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| A fractional viscoelastic-plastic creep damage model for salt rock considering temperature effect |
| ZHANG Shengli1，LIANG Weiguo1，2，XIAO Ning1，ZHAO Desheng1，LI Jing1，LI Chao1 |
| (1. Key Laboratory of In-situ Property-improving Mining of Ministry of Education，Taiyuan University of Technology，
Taiyuan，Shanxi 030024，China；2. College of Mining Engineering，Taiyuan University of Technology，
Taiyuan，Shanxi 030024，China) |
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Abstract The surrounding rock of salt caverns，being ideal locations for the storage of energy and disposal of nuclear waste，presents with significant creep deformation over a long period of time due to being continually affected by a combination of stress and temperature. To determine the effects of temperature and stress on the creep of salt rock，triaxial creep tests at varying conditions were conducted，the mechanisms of the effects of temperature and deviatoric stress at steady-state creep rate were determined，and fitting was conducted to obtain the parameters of steady state creep rate constitutive equation. The linear dashpot of the Maxwell model was replaced by a fractional Abel dashpot to establish a fractional Maxwell model that can be used to consider the effects of temperature. A new fractional viscoelastic-plastic creep damage model considering temperature was achieved by connecting the viscoplastic damage model to the fractional Maxwell model. The parameters of the creep damage model were extracted from the results of the experimental triaxial creep test using 1stOpt software. The theoretical model results and tests data were compared to determine the validity of the creep damage model. The new model can well simulate the creep deformation in whole evolution.
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| [1] 杨春和，白世伟，吴益民. 应力水平及加载路径对盐岩时效的影响[J]. 岩石力学与工程学报，2000，19(3)：270–275.(YANG Chunhe，BAI Shiwei，WU Yimin. Stress level and loading path effect on time dependent properties of salt rock[J]. Chinese Journal of Rock Mechanics and Engineering，2000，19(3)：270–275.(in Chinese))
[2] 李 哲. 应力、温度耦合下盐岩力学特性试验研究[硕士学位论文][D]. 重庆：重庆大学，2012.(LI Zhe. Experimental research on mechanical characteristics of rock salt under coupling between stress and temperature[M. S. Thesis][D]. Chongqing：Chongqing University，2012.(in Chinese))
[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] 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))
[5] 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))
[6] 万 玲. 岩石类材料黏弹塑性损伤本构模型及其应用[博士学位论文][D]. 重庆：重庆大学，2004.(WAN Ling. A visco-elastoplastic damage constitutive model of rock and rock-like materials and applications[Ph. D. Thesis][D]. Chongqing：Chongqing University，2004.(in Chinese))
[7] 张天才. 岩盐蠕变特性试验研究及理论分析[硕士学位论文][D]. 重庆：重庆大学，2015.(ZHANG Tiancai. Experimental investigation and theoretical analysis of rock salt creep[M. S. Thesis][D]. Chongqing：Chongqing University，2015.(in Chinese))
[8] 蒋昱州，张明鸣，李良权. 岩石非线性黏弹塑性蠕变模型研究及其参数识别[J]. 岩石力学与工程学报，2008，27(4)：832–839.(JIANG Yuzhou，ZHANG Mingming，LI Liangquan. Study on nonlinear viscoelasto- plastic creep model of rock and its parameter identification[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(4)：832–839.(in Chinese))
[9] 王军保，刘新荣，郭建强，等. 盐岩蠕变特性及其非线性本构模型[J]. 煤炭学报，2014，39(3)：445–451.(WANG Junbao，LIU Xinrong，GUO Jianqiang，et al. Creep properties of salt rock and its nonlinear constitutive model[J]. Journal of China Coal Society，2014，39(3)：445–451.(in Chinese))
[10] 康永刚，张秀娥. 一种改进的岩石蠕变本构模型[J]. 岩土力学，2014，35(4)：1 049–1 055.(KANG Yonggang，ZHANG Xiue. An improved constitutive model for rock creep[J]. Rock and Soil Mechanics，2014，35(4)：1 049–1 055.(in Chinese))
[11] 熊良宵，杨林德，张 尧. 岩石的非定常Burgers模型[J]. 中南大学学报：自然科学版，2010，41(2)：679–684.(XIONG Liangxiao，YANG Linde，ZHANG Yao. Non-stationary Burgers model for rock[J]. Journal of Central South University：Science and Technology，2010，41(2)：679–684.(in Chinese))
[12] 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.
[13] 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))
[14] 丁靖洋，周宏伟，刘 迪，等. 盐岩分数阶三元件本构模型研究[J]. 岩石力学与工程学报，2014，33(4)：672–678.(DING Jingyang，ZHOU Hongwei，LIU Di，et al. Research on fractional derivative three elements model of salt rock[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(4)：672–678.(in Chinese))
[15] 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 model of salt rock based on Weibull distribution[J]. Chinese Journal of Solid Mechanics，2013，34(5)：473–480.(in Chinese))
[16] 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 Xiong，et al. Characters of rheological damage and constitutive model of salt rock[J]. Rock and Soil Mechanics，2015，36(3)：769–776.(in Chinese))
[17] 吴 斐，刘建锋，边 宇，等. 盐岩的分数阶导数蠕变模型[J]. 四川大学学报：工程科学版，2014，46(5)：22–27.(WU Fei，LIU Jianfeng，BIAN Yu，et al. Fractional derivative creep model of salt rock[J]. Journal of Sichuan University：Engineering Science，2014，46(5)：22–27.(in Chinese))
[18] 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))
[19] WU F，LIU J，ZOU Q，et al. A triaxial creep model for salt rocks based on variable-order fractional derivative[J]. Mechanics of Time-Dependent Materials，2021，25(1)：101–118.
[20] 佘成学. 岩石非线性黏弹塑性蠕变模型研究[J]. 岩石力学与工程学报，2009，28(10)：2 006–2 011.(SHE Chengxue. Research on nonlinear viscoelasto-plastic creep model of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(10)：2 006–2 011.(in Chinese))
[21] 曹文贵，袁靖周，王江营，等. 考虑加速蠕变的岩石蠕变过程损伤模拟方法[J]. 湖南大学学报：自然科学版，2013，40(2)：15–21. (CAO Wengui，YUAN Jingzhou，WANG Jiangying，et al. A damage simulation technique of the full rock creep process considering accelerated creep[J]. Journal of Hunan University：Natural Science，2013，40(2)：15–21.(in Chinese))
[22] ZHAO Y，ZHANG L，WANG W，et al. Separation of viscoelastic plastic strains of rock and a nonlinear creep model[J]. International Journal of Geomechanics，2018，18(1)：04017129.
[23] 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))
[24] 张强勇，杨文东，张建国，等. 变参数蠕变损伤本构模型及其工程应用[J]. 岩石力学与工程学报，2009，28(4)：732–739.(ZHANG Qiangyong，YANG Wendong，ZHANG Jianguo，et al. Variable parameters- based creep damage constitutive model and its engineering application[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(4)：732–739.(in Chinese))
[25] 蒲志成，曹 平，张春阳，等. 考虑时效损伤劣化的变参数非线性蠕变损伤模型[J]. 工程力学，2017，34(6)：17–27.(PU Zhicheng，CAO Ping，ZHANG Chunyang，et al. Variable parameters nonlinear creep damage model of rock with consideration of aging，damage and deterioration[J]. Engineering Mechanic，2017，34(6)：17–27.(in Chinese))
[26] WANG J B，LIU X R，SONG Z P，et al. An improved Maxwell creep model for salt rock[J]. Geomechanics and Engineering，2015，9(4)：499–511.
[27] 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))
[28] 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))
[29] 江力宇. 考虑温度影响的片麻状花岗岩蠕变力学特性与理论分析研究[硕士学位论文][D]. 济南：山东大学，2016.(JIANG Liyu. Creep mechanical properties and Theoretical analysis research to Gneissic granite with considering the effects of temperature[M. S. Thesis][D]. Jinan：Shandong University，2016.(in Chinese))
[30] 薛东杰，路乐乐，易海洋，等. 考虑温度和体积应力的分数阶蠕变损伤Burgers模型[J]. 岩石力学与工程学报，2021，40(2)：315–329. (XUE Dongjie，LU Lele，YI Haiyang，et al. A fractional Burgers model for uniaxial and triaxial creep of damaged salt-rock considering temperature and volume-stress[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(2)：315–329.(in Chinese))
[31] ISRM. Suggested methods for determining the uniaxial compressive strength and deformation of rock material[S]. [S. l.]：[s. n.]，1979.
[32] 刘 雄. 岩石流变学概论[M]. 北京：地质出版社，1994：1–66. (LIU Xiong. The conspectus of rock rheology[M]. Beijing：Geology Press，1994：1–66.(in Chinese))
[33] 吴 文. 盐岩的静、动力学特性实验研究与理论分析[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 studies and theoretic analysis of static and dynamic mechanical characteristics of rock salt [Ph. D. Thesis][D]. Wuhan：Chinese Academy of Sciences，Institute of Rock and Soil Mechanics，2003.(in Chinese))
[34] 刘 迪. 盐岩蠕变微细观机制及分数阶本构模型研究[博士学位论文][D]. 北京：中国矿业大学(北京)，2019.(LIU Di. The fractional derivative constitutive model and micro-mechanisms of salt rock during creep[Ph. D. Thesis][D]. Beijing：China University of Mining and Technology(Beijing)，2019.(in Chinese))
[35] WU F，ZHANG H，ZOU Q，et al. Viscoelastic-plastic damage creep model for salt rock based on fractional derivative theory[J]. Mechanics of Materials，2020，150(6)：103600.
[36] 赵延林，曹 平，文有道，等. 岩石弹黏塑性流变试验和非线性流变模型研究[J]. 岩石力学与工程学报，2008，27(3)：477–486. (ZHAO Yanlin，CAO Ping，WEN Youdao，et a1. Viscoelasto-plastic rheological experimental and nonlinear rheological model of rocks[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(3)：477–486.(in Chinese))
[37] 孙 钧. 岩土材料流变及其工程应用[M]. 北京：中国建筑工业出版社，1999：3–80.(SUN Jun. Rheology of rock and soil materials and its application in engineering[M]. Beijing：Chinese Architecture and Building Press，1999：3–80.(in Chinese))
[38] 苏 彦，张向东，周林林. 岩石分数阶蠕变损伤本构模型研究[J]. 河北工程大学学报：自然科学版，2020，37(1)：19–23.(SU Yan，ZHANG Xiangdong，ZHOU Linlin. Study on constitutive model of fractional creep damage of rock[J]. Journal of Hebei University of Engineering：Natural Science，2020，37(1)：19–23.(in Chinese)) |
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2022, Vol. 41 
