含铜石榴黑云片岩动态力学特性及损伤本构模型

doi:10.12382/bgxb.2023.0690

摘要/Abstract

摘要：

为探究深部矿岩在不同加载条件下的动态力学特性及损伤规律,以深部回采的含铜石榴黑云片岩为对象,开展6种轴压σ_ap(0MPa、6MPa、12MPa、18MPa、24MPa、30MPa)、6种围压σ_p(0MPa、4MPa、8MPa、12MPa、16MPa、20MPa)及6种冲击速度v(18.68m/s、20.9m/s、23.54m/s、26.63m/s、29.26m/s、31.95m/s)条件下的动静组合冲击试验,并考虑冲击速度、轴压、围压及应变率因素,基于统计损伤理论和Drucker-Prager破坏准则建立动静组合加载下含铜石榴黑云片岩的动态损伤本构模型。研究结果表明:矿岩试件的应力-应变曲线几乎无压密阶段,当应力增加至峰值应力的65%~80%时,该阶段的应力-应变曲线出现阶跃现象;不同埋深矿岩的受力状态和冲击速度显著影响了深部围岩的动态破坏模式,当σ_p=12MPa、v=31.95m/s时,随着轴压σ_ap的增加,动态抗压强度先增加、后降低,而峰值应变线性递减,当σ_p=12MPa、σ_ap=24MPa时,动态抗压强度随应变率的增大线性增加,而峰值应变随应变率的增加呈二次多项式增长;模型理论曲线与试验曲线吻合度均较高,验证了该动态本构模型的可靠性,可为深埋岩体动态本构模型研究及工程应用提供一定的参考。

关键词: 含铜石榴黑云片岩, 动静组合加载, 破坏模式, Drucker-Prager破坏准则, 动态损伤本构模型

Abstract:

The dynamic mechanical properties and damage law of deep ore rock under different loading conditions are explored by taking the copper-bearing garnet biotite schist in deep mining as an object of study. A combined dynamic and static impact test is performed under the conditions of six kinds of axial pressure σ_ap(0MPa, 6MPa, 12MPa, 18MPa, 24MPa, 30MPa), six kinds of confining pressure σ_p (0MPa, 4MPa, 8MPa, 12MPa, 16MPa, 20MPa) and six kinds of impact velocity v (18.68m/s, 20.93m/s, 23.54m/s, 26.63m/s, 29.26m/s, 31.95m/s), and the factors of impact velocity, axial pressure, confining pressure and strain rate are considered. Based on the statistical damage theory and Drucker-Prager failure criterion, a dynamic damage constitutive model of copper-bearing garnet-biotite schist under combined static and dynamic loading is established. The results show that there is almost no compaction stage in the stress-strain curve of ore rock specimen. When the stress increases to 65%-80% of peak stress, the stress-strain curve of this stage shows a step phenomenon. The dynamic failure mode of deep surrounding rock is significantly affected by the stress state and impact velocity of ore rock at different buried depths.When σ_p=12MPa and v=31.95m/s, the dynamic compressive strength increases first and then decreases with the increase of axial compression σ_ap, while the peak strain decreases linearly. When σ_p=12MPa and σ_ap=24MPa, the dynamic compressive strength increases linearly with the increase of strain rate, while the peak strain increases as quadratic polynomial with the increase of strain rate. The theoretical curve of the model is in good agreement with the experimental curve, which verifies the reliability of the dynamic constitutive model, and can provide some reference for the research and engineering application of the dynamic constitutive model of deep buried rock mass.

Key words: copper-bearing garnet-biotite schist, static-dynamic coupling loading, failure mode, Drucker-Prager failure criterion, dynamic damage constitutive model

中图分类号:

DT235

赵泽虎, 李祥龙, 胡启文, 王建国. 含铜石榴黑云片岩动态力学特性及损伤本构模型[J]. 兵工学报, 2023, 44(12): 3805-3814.

ZHAO Zehu, LI Xianglong, HU Qiwen, WANG Jianguo. Dynamic Mechanical Properties and Damage Constitutive Model of Copper-bearing Garnet-biotite Schist[J]. Acta Armamentarii, 2023, 44(12): 3805-3814.

图/表 9

表1 含铜石榴片岩的静力学参数

Table 1 Static parameters of copper-bearing garnet schist

抗压强度/MPa	抗拉强度/MPa	弹性模量/GPa	内聚力/ MPa	内摩擦角/(°)	泊松比	容重/ (kN·m^-3)
59.82	7.54	31.0	3.76	58.34	0.31	33.8

图1 部分加工完成的试件

Fig.1 Partially processed specimen

图2 三维动静组合加载SHPB试验设备

Fig.2 Three-dimensional dynamic and static combined loading SHPB test equipment

图3 不同方案下应力波传播规律

Fig.3 Propagation law of stress wave under different schemes

图4 不同组合加载条件下应力-应变曲线

Fig.4 Stress-strain curves under different combined loading

图5 不同受力条件下动态抗压强度、峰值应变的变化关系

Fig.5 The relationship between dynamic compressive strength and peak strain under different stress conditions

图6 微元体模型图

Fig.6 Micro-element model diagram

表2 本构模型参数计算结果

Table 2 Calculated results of constitutive model parameters

σ_ap/ MPa	σ_p/ MPa	v/ (m·s^-1)	E/ GPa	S_E/ %	m	S_m/ %	F₀/ MPa	$S F 0$ / %
0	12	31.95	57.82	49.56	2.28	25.75	428.72	16.53
6	12	31.95	59.5	75.32	3.56	120.10	323.89	60.70
12	12	31.95	77.05	2.30	3.04	161.60	466.85	178.90
18	12	31.95	81.20	56.10	2.42	75.28	490.15	237.70
24	12	31.95	80.53	476.00	2.35	34.01	467.44	60.13
30	12	31.95	105.10	73.52	2.05	43.33	198.95	99.52
24	0	31.95	59.13	36.76	1.67	78.32	453.53	14.79
24	4	31.95	62.90	43.92	1.98	92.98	443.33	16.60
24	8	31.95	60.39	166.40	2.80	20.04	397.49	58.74
24	12	31.95	80.53	111.60	2.35	143.90	467.44	106.90
24	16	31.95	74.20	8.10	3.55	97.75	416.11	4.88
24	20	31.95	97.52	69.20	4.12	100.20	355.88	31.46
24	12	18.68	121.30	51.36	2.24	48.83	238.33	60.73
24	12	20.93	93.51	11.18	3.26	33.87	226.39	104.00
24	12	23.54	94.04	24.65	2.87	19.99	337.76	2.79
24	12	26.63	95.52	13.54	2.75	59.11	342.22	8.82
24	12	29.26	96.90	2.30	4.18	136.40	421.38	78.84
24	12	31.95	80.53	33.15	2.35	39.36	467.44	74.16

表2 本构模型参数计算结果

Table 2 Calculated results of constitutive model parameters

σ_ap/ MPa	σ_p/ MPa	v/ (m·s^-1)	E/ GPa	S_E/ %	m	S_m/ %	F₀/ MPa	$S F 0$ / %
0	12	31.95	57.82	49.56	2.28	25.75	428.72	16.53
6	12	31.95	59.5	75.32	3.56	120.10	323.89	60.70
12	12	31.95	77.05	2.30	3.04	161.60	466.85	178.90
18	12	31.95	81.20	56.10	2.42	75.28	490.15	237.70
24	12	31.95	80.53	476.00	2.35	34.01	467.44	60.13
30	12	31.95	105.10	73.52	2.05	43.33	198.95	99.52
24	0	31.95	59.13	36.76	1.67	78.32	453.53	14.79
24	4	31.95	62.90	43.92	1.98	92.98	443.33	16.60
24	8	31.95	60.39	166.40	2.80	20.04	397.49	58.74
24	12	31.95	80.53	111.60	2.35	143.90	467.44	106.90
24	16	31.95	74.20	8.10	3.55	97.75	416.11	4.88
24	20	31.95	97.52	69.20	4.12	100.20	355.88	31.46
24	12	18.68	121.30	51.36	2.24	48.83	238.33	60.73
24	12	20.93	93.51	11.18	3.26	33.87	226.39	104.00
24	12	23.54	94.04	24.65	2.87	19.99	337.76	2.79
24	12	26.63	95.52	13.54	2.75	59.11	342.22	8.82
24	12	29.26	96.90	2.30	4.18	136.40	421.38	78.84
24	12	31.95	80.53	33.15	2.35	39.36	467.44	74.16

图7 不同组合加载条件下理论曲线与试验结果的比较

Fig.7 Comparison of theoretical curves and experimental results under different combined loading conditions

参考文献 25

[1]	李夕兵, 宫凤强. 基于动静组合加载力学试验的深部开采岩石力学研究进展与展望[J]. 煤炭学报, 2021, 46(3):846-866.
	LI X B, GONG F Q. Research progress and prospect of deep mining rock mechanics based on dynamic and static combined loading mechanical test[J]. Journal of China Coal Society, 2021, 46(3):846-866. (in Chinese)
[2]	郭瑞奇, 任辉启, 张磊, 等. 分离式大直径Hopkinson杆实验技术研究进展[J]. 兵工学报, 2019, 40(7):1518-1536. doi: 10.3969/j.issn.1000-1093.2019.07.023
	GUO R Q, REN H Q, ZHANG L, et al. Research progress of split large-diameter Hopkinson bar experimental technique[J]. Acta Armamentarii, 2019, 40 (7): 1518-1536. (in Chinese)
[3]	刘军忠, 许金余, 吕晓聪, 等. 围压下岩石的冲击力学行为及动态统计损伤本构模型研究[J]. 工程力学, 2012, 29(1):55-63.
	LIU J Z, XU J Y, LÜ X C, et al. Research on impact mechanics behavior and dynamic statistical damage constitutive model of rock under confining pressure[J]. Engineering Mechanics, 2012, 29(1): 55-63. (in Chinese)
[4]	王恩元, 孔祥国, 何学秋, 等. 冲击载荷下三轴煤体动力学分析及损伤本构方程[J]. 煤炭学报, 2019, 44(7):2049-2056.
	WANG E Y, KONG X G, HE X Q, et al. Dynamic analysis and damage constitutive equation of triaxial coal under impact load[J]. Journal of China Coal Society, 2019, 44 (7): 2049-2056. (in Chinese)
[5]	闻磊, 梁旭黎, 冯文杰, 等. 冲击损伤砂岩动静组合加载力学特性研究[J]. 岩土力学, 2020, 41(11):3540-3552.
	WEN L, LIANG X L, FENG W J, et al. Study on dynamic and static combined loading mechanical properties of impact damaged sandstone[J]. Rock and Soil Mechanics, 2020, 41(11): 3540-3552. (in Chinese)
[6]	TIAN Y K, WEIJERMARS R, ZHOU F J, et al. Advances in stress-strain constitutive models for rock failure: Review and new dynamic constitutive failure (DCF) model using core data from the Tarim Basin (China)[J]. Earth-Science Reviews, 2023, 243:104473. doi: 10.1016/j.earscirev.2023.104473 URL
[7]	王春, 唐礼忠, 程露萍, 等. 三维高静载频繁动态扰动时岩石损伤特性及本构模型[J]. 岩土力学, 2017, 38(8):2286-2296, 2305.
	WANG C, TANG L Z, CHENG L P, et al. Damage characteristics and constitutive model of rock under three-dimensional high static load and frequent dynamic disturbance[J]. Rock and Soil Mechanics, 2017, 38(8):2286-2296,2305. (in Chinese)
[8]	张茹, 张安林, 谢和平, 等. 不同赋存深度岩石力学行为差异及本构模型研究[J]. 中国科学基金, 2022, 36(6):1008-1015.
	ZHANG R, ZHANG A L, XIE H P, et al. Study on the difference of rock mechanical behavior and constitutive model at different depths[J]. Bulletin of National Natural Science Foundation of China, 2022, 36 (6): 1008-1015. (in Chinese)
[9]	SUBBIAH S K, MOHAMAD-HUSSEIN A, SAMSURI A, et al. Development of new novel constitutive model for deep reservoir sandstone rock for sand production application[J]. IOP Conference Series: Materials Science and Engineering, 2021, 1051(1): 012093. doi: 10.1088/1757-899X/1051/1/012093
[10]	SHEN P W, TANG H M, NING Y B, et al. A damage mechanics based on the constitutive model for strain-softening rocks[J]. Engineering Fracture Mechanics, 2019, 216: 106521. doi: 10.1016/j.engfracmech.2019.106521 URL
[11]	刘志义, 甘德清, 于泽皞, 等. 一维动静组合加载下磁铁矿石力学特性及破碎特征试验研究[J]. 岩石力学与工程学报, 2022, 41(增刊1):2869-2880.
	LIU Z Y, GAN D Q, YU Z H, et al. Experimental research on the dynamic mechanical properties and breakage behavior of magnetite under one-dimensional coupled dynamic and static loads[J]. Chinese Journal of Rock Mechanics and Engineering, 2022, 41(S1): 2869-2880. (in Chinese)
[12]	李晓照, 戚承志. 基于裂纹扩展脆性岩石动力压缩力学特性研究[J]. 爆炸与冲击, 2019, 39(8):52-62.
	LI X Z, QI C Z. Study on dynamic compressive mechanical properties of brittle rocks based on crack propagation[J]. Explosion and shock Waves, 2019, 39(8): 52-62. (in Chinese)
[13]	周宗红, 章雅琦, 杨安国, 等. 白云岩三维动静组合加载力学特性试验研究[J]. 煤炭学报, 2015, 40(5):1030-1036.
	ZHOU Z H, ZHANG Y Q, YANG A G, et al. Experimental study on mechanical properties of dolomite under three-dimensional dynamic and static combined loading[J]. Journal of China Coal Society, 2015, 40(5): 1030-1036. (in Chinese)
[14]	ZHOU Z L, LI X B, ZOU Y, et al. Dynamic brazilian tests of granite under coupled static and dynamic loads[J]. Rock Mechanics and Rock Engineering, 2014, 47(2):495-505. doi: 10.1007/s00603-013-0441-4 URL
[15]	中国岩石力学与工程学会. 岩石动力特性试验规程:T/CSRME 00—2019[S]. 北京: 中国标准出版社, 2019.
	Chinese Society of Rock Mechanics and Engineering. Rock dynamic characteristics test procedures: T/CSRME 00—2019[S]. Beijing: China Standards Press, 2019. (in Chinese)
[16]	GONG F Q, ZHONG W H, GAO M Z, et al. Dynamic characteristics of high stressed red sandstone subjected to unloading and impact loads[J]. Journal of Central South University, 2022, 29(2): 596-610. doi: 10.1007/s11771-022-4944-6
[17]	余永强, 余雳伟, 范利丹, 等. 三维动静组合加载下石灰岩力学特性研究[J]. 金属矿山, 2022, 25(11):84-91.
	YU Y Q, YU L W, FAN L D, et al. Study on the mechanical properties of limestone under three-dimensional combined static and dynamic loading[J]. Metal Mines, 2022, 25(11) : 84-91. (in Chinese)
[18]	范勇, 吴凡, 冷振东, 等. 径向不耦合装药爆压消峰作用及其对岩石破裂范围影响[J/OL]. 兵工学报, 2022(2022-10-21):https://doi.org/10.12382/bgxb.2022.0431.
	FAN Y, WU F, LENG Z D, et al. Detonation peak effect of radial uncoupled charge and its influence on rock fracture range[J/OL]. Acta Armamentarii, 2022(2022-10-21):https://doi.org/10.12382/bgxb.2022.0431. (in Chinese)
[19]	马东方, 侯远, 陈大年, 等. 冲击载荷下细砂岩压缩试验和破坏特性研究[J]. 兵工学报, 2016, 37(增刊2):42-48.
	MA D F, HOU Y, CHEN D N, et al. Compression test and failure characteristics of fine sandstone under impact load[J]. Acta Armamentarii, 2016, 37 (S2): 42-48. (in Chinese)
[20]	LI X B, ZOU Y, ZHOU Z L. Numerical simulation of the rock SHPB test with a special shape striker based on the discrete element method[J]. Rock Mechanics and Rock Engineering, 2014, 47(5): 1693-1709. doi: 10.1007/s00603-013-0484-6 URL
[21]	KONG X G, LI S G, WANG E Y, et al. Dynamics behaviour of gas-bearing coal subjected to SHPB tests[J]. Composite Structures, 2021, 256: 113088-113098. doi: 10.1016/j.compstruct.2020.113088 URL
[22]	何成龙, 杨军. 主动围压和爆炸加载作用下岩石动态响应研究[J]. 兵工学报, 2017, 38(12):2395-2405. doi: 10.3969/j.issn.1000-1093.2017.12.013
	HE C L, YANG J. Study on the dynamic response of rock under active confining pressure and explosive loading[J]. Acta Armamentarii, 2017, 38 (12):2395-2405. (in Chinese)
[23]	徐泽辉, 何童, 杜光钢, 等. 恒定动载下高温水冷后玄武岩的动力特性及本构模型[J]. 爆炸与冲击, 2023, 43(6):62-75.
	XU Z H, HE T, DU G G, et al. Dynamic characteristics and constitutive model of basalt after high temperature water cooling under constant dynamic load[J]. Explosion and Shock Waves, 2023, 43 (6): 62-75. (in Chinese) doi: 10.1007/s10573-007-0010-9 URL
[24]	ZHAO B Y, HUANG T Z, LIU D Y, et al. Study on the mechanical properties test and constitutive model of rock salt[J]. Geomechanics and Engineering, 2019, 18(3): 291-298.
[25]	牛向东, 杨志全, 侯克鹏. 高程对强风化灰岩抗剪强度敏感性分析[J]. 工程勘察, 2016, 44(6):1-4,23.
	NIU X D, YANG Z Q, HOU K P. Sensitivity analysis of elevation on shear strength of strongly weathered limestone[J]. Geotechnical Investigation & Surveying, 2016, 44(6): 1-4,23.