A dynamic damage constitutive model for rockmass with intermittent joints under uniaxial compression
-
摘要: 断续节理将对工程岩体的强度及变形等力学特性产生显著影响，损伤力学中视节理为岩体的一种宏观损伤，因而采用损伤张量来刻画其对岩体的影响。目前学术界提出了用节理的几何、强度及变形等3类参数来描述节理的物理力学性质，而目前的岩体损伤张量计算方法都只涉及前2类参数，均没有涉及其变形参数即法向及切向刚度。为此，在前人研究的基础上，基于断裂及损伤理论提出了考虑节理法向及切向刚度的单轴压缩下单条断续节理引起的损伤张量计算公式，进而通过考虑节理间相互作用给出了单组单排或多排节理岩体损伤张量计算公式。其次，以岩石细观动态损伤模型为基础，结合宏细观损伤耦合观点提出了一个能够同时考虑节理几何、强度及变形参数的断续节理岩体动态损伤本构模型。最后，利用该模型讨论了节理参数及载荷应变率等对岩体动态力学特性的影响，认为节理长度减小及摩擦角增大将导致岩体动态峰值强度及弹性模量增大；岩体动态峰值强度及弹性模量则随着节理法向及切向刚度的增大分别减小或增大；而当节理法向及切向刚度按照同一比例增大时，岩体动态峰值强度及弹性模量则是增大的。岩体动态峰值强度与载荷应变率呈正相关。Abstract: The intermittent joints have obvious effect on the strength and deformability of engineering rockmass. The joint is assumed to be a kind of macroscopic damage to the rockmass in the damage mechanics, therefore the damage tensor is adopted to describe its effect on the rockmass. Now three kinds of joint parameters such as the geometrical ones, strength ones and deformational ones are proposed in the academic circles to describe the joint physical and mechanical properties. However, the existing calculation methods of the rockmass damage tensor consider only the joint geometrical or strength parameters, not its deformational parameters such as normal stiffness and shear stiffness. Therefore, on the basis of the existing studies, the fracture and damage theory is adopted to propose the damage tensor calculation formula of the rockmass caused by an intermittent joint under uniaxial compression, and then that caused by one row or multi-row of joints in one set is given by considering the interaction of the joints. Secondly, based on the rock mesoscopic dynamic damage constitutive model and the viewpoint of macroscopic and mesoscopic damage coupling, a dynamic damage constitutive model for the rockmass with intermittent joints is proposed which can consider the joint geometrical, strength or deformational parameters at the same time. Finally, the effects of joint parameters and load strain rate on the rockmass dynamic mechanical behaviors are discussed with the proposed model. It is found the decrease in the joint length and the increase in the joint friction angle will increase the dynamic climax strength and elastic modulus of the rockmass. While with increasing the joint normal stiffness and shear stiffness, the dynamic climax strength and elastic modulus of the rockmass decrease and increase, respectively. While when the joint normal stiffness and shear stiffness increase in the same proportion, the dynamic climax strength and elastic modulus of the rockmass increase. The dynamic climax strength of the rockmass has a positive correlation with the load strain rate.
-
图 2 含单排及多排断续节理的岩体模型
Figure 2. A model of the jointed rockmass with one or more rows of intermittent joints
图 4 岩体单轴压缩动态应力应变计算曲线
Figure 4. Calculated dynamic stress-strain curves of rockmass under axial compression
图 5 不同节理摩擦角的试件动态应力应变曲线
Figure 5. Dynamic stress-strain curves of the samples with different joint friction angles
图 6a 不同节理法向刚度试件的动态应力应变曲线
Figure 6a. Dynamic stress-strain curves of the samples with different joint normal stiffnesses
6b 不同节理切向刚度试件的动态应力应变曲线
6b. Dynamic stress-strain curves of the samples with different joint shear stiffnesses
6c 节理法向及切向刚度按相同比例变化时的试件动态应力应变曲线
6c. Dynamic stress-strain curves of the samples at the same joint normal-to-shear stiffnesses ratios
图 7 节理长度对试件动态特性的影响
Figure 7. Effects of joint length on dynamic mechanical behaviors of the samples
-
[1] AKIN M. Slope stability problems and back analysis in heavily jointed rock mass: A case study from Manisa, Turkey[J]. Rock Mechanics and Rock Engineering, 2013, 46(2):359-371. doi: 10.1007/s00603-012-0262-x [2] 张力民, 吕淑然, 刘红岩.综合考虑宏细观缺陷的岩体动态损伤本构模型[J].爆炸与冲击, 2015, 35(3):428-436. doi: 10.11883/1001-1455-(2015)03-0428-09ZHANG Limin, LV Shuran, LIU Hongyan. A dynamic damage constitutive model for rock mass by comprehensively considering macroscopic and mesoscopic flaws[J]. Explosion and Shock Waves, 2015, 35(3):428-436. doi: 10.11883/1001-1455-(2015)03-0428-09 [3] 刘红岩, 杨艳, 李俊峰, 等.基于TCK模型的断续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)03-0319-07LIU Hongyan, YANG Yan, LI Junfeng, 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 [4] KYOYA T, ICHIKAWA Y, KAWAMOTO T. A damage mechanics theory for discontinuous rock mass[C]//Proceedings of the 5th International Conference on Numerical Methods in Geomechanics. Nagoya, 1985: 469-480. [5] KAWAMOTO T, ICHIKAWA Y, KYOYA T. Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory[J]. International Journal for Numerical Analysis Method in Geomechanics, 1988, 12(1):1-30. doi: 10.1002/(ISSN)1096-9853 [6] SWOBODA G, SHEN X P, ROSAS L. Damage model for jointed rock mass and its application to tunneling[J]. Computers and Geotechnics, 1998, 22(3/4):183-203. https://www.sciencedirect.com/science/article/pii/S0266352X98000093 [7] YUAN X P, LIU H Y, WANG Z Q. An interacting joint-mechanics based model for elastoplastic damage model of rock-like materials under compression[J]. International Journal of Rock Mechanics & Mining Sciences, 2013, 58(9):92-102. https://www.sciencedirect.com/science/article/pii/S1365160912002092 [8] SWOBODA G, YANG Q. An energy-based damage model of geomaterials:Ⅰ: Formulation and numerical results[J]. International Journal of Solids and Structures, 1999, 36(9):1719-1734. https://www.sciencedirect.com/science/article/pii/S0020768398000365 [9] LI N, CHEN W, ZHANG P, et al. The mechanical properties and a fatigue-damage model for jointed rock mass subjected to dynamic cyclical loading[J]. International Journal of Rock Mechanics & Mining Sciences, 2001, 38(7):1071-1079. https://www.researchgate.net/publication/248165191_The_mechanical_properties_and_a_fatigue-damage_model_for_jointed_rock_masses_subjected_to_dynamic_cyclical_loading [10] LIU Hongyan, ZHANG Limin. A damage constitutive model for rock mass with non-persistently closed joints under uniaxial compression[J]. Arabian Journal for Science and Engineering, 2015, 40(1):3107-3117. doi: 10.1007/s13369-015-1777-8 [11] 刘红岩, 王新生, 张力民, 等.断续节理岩体单轴压缩动态损伤本构模型[J].岩土工程学报, 2016, 38(3):426-436. http://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ201802011.htmLIU Hongyan, WANG Xinsheng, ZHANG Limin, et al. A dynamic damage constitutive model for rock mass with non-persistent joints under uniaxial compression[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(3):426-436. http://www.cnki.com.cn/Article/CJFDTOTAL-BZCJ201802011.htm [12] PRUDENCIO M, JAN M V S. Strength and failure modes of rock mass models with non-persistent joints[J]. International Journal of Rock mechanics & Mining Sciences, 2007, 46(6):890-902. https://www.sciencedirect.com/science/article/pii/S1365160907000160 [13] TAYLOR L M, CHEN E P, KUSZMAUL J S. Microjoint induced damage accumulation in brittle rock under dynamic loading[J]. Computer Method in Applied Mechanics & Engineering, 1986, 55:301-320. http://www.sciencedirect.com/science/article/pii/0045782586900575 [14] GRADY D E, KIPP M E. Continuum modeling of explosive fracture in oil shale[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1987, 17(3):147-157. http://www.oalib.com/references/17407042 [15] HUANG C, 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 [16] HUANG C, 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 [17] PALIWAL B, RAMESH K T. An interacting micro-joint damage model for failure of brittle materials under compression[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(3):896-923. doi: 10.1016/j.jmps.2007.06.012 [18] LIU Taoying, CAO Ping, LIN Hang. 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 [19] LEE S, RAVICHANDRAN G. Joint initiation in brittle solids under multiaxial compression[J]. Engineering Fracture Mechanics, 2003, 70(13):1645-1658. doi: 10.1016/S0013-7944(02)00203-5 [20] 李建林, 哈秋瓴.节理岩体拉剪断裂与强度研究[J].岩石力学与工程学报, 1998, 17(3):259-266. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX904.028.htmLI Jianlin, HA Qiuling. A study of tensile-shear joint and strength related to jointed rock mass[J]. Chinese Journal of Rock Mechanics and Engineering, 1998, 17(3):259-266. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX904.028.htm [21] 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. http://www.cqvip.com/QK/96026X/199202/918156.htmlFAN Jingwei, HE Jiangda. The strength behavior of rockmasses containing oriented and closed intermittent joints[J]. Chinese Journal of Rock Mechanics and Engineering, 1992, 11(2):190-199. http://www.cqvip.com/QK/96026X/199202/918156.html [22] CHEN W, LA BORDERIE C, MAUREL O, et al. Simulation of damage-permeability coupling for mortar under dynamic loads[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38(5):457-474. doi: 10.1002/nag.v38.5 [23] GOODMAN R E. The mechanical properties of joints[C]//Proceeding of the 3rd Congress ISRM. Denver, 1974, Ⅰ(A): 127-140. [24] GOODMAN R E, TAYLOR R L, BREKKE T. A model for the mechanics of jointed rock[J]. Journal of Soil Mechanics and Foundations Division, 1968, 94:637-659. http://www.researchgate.net/publication/304714966_A_model_for_the_mechanics_of_jointed_rock?_sg=b8MO0PmdTRgxCnEO-TU_wZBP08GTw-SFYMaeUaPKFm6T503iva1D1R55D4t_A2-i31ZvUYvizDCpxoS7YpGA9npvef9GcG4jLRU_V82J8FI [25] BANDIS S C, LUMSDEN A C, BARTON N R. Fundamentals of rock joint deformation[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1983, 20:249-268. https://www.sciencedirect.com/science/article/pii/0148906283905958 [26] KUMAR A. The effect of stress rate and temperature on the strength of basalt and granite[J]. Geophysics, 1968, 33(3):501-510. doi: 10.1190/1.1439947 -
下载:
点击查看大图
图(10)
计量
- 文章访问数: 5313
- HTML全文浏览量: 1918
- PDF下载量: 306
- 被引次数: 0