An Elasto-plastic Coupling Model for Rock Based on Triple Shear Energy Yield Criterion

LIU Zhen-yang; WANG Ai-wen; LIU Xiao-lin

doi:10.11988/ckyyb.20221608

Journal of Changjiang River Scientific Research Institute >

2024 , Vol. 41 >Issue 5: 139 - 148

DOI: https://doi.org/10.11988/ckyyb.20221608

Rock-Soil Engineering

An Elasto-plastic Coupling Model for Rock Based on Triple Shear Energy Yield Criterion

LIU Zhen-yang ,
WANG Ai-wen ,
LIU Xiao-lin

Expand

1. School of Mechanics and Engineering, Liaoning Technical University, Fuxin 123000, China;
2. Institute of Disaster Rock Mechanics, Liaoning University, Shenyang 110036, China;
3. School of Resources Environment and Architectural Engineering, Chifeng University, Chifeng 024000, China

Received date: 2022-11-25

Revised date: 2023-03-02

Online published: 2023-10-12

Fold

Abstract

To accurately depict energy evolution during rock deformation, we propose methodologies for computing rock cohesion and internal friction angle using elastic shear strain energy and the triple shear energy yield criterion. Additionally, we introduce a method for determining the dilatancy angle based on the triple shear energy plastic potential function. Leveraging these approaches alongside data from cyclic loading and unloading tests on rocks, we derive the elastic modulus, cohesion, internal friction angle, and dilatancy angle at various plastic accumulation stages under different confining pressures. Our findings reveal a negative exponential decrease in elastic modulus with increasing plastic deformation, linear increases in pre-peak cohesion, and negative exponential decreases in post-peak cohesion. The internal friction angle conforms to a Weibull function with proportional and shape parameters of 1 and 1.5, respectively, while the dilatancy angle decreases linearly. Furthermore, elevating confining pressure leads to linear increases in elastic modulus and cohesion, accompanied by a linear decrease in the dilatancy angle. We establish a triple shear energy elasto-plastic coupling mechanical model and integrate it into finite difference software, developing code to monitor energy evolution. Through simulated triaxial compression tests on rocks, our model accurately captures rock mechanical behaviors during subsequent yielding, encompassing phenomena such as hardening, softening, dilatancy, confining pressure effects, and energy evolution. These findings furnish both theoretical insights and practical tools for examining rock mass instability from an energy perspective.

Key words： rock mechanics; triple shear energy yield criterion; elasto-plastic coupling model; elastic shear strain energy; confining pressure effect; secondary development

Cite this article

LIU Zhen-yang , WANG Ai-wen , LIU Xiao-lin . An Elasto-plastic Coupling Model for Rock Based on Triple Shear Energy Yield Criterion[J]. Journal of Changjiang River Scientific Research Institute, 2024 , 41(5) : 139 -148 . DOI: 10.11988/ckyyb.20221608

References

[1] 周辉,张凯,冯夏庭,等.脆性大理岩弹塑性耦合力学模型研究[J].岩石力学与工程学报,2010,29(12):2398-2409.(ZHOU Hui,ZHANG Kai,FENG Xia-ting,et al. Elastoplastic Coupling Mechanical Model for Brittle Marble[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(12): 2398-2409.(in Chinese))
[2] 王红才, 赵卫华, 孙东生, 等. 岩石塑性变形条件下的Mohr-Coulomb屈服准则[J]. 地球物理学报, 2012, 55(12): 4231-4238. (WANG Hong-cai, ZHAO Wei-hua, SUN Dong-sheng, et al. Mohr-coulomb Yield Criterion in Rock Plastic Mechanics[J]. Chinese Journal of Geophysics, 2012, 55(12): 4231-4238.(in Chinese))
[3] 陆银龙, 王连国, 杨峰, 等. 软弱岩石峰后应变软化力学特性研究[J]. 岩石力学与工程学报, 2010, 29(3): 640-648. (LU Yin-long, WANG Lian-guo, YANG Feng, et al. Post-peak Strain Softening Mechanical Properties of Weak Rock[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(3): 640-648.(in Chinese))
[4] 李鹏飞, 赵星光, 郭政, 等. 北山花岗岩在三轴压缩条件下的强度参数演化[J]. 岩石力学与工程学报, 2017, 36(7): 1599-1610. (LI Peng-fei, ZHAO Xing-guang, GUO Zheng, et al. Variation of Strength Parameters of Beishan Granite under Triaxial Compression[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(7): 1599-1610.(in Chinese))
[5] 张振杰, 汪斌, 朱杰兵, 等. 基于全过程曲线循环加卸载的岩石塑性硬化软化模型研究[J]. 长江科学院院报, 2018, 35(1): 95-100. (ZHANG Zhen-jie, WANG Bin, ZHU Jie-bing, et al. Plastic Hardening and Softening Model of Rock Based on Cyclic Loading and Unloading Testing Throughout Failure Process[J]. Journal of Yangtze River Scientific Research Institute, 2018, 35(1): 95-100.(in Chinese))
[6] WU X, JIANG Y, GUAN Z. AModified Strain-softening Model with Multi-post-peak Behaviours and Its Application in Circular Tunnel[J]. Engineering Geology, 2018, 240: 21-33.
[7] 金俊超, 佘成学, 尚朋阳. 硬岩弹塑性变形破坏过程中强度参数及剪胀角演化模型研究[J]. 岩土力学, 2019, 40(11): 4401-4411. (JIN Jun-chao, SHE Cheng-xue, SHANG Peng-yang. Study on Strength Parameters and Dilation Angle Evolution Models in Hard Rock Elasto-plastic Deformation and Failure Process[J]. Rock and Soil Mechanics, 2019, 40(11): 4401-4411.(in Chinese))
[8] 殷有泉, 曲圣年. 弹塑性耦合和广义正交法则[J]. 力学学报, 1982, 14(1): 63-70. (YIN You-quan, QU Sheng-nian. Elastoplastic Coupling and Generalized Normality Rule[J]. Acta Mechanica Sinica, 1982, 14(1): 63-70.(in Chinese))
[9] 李震,周辉,杨凡杰,等.弹塑性耦合应变定义与本构方程[J].岩土力学,2018,39(3):917-925.(LI Zhen, ZHOU Hui, YANG Fan-jie, et al. Elastoplastic Coupling Strain Definition and Constitutive Function[J]. Rock and Soil Mechanics, 2018, 39(3): 917-925.(in Chinese))
[10]ZHANG K, ZHOU H, SHAO J. An Experimental Investigation and an Elastoplastic Constitutive Model for a Porous Rock[J]. Rock Mechanics and Rock Engineering, 2013, 46(6): 1499-1511.
[11]周辉, 杨凡杰, 张传庆, 等. 考虑围压效应的大理岩弹塑性耦合力学模型研究[J]. 岩石力学与工程学报, 2012, 31(12): 2389-2399. (ZHOU Hui, YANG Fan-jie, ZHANG Chuan-qing, et al. An Elastoplastic Coupling Mechanical Model for Marble Considering Confining Pressure Effect[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(12): 2389-2399.(in Chinese))
[12]YANG F, ZHOU H, ZHANG C,et al. An Elastoplastic Coupling Mechanical Model for Hard and Brittle Marble with Consideration of the First Stress Invariant Effect[J]. European Journal of Environmental and Civil Engineering, 2018, 22(4): 405-428.
[13]周宏伟, 谢和平, 左建平, 等. 赋存深度对岩石力学参数影响的实验研究[J]. 科学通报, 2010, 55(34): 3276-3284. (ZHOU Hong-wei, XIE He-ping, ZUO Jian-ping, et al. Experimental Study of the Effect of Depth on Mechanical Parameters of Rock[J]. Chinese Science Bulletin, 2010, 55(34): 3276-3284.(in Chinese))
[14]王延宁, 张强, 李子仪, 等. 考虑弹塑性耦合效应的应变软化模型[J]. 煤炭学报, 2020, 45(12): 4037-4051. (WANG Yan-ning, ZHANG Qiang, LI Zi-yi, et al. Strain Softening Model Considering Elastic-plastic Coupling Effect[J]. Journal of China Coal Society, 2020, 45(12): 4037-4051.(in Chinese))
[15]孙闯, 张向东, 刘家顺. 基于Hoek-Brown强度准则的应变软化模型在隧道工程中的应用[J]. 岩土力学, 2013, 34(10): 2954-2960, 2970. (SUN Chuang, ZHANG Xiang-dong, LIU Jia-shun. Application of Strain Softening Model to Tunnels Based on Hoek-brown Strength Criterion[J]. Rock and Soil Mechanics, 2013, 34(10): 2954-2960, 2970.(in Chinese))
[16]金俊超, 佘成学, 尚朋阳. 基于Hoek-Brown准则的岩石应变软化模型研究[J]. 岩土力学, 2020, 41(3): 939-951. (JIN Jun-chao, SHE Cheng-xue, SHANG Peng-yang. A Strain-softening Model of Rock Based on Hoek-Brown Criterion[J]. Rock and Soil Mechanics, 2020, 41(3): 939-951.(in Chinese))
[17]姚再兴. 软化Drucker-Prager材料强度参数的测定方法[J]. 岩石力学与工程学报, 2014, 33(6): 1187-1193. (YAO Zai-xing. A Method for Measuring Strength Parameters of Softening Drucker-Prager Material[J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(6): 1187-1193.(in Chinese))
[18]丁祥,张广清.等向强化–软化Drucker-Prager材料强度参数演化[J].岩石力学与工程学报,2017,36(4):910-916.(DING Xiang, ZHANG Guang-qing. Variation of Strength Parameters of Drucker-Prager Material with Isotropic Hardening and Softening[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(4): 910-916.(in Chinese))
[19]白冰,李小春,石露,等.基于虚强度参数的塑性硬化模式[J].长江科学院院报,2012,29(8):24-28.(BAI Bing, LI Xiao-chun, SHI Lu, et al. A Plastic Hardening Mode Based on Virtual Strength Parameters[J]. Journal of Yangtze River Scientific Research Institute, 2012, 29(8): 24-28.(in Chinese))
[20]XIE H, LI L, PENG R,et al. Energy Analysis and Criteria for Structural Failure of Rocks[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2009, 1(1): 11-20.
[21]张后全,徐建峰,贺永年,等.脆性岩石真三轴能量强度准则研究[J].中国矿业大学学报,2012,41(4):564-570.(ZHANG Hou-quan, XU Jian-feng, HE Yong-nian, et al. Study of Triaxial Energy Strength Criterion for Brittle Rock Materials[J]. Journal of China University of Mining & Technology, 2012, 41(4): 564-570.(in Chinese))
[22]牛超颖, 贾洪彪, 马淑芝, 等. 基于能量原理与中间主应力效应的新岩石强度准则探讨[J]. 长江科学院院报, 2015, 32(11): 93-98. (NIU Chao-ying, JIA Hong-biao, MA Shu-zhi, et al. Discussion on New Rock Strength Criterion Based on Energy Principle and Intermediate Principal Stress Effect[J]. Journal of Yangtze River Scientific Research Institute, 2015, 32(11): 93-98.(in Chinese))
[23]高红, 郑颖人, 冯夏庭. 岩土材料能量屈服准则研究[J]. 岩石力学与工程学报, 2007, 26(12): 2437-2443. (GAO Hong, ZHENG Ying-ren, FENG Xia-ting. Study on Energy Yield Criterion of Geomaterials[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(12): 2437-2443.(in Chinese))
[24]裴峰.纱岭金矿深部地层岩体力学性能与深竖井围岩稳定性分析及控制[D].北京:北京科技大学,2020.(PEI Feng. Mechanical Properties of Rock in Deep Stratum and Analysis and Control of Shaft Surrounding Rock Stability in Shaling Gold Mine[D].Beijing: University of Science and Technology Beijing, 2020. (in Chinese))
[25]马秋峰. 基于能量耗散原理三轴条件下岩石损伤模型研究[D]. 北京: 中国矿业大学(北京), 2020. (MA Qiu-feng. Rock Damage Model under Triaxial Condition Based on Energy Dissipation Principle[D].Beijing: China University of Mining & Technology, Beijing, 2020. (in Chinese))
[26]DZ/T 0276.20—2015, 岩石物理力学性质试验规程第20部分:岩石三轴压缩强度试验[S]. 北京: 中国标准出版社, 2015. (DZ/T 0276.20—2015, Regulation for Testing the Physical and Mechanical Properties Of Rock—Part 20: Test for Determining the Strength of Rock in Triaxial Compression[S]. Beijing: Standards Press of China, 2015. (in Chinese))

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article

References