完整岩石拉压应力状态下的张裂破坏准则

吕爱钟; 刘宜杰; 尹崇林

doi:10.6052/0459-1879-21-026

完整岩石拉压应力状态下的张裂破坏准则

doi: 10.6052/0459-1879-21-026

华北电力大学水电与岩土工程研究所, 北京 102206

基金项目: 1)国家自然科学基金资助项目(51974124)

详细信息

作者简介:
2)吕爱钟, 教授, 主要研究方向: 地下隧洞力学分析的解析方法. E-mail: lvaizhong@ncepu.edu.cn

通讯作者:
吕爱钟

中图分类号: O343.3
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出版历程
- 收稿日期: 2021-01-16
- 刊出日期: 2021-06-01

EXTENSION FAILURE CRITERION FOR INTACT ROCK UNDER TENSION AND COMPRESSION STRESS

Institute of Hydroelectric and Geotechnical Engineering, North China Electric Power University, Beijing 102206, China

摘要

摘要: 一点的应力状态可由3个主应力$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$来表示, 当规定主应力以压为正时, 沿最大主应力$\sigma_{1}$方向将产生收缩变形, 若中间主应力$\sigma_{2}$和最小主应力$\sigma_{3}$都远小于$\sigma_{1}$, 则沿$\sigma_{2}$和$\sigma_{3}$方向会产生横向扩张变形, 当横向扩张变形达到一定极限时, 将会在平行于$\sigma _{1}$的方向产生张裂破坏. 如何建立这种张裂破坏的强度准则目前尚缺乏研究, 最大拉应变理论(第二强度理论)有时被用来解释张裂破坏, 但最大拉应变理论难以应用于三向受力状态. 本文分别用$\varepsilon_{1}$, $\varepsilon_{2}$表示最大张应变和次大张应变, 则最大拉应变理论认为当$\varepsilon_{1}$达到单向拉伸屈服应变时, 材料将产生破坏. 而本文将根据$\varepsilon_{1}+\varepsilon_{2}$之和达到极限值$\varepsilon_u$来建立张裂破坏准则. 可以证明$\varepsilon_{1} +\varepsilon_{2}$所表示的是$\sigma_{1}$主平面的面积增长率. 当$\sigma_{3}<\sigma_{2} \ll \sigma_{1}$时, 大部分岩石都具有脆性破坏的特点, 所以可将破坏前的岩石视为满足广义胡克定律的线弹性材料, 这样用$\varepsilon_{1}$, $\varepsilon_{2}$表示的强度准则可通过$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$来表示. 在这个过程中还可考虑岩石在拉伸和压缩时具有不同弹性参数和强度的特点, 并可通过单向拉伸和单向压缩的破坏状态来确定$\varepsilon_u$. 不管$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$是压应力, 还是拉应力, 或者$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$中有拉有压的情形, 基于$\varepsilon_{1} +\varepsilon_{2} =\varepsilon_u$都可建立相应的强度准则. 所建立的准则可以反映中间应力$\sigma_{2}$对强度的影响规律, 通过建立的强度准则还可以证明: 静水拉力能引起屈服, 而静水压力不能产生屈服; 压缩破坏能使塑性体积增大, 其结果比Mohr-Coulomb准则更能反映实际情形. 并通过拉压应力状态下的试验数据验证了所建立的强度准则, 所得理论计算结果和已有的试验数据吻合得很好. 通过提出的强度准则和圆盘劈裂的试验结果, 可获得更为可靠的岩石单轴抗拉强度.
- 完整岩石 /
- 拉压应力 /
- 面积增长率 /
- 张裂破坏 /
- 强度准则
Abstract: The stress state at a point in the material can be represented by three principal stresses $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$. When it is specified that the principal stress is positive in pressure, the shrinkage deformation occurs along the direction of the maximum principal stress $\sigma_{1}$. If both the intermediate principal stress $\sigma_{2}$ and the minimum principal stress $\sigma _{3}$ are far less than $\sigma_{1}$, the lateral extending deformation will occur along the direction of $\sigma_{2}$ and $\sigma_{3}$. When the lateral extending deformation reaches a certain limit, the extending tension failure will occur in the direction parallel to $\sigma_{1}$. There is still a lack of research on how to establish the strength criterion of this kind of extending tension failure, the maximum tensile strain theory (the second strength theory) is sometimes used to explain the extending tension failure, but it is difficult to apply it to the triaxial stress state. In this paper, $\varepsilon_{1}$, $\varepsilon_{2}$ are used to represent the maximum tensile strain and the intermediate tensile strain respectively. Based on the maximum strain theory, the failure will occur if $\varepsilon_{1}$ reaches the uniaxial tensile yield strain. The extension failure criterion will be established herein when the sum of $\varepsilon _{1} +\varepsilon_{2}$ reaches the critical value $\varepsilon_u$ and it can be proved that $\varepsilon_{1} +\varepsilon_{2}$ actually denotes the extension rate of the $\sigma_{1}$-plane. When $\sigma_{3} <\sigma_{2} \ll \sigma_{1}$, most rocks have the characteristics of brittle failure, so the rock material in prefailure stage can be assumed as linear elastic that satisfies the generalized Hooke's law. Thus, the strength criterion expressed by $\varepsilon_{1}$ and $\varepsilon_{2}$ can be expressed by $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$. In this process, the rock's characteristics of different elastic parameters and strength under tension and compression can also be considered, and the failure state of uniaxial tension and uniaxial compression can be used to determine $\varepsilon_u$. Regardless of whether $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$ are compressive stress or tensile stress, or there is tension and compression in $\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$, corresponding strength criteria can be established based on $\varepsilon_{1} +\varepsilon_{2} =\varepsilon_u$. The established criterion can reflect the effect of intermediate principal stress $\sigma_{2}$ on the strength. It can also be proved that: like yielding which will happen under the hydrostatic tension but not under the hydrostatic compression; compression failure can increase the plastic volume, and the results can better reflect the actual situation than Mohr-Coulomb criterion. The established strength criterion is verified by experimental data under tension-compression stress state and the theoretical calculation results are in good agreement with the existing test data. Through the proposed strength criterion and the test results of disc splitting, a more reliable uniaxial tensile strength of rock can be obtained.
- intact rock /
- tension and compression stress /
- extension rate /
- tensile failure /
- strength criterion

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参考文献(42)

[1]	Jaeger JC, Cook NG, Zimmerman R. Fundamentals of Rock Mechanics. New Jersey: John Wiley & Sons, 2009
[2]	Griffith AA. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 1921, 221(582-593): 163-198
[3]	Hoek E, Brown ET. Empirical strength criterion for rock masses. Journal of Geotechnical Engineering Division, 1980, 106(9): 1013-1035
[4]	Bineshian H, Ghazvinian A, Bineshian Z. Comprehensive compressive-tensile strength criterion for intact rock. Journal of Rock Mechanics and Geotechnical Engineering, 2012, 4(2): 140-148
[5]	Mohr O. Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materials. Zeitschrift des Vereins Deutscher Ingenieure, 1900, 46(1524-1530): 1572-1577 (Mohr O. What are the conditions for the elastic limit and the fracturing of a material. Journal of the Association of German Engineers, 1900, 46(1524-1530): 1572-1577 (in German))
[6]	Drucker DC, Prager W. Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics, 1952, 10(2): 157-165
[7]	俞茂宏. 双剪理论及其应用. 北京: 科学出版社, 1998 (Yu Maohong. Twin-shear Theory and Its Application. Beijing: Science Press, 1998 (in Chinese))
[8]	Yu MH, Zan YW, Zhao J, et al. A unified strength criterion for rock material. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(8): 975-989
[9]	Sheorey PR, Biswas AK, Choubey VD. An empirical failure criterion for rocks and jointed rock masses. Engineering Geology, 1989, 26(2): 141-159
[10]	Johnston IW. Strength of intact geomechanical materials. Journal of Geotechnical Engineering, 1985, 111(6): 730-749
[11]	Singh M, Singh B. A strength criterion based on critical state mechanics for intact rocks. Rock Mechanics and Rock Engineering, 2005, 38(3): 243-248
[12]	Singh M, Raj A, Singh B. Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks. International Journal of Rock Mechanics and Mining Sciences, 2011, 48(4): 546-555
[13]	Barton N. Shear strength criteria for rock, rock joints, rock fill and rock masses: Problems and some solutions. Journal of Rock Mechanics and Geotechnical Engineering, 2013, 5(4): 249-261
[14]	Liu MD, Carter JP. General strength criterion for geomaterials. International Journal of Geomechanics, 2003, 3(2): 253-259
[15]	Liu MD, Indraratna B. Strength criterion for intact rock. Indian Geotechnical Journal, 2017, 47(3): 261-264
[16]	You, MQ. True-triaxial strength criteria for rock. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(1): 115-127
[17]	Sriapai T, Walsri C, Fuenkajorn K. True-triaxial compressive strength of Maha Sarakham salt. International Journal of Rock Mechanics and Mining Sciences, 2013, 61: 256-265
[18]	Haimson B. True triaxial stresses and the brittle fracture of rock. Pure and Applied Geophysics, 2006, 163(5): 1101-1130
[19]	蔡美峰, 何满潮, 刘东燕. 岩石力学与工程. 北京: 科学出版社, 2002 (Cai Meifeng, He Manchao, Liu Dongyan. Rock Mechanics and Engineering. Beijing: Science Press, 2002 (in Chinese))
[20]	Yu MH. Advances in strength theories for materials under complex stress state in the 20th century. Applied Mechanics Reviews, 2002, 55(3): 169-218
[21]	Lu AZ, Zhang N, Zeng GS. An extension failure criterion for brittle rock. Advances in Civil Engineering, 2020.DOI: 10.1155/2020/8891248
[22]	Hallbauer DK, Wagner H, Cook N. Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in stiff, triaxial compression tests. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1973, 10(6): 713-726
[23]	周维垣. 高等岩石力学. 北京: 水利电力出版社, 1990 (Zhou Weiyuan. Advanced Rock Mechanics. Beijing: Water Conservancy and Electric Power Press, 1990(in Chinese))
[24]	陶振宇. 岩石力学的理论与实践. 武汉: 武汉大学出版社, 2013 (Tao Zhenyu. Theory and Practice of Rock Mechanics. Wuhan: Wuhan University Press, 2013 (in Chinese))
[25]	翟越, 赵均海, 艾晓芹等. 基于统一强度理论的巴西圆盘劈裂强度分析. 建筑科学与工程学报, 2015, 32(3): 46-51 (Zhai Yue, Zhao Junhai, Ai Xiaoqin, et al. Analysis on splitting strength of Brazilian disc based on unified strength theory. Journal of Architecture and Civil Engineering, 2015, 32(3): 46-51 (in Chinese))
[26]	Hawkes I, Mellor M, Gariepy S. Deformation of rocks under uniaxial tension. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1973, 10(6): 493-507
[27]	Stimpson B, Chen R. Measurement of rock elastic moduli in tension and in compression and its practical significance. Canadian Geotechnical Journal, 1993, 30(2): 338-347
[28]	余贤斌, 王青蓉, 李心一等. 岩石直接拉伸与压缩变形的试验研究. 岩土力学, 2008, 29(1): 18-22 (Yu Xianbin, Wang Qingrong, Li Xinyi, et al. Experimental research on deformation of rocks in direct tension and compression. Rock and Solid Mechanics, 2008, 29(1): 18-22 (in Chinese))
[29]	李地元, 李夕兵, Li CC. 2种岩石直接拉压作用下的力学性能试验研究. 岩石力学与工程学报, 2010, 29(3): 624-632 (Li Diyuan, Li Xibin, Li Charlie. Exprimental studies of mechanical properties of two rocks under direct compression and tension. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(3): 624-632 (in Chinese))
[30]	Fuenkajorn K, Klanphumeesri S. Laboratory determination of direct tensile strength and deformability of intact rocks. Geotechnical Testing Journal, 2011, 34(1): 97-102
[31]	蒋伟. 不同岩石抗拉与抗压实验对比研究. [硕士论文]. 南京: 南京大学, 2014 (Jiang Wei. Comparative study on tensile and compressive tests of different rocks. [Master Thesis]. Nanjing: Nanjing University, 2014 (in Chinese))
[32]	袁圣渤. 硬脆性岩石直接拉伸力学试验与计算分析研究. [硕士论文]. 济南: 山东大学, 2016 (Yuan Shengbo. Experimental and numerical analysis study on direct tensile test of hard brittle rocks. [Master Thesis]. Jinan: Shandong University, 2016 (in Chinese))
[33]	阿姆巴尔楚米扬. 不同模量弹性理论. 邬瑞锋, 张允真译校. 北京: 中国铁道出版社, 1986 (Ambartsumyan S. Elasticity Theory of Different Modulus. Translated by Wu Ruifeng, Zhang Yunzhen. Beijing: China Railway Press, 1986 (in Chinese))
[34]	郑颖人, 孔亮. 岩土弹塑性力学. 北京: 中国建筑工业出版社, 2010 (Zheng Yingren, Kong Liang, Geotechnical Plastic Mechanicas. Beijing: China Construction Industry Press, 2010 (in Chinese))
[35]	熊祝华. 塑性力学基础知识. 北京: 高等教育出版社, 1986 (Xiong Zhuhua. Basic Knowledge of Plastic Mechanics. Beijing: China Higher Education Press, 1986 (in Chinese))
[36]	邓楚键, 郑颖人, 王凯等. 有关岩土材料剪胀的讨论. 岩土工程学报, 2009, 31(7): 1111-1114 (Deng Chujian, Zheng Yingren, Wang Kai, et al. Some discussion on the dilatancy materials. Chinese Journal of Geotechnical Engineering, 2009, 31(7): 1111-1114 (in Chinese))
[37]	尤明庆. 统一强度理论的试验数据拟合及评价. 岩石力学与工程学报, 2008, 27(11): 2193-2204 (You Mingqing. Fitting and evaluation of test data using unified strength theory. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(11): 2193-2204 (in Chinese))
[38]	Sheorey PR. Empirical Rock Failure Criteria. Rotterdam: CRC Press Balkema, 1997
[39]	Gercek H. Posson's ratio values for rocks. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(1): 1-13
[40]	陶纪南. 岩石轴向拉伸与劈裂法试验结果的比较分析. 金属矿山, 1995, 3: 28-31 (Tao Jinan. Comparative analysis of test results by axial tension method and splitting method. Metal Mine, 1995, 3: 28-31 (in Chinese))
[41]	Lu AZ, Wang SJ, Cai H. Closed-form solution for the stresses in Brazilian disc tests under vertical uniform loads. Rock Mechanics and Rock Engineering, 2018, 51(11): 3489-3503
[42]	何满潮, 胡江春, 熊伟等. 岩石抗拉强度特性的劈裂试验分析. 矿业研究与开发, 2005, 25(2): 12-16 (He Manchao, Hu Jiangchun, Xiong Wei. Splitting test and analysis of rock tensile strength. Mining Research and Development, 2005, 25(2): 12-16 (in Chinese))