考虑温度和体积应力的分数阶蠕变损伤Burgers模型

doi:10.13722/j.cnki.jrme.2020.0734

Abstract
Figure/Table
References (0)
Related Citation (15)

Download: PDF (664 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract Salt cavern is an ideal shielding rock for deep storage of oil，natural gas and high-level radioactive nuclear waste. Considering the combined influence of temperature and volume-stress in deep，a damage variable is proposed based on the Weibull distribution of random failure of meso-scale element. The Drucker-Prager criterion is used to describe the brittle failure in the linear deformation at meso-scale，and the generalized Hook's Law considering the plastic damage is introduced to describe the sample-scale damage. As a result，a static constitutive model under triaxial compression is effectively established. Furthermore，introducing both the static constitutive model and the nonlinear fractional viscosity dashpot into Burgers model，a fractional Burgers model with creep damage considering the temperature and the volume stress is effectively established. The results show that the new model，sensitive to the temperature and the volume stress，can well simulate the creep deformation in whole evolution，especially for the accelerated creep deformation.

Key words： rock mechanics full-stage modeling triaxial creep fractional creep Burgers model

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	XUE Dongjie1
	2
	LU Lele1
	YI Haiyang3
	WU Zhide4
	ZHANG Qingsen1
	ZHANG Zepeng1

Cite this article:

XUE Dongjie1,2,LU Lele1, et al. A fractional Burgers model for uniaxial and triaxial creep of damaged salt-rock considering temperature and volume-stress[J]. , 2021, 40(2): 315-329.

URL:

https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2020.0734 OR https://rockmech.whrsm.ac.cn/EN/Y2021/V40/I2/315

[1] 王新志，汪稔，杨春和，等. 盐岩渗透性影响因素研究综述[J]. 岩石力学与工程学报，2007，26(增1)：2 678–2 686.(WANG Xinzhi，WANG Ren，YANG Chunhe，et al. Summary on influence of permeability of salt rock[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(Supp.1)：2 678–2 686.(in Chinese))
[2] COSENZA P，GHOREYCHI M，BAZARGAN-SABET B，et al. In-situ rock salt permeability measurement for long-term safety assessment of storage[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36(4)：509–526.
[3] 井文君，杨春和，陈锋. 基于事故统计分析的盐岩地下油/气储库风险评价[J]. 岩土力学，2011，32(6)：1 787–1 793.(JING Wenjun，YANG Chunhe，CHEN Feng. Risk assessment of salt cavern oil/gas storage based on accident statistical analysis[J]. Rock and Soil Mechanics，2011，32(6)：1 787–1 793.(in Chinese))
[4] 武志德. 考虑渗流及时间效应的层状盐岩溶腔稳定分析[博士学位论文][D]. 北京：中国矿业大学，2011.(WU Zhide. Research on the stability of cavern in bedded rock salt based on permeability and time dependent behavior[Ph. D. Thesis][D]. Beijing：China University of Mining and Technology，2011.(in Chinese))
[5] 王贵君. 盐岩油气储库与核废料处置库力学问题研究新进展[M]. 北京：科学出版社，2013：1–50.(WANG Guijun. New research progress on rock salt oil and gas reservoirs and nuclear waste repositories mechanical problems[M]. Beijing：Science Press，2013：1–50.(in Chinese))
[6] 万文，王敏，赵延林. 损伤层状盐岩蠕变-渗透的流固耦合试验研究[J]. 中南大学学报：自然科学版，2016，47(7)：2 341–2 346. (WAN Wen，WANG Min，ZHAO Yanlin. Fluid-solid coupling experimental study on damage bedded rock salt[J]. Journal of Central South University：Science and Technology，2016，47(7)：2 341–      2 346.(in Chinese))
[7] WANG G J，ZHANG L，ZHANG Y W，et al. Experimental investigations of the creep–damage–rupture behavior of rock salt[J]. International Journal of Rock Mechanics and Mining Sciences，2014，66：181–187.
[8] CHAN K S，BODNER S R，FOSSUM A F，et al. A damage mechanics treatment of creep failure in rock salt[J]. International Journal of Damage Mechanics，1997，6(1)：121–152.
[9] 郤保平，赵阳升，赵金昌，等. 层状盐岩温度应力耦合作用蠕变特性研究[J]. 岩石力学与工程学报，2008，27(1)：90–96.(XI Baoping，ZHAO Yangsheng，ZHAO Jinchang，et al. Study on coupled thermomechanical creep properties of bedded rock salt[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(1)：90–96.(in Chinese))
[10] 梁卫国，赵阳升，徐素国. 240 ℃内盐岩物理力学特性的试验研究[J]. 岩石力学与工程学报，2004，23(14)：2 365–2 369.(LIANG Weiguo，ZHAO Yangsheng，XU Suguo. Testing study on physical and mechanical properties of heated salt rock within 240 ℃[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(14)：2 365–2 369.(in Chinese))
[11] 邓广哲，王广地. 北山花岗岩热黏弹性流变特性分析[J]. 岩石力学与工程学报，2004，23(增1)：4 368–4 372.(DENG Guangzhe，WANG Guangdi. Analysis of characteristics of thermo-viscoelasto rheology of Beishan granite[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(Supp.1)：4 368–4 372.(in Chinese))
[12] 杨玉良，梁卫国，杨晓琴，等. 钙芒硝盐岩多场耦合作用下蠕变的温度效应研究[J]. 煤炭学报，2020，45(3)：1 070–1 080.(YANG Yuliang，LIANG Weiguo，YANG Xiaoqin，et al. Study on temperature effect of creep of glauberite salt rock under multi-field coupling[J]. Journal of China Coal Society，2020，45(3)：1 070–1 080.(in Chinese))
[13] ZHOU H W，LIU D，LEI G，et al. The creep-damage model of salt rock based on fractional derivative[J]. Energies，2018，11：2 349.
[14] 周宏伟，王春萍，段志强，等. 基于分数阶导数的盐岩流变本构模型[J]. 中国科学：物理学力学天文学，2012，42(3)：310–318.(ZHOU Hongwei，WANG Chunping，DUAN Zhiqiang，et al. Time-based fractional derivative approach to creep constitutive model of salt rock[J]. Scientia Sinica Physica，Mechanica and Astronomica，2012，42(3)：310–318.(in Chinese))
[15] WANG G J. A new constitutive creep-damage model for salt rock and its characteristics[J]. International Journal of Rock Mechanics and Mining Sciences，2004，41(Supp.1)：61–67.
[16] WU F，GAO R B，ZOU Q. Long‐term strength determination and nonlinear creep damage constitutive model of salt rock based on multistage creep test：Implications for underground natural gas storage in salt cavern[J]. Energy Science and Engineering，2020，8(5)：1 592–1 603.
[17] 张向东，蔡冀奇，唐楠楠，等. 深部砂岩力学特性试验与本构模型[J]. 煤炭学报，2019，44(7)：2 087–2 093.(ZHANG Xiangdong，CAI Jiqi，TANG Nannan，et al. Experimental study on mechanical properties of deep sandstone and its constitutive model[J]. Journal of China Coal Society，2019，44(7)：2 087–2 093.(in Chinese))
[18] JIN J S，CRISTESCU N D. An elastic/viscoplastic model for transient creep of rock salt[J]. International Journal of Plasticity，1998，14(1/3)：85–107.
[19] YANG C H，DAEMEN J J K，YIN J H. Experimental investigation of creep behavior of salt rock[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36：233–242.
[20] HOU Z. Mechanical and hydraulic behaviour of salt in the excavation disturbed zone around underground facilities[J]. International Journal of Rock Mechanics and Mining Sciences，2003，40(5)：725–738.
[21] ZHOU H W，WANG C P，HAN B B，et al. A creep constitutive model for salt rock based on fractional derivatives[J]. International Journal of Rock Mechanics and Mining Sciences，2011，48(1)：116–121.
[22] 丁靖洋，周宏伟，陈琼，等. 盐岩流变损伤特性及本构模型研究[J]. 岩土力学，2015，36(3)：769–776.(DING Jingyang，ZHOU Hongwei，CHEN Qiong，et al. Characters of rheological damage and constitutive model of salt rock[J]. Rock and Soil Mechanics，2015，36(3)：769–776.(in Chinese))
[23] 周倩瑶，秦志军，王伟，等. 考虑塑性变形的分数阶岩石蠕变损伤模型研究[J]. 三峡大学学报：自然科学版，2019，41(5)：53–58.(ZHOU Qianyao，QIN Zhijun，WANG Wei，et al. Study of fractional rock creep damage model considering plastic deformation[J]. Journal of China Three Gorges University：Natural Sciences，2019，41(5)：53–58.(in Chinese))
[24] 吴斐，谢和平，刘建锋，等. 分数阶黏弹塑性蠕变模型试验研究[J]. 岩石力学与工程学报，2014，33(5)：964–970.(WU Fei，XIE Heping，LIU Jianfeng，et al. Experimental study of fractional viscoelasticplastic creep model[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(5)：964–970.(in Chinese))
[25] 高小平. 盐岩力学特性时温效应试验研究及其本构方程[硕士学位论文][D]. 武汉：中国科学院武汉岩土力学研究所，2005：36–48.(GAO Xiaoping. Experiment studies on time and temperature effect of mechanical properties and constitutive relation of rock salt[M. S. Thesis][D]. Wuhan：Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，2005：36–48.(in Chinese))
[26] 高小平，杨春和，吴文，等. 盐岩蠕变特性温度效应的试验研究[J]. 岩石力学与工程学报，2005，24(12)：2 054–2 059.(GAO Xiaoping，YANG Chunhe，WU Wen，et al. Experimental studies on temperature dependent properties of creep of rock salt[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(12)：2 054–2 059.(in Chinese))
[27] 胡其志，冯夏庭，周辉. 考虑温度损伤的盐岩蠕变本构关系研究[J]. 岩土力学，2009，30(8)：2 245–2 248.(HU Qizhi，FENG Xiating，ZHOU Hui. Study of creep model of rock salt with thermal damage considered[J]. Rock and Soil Mechanics，2009，30(8)：2 245–   2 248.(in Chinese))
[28] XUE D J，ZHOU H W，ZHAO Y W，et al. Real-time SEM observation of mesoscale failures under thermal-mechanical coupling sequences in granite[J]. International Journal of Rock Mechanics and Mining Sciences，2018，112：35–46.
[29] XUE D J，LIU Y T，ZHOU H W，et al. Fractal characterization on anisotropy and fractal reconstruction of rough surface of granite under orthogonal shear[J]. Rock Mechanics and Rock Engineering，2020，53：1 225–1 242.
[30] KACHANOV L M. Time of the rupture process under creep conditions[J]. Izvestiia Akademii Nauk SSSR，Otdelenie Teckhnicheskikh Nauk，1958，(8)：26–31.
[31] 梁正召，唐春安，张永彬，等. 准脆性材料的物理力学参数随机概率模型及破坏力学行为特征[J]. 岩石力学与工程学报，2008，27(4)：718–727.(LIANG Zhengzhao，TANG Chun¢an，ZHANG Yongbin，et al. Stochastic probability model of physical and mechanical parameters of quasi brittle materials and characteristics of failure mechanics[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(4)：718–727.(in Chinese))
[32] 丁靖洋，周宏伟，李潮，等. 基于Weibull分布的盐岩分数阶蠕变本构模型研究[J]. 固体力学学报，2013，34(5)：473–480.(DING Jingyang，ZHOU Hongwei，LI Chao，et al. The fractional derivative approach to creep constitutive mode of salt rock based on Weibull distribution[J]. Chinese Journal of Solid Mechanics，2013，34(5)：473–480.(in Chinese))
[33] 吴文. 盐岩的静、动力学特性试验研究与理论分析[博士学位论文][D]. 武汉：中国科学院武汉岩土力学研究所，2003.(WU Wen. Experimental and theoretical analysis of static and dynamic characteristics of salt rock[Ph. D. Thesis][D]. Wuhan：Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，2003.(in Chinese))
[34] 白晨光，魏一鸣. 岩石材料初始缺陷的分维数与损伤演化的关系[J]. 矿冶，1996，5(4)：17–19.(BAI Chenguang，WEI Yiming. The relation between dimension of defects of rock material and its damage evolution[J]. Mining and Metallurgy，1996，5(4)：17–19.(in Chinese))
[35] 陈剑文，杨春和，高小平，等. 盐岩温度与应力耦合损伤研究[J]. 岩石力学与工程学报，2005，24(11)：1 986–1 991.(CHEN Jianwen，YANG Chunhe，GAO Xiaoping，et al. Study on the couple damage of temperature and mechanics for salt rock[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(11)：1 986–1 991.(in Chinese))
[36] 姚院峰，杨春和，纪文栋，等. 两种不同沉积类型界面盐岩力学特性试验研究[J]. 岩石力学与工程学报，2012，31(2)：265–272.(YAO Yuanfeng，YANG Chunhe，JI Wendong，et al. Experimental study of mechanical property of two types of sedimentary salt rock with interface[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(2)：265–272.(in Chinese))
[37] 徐杨梦迪，刘建锋，徐慧宁，等. 单轴压缩下含杂质盐岩的声发射特征试验研究[J]. 四川大学学报：工程科学版，2016，48(6)：37–45.(XU Yangmengdi，LIU Jianfeng，XU Huining，et al. Experimental study on acoustic emission characteristics of salt rock with impurities under uniaxial compression[J]. Journal of Sichuan University：Engineering Science Edition，2016，48(6)：37–45.(in Chinese))
[38] 吴文，杨春和. 盐岩的压缩试验研究与损伤模型模拟[J]. 岩石力学与工程学报，2006，25(增2)：3 709–3 713.(WU Wen，YANG Chunhe. Experimental study on salt rock under compression and damage model simulation[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(Supp.2)：3 709–3 713.(in Chinese))
[39] 张学言. 岩土塑性力学[M]. 北京：人民交通出版社，1993：76–81.(ZHANG Xueyan. Geotechnical plastic mechanics[M]. Beijing：China Communications Press，1993：76–81.(in Chinese))
[40] LIU J H，ZHU W S. A new elastic-plasticity yield criterion for rock and soil[J]. Advanced Materials Research，2011，250–253：1 342–    1 347.
[41] OZTEKIN E，PUL S，HUSEM M. Experimental determination of Drucker-Prager yield criterion parameters for normal and high strength concretes under triaxial compression[J]. Construction and Building Materials，2016，112：725–732.
[42] 周凤玺，李世荣. 广义Drucker-Prager强度准则[J]. 岩土力学，2008，29(3)：747–751.(ZHOU Fengxi，LI Shirong. Generalized Drucker- Prager strength criterion[J]. Rock and Soil Mechanics，2008，29(3)：747–751.(in Chinese))
[43] 曹文贵，方祖烈. 岩石损伤软化统计本构模型之研究[J]. 岩石力学与工程学报，1998，17(6)：628–633.(CAO Wengui，FANG Zulie. A study of statistical constitutive model for soft and damage rocks[J]. Chinese Journal of Rock Mechanics and Engineering，1998，17(6)：628–633.(in Chinese))
[44] KILBAS A A，SRIVASTAVA H M，TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam：Elsevier，2006：69–132.
[45] 邓荣贵，周德培，张倬元，等. 一种新的岩石流变模型[J]. 岩石力学与工程学报，2001，20(6)：780–784.(DENG Ronggui，ZHOU Depei，ZHANG Zuoyuan，et al. A new rheological model for rocks[J]. Chinese Journal of Rock Mechanics and Engineering，2001，20(6)：780–784.(in Chinese))
[46] 齐亚静，姜清辉，王志俭，等. 改进西原模型的三维蠕变本构方程及其参数辨识[J]. 岩石力学与工程学报，2012，31(2)：347–355.(QI Yajing，JIANG Qinghui，WANG Zhijian，et al. 3D creep constitutive equation of modified Nishihara model and its parameters identification[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(2)：347–355.(in Chinese))
[47] 吴斐，刘建锋，武志德，等. 盐岩的分数阶非线性蠕变本构模型[J]. 岩土力学，2014，35(增2)：162–167.(WU Fei，LIU Jianfeng，WU Zhide，et al. Fractional nonlinear creep constitutive model of salt rock[J]. Rock and Soil Mechanics，2014，35(Supp.2)：162–167.(in Chinese))
[48] 汪妍妍，盛冬发. 基于Burgers模型考虑损伤的岩石蠕变全过程研究[J]. 力学季刊，2019，40(1)：143–148.(WANG Yanyan，SHENG Dongfa. Study on the whole process of rock creep considering damage based on burgers model[J]. Chinese Quarterly of Mechanics，2019，40(1)：143–148.(in Chinese))
[49] 吴池，刘建锋，周志威，等. 含杂质盐岩三轴蠕变特性试验研究[J]. 工程科学与技术，2017，49(增2)：165–172.(WU Chi，LIU Jianfeng，ZHOU Zhiwei，et al. Study on creep properties of salt rock with impurities during triaxial creep test[J]. Advanced Engineering Sciences，2017，49(Supp.2)：165–172.(in Chinese))
[50] 蔡煜，曹平. 基于Burgers模型考虑损伤的非定常岩石蠕变模型[J]. 岩土力学，2016，37(增2)：369–374.(CAI Yu，CAO Ping. A non-stationary model for rock creep considering damage based on Burgers mode[J]. Rock and Soil Mechanics，2016，37(Supp.2)：369–374.(in Chinese))
[51] 马洪岭. 超深地层盐岩地下储气库可行性研究[博士学位论文][D]. 武汉：中国科学院武汉岩土力学研究所，2010.(MA Hongling. Study of feasibility of rock salt underground gas storage in ultra-deep formation[Ph. D. Thesis][D]. Wuhan：Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，2010.(in Chinese))