30	3.63	4.6	14
	33.09	47.35	50.77	1.522	13.44	0.49	4.85
	33.77	47.92	50.97	1.404	8.37	0.35	4.42
0.34	38.78	48.33	51.09	1.367	7.72	0.25	3.84	2.4	10
	42.32	47.73	50.02	1.431	12.72	0.56	4.62
	42.51	47.65	50.85	1.418	7.53	0.30	4.04
0.36	46.22	47.51	51.15	1.294	13.58	0.44	5.49	7.4	5
	52.05	47.63	51.03	1.502	22.50	0.37	4.99
	57.66	48.21	50.07	1.418	24.19	0.74	5.26
0.38	53.77	47.53	52.01	1.513	17.09	0.51	7.74	11.5	2
	60.61	47.43	51.15	1.291	20.33	0.65	7.55
	61.59	47.63	50.49	1.218	28.31	0.70	7.82
0.40	69.36	47.37	51.94	1.492	18.49	0.63	6.03	2.2	12
	69.49	47.96	51.60	1.438	14.48	0.34	6.97
	71.90	47.49	52.31	1.495	20.99	0.42	7.70
0.42	72.82	47.94	50.95	1.442	20.01	0.74	9.19	1.2	16
	76.09	47.81	50.75	1.455	23.29	0.75	7.40
	87.59	47.60	51.62	1.476	18.54	0.93	6.86
0.44	70.44	47.47	50.08	1.507	25.92	0.48	9.21	3.8	15
	77.12	48.27	50.55	1.396	21.05	0.72	8.36
	90.15	47.91	51.65	1.461	26.05	0.67	6.82
0.46	91.51	47.35	51.56	1.477	32.82	1.06	10.99	2.1	13
	95.69	47.47	49.74	1.489	30.96	0.64	12.41
	98.48	48.23	50.95	1.430	32.50	0.74	9.47

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表 2 不同应变率下煤岩的破碎特征

Table 2. Fragmentation characteristics of coal rock at different strain rates

应变率/s⁻¹	α	相关系数	分形维数	平均块度/mm
24.84	0.864	0.655	2.136	47.36
33.77	0.967	0.994	2.033	36.52
42.32	1.092	0.993	1.908	37.08
46.22	0.777	0.952	2.223	37.11
53.77	1.031	0.980	1.969	35.37
69.36	0.897	0.983	2.103	32.31
72.82	1.004	0.976	1.996	33.02
77.12	0.817	0.983	2.184	31.62
91.51	0.846	0.974	2.154	31.16

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表 3 本构模型参数计算结果

Table 3. Computational results of constitutive model parameters

$\dot \varepsilon $/s⁻¹	F₀/MPa	m
24.84	12.757	2.945
33.77	14.698	1.627
42.32	23.240	1.407
46.22	23.372	1.736
53.77	32.253	1.195
69.36	33.884	1.389
72.82	37.423	0.818
77.12	40.240	0.952
91.51	60.800	0.790

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