考虑裂隙粗糙度的岩体单轴压缩动态损伤模型

刘红岩; 薛雷; 张光雄; 王光兵; 王基禹; 和铁柱; 邹宗山

doi:10.11883/bzycj-2024-0335

考虑裂隙粗糙度的岩体单轴压缩动态损伤模型

doi: 10.11883/bzycj-2024-0335

1.
中国地质大学(北京)工程技术学院，北京 100083
2.
中国科学院地质与地球物理研究所页岩气与地质工程重点实验室，北京 100083
3.
保利民爆哈密有限公司，新疆哈密 839000

基金项目: 北京市自然科学基金项目（8222031）；2024年河南省重点研发与推广专项（科技攻关）（242103220059）；河南省高等学校青年骨干教师培养计划项目（2024GGJS200）；新疆维吾尔自治区“天池英才”领军人才计划项目（2023）

详细信息

作者简介:
刘红岩（1975－　），男，博士、教授，Lhyan1204@126.com

中图分类号: O346
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- 被引次数: 0
出版历程
- 收稿日期: 2024-09-10
- 修回日期: 2024-11-13
- 网络出版日期: 2024-11-13

A uniaxial compressive dynamic damage model for rockmass considering the crack roughness

1.
School of Engineering & Technology, China University of Geosciences (Beijing), Beijing 100083, China
2.
Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
3.
Poly Explosive Hami Co., Ltd., Hami 839000, Xinjiang, China

摘要

摘要: 为了在裂隙岩体动态损伤模型中考虑裂隙粗糙度的影响：首先，基于前人提出的能够同时考虑裂隙几何参数、强度参数及变形参数的岩体宏观损伤变量计算模型，通过引入Barton建立的粗糙裂隙JRC-JCS抗剪强度模型，提出了能够同时考虑裂隙粗糙度的岩体宏观损伤变量计算模型；其次，将该计算模型引入到前人提出的考虑宏细观缺陷耦合的非贯通裂隙岩体单轴压缩动态损伤模型中，建立了能够同时考虑裂隙粗糙度的非贯通裂隙岩体单轴压缩动态损伤模型；最后，通过参数敏感性分析研究了裂隙粗糙度JRC、裂隙面基本摩擦角φ_b、裂隙长度2a对岩体动态力学特性的影响。结果显示，当JRC由0分别增加到10和20时，岩体动态峰值强度由26.42分别增加到27.28和28.37 MPa；当φ_b由0°分别增加到15°和30°时，岩体动态峰值强度由26.24 MPa分别增加到27.28和28.80 MPa；当2a由1 cm分别增加到2和3 cm时，岩体动态峰值强度由31.37 MPa分别降低至27.28和23.90 MPa。同时为了更精确地刻画裂隙面粗糙度的影响，将裂隙面分形维数引入到岩体动态损伤模型中，不但提高了模型计算精度，而且拓宽了其应用范围，更便于实际工程应用。
- 非贯通裂隙岩体 /
- 裂隙粗糙度系数 /
- 应力强度因子 /
- JRC-JCS抗剪强度模型 /
- 单轴压缩动态损伤模型
Abstract: In order to take into account the influence of the crack roughness, first of all, on basis of the calculation model for the rockmass macroscopic damage variable which can take into account the crack geometry parameter, strength parameter and deformation parameter, a calculation model for the rockmass macroscopic damage variable is proposed by introducing the JRC-JCS shear strength model for the rough crack established by Barton, which can consider the crack roughness. Secondly, the proposed calculation model is introduced into the uniaxial compressive dynamic damage model for the rock mass with the non-persistent crack, which both considers the coupling of the macroscopic and microscopic defects, and then a uniaxial compressive dynamic damage model for the rock mass with the non-persistent crack is established which can consider the crack roughness at the same time. Finally, the effect of crack roughness JRC and crack basic friction angle φ_b and crack length 2a on rockmass dynamic mechanical property is studied with the parametric sensitivity analysis. The result shows that the rockmass dynamic climax strength increases from 26.42 MPa to 27.28 and 28.37 MPa with JRC increasing from 0 to 10 and 20 respectively. The rockmass dynamic climax strength increases from 26.42 MPa to 27.28 and 28.80 MPa with φ_b increasing from 0° to 15° and 30° respectively. The rockmass dynamic climax strength decreases from 31.37 MPa to 27.28 and 23.90 MPa with 2a increasing from 1cm to 2 and 3cm respectively. At the same time, in order to describe the influence of the crack roughness more accurately, the crack fractal dimension is introduced into the dynamic damage model for the rock mass, which not only improves the calculation accuracy of the model, but also broadens its application range, which is more convenient for practical engineering application.
- the rockmass with the non-persistent crack /
- crack roughness coefficient /
- stress intensity factor /
- JRC-JCS shear strength model /
- a uniaxial compressive dynamic damage model

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图 1 单轴压缩下含单条非贯通裂隙的岩体

Figure 1. Rockmass with single non-persistent crack under uniaxial compression

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图 2 含单组断续裂隙的岩体模型

Figure 2. The rockmass model with one set of intermittent cracks

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图 3 求解流程示意图

Figure 3. Scheme of the solution flow

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图 4 计算模型及施加的动荷载

Figure 4. The calculation model and applied dynamic load

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图 5 岩体单轴压缩动态应力应变计算曲线

Figure 5. the calculation curve of rock axial compression dynamic stress-strain

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图 6 裂隙粗糙度μ对岩体动态力学特性的影响

Figure 6. Effect of the crack roughness μ on the rockmass dynamic mechanical behavior

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图 7 裂隙面分形维数η对岩体动态力学特性的影响

Figure 7. Effect of the crack fractal dimension η on the rockmasµμs dynamic mechanical behavior

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图 8 裂隙面基本摩擦角φ_b对岩体动态力学特性的影响

Figure 8. Effect of the crack face basic friction angle φ_b on the rockmass dynamic mechanical behavior

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图 9 裂隙长度2a对岩体动态力学特性的影响

Figure 9. Effect of the crack length 2a on the rockmass dynamic mechanical behavior

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表 1 岩块参数

Table 1. Parameters of the intact rock

ρ/(kg·m⁻³)	E/GPa	ν	$ \dot{\varepsilon } $/s⁻¹	k	m	h/mm	w/mm
2270	10.8	0.2	100	5.115×10²²	7	100	50

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表 2 裂隙参数

Table 2. Crack parameters

n	2a/mm	d/mm	b/mm	δ/mm	α/(°)	φ_b/(°)	k_n/(GPa·cm⁻¹)	k_s/(GPa·cm⁻¹)	f_JRC	σ_JCS/MPa
8	20	20	40	10	45	15	20	8	10	30

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表 3 典型粗糙裂隙剖面及其粗糙度系数$ {f}_{\mathrm{J}\mathrm{R}\mathrm{C}} $与分形维数$ \eta $

Table 3. The typical rough crack profile and its JRC ($ {f}_{\mathrm{J}\mathrm{R}\mathrm{C}} $) and fractal dimension ($ \eta $)

编号	典型裂隙剖面	$ {f}_{\mathrm{J}\mathrm{R}\mathrm{C}} $	$ \eta $	编号	典型裂隙剖面	$ {f}_{\mathrm{J}\mathrm{R}\mathrm{C}} $	$ \eta $
1		0～2	1.002	6		10～12	1.036
2		2～4	1.005	7		12～14	1.043
3		4～6	1.011	8		14～16	1.051
4		6～8	1.018	9		16～18	1.062
5		8～10	1.025	10		18～20	1.069

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参考文献(26)

[1]	LIU H Y, LV S R, ZHANG L M, et al. A dynamic damage constitutive model for a rock mass with persistent joints [J]. International Journal of Rock Mechanics and Mining Sciences, 2015, 75: 132–139. DOI: 10.1016/j.ijrmms.2015.01.013.
[2]	刘红岩, 杨艳, 李俊峰, 等. 基于TCK模型的非贯通节理岩体动态损伤本构模型 [J]. 爆炸与冲击, 2016, 36(3): 319–325. DOI: 10.11883/1001-1455(2016)03-0319-07. LIU H Y, YANG Y, LI J F, et al. Dynamic damage constitutive model for rock mass with non-persistent joints based on the TCK model [J]. Explosion and Shock Waves, 2016, 36(3): 319–325. DOI: 10.11883/1001-1455(2016)03-0319-07.
[3]	YAN Z L, DAI F, LIU Y, et al. Experimental investigations of the dynamic mechanical properties and fracturing behavior of cracked rocks under dynamic loading [J]. Bulletin of Engineering Geology and The Environment, 2020, 79(10): 5535–5552. DOI: 10.1007/s10064-020-01914-8.
[4]	闻磊, 冯文杰, 李明烨, 等. 应变率对含裂隙红砂岩裂纹扩展模式及破碎特征的影响 [J]. 爆炸与冲击, 2023, 43(11): 113103. DOI: 10.11883/bzycj-2023-0061. WEN L, FENG W J, LI M Y, et al. Strain rate effect on crack propagation and fragmentation characteristics of red sandstone containing pre-cracks [J]. Explosion and Shock Waves, 2023, 43(11): 113103. DOI: 10.11883/bzycj-2023-0061.
[5]	YUAN G T, ZHANG M W, ZHANG K, et al. Dynamic mechanical response characteristics and cracking behavior of randomly distributed cracked sandstone [J]. Computational Particle Mechanics, 2024, 11(1): 119–139. DOI: 10.1007/s40571-023-00612-y.
[6]	JIA Z M, ZHOU X P. Modelling fracture of rock masses around tunnels and slopes by field-enriched finite element method [J]. Computers and Geotechnics, 2023, 163: 105756. DOI: 10.1016/j.compgeo.2023.105756.
[7]	KYOYA T, ICHIKAWA Y, KAWAMOTO T. Damage mechanics theory for discontinuous rock mass [C]//Proceedings of the 5th International Conference on Numerical Methods in Geomechanics. Nagoya, 1985: 469–480.
[8]	KAWAMOTO T, ICHIKAWA Y, KYOYA T. Deformation and fracturing behaviour of discontinuous rock mass and damage mechanics theory [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(1): 1–30. DOI: 10.1002/nag.1610120102.
[9]	SWOBODA G, SHEN X P, ROSAS L. Damage model for jointed rock mass and its application to tunnelling [J]. Computers and Geotechnics, 1998, 22(3/4): 183–203. DOI: 10.1016/S0266-352X(98)00009-3.
[10]	LI N, CHEN W, ZHANG P, et al. The mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(7): 1071–1079. DOI: 10.1016/S1365-1609(01)00058-2.
[11]	LIU H Y, ZHANG L M. A damage constitutive model for rock mass with nonpersistently closed joints under uniaxial compression [J]. Arabian Journal for Science and Engineering, 2015, 40(11): 3107–3117. DOI: 10.1007/s13369-015-1777-8.
[12]	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 H Y, LI J F, PEI X L. A dynamic damage constitutive model for rockmass with intermittent joints under uniaxial compression [J]. Explosion and Shock Waves, 2018, 38(2): 316–323. DOI: 10.11883/bzycj-2016-0261.
[13]	杨圣奇, 陆家炜, 田文岭, 等. 不同节理粗糙度类岩石材料三轴压缩力学特性试验研究 [J]. 岩土力学, 2018, 39(S1): 21–32. DOI: 10.16285/j.rsm.2017.2293. YANG S Q, LU J W, TIAN W L, et al. Experimental study of mechanical behavior of rock specimens with different joint roughness coefficient under conventional triaxial compression [J]. Rock and Soil Mechanics, 2018, 39(S1): 21–32. DOI: 10.16285/j.rsm.2017.2293.
[14]	王本鑫, 金爱兵, 赵怡晴, 等. 基于DIC的含3D打印起伏节理试样破裂特性及损伤本构 [J]. 工程科学学报, 2022, 44(12): 2029–2039. DOI: 10.13374/j.issn2095-9389.2021.04.11.001. WANG B X, JIN A B, ZHAO Y Q, et al. Fracture characteristics and the damage constitutive model of 3D printing undulating joint samples based on DIC [J]. Chinese Journal of Engineering, 2022, 44(12): 2029–2039. DOI: 10.13374/j.issn2095-9389.2021.04.11.001.
[15]	KIM D H, GRATCHEV I, BALASUBRAMANIAM A. Determination of joint roughness coefficient (JRC) for slope stability analysis: a case study from the Gold Coast area, Australia [J]. Landslides, 2013, 10(5): 657–664. DOI: 10.1007/s10346-013-0410-8.
[16]	BARTON N. Review of a new shear-strength criterion for rock joints [J]. Engineering Geology, 1973, 7(4): 287–332. DOI: 10.1016/0013-7952(73)90013-6.
[17]	谢和平, PARISEAU W G. 岩石节理粗糙系数(JRC)的分形估计 [J]. 中国科学(B辑), 1994, 24(5): 524–530. XIE H P, PARISEAU W G. The fractal estimation of rock joint roughness coefficient [J]. Science in China (Series B), 1994, 24(5): 524–530.
[18]	陈世江, 朱万成, 王创业, 等. 岩体结构面粗糙度系数定量表征研究进展 [J]. 力学学报, 2017, 49(2): 239–256. DOI: 10.6052/0459-1879-16-255. CHEN S J, ZHU W C, WANG C Y, et al. Review of research progresses of the quantifying joint roughness coefficient [J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 239–256. DOI: 10.6052/0459-1879-16-255.
[19]	TAYLOR L M, CHEN E P, KUSZMAUL J S. Microcrack-induced damage accumulation in brittle rock under dynamic loading [J]. Computer Methods in Applied Mechanics and Engineering, 1986, 55(3): 301–320. DOI: 10.1016/0045-7825(86)90057-5.
[20]	GRADY D E, KIPP M E. Continuum modelling of explosive fracture in oil shale [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1980, 17(3): 147–157. DOI: 10.1016/0148-9062(80)91361-3.
[21]	贺红亮. 冲击波极端条件下脆性介质的力学响应特性及其细观结构破坏特征 [D]. 绵阳: 中国工程物理研究院, 1999. HE H L. Mechanical response and microstructure failure characteristics of brittle medium under extreme shock wave conditions (Doctoral dissertation) [D]. Mianyang: China Academy of Engineering Physics, 1999.
[22]	LIU T Y, CAO P, LIN H. Damage and fracture evolution of hydraulic fracturing in compression-shear rock cracks [J]. Theoretical and Applied Fracture Mechanics, 2014, 74: 55–63. DOI: 10.1016/j.tafmec.2014.06.013.
[23]	LEE S, RAVICHANDRAN G. Crack initiation in brittle solids under multiaxial compression [J]. Engineering Fracture Mechanics, 2003, 70(13): 1645–1658. DOI: 10.1016/S0013-7944(02)00203-5.
[24]	HUANG C Y, SUBHASH G, VITTON S J. A dynamic damage growth model for uniaxial compressive response of rock aggregates [J]. Mechanics of Materials, 2002, 34(5): 267–277. DOI: 10.1016/S0167-6636(02)00112-6.
[25]	HUANG C Y, SUBHASH G. Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids [J]. Journal of the Mechanics and Physics of Solids, 2003, 51(6): 1089–1105. DOI: 10.1016/S0022-5096(03)00002-4.
[26]	范景伟, 何江达. 含定向闭合断续节理岩体的强度特性 [J]. 岩石力学与工程学报, 1992, 11(2): 190–199. FAN J W, HE J D. The strength behavior of rockmasses containing oriented and closed intermittent joints [J]. Chinese Journal of Rock Mechanics and Engineering, 1992, 11(2): 190–199.