Elastoplastic constitutive model and parameter determination for transversely isotropic rocks
-
摘要: 地层中普遍存在层理状岩石,这些岩石细观结构具有显著的方向性,从而引起了其变形与强度具有横观各向同性。采用弹性力学与广义塑性力学基本理论,建立了岩石横观各向同性弹塑性本构模型：弹性部分采用广义胡克定律描述,塑性部分采用基于广义八面体剪应力的屈服准则和势函数、非关联流动法则和应变硬化准则描述。该模型屈服面为外凸的非等截距椭圆截面角锥体,在各向同性条件下可退化为米塞斯屈服准则。提出了模型参数求解方法：弹性参数采用三轴压缩和扭转试验联合求解;塑性参数采用不同层理方向试样的三轴压缩试验求解。以炭质板岩为例,验证了所提出的横观各向同性弹塑性模型和参数求解方法,验证结果表明所提模型较好地反映了岩石的横观各向同性,参数求解方法简单有效。此外,还根据试验数据分析了炭质板岩塑性势方向性和弹塑性参数耦合特征。研究成果将为丰富岩石力学基本理论和解决相关工程问题提供理论基础。Abstract: Layered rocks are widely distributed in formations. The macro-structure of the layered rocks is characterized with transversely isotropy, which will induce the transverse isotropy in deformation and strength. Based on the basic theory of elasticity and generalized plastic mechanics, an elastoplastic constitutive model for transversely isotropic rock is proposed. In the model, the generalized Hooke's law is adopted for the elastic behavior. For the plastic behavior, the yield criterion and potential function formulated as a function of the generalized octahedral shear stress, the non-associated flow rule and the stress-dependent hardening criterion are used. The yield surface of the model is convex with non-equal intercept elliptical cross-section pyramid, which can be simplified under isotropic condition as that for the Mises yield criterion. A method for determination of the model parameters is proposed, that is, the elastic parameters are obtained by combining the triaxial compression tests with a torsion test. The plastic parameters are obtained by using the triaxial compression tests on samples with different bedding directions. Taking the carbonaceous slate as an example, the proposed transversely isotropic elastic-plastic model and the parameter determination method are verified. The results show that the proposed model can reflect the transversal isotropy of the rock well, and the parameter determination method is simple and effective. The direction of plastic potential and the coupling between elastic and plastic behaviors of carbonaceous slate are also discussed according to the test data. This research provides a theoretical basis for enriching the basic theory of rock mechanics and solving engineering problems.
-
[1] BARTON N, QUADROS E.Anisotropy is everywhere, to see, to measure, and to model[J]. Rock Mech Rock Eng, 2015, 48(4): 1323-1339. [2] AMADEI B.Importance of anisotropy when estimating and measuring in situ stresses in rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1996, 33(3): 293-325. [3] 秦二涛. 深埋层状岩体地下硐室稳定性及支护技术研究[D].长沙: 中南大学, 2012.
(QIN Er-tao.Study on stability of underground caverns and support technology in deep layered rock mass[D]. Changsha: Central South University, 2012. (in Chinese))[4] 刘运思, 傅鹤林, 伍毅敏, 等. 横观各向同性岩石弹性参数及抗压强度的试验研究[J]. 中南大学学报(自然科学版), 2013, 8: 3398-3404.
(LIU Yun-si, FU He-lin, WU Yi-min, et al.Experimental study of elastic parameters and compressive strength for transversely isotropic rocks[J]. Journal of Central South University, 2013, 8: 3398-3404. (in Chinese))[5] 段靓靓, 梁锴, 方理刚. 岩石横观各向同性参数试验研究[J]. 土工基础, 2008(3): 80-82, 85.
(DUAN Liang-liang, LIANG Kai, FANG Li-gang.Test research for transverse isotropy parameter of rock[J]. Soil Engineering and Foundation, 2008(3): 80-82, 85. (in Chinese))[6] CHOU Y C, CHEN C S.Determining elastic constants of transversely isotropic rocks using Brazilian test and iterative procedure[J]. Int J Numer Anal Meth Geomech, 2008, 32(3): 219-234. [7] TALESNICK M L, LEE M Y, HAIMSON B C.On the determination of elastic material parameters of transverse isotropic rocks from a single test specimen[J]. Rock Mech Rock Eng, 1995, 28(1): 17-35. [8] 卢应发, 杨丽平, 陈高峰, 等. 层状地质材料弹性张量求解及应用[J]. 岩石力学与工程学报, 2008, 27(5): 922-930.
(LU Ying-fa, YANG Li-ping, CHEN Gao-feng, et al.Research on elastic tensor resolution in stratified geomaterial and tis application[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(5): 922-930. (in Chinese))[9] BOBET A.Lined circular tunnels in elastic transversely anisotropic rock at depth[J]. Rock Mech Rock Eng, 2011, 44(2): 149-167. [10] HEFNY A M, LO K Y.Analytical solutions for stresses and displacements around tunnels driven in cross-anisotropic rocks[J]. Int J Numer Anal Meth Geomech, 1999, 23(2): 161-177. [11] VU T M, SULEM J, SUBRIN D, et al.Semi-analytical solution for stresses and displacements in a tunnel excavated in transversely isotropic formation with non-linear behavior[J]. Rock Mech Rock Eng, 2013, 46(2): 213-229. [12] 张志增, 李仲奎. 横观各向同性岩体中圆形巷道反分析的惟一性[J]. 岩土力学, 2011, 32(7): 2066-2072.
(ZHANG Zhi-zeng, LI Zhong-kui.Uniqueness of displacement back analysis of a circular tunnel in transversely isotropic rock mass[J]. Rock and Soil Mechanics, 2011, 32(7): 2066-2072. (in Chinese))[13] 王永刚, 丁文其, 贾善坡, 等. 考虑结构面特性的层状岩体各向异性模型[J]. 公路交通科技, 2014(10): 85-92.
(WANG Yong-gang, DING Wen-qi, JIA Shan-po, et al.Anisotropic model of layered rock mass considering characteristics of structural interface[J]. Journal of Highway and Transportation Research and Development, 2014(10): 85-92. (in Chinese))[14] LONG N M A N, KHALDJIGITOV A A, ADAMBAEV U. On the constitutive relations for isotropic and transversely isotropic materials[J]. Applied Mathematical Modelling, 2013, 37: 7726-7740. [15] 徐磊, 任青文, 杜小凯, 等. 层状岩体各向异性弹塑性模型及其数值实现[J]. 地下空间与工程学报, 2010(4): 763-769.
(XU Lei, REN Qing-wen, DU Xiao-kai, et al.An anisotropic elastoplastic constitutive model for layered rock masses and its implementation[J]. Chinese Journal of Underground Space and Engineering, 2010(4): 763-769. (in Chinese))[16] HILL R.The mathematical theory of plasticity[M]. Oxford: Clarendon Press, 1950. [17] 郑颖人, 孔亮. 岩土塑性力学[M]. 北京: 中国建筑工业出版社, 2010.
(ZHENG Yin-ren, KONG Liang.Geotechnical plastic mechanics[M]. Beijing: China Architecture and Building Press, 2010. (in Chinese))[18] 王者超, 乔丽苹, 李术才, 等. 土的内变量蠕变模型研究[J]. 岩土工程学报2011, 33(10): 1569-1575.
(WANG Zhe-chao, QIAO Li-ping, LI Shu-cai, et al.An internal-variable creep model for soil[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(10): 1569-1575. (in Chinese)) -
期刊类型引用(24)
1. 李东明，聂一丹，晁阳，齐慧君，林潮宁. 基于改进聚类方法的大坝安全监测算法. 水力发电. 2025(04): 97-103+110 . 
百度学术
2. 李扬涛，包腾飞，李田雨. 深水大坝缺陷鲁棒实时检测方法. 武汉大学学报(信息科学版). 2025(04): 684-698 . 百度学术
3. 穆明垚，王岳航，冯国磊. 水库除险加固方案设计与技术优化及坝体稳定性分析. 粘接. 2025(04): 163-165+169 . 百度学术
4. 邓鹏. 物联网技术在小水库大坝安全监测中的应用现状. 中国宽带. 2025(04): 95-97 . 百度学术
5. 董蕊. 基于BIM技术在土石坝渗流安全监控与预警. 地下水. 2025(02): 260-262 . 百度学术
6. 高寒. 机电设备中智能故障检测诊断技术的运用. 黑龙江科学. 2024(02): 64-66 . 百度学术
7. 徐新超，张若冰. 降水极端情况下某闸坝的自适应防洪安全运行管理研究. 珠江水运. 2024(02): 119-121 . 百度学术
8. 海日姑·阿布都热西提. 小型水库雨水情测报和大坝安全监测系统设计与实践. 中国水运(下半月). 2024(03): 88-90 . 百度学术
9. 尹光景，李晨玉，曾子彬，赵芃芃，雷鹏，常留红. 基于Vue.js+Django的大坝安全监测信息管理系统开发. 软件. 2024(01): 47-49+82 . 百度学术
10. 王猛，刘英英，周明明. 浅析大坝失事主要原因及应对措施方案. 水利规划与设计. 2024(05): 81-83+105 . 百度学术
11. 刘郴玲，蒋光灿. 基于龟石水库监测资料的大坝安全性态评估分析. 人民珠江. 2024(S1): 29-33 . 百度学术
12. 李东明，李龙龙，晁阳，李同春，齐慧君，林潮宁. 大坝安全监测数字孪生系统应用研究. 水力发电. 2024(09): 110-117 . 百度学术
13. 沈晓雷，余泉，季昊巍. 基于传感器的海上风电钢结构腐蚀检测方法. 中国水运. 2024(06): 91-92 . 百度学术
14. 盛金保，李宏恩，王芳. 智能大坝建设与韧性提升发展路径研究. 中国水利. 2024(24): 68-77 . 百度学术
15. 王琛，陈锦，谢应兵. 浅析现代水利工程成本控制理论及其存在问题. 红水河. 2023(01): 7-10 . 百度学术
16. 李松培，周江，黎海波，熊静，杨志虎，刘家森. 大坝安全在线监控及智能管理平台探索与应用. 云南水力发电. 2023(06): 173-176 . 百度学术
17. 窦飞，薛江寒. 岱山大坝渗流预测模型研究及渗漏问题分析. 海河水利. 2023(06): 61-68+112 . 百度学术
18. 李宗坤，王特，葛巍，景来红，罗秋实，杨风威，宋志宇，马福恒. 黄河流域梯级水库大坝风险评估与管控的战略思考. 人民黄河. 2023(07): 1-6 . 百度学术
19. 刘越，周志维. 基于小概率法的大坝多源监测预警阈值研究. 江西水利科技. 2023(04): 252-256 . 百度学术
20. 热米拉·塔什珀拉提. 溢洪道水流特性的性能模拟研究. 水利科技与经济. 2023(07): 122-127 . 百度学术
21. 何永祥. 甘肃永昌皇城水库大坝安全评价分析. 水利科学与寒区工程. 2023(09): 142-144 . 百度学术
22. 李宇文. 小型病险水库安全鉴定及加固改造实践——以水磨坑水库为例. 湖南水利水电. 2023(05): 75-78 . 百度学术
23. 李宗坤，王特，葛巍，景来红，崔秋晶，焦余铁. 考虑溃坝后果的水库工程等级划分方法. 水科学进展. 2023(05): 753-765 . 百度学术
24. 唐忠海，陈章傑，刘书婷，廖渝，李欣艺，李滟浩，袁士才. 无人机航测技术在大坝裂缝检测中的应用研究. 科技创新与生产力. 2022(10): 63-65 . 百度学术
其他类型引用(9)
计量
- 文章访问数: 320
- HTML全文浏览量: 9
- PDF下载量: 209
- 被引次数: 33
下载:
