基于颗粒流软件探究不同CFRP布层数对轴压煤圆柱能量演化的影响

李庆文; 潘创创; 张学磊; 钟宇奇; 李玲; 聂帆帆; 李雯霞; 徐梦娇

doi:10.11858/gywlxb.20240931

基于颗粒流软件探究不同CFRP布层数对轴压煤圆柱能量演化的影响

doi: 10.11858/gywlxb.20240931

1.
辽宁工业大学土木建筑工程学院, 辽宁锦州　121001
2.
中国建筑材料工业地质勘查中心辽宁总队, 辽宁沈阳　110004

基金项目: 辽宁省自然科学基金（2023-MS-298，20180550297）；辽宁省教育厅基本科研面上项目（JYTMS20230866）；辽宁省博士科研启动基金（2019-BS-120）

详细信息

作者简介:
李庆文（1987－），男，博士，副教授，主要从事岩石力学、新材料与新型组合结构及离散元-有限差分跨尺度耦合细观模拟研究. E-mail：lgjzlqw@163.com

通讯作者:
潘创创（1997－），男，硕士研究生，主要从事计算颗粒力学研究. E-mail：panguoguo0602@163.com

中图分类号: TU45; O521.9
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出版历程
- 收稿日期: 2024-11-05
- 修回日期: 2024-11-22
- 网络出版日期: 2025-03-25
- 刊出日期: 2025-04-05

Effect of CFRP Layers on the Energy Evolution of Axial Compressed Cylindrical Coal Based on Particle Flow Software

1.
School of Civil and Architectural Engineering, Liaoning University of Technology, Jinzhou 121001, Liaoning, China
2.
China Building Materials Industry Geologic Exploration Center Liaoning Branch, Shenyang 110004, Liaoning, China

摘要

摘要: 为探究不同碳纤维增强复合材料（carbon fiber reinforced plastic，CFRP）布层数对轴压煤圆柱力学特性及能量演化的影响，结合室内单轴压缩试验，采用有限差分-离散元法（FDM-DEM）进行数值模拟。试验结果表明，无论是未约束煤圆柱，还是CFRP约束样本，应力-应变曲线均经历了压密、弹性、屈服和峰后4个阶段。CFRP布约束样本在屈服和峰后阶段表现出明显的延性破坏，其平均峰值应力、峰值应变和弹性模量分别比未约束样本高出约2、2.5和1倍。数值模拟结果显示：随着CFRP布层数增加，峰值应变和峰值应力分别提升至733%和548%；而弹性模量并未单调上升，表明在设计CFRP布层数时需平衡强度与刚度。此外，CFRP布层数的增加导致破坏机制由张拉破坏转变为剪切破坏，表明其对煤圆柱的应力分布和破坏过程影响显著。煤圆柱的总能量和耗散能随着CFRP布层数的增加显著提升，能量吸收效率最高可达10.51倍，显示其抗失稳能力显著增强。为量化CFRP布的约束效应，引入了“等效厚度”概念，发现其随着CFRP布层数增加呈非线性增长趋势，且在6.78层时，等效厚度趋近于无穷大，说明了CFRP布在提升煤圆柱结构稳定性方面的重要性，为未来研究提供了重要参考。
- 单轴压缩 /
- 碳纤维增强复合材料布 /
- 煤圆柱 /
- 有限差分-离散元法 /
- 能量演化 /
- 等效厚度
Abstract: To investigate the effects of different layers of carbon fiber reinforced plastic (CFRP) on the mechanical properties and energy evolution of axially compressed cylindrical coal samples, the finite difference method-discrete element method (FDM-DEM) coupled numerical simulation and laboratory uniaxial compression tests are combined in this paper. The test results show that both unconfined cylindrical coal samples and CFRP-confined samples undergo four stages in the stress-strain curve, namely, compression-tightness, elasticity, yielding, and post-peak. The CFRP-confined samples show obvious ductile damage in the yielding and post-peak stages, and their average peak stresses, peak strains, and elasticity modulus are about 2, 2.5 and 1 times higher than those of the unconfined samples, respectively. Numerical simulations show that the peak strain and peak stress increased to 733% and 548%, respectively, with the increase in the number of CFRP layers. The elastic modulus does not increase monotonically, indicating that a balance between strength and stiffness is required when designing the CFRP layers. In addition, the increase of CFRP layers leads to the change of the damage mechanism from tensile damage to shear damage, indicating that it has a significant effect on the stress distribution and damage process of the cylindrical coal samples. The total and dissipated energy of the cylindrical coal samples significantly increased with the increase of CFRP layers, and the energy absorption efficiency reaches up to 10.51 times, showing a significant enhancement of their destabilization resistance. To quantify the confinement effect of CFRP sheets, the concept of “equivalent thickness” is introduced. It is found that the equivalent thickness increases nonlinearly with the number of CFRP layers, and at 6.78 layers, the equivalent thickness approaches infinity, which emphasizes the importance of CFRP sheet in improving the stability of cylindrical coal sample structure, and provides an important reference for future research.
- uniaxial compression /
- carbon fiber reinforced plastic sheet /
- cylindrical coal /
- finite difference method-discrete element method /
- energy evolution /
- equivalent thickness

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图 1 煤圆柱的能量转换过程

Figure 1. Energy conversion process of cylindrical coal samples

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图 2 CFRP条带制作

Figure 2. Preparation of CFRP strips

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图 3 CFRP条带荷载-应变曲线

Figure 3. Load-strain curves of CFRP strips

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图 4 试验设备及采集系统

Figure 4. Test equipment and acquisition systems

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图 5 单轴压缩试验的应力-应变曲线

Figure 5. Stress-strain curves of uniaxial compression tests

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图 6 PFC^3D-FLAC^3D耦合计算原理

Figure 6. Calculation principle of PFC^3D-FLAC^3D coupling

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图 7 平行黏结模型^[33–34]

Figure 7. Parallel bonding model^[33–34]

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图 8 煤圆柱模型

Figure 8. Model of cylindrical coal samples

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图 9 CFRP条带的应力-应变模拟曲线

Figure 9. Simulated stress-strain curves of CFRP strips

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图 10 试验与模拟验证

Figure 10. Verification of tests and simulations

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图 11 模拟不同CFRP层数下煤圆柱的应力-应变曲线

Figure 11. Numerical simulated stress-strain curves of cylindrical coal samples with different CFRP layers

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图 12 煤圆柱的破坏形态

Figure 12. Damage patterns of the cylindrical coal samples

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图 13 不同CFRP层数下煤圆柱的裂纹数量

Figure 13. Number of cracks in cylindrical coal samples with different CFRP layers

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图 14 不同CFRP层数下煤圆柱的能量演化规律

Figure 14. Energy evolution law of cylindrical coal samples with different CFRP layers

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图 15 不同CFRP层数下煤圆柱的能量吸收效率曲线

Figure 15. Energy absorption efficiency curves of cylindrical coal samples with different CFRP layers

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图 16 CFRP约束煤圆柱的弹性能与耗散能的关系^[20]

Figure 16. Relationship between elastic strain energy and dissipated energy of CFRP-confined cylindrical coal samples^[20]

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图 17 未约束煤圆柱的弹性能耗比曲线

Figure 17. Elastic energy consumption ratio curves of unconfined cylindrical coal sample

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图 18 不同CFRP层数下煤圆柱的弹性能耗比曲线

Figure 18. Elastic energy consumption ratio curves of cylindrical coal samples with different CFRP layers

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图 19 CFRP布约束煤圆柱的机制

Figure 19. Mechanism of CFRP-confined cylindrical coal samples

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图 20 等效厚度柱状图及拟合曲线

Figure 20. Equivalent thickness histograms and fitting curve

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表 1 CFRP布的力学参数

Table 1. Mechanical parameters of CFRP sheets

CFRP No.	F_CFRP/N	x/mm	ε_CFRP/%	T_CFRP/MPa
CFRP-1	3846.0	4.71	1.88	921.2
CFRP-2	3880.5	5.19	2.07	929.5
CFRP-3	3889.5	5.18	2.07	931.6
CFRP-4	3877.5	4.57	1.83	928.7
CFRP-5	4462.5	5.35	2.14	1068.9
CFRP-6	3466.5	5.05	2.02	830.3
CFRP-7	3408.0	3.91	1.56	816.3
Average value	3832.9	4.85	1.94	918.1

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表 2 单轴压缩试验方案

Table 2. Uniaxial compression test scheme

Specimen No.	Layer	Number of samples	Loading rate/(mm·min^–1)
C0	0	3	0.12
C1	1	3	0.12

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表 3 煤圆柱单轴压缩试验结果

Table 3. Uniaxial compression test results of cylindrical coal specimens

Test No.	Layer	D/mm	H/mm	σ/MPa	ε/10⁻³	E/GPa
C0-1	0	50.05	100.21	19.50	13.53	1.72
C0-2	0	49.08	100.06	21.00	14.10	1.79
C0-3	0	50.01	100.13	19.81	13.46	1.95
Average				20.10	13.70	1.82
C1-1	1	49.04	100.00	42.14	38.04	1.61
C1-2	1	49.06	100.04	42.12	33.49	1.95
C1-3	1	49.81	100.37	39.38	29.55	1.92
Average				41.21	33.69	1.83

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表 4 试验与模拟煤圆柱样品的力学参数对比

Table 4. Comparison of mechanical parameters of cylindrical coal sample between test and simulation

Sample	σ_p			ε_p			E
Sample	Test/MPa	Sim./MPa	Error/%	Test/10⁻³	Sim./10⁻³	Error/%	Test/GPa	Sim./GPa	Error/%
Unconfined	19.50	20.08	3.0	13.53	12.71	6.1	1.72	1.63	5.2
CFRP confined	42.14	41.63	1.2	37.04	33.40	9.8	1.61	1.48	8.10

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表 5 煤圆柱和CFRP布的细观参数

Table 5. Microscopic parameters of cylindrical coal sample and CFRP sheet

Sample	E_c/GPa	$ \overline{E}_{\mathrm{c}} $/GPa	k	σ_b/MPa	τ_b/MPa	φ/(°)	μ
Cylindrical coal	1.2	1	1	18.9	11	50	0.5

Sample	T_g/MPa	ε_g/%	E_g/GPa	d/mm	K_s/(N·m⁻³)	c_i/kPa	φ_i/(°)
CFRP sheet	918.07	1.94	47.54	0.168	3.5×10⁶	10	30

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表 6 数值模拟方案

Table 6. Numerical simulation scheme

Sample	Size/(mm×mm)	Layer	Number of particles	Loading rate/(mm·min⁻¹)
DZ-C0–DZ-C6	50×100	0–6	8881	0.12

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表 7 不同CFRP布层数下煤圆柱的力学参数

Table 7. Mechanical parameters of cylindrical coal samples with different CFRP sheet layers

Sample	n	ε_p/10⁻³	σ_p/MPa	E/GPa
DZ-C0	0	12.71	20.08311	1.63
DZ-C1	1	33.40	41.63361	1.48
DZ-C2	2	48.31	60.29511	1.30
DZ-C3	3	63.95	84.83669	1.38
DZ-C4	4	75.46	101.03746	1.41
DZ-C5	5	88.68	114.25265	1.35
DZ-C6	6	105.91	130.26486	1.29

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表 8 不同CFRP层数煤圆柱的约束刚度及等效厚度

Table 8. Confinement stiffness and equivalent thickness of cylindrical coal samples with different CFRP layers

n	d/mm	E_CFRP/GPa	K_CFRP/MPa	λ	d_eq/mm
1	0.167	47.54	317.57	0.165	1.86
2	0.334	47.54	635.13	0.329	4.37
3	0.501	47.54	952.70	0.494	7.99
4	0.668	47.54	1270.27	0.658	13.83
5	0.835	47.54	1587.84	0.823	25.53
6	1.002	47.54	1905.40	0.987	74.05

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