循环加卸载损伤大理岩的动力学特性

蔚立元; 朱子涵; 孟庆彬; 靖洪文; 苏海健; 何明

doi:10.11883/bzycj-2019-0164

循环加卸载损伤大理岩的动力学特性

doi: 10.11883/bzycj-2019-0164

1.
中国矿业大学深部岩土力学与地下工程国家重点实验室，江苏徐州 221116
2.
陆军工程大学爆炸冲击防灾减灾国家重点实验室，江苏南京 210007

基金项目: 国家自然科学基金（51579239，51704280，51704279）；国家重点研究发展计划（2017YFC0603001）

详细信息

作者简介:
蔚立元（1982－　），男，博士，教授，博导，yuliyuan@cumt.edu.cn

中图分类号: O347.3
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- 被引次数: 0
出版历程
- 收稿日期: 2019-04-25
- 修回日期: 2019-05-21
- 刊出日期: 2019-08-01

Dynamic characteristics of marble damaged by cyclic loading

1.
State key laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and technology, Xuzhou 221116, Jiangsu China
2.
State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, Army University of Engineering, Nanjing 210007, Jiangsu, China

摘要

摘要: 利用MTS 815电液伺服岩石实验系统进行上限应力为80%、85%、90%、95%单轴抗压强度的大理岩单轴压缩循环加卸载实验，每种上限应力条件分别设置20、40、60、80次循环。再利用分离式Hopkinson压杆对损伤岩样进行动力学实验。分析了循环加卸载上限应力及循环次数对大理岩塑性应变的影响，揭示了大理岩动态力学参数和破碎吸收能随损伤变量的演化规律。实验结果表明:塑性应变与循环次数呈正相关，且上限应力越大，塑性应变趋于稳定所需的循环次数也会增大；动态单轴抗压强度、动态弹性模量随损伤变量增加呈指数衰减；破碎吸能占比以损伤变量D=0.343为临界点分为两个阶段，D＜0.343时，破碎吸能占比稳定在10%左右，数值约为13 J，当D＞0.343时破碎吸能占比随损伤变量增加不断增大。研究结果可为岩体工程的设计、施工及支护参数的选取提供参考。
- 岩石力学 /
- 循环加卸载 /
- 分离式Hopkinson压杆 /
- 损伤变量 /
- 动态力学特性 /
- 能量
Abstract: The rock mass will bear the cyclic loading during the construction of underground engineering. Mechanical properties of the damaged rock mass under disturbance of cyclic loading are important for supporting capacity of the surrounding rock. Moreover, the disturbed rock mass is also potentially threatened by impact loads such as blasting. Therefore, it is necessary to investigate the re-bearing mechanical behavior of disturbing rock mass under cyclic loading. The cyclic loading experiments with four various maximum cyclic stress levels were carried out by using MTS 815 test system. The maximum cycling stresses are 80%, 85%, 90%, and 95% of uniaxial compressive strength respectively and the numbers of cycle are set to be 20, 40, 60 and 80 for each maximum cyclic stresses. The dynamic tests of the disturbed rock sample were conducted by using split Hopkinson pressure bar (SHPB). We analyzed the effects of maximum cyclic stress and the numbers of cycle on plastic strain and revealed the evolution law of dynamic strength and dynamic elastic modulus of marble with damage variable. The test results show that the plastic strain positively correlated with cycles, and the larger the maximum cycling stress, the more the cycles required to reach the stable plastic strain. The dynamic uniaxial compressive strength and dynamic elastic modulus decrease exponentially with the increase of the damage variable. The ratio of breakage energy divided into two stages and the critical point of damage variable is D=0.343. When D<0.343, the breakage energy ratio is stable at about 10%, and the value is about 13 J. When D>0.343, the ratio of breakage energy increases with the increase of damage variable. The findings of this research can provide guidelines for the selection of the mechanical parameters of the surrounding rock and the optimization of the support scheme.
- rock mechanics /
- cyclic loading /
- SHPB /
- damage variable /
- dynamic properties /
- energy

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图 1 大理岩8个等距横截面的CT图像

注：CT_a和CT_sd分别是每个图像中所有CT值的平均值和标准差。

Figure 1. CT images of eight equidistant cross-sections

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图 2 MTS 815、SHPB实验系统

Figure 2. MTS 815 and SHPB testing systems

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图 3 单轴抗压强度曲线

Figure 3. Axial stress-axial strain curves

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图 4 大理岩损伤强度

Figure 4. Determination of the damage strength

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图 5 等荷载循环实验典型应力应变曲线

Figure 5. Stress-strain curves for cyclic loadingwith constant amplitude

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图 6 岩石在应力水平σ′处能量计算示意图

Figure 6. Schematic diagram of energy calculation at σ′

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图 7 不同上限应力累积耗散能密度与循环次数关系曲线

Figure 7. Relation between cumulative dissipation energy density and number of cycles under different upper limit stress levels

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图 8 塑性应变与循环次数关系曲线

Figure 8. Relationship between plastic strain and number of cycles

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图 9 整形后的应变波

Figure 9. Strain waves after shaping

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图 10 动态应力应变曲线

Figure 10. Dynamic stress-strain curves

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图 11 动态抗压强度随上限应力变化规律

Figure 11. Relationship between dynamic compressive strength and upper limit stress

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图 12 动态弹性模量随上限应力变化规律

Figure 12. Relationship between dynamic elastic modulus and upper limit stress

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图 13 损伤变量与上限应力关系曲线

Figure 13. Relationship between damage variable and upper limit stress

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图 14 动态抗压强度随损伤变量演化过程

Figure 14. Relationship between dynamic compressive strength and damage variable

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图 15 动态弹性模量随损伤变量演化过程

Figure 15. Relationship between dynamic elastic modulus and damage variable

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图 16 能量分配随损伤变量演化规律

Figure 16. Evolution curves of energy under different damage variables

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图 17 破碎吸能随损伤变量演化规律

Figure 17. Relationship between W_FD and damage variable

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表 1 等荷载循环加卸载试样

Table 1. Cyclic loading and unloading specimens under equal load

σ_uls/σ_ucs	循环次数
σ_uls/σ_ucs	80	60	40	20
80%	T37	T40	T43	T46
	T38	T41	T44	T47
	T39	T42	T45	T48
85%	T25	T28	T31	T34
	T26	T29	T32	T35
	T27	T30	T33	T36
90%	T4	T1	T7	T10
	T5	T2	T8	T11
	T6	T3	T9	T12
95%	T13	T16	T19	T22
	T14	T17	T20	T23
	T15	T18	T21	T24

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表 2 不同上限应力及循环次数下波速

Table 2. Wave speed for different upper limit stress and number of cycles

σ_uls/σ_ucs	循环次数	平均波速/(km·s⁻¹)	损伤变量
80%	20	4.951	0.124
	40	4.774	0.186
	60	4.605	0.242
	80	4.288	0.343
85%	20	4.639	0.231
	40	4.513	0.273
	60	4.288	0.343
	80	4.117	0.395
90%	20	4.513	0.273
	40	4.401	0.308
	60	4.178	0.377
	80	3.989	0.432
95%	20	4.362	0.320
	40	4.288	0.343
	60	4.083	0.405
	80	3.844	0.472
0	0	5.291	0

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参考文献(31)

[1]	王刚, 李术才, 王书刚, 等. 节理岩体大型地下洞室群稳定性分析 [J]. 岩土力学, 2010, 29(1): 261–268. WANG Gang, LI Shucai, WANG Shugang, et al. Stability analysis of huge underground cavern group in jointed rockmass [J]. Rock and Soil Mechanics, 2010, 29(1): 261–268.
[2]	王者超, 赵建纲, 李术才, 等. 循环荷载作用下花岗岩疲劳力学性质及其本构模型 [J]. 岩石力学与工程学报, 2012, 31(9): 1888–1900. doi: 10.3969/j.issn.1000-6915.2012.09.021 WANG Zhechao, ZHAO Jiangang, LI Shucai, et al. Fatigue mechanical behavior of granite subject to cyclic load and its constitutive model [J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(9): 1888–1900. doi: 10.3969/j.issn.1000-6915.2012.09.021
[3]	潘一山, 李忠华, 章梦涛. 我国冲击地压分布、类型、机理及防治研究 [J]. 岩石力学与工程学报, 2003, 22(11): 1844–1851. doi: 10.3321/j.issn:1000-6915.2003.11.019 PAN Yishan, LI Zhonghua, ZHANG Mengtao. Distribution, type, mechanism and prevention of rock brust in China [J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(11): 1844–1851. doi: 10.3321/j.issn:1000-6915.2003.11.019
[4]	YU L, SU H, JING H, et al. Experimental study of the mechanical behavior of sandstone affected by blasting [J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 93(3): 234–241.
[5]	葛修润, 蒋宇, 卢允德, 等. 周期荷载作用下岩石疲劳变形特性试验研究 [J]. 岩石力学与工程学报, 2003, 22(10): 1581–1585. doi: 10.3321/j.issn:1000-6915.2003.10.001 GE Xiurun, JIANG Yu, LU Yunde, et al. Testing study on fatigue deformation law of rock under cyclic loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(10): 1581–1585. doi: 10.3321/j.issn:1000-6915.2003.10.001
[6]	谢和平, 鞠杨, 黎立云. 基于能量耗散与释放原理的岩石强度与整体破坏准则 [J]. 岩石力学与工程学报, 2005, 24(17): 3003–3010. doi: 10.3321/j.issn:1000-6915.2005.17.001 XIE Heping, JU Yang, LI Liyun. Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles [J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(17): 3003–3010. doi: 10.3321/j.issn:1000-6915.2005.17.001
[7]	张志镇, 高峰. 单轴压缩下红砂岩能量演化试验研究 [J]. 岩石力学与工程学报, 2012, 31(5): 953–962. doi: 10.3969/j.issn.1000-6915.2012.05.012 ZHANG Zhizhen, GAO Feng. Experimental research on energy evolution of red sandstone samples under uniaxial compression [J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(5): 953–962. doi: 10.3969/j.issn.1000-6915.2012.05.012
[8]	邓华锋, 胡玉, 李建林, 等. 循环荷载的频率和幅值对砂岩动力特性的影响 [J]. 岩土力学, 2017, 38(12): 3402–3409. DENG Huafeng, HU Yu, LI Jianlin, et al. Effects of frequency and amplitude of cyclic loading on the dynamic characteristics of sandstone [J]. Rock and Soil Mechanics, 2017, 38(12): 3402–3409.
[9]	郭印同, 赵克烈, 孙冠华, 等. 周期荷载下盐岩的疲劳变形及损伤特性研究 [J]. 岩土力学, 2011, 32(5): 1353–1359. doi: 10.3969/j.issn.1000-7598.2011.05.012 GUO Yintong, ZHAO Kelie, SUN Guanhua, et al. Experimental study of fatigue deformation and damage characteristics of salt rock under cyclic loading [J]. Rock and Soil Mechanics, 2011, 32(5): 1353–1359. doi: 10.3969/j.issn.1000-7598.2011.05.012
[10]	SHALEV E, LYAKHOVSKY V, QUGIER-SIMONINAUDREY A, et al. Inelastic compaction, dilation and hysteresis of sandstones under hydrostatic conditions [J]. Geophysical Journal International, 2014, 197(2): 920–925. doi: 10.1093/gji/ggu052
[11]	周家文, 杨兴国, 符文熹, 等. 脆性岩石单轴循环加卸载试验及断裂损伤力学特性研究 [J]. 岩石力学与工程学报, 2010, 29(6): 1172–1183. ZHOU Jiawen, YANG Xingguo, FU Wenxi, et al. Experimental test and fracture damage mechanical characteristics of brittle rock under uniaxial cyclic loading and unloading condition [J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(6): 1172–1183.
[12]	张媛, 许江, 杨红伟, 等. 循环荷载作用下围压对砂岩滞回环演化规律的影响 [J]. 岩石力学与工程学报, 2011, 30(2): 320–326. ZHANG Yuan, XU Jiang, YANG Hongwei, et al. Effect of confining pressure on evolution law of hysteresis loop of sandstone under cyclic loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(2): 320–326.
[13]	黎立云, 王荣新, 马旭, 等. 双向加压下岩石能量规律的试验研究 [J]. 煤炭学报, 2010, 35(12): 2033–2038. LI Liyun, WANG Rongxin, MA Xu, et al. Energy variety analysis of rock under biaxial compression [J]. Journal of China Coal Society, 2010, 35(12): 2033–2038.
[14]	朱珍德, 孙林柱, 王明洋. 不同频率循环荷载作用下岩石尼比试验与变形破坏机制细观分析 [J]. 岩土力学, 2010, 31(增1): 8–12. ZHU Zhende, SUN Linzhu, WANG Mingyang. Experiment and mesomechanical analysis of deformation failure mechanism on rock under different frequency cyclic loadings [J]. Rock and Soil Mechanics, 2010, 31(S1): 8–12.
[15]	章根德. 岩石对冲击载荷的动态响应 [J]. 爆炸与冲击, 1982, 2(2): 1–9. ZHANG Gende. Dynamic response of rock impulse loads [J]. Explosion and Shock Waves, 1982, 2(2): 1–9.
[16]	黎立云, 徐志强, 谢和平, 等. 不同冲击速度下岩石破坏能量规律的实验研究 [J]. 煤炭学报, 2011, 36(12): 2007–2011. LI Liyun, XU Zhiqiang, XIE Heping, et al. Failure experimental study on energy laws of rock under differential dynamic impact velocities [J]. JOURNAL OF CHINA COAL SOCIETY, 2011, 36(12): 2007–2011.
[17]	刘红岩, 李俊峰, 裴小龙. 单轴压缩下断续节理岩体动态损伤本构模型 [J]. 爆炸与冲击, 2018, 38(2): 316–323. DOI: 10.11883/bzycj-2016-0261. LIU Hongyan, LI Junfeng, PEI Xiaolong. A dynamic damage constitutive model for rock mass with intermittent joints [J]. Explosion and Shock Waves, 2018, 38(2): 316–323. DOI: 10.11883/bzycj-2016-0261.
[18]	宫凤强, 陆道辉, 李夕兵, 等. 不同应变率下砂岩动态强度准则的试验研究 [J]. 岩土力学, 2013, 34(9): 2433–2441. GONG Fengqiang, LU Daohui, LI Xibing, et al. Experimental research of sandstone dynamic strength criterion under different strain rates [J]. Rock and Soil Mechanics, 2013, 34(9): 2433–2441.
[19]	胡柳青, 李夕兵, 赵伏军. 冲击荷载作用下岩石破裂损伤的耗能规律 [J]. 岩石力学与工程学报, 2002, 21(增2): 2304–2308. Hu Liuqing, Li Xibing, Zhao Fujun. Study on energy consumption in fracture and damage of rock induced by impact loadings [J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21(S2): 2304–2308.
[20]	刘军忠, 许金余, 吕晓聪, 等. 冲击压缩荷载下角闪岩的动态力学性能试验研究 [J]. 岩石力学与工程学报, 2009, 28(10): 2113–2120. doi: 10.3321/j.issn:1000-6915.2009.10.020 LIU Junzhong, XU Jinyu, LYU Xiaocong, et al. Experimental study on dynamic mechanical properties of amphibolites under impact compressive loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(10): 2113–2120. doi: 10.3321/j.issn:1000-6915.2009.10.020
[21]	李夕兵, 宫凤强, 高科, 等. 一维动静组合加载下岩石冲击破坏试验研究 [J]. 岩石力学与工程学报, 2010, 29(2): 251–260. LI Xibing, GONG Fengqiang, GAO Ke, et al. Test study of impact failure of rock subjected to one-dimensional coupled static and dynamic loads [J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(2): 251–260.
[22]	汪斌, 朱杰兵, 严鹏, 等. 大理岩损伤强度的识别及基于损伤控制的参数演化规律 [J]. 岩石力学与工程学报, 2012, 31(S2): 3968–3973. WANG Bin, ZHU Jiebing, YAN Peng, et al. Damage strength determination of marble and its parameters evaluation based on damage control test [J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(S2): 3968–3973.
[23]	FREW D J, FORRESTAL M J, CHEN W. Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar [J]. Experimental Mechanics, 2002, 42(1): 93–106. doi: 10.1007/BF02411056
[24]	周子龙, 李夕兵, 岩小明. 岩石SHPB测试中试样恒应变率变形的加载条件 [J]. 岩石力学与工程学报, 2009, 28(12): 2445–2452. doi: 10.3321/j.issn:1000-6915.2009.12.009 ZHOU Zilong, LI Xibing, YAN Xiaoming. Loading condition for specimen deformation at constant stain rate in SHPB test of rock [J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(12): 2445–2452. doi: 10.3321/j.issn:1000-6915.2009.12.009
[25]	蔚立元, 李光雷, 苏海健, 等. 高温后无烟煤静动态压缩力学特性研究 [J]. 岩石力学与工程学报, 2017, 36(11): 2712–2719. YU Liyuan, LI Guanglei, SU Haijian, et al. Experimental study on static and dynamic mechanical properties of anthracite after high temperature heating [J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(11): 2712–2719.
[26]	肖大武, 胡时胜. SHPB实验试件横截面积不匹配效应的研究 [J]. 爆炸与冲击, 2007, 27(1): 87–90. DOI: 10.11883/1001-1455(2007)01-0087-04. XIAO Dawu, HU Shisheng. Study of two-dimensional effect on SHPB experiment [J]. Explosion and Shock Waves, 2007, 27(1): 87–90. DOI: 10.11883/1001-1455(2007)01-0087-04.
[27]	王礼立. 应力波基础 [M]. 北京: 国防工业出版社, 2005: 52−60.
[28]	ZHOU Y X, XIA K, LI X B, et al. Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials [J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 49(1): 105–112.
[29]	赵奎, 金解放, 王晓军, 等. 岩石声速与其损伤及声发射关系研究 [J]. 岩土力学, 2007, 28(10): 2105–2109. doi: 10.3969/j.issn.1000-7598.2007.10.019 ZHAO Kui, JIN Jiefang, WANG Xiaojun, et al. Study on rock damage and acoustic emission based on ultrasonic velocity test of rock specimen under uniaxial compression [J]. Rock and Soil Mechanics, 2007, 28(10): 2105–2109. doi: 10.3969/j.issn.1000-7598.2007.10.019
[30]	ZHANG Z X, KOU S Q, YU J, et al. Effects of loading rate on rock fracture [J]. International Journal of Rock Mechanics & Mining Sciences, 2000, 37(5): 745–762.
[31]	洪亮. 冲击荷载下岩石强度及破碎吸能耗特征的尺寸效应研究 [D]. 长沙: 中南大学, 2008.