理论与试验研究

卸荷损伤泥岩应力松弛特征及本构模型研究

  • 王宇 ,
  • 黎瑾 ,
  • 闫亮 ,
  • 茆苏徽
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  • 1.三峡库区地质灾害教育部重点实验室,湖北 宜昌 443002;
    2.三峡大学 土木与建筑学院,湖北 宜昌 443002;
    3.三峡大学防灾减灾湖北省重点实验室,湖北 宜昌 443002
王宇(1981—),女,湖北荆州人,博士,副教授,主要从事岩土工程方面的教学与研究工作。E-mail:wangyu@ctgu.edu.cn

收稿日期: 2024-04-17

  网络出版日期: 2024-10-31

基金资助

国家自然科学基金(U2034203);防灾减灾湖北省重点实验室(三峡大学)开放研究基金(2020KJZ07)

Study on the Stress Relaxation Characteristics and Constitutive Model of Unloading Damage Mudstone

  • Wang Yu ,
  • Li Jin ,
  • Yan Liang ,
  • Mao Suhui
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  • 1. Key Laboratory of Geological Hazards on Three Gorges Reservoir Area, Ministry of Education, Yichang, Hubei 443002, P.R. China;
    2. College of Civil Engineering & Architecture, China Three Gorges University, Yichang, Hubei 443002, P.R. China;
    3. Hubei Key Laboratory of Disaster Prevention and Mitigation, China Three Gorges University, Yichang, Hubei 443002, P.R. China

Received date: 2024-04-17

  Online published: 2024-10-31

摘要

软弱岩体开挖卸荷形成的损伤对其支护加固后的应力松弛特性影响不可忽视。以红层泥岩为研究对象,开展了不同卸荷损伤程度泥岩的单轴应力松弛破坏试验,研究了不同应变水平及卸荷损伤程度对泥岩松弛特性的影响规律。结果表明:卸荷损伤泥岩在破坏前后的分级应力松弛试验中应力曲线均表现为不完全松弛,应力松弛曲线主要包含减速及稳定松弛两阶段,且各级应变水平下松弛量和松弛时间均随卸荷损伤程度增加呈线性增大趋势。基于分数阶微积分理论,选取R-L分数阶弹黏性元件(F元件),提出考虑黏滞系数时变特征的弹黏性时变元件(FT元件),然后引入卸荷损伤程度因子,提出考虑卸荷损伤的分数阶弹黏性时变元件(UFT元件),最后将该元件引入传统Burgers模型,建立了基于分数阶的非线性松弛本构模型。基于不同分数阶元件的理论本构模型计算值与试验数据对比表明,基于UFT元件的松弛本构模型具有更高的精确性,且不同应力水平及卸荷损伤程度下的模型理论计算成果与试验数据均较吻合,表明该松弛本构模型能够精确地描述卸荷损伤泥岩松弛特征。

本文引用格式

王宇 , 黎瑾 , 闫亮 , 茆苏徽 . 卸荷损伤泥岩应力松弛特征及本构模型研究[J]. 地下空间与工程学报, 2024 , 20(5) : 1515 -1527 . DOI: 10.20174/j.JUSE.2024.05.10

Abstract

The influence of the damage caused by excavation and unloading of soft rock mass on the stress relaxation characteristics of its support reinforcement cannot be ignored. Taking the red layer mudstone as the research object, the uniaxial stress relaxation failure test of unloading damaged mudstone was carried out, and the influence of different strain levels and unloading damage degrees on the relaxation characteristics of mudstone was studied. The results show that: The stress curves of the graded stress relaxation test of the unloading damaged mudstone before and after failure are all incomplete relaxation, and the stress relaxation curve mainly includes two stages: deceleration and stable relaxation, and the relaxation amount and relaxation time at all levels of strain level show a linear increase trend with the increase of the degree of unloading damage. Based on the fractional calculus theory, the R-L fractional order elastic viscous element (F element) is selected, and an elastic viscous time-varying element (FT element) considering the time-varying characteristics of viscosity coefficient is proposed, and then the unloading damage degree factor is introduced, and a fractional order elastic viscous time-varying element (UFT element) considering the initial unloading damage degree is proposed. Finally, the component is introduced into the traditional Burgers model to establish a nonlinear relaxation constitutive model based on fractional order. The comparison and discussion of the calculation values and experimental data of the theoretical constitutive model based on the three fractional order elements shows that the relaxation constitutive model based on UFT elements has higher accuracy, and the theoretical calculation results of the model under different stress levels and unloading damage degrees are consistent with the experimental data, indicating that the relaxation constitutive model can better and accurately describe the relaxation characteristics of unloading damage mudstone.

参考文献

[1] 冯涛,王文星,潘长良.岩石应力松弛试验及两类岩爆研究[J].湘潭矿业学院学报,2000,15(1):27-31. (Feng Tao, Wang Wenxing, Pan Changliang. Stress relaxation tests of rock and research on two types of rock bursts [J].Journal of Xiangtan Mining Institute, 2000, 15(1):27-31. (in Chinese))
[2] 唐礼忠,潘长良.岩石在峰值荷载变形条件下的松弛试验研究[J].岩土力学,2003,24(6):940-942. (Tang Lizhong, Pan Changliang. Experiment study on properties of stress relaxation of rock under deformation at peak load[J]. Rock and Soil Mechanics,2003,24(6):940-942. (in Chinese))
[3] 邱士利,冯夏庭,张传庆,等.不同初始损伤和卸荷路径下深埋大理岩卸荷力学特性试验研究[J].岩石力学与工程学报,2012,31(8):1686-1697. (Qiu Shili, Feng Xiating, Zhang Chuanqing, et al. Experimental research on mechanical properties of deep marble under different initial damage levels and unloading path[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(8):1686-1697. (in Chinese))
[4] 秦虎,黄滚,王维忠.不同含水率煤岩受压变形破坏全过程声发射特征试验研究[J].岩石力学与工程学报,2012,31(6):1115-1120. (Qin Hu, Huang Gun, Wang Weizhong. Experimental study of acoustic emission characteristics of coal samples with different moisture contents in process of compression deformation and failure[J].Chinese Journal of Rock Mechanics and Engineering, 2012, 31(6):1115-1120. (in Chinese))
[5] 黄涛.裂隙岩体渗流—应力—温度耦合作用研究[J].岩石力学与工程学报,2002,21(1):77-82. (Huang Tao. Coupling study among seepage-stress-temperature in fractured rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(1):77-82. (in Chinese))
[6] 张慧梅,杨更社.冻融与荷载耦合作用下岩石损伤模型的研究[J].岩石力学与工程学报,2010,29(3):471-476. (Zhang Huimei,Yang Gengshe. Research on damage model of rock under coupling action of freeze-thaw and load [J]. Chinese Journal of Rock Mechanics and Engineering, 2010,29(3):471-476. (in Chinese))
[7] 王浩,王晓东,泮俊.超高路堑边坡治理工程案例研究Ⅰ:边坡失稳机制模拟分析[J].岩石力学与工程学报,2017,36(4):899-909. (Wang Hao, Wang Xiaodong, Pan Jun. A case study of super-high cut slope I: simulation and analysis of instability mechanism of slopes [J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(4):899-909. (in Chinese))
[8] 孟国涛,樊义林,江亚丽,等.白鹤滩水电站巨型地下洞室群关键岩石力学问题与工程对策研究[J].岩石力学与工程学报,2016,35(12):2549-2560. (Meng Guotao, Fan Yilin, Jiang Yali, et al. Key rock mechanical problems and measures for huge caverns of Baihetan hydropower plant[J]. Chinese Journal of Rock Mechanics and Engineering,2016,35(12): 2549-2560. (in Chinese))
[9] 魏进兵,邓建辉,王俤剀,等.锦屏一级水电站地下厂房围岩变形与破坏特征分析[J].岩石力学与工程学报,2010,29(6):1198-1205. (Wei Jinbing,Deng Jianhui,Wang Dikai,et al. Characterization of deformation and fracture for rock mass in underground powerhouse of Jinping I Hydropower Station[J].Chinese Journal of Rock Mechanics and Engineering,2010,29 (6) :1198-1205. (in Chinese))
[10] Chrysothemis P, Matthew P, Mark D, et al. The three stages of stress relaxation-observations for the time-dependent behavior of brittle rocks based on laboratory testing[J]. Engineering Geology,2017,216: 56-75.
[11] Yu J, Zhu Y L, Yao W, et al. Stress relaxation behavior of marble under cyclic weak disturbance and confining pressures[J]. Measurement, 2021,182: 109777.
[12] 刘志勇,肖明砾,谢红强,等.基于损伤演化的片岩应力松弛特性[J].岩土力学,2016,37(增1):101-107. (Liu Zhiyong, Xiao Mingli, Xie Hongqiang,et al. Stress relaxation properties of schist based on damage evolution[J].Rock and Soil Mechanics,2016,37(Supp.1):101-107. (in Chinese))
[13] 于怀昌,赵阳,刘汉东,等.三轴应力作用下水对岩石应力松弛特性影响作用试验研究[J].岩石力学与工程学报,2015,34(2):313-322. (Yu Huaichang, Zhao Yang, Liu Handong, et al. Experimental study of influence of water on stress relaxation of rock under triaxial stress[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(2):313-322. (in Chinese))
[14] 李铀,朱维申,彭意,等.某地红砂岩多轴受力状态蠕变松弛特性试验研究[J].岩土力学,2006,27(8):1248-1252. (Li You, Zhu Weishen, Peng Yi, et al. Multi-axial experimental study on creep and relaxation properties of red sandstone from somewhere[J]. Rock and Soil Mechanics,2006,27(8):1248-1252. (in Chinese))
[15] 于怀昌,周敏,刘汉东,等.粉砂质泥岩三轴压缩应力松弛特性试验研究[J].岩石力学与工程学报,2011,30(4):803-811. (Yu Huaichang, Zhou Min, Liu Handong, et al. Experimental investigation on stress relaxation properties of silty mudstone under triaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(4):803-811. (in Chinese))
[16] 田洪铭,陈卫忠,赵武胜,等.宜-巴高速公路泥质红砂岩三轴应力松弛特性研究[J].岩土力学,2013,34(4):981-986. (Tian Hongming, Chen Weizhong, Zhao Wusheng, et al. Analysis of triaxial stress relaxation properties of red silty mudstone of Yichang-Badong highway[J]. Rock and Soil Mechanics, 2013,34(4):981-986. (in Chinese))
[17] Koeller R C. Applications of fractional calculus to the theory of viscoelasticity [J]. Journal of Applied Mechanics, 1984, 51(2):299-307.
[18] 郭佳奇,乔春生,徐冲,等.基于分数阶微积分的Kelvin-Voigt流变模型[J].中国铁道科学,2009,30(4):1-6. (Guo Jiaqi, Qiao Chunsheng, Xu Chong, et al. The Kelvin-Voigt rheological model based on fractional calculus[J].China Railway Science,2009,30(4):1-6. (in Chinese))
[19] 苏腾,周宏伟,赵家魏,等.基于变阶分数阶导数的岩石蠕变模型[J].岩石力学与工程学报,2019,38(7):1355-1363. (Su Teng,Zhou Hongwei,Zhao Jiawei,et al. A creep model of rock based on variable order fractional derivative[J].Chinese Journal of Rock Mechanics and Engineering,2019,38(7):1355-1363. (in Chinese))
[20] 李德建,刘校麟,韩超. 基于等效黏弹性的变阶分数阶岩石损伤蠕变模型[J].岩土力学,2020,41(12):3831-3839. (Li Dejian,Liu Xiaolin,Han Chao. Variable-order fractional damage creep model based on equivalent viscoelasticity for rock[J].Rock and Soil Mechanics,2020,41(12):3831-3839. (in Chinese))
[21] 于怀昌,史广诚,刘汉东,等.基于分数阶微积分的岩石非线性黏弹性应力松弛模型研究[J].应用基础与工程科学学报,2019,27(1):194-204. (Yu Huaichang, Shi Guangcheng, Liu Handong, et al. Study on nonlinear viscoelastic stress relaxation model of rock based on fractional order calculus[J].Journal of Applied Foundation and Engineering Science, 2019, 27(1):194-204. (in Chinese))
[22] Yin D S,Zhang W,Cheng C, et al. Fractional time-dependent Bingham model for muddy clay[J]. Journal of Non-Newtonian Fluid Mechanics,2012,187-188: 32-35.
[23] Zhang S G, Chen L, Liu W B. Unsteady fractional stress relaxation time effect model[J]. Arabian Journal of Geosciences,2020,13(22): 1206.
[24] International Society for Rock Mechanics Commission on Standardization of Laboratory and Field Tests. Suggested methods for determining the strength of rock material in triaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1978,15(2):47-51.
[25] 周维垣.高等岩石力学[M].北京:水利电力出版社, 1990. (Zhou Weiyuan. Advanced rock mechanics[M].Beijing: Water Conservancy and Electric Power Press,1990. (in Chinese))
[26] 沈明荣,陈建峰.岩体力学[M].上海:同济大学出版社,2015. (Shen Mingrong, Chen Jianfeng. Rock mechanics[M]. Shanghai: Tongji University Press, 2015. (in Chinese))
[27] 朱子涵,蔚立元,孟庆彬,等.峰前卸荷损伤大理岩的动静力学特性试验研究[J].岩石力学与工程学报,2019,38(4):747-756. (Zhu Zihan, Wei Liyuan, Meng Qingbin, et al. Experimental study on dynamic and static mechanical properties of marble damaged by pre-peak unloading [J]. Chinese Journal of Rock Mechanics and Engineering, 2019,38(4):747-756. (in Chinese))
[28] 李景龙,朱子涵,蔚立元,等.大理岩峰前卸荷损伤表征及再承载破坏耗能特征[J].岩石力学与工程学报,2020,39(12):2429-2438. (Li Jinglong, Zhu Zihan, Wei Liyuan, et al. Unloading damage characterization and reloading failure energy dissipation characteristics of marble in front of peaks[J]. Chinese Journal of Rock Mechanics and Engineering, 2020,39(12):2429-2438. (in Chinese))
[29] 王春萍,刘建锋,刘健,等.含卸荷裂隙北山花岗岩蠕变特征试验研究[J].地下空间与工程学报,2023,19(3):888-896.(Wang Chunping,Liu Jianfegn,Liu Jian,et al.Experimental study on creep behavior of unloading-cracked Beishan granite[J].Chinese Journal of Underground Space and Engineering,2023,19(3):888-896.(in Chinese))
[30] 付宏渊,邱祥,史振宁,等.基于弹塑性损伤模型的岩石加卸载计算研究[J].地下空间与工程学报,2018,14(1):12-18.(Fu Hongyuan,Qiu Xiang,Shi Zhenning,et al.Computing research on rock loading and unloading based on coupled elastoplasticity damage model[J].Chinese Journal of Underground Space and Engineering,2018,14(1):12-18.(in Chinese))
[31] 张全胜,杨更社,任建喜.岩石损伤变量及本构方程的新探讨[J].岩石力学与工程学报,2003,22(1):30-34. (Zhang Quansheng, Yang Gengshe, Ren Jian-xi. New study of damage variable and constitutive equation of rock [J]. Chinese Journal of Rock Mechanics and Engineering,2003, 22(1):30-34. (in Chinese))
[32] Lemaitre J. How to use damage mechanics[J].Nuclear Engineering & Design, 1984, 80(1):233-245.
[33] 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. (Sun Jun. Rheological behavior of geomaterials and its engineering applications[M]. Beijing:China Architecture and Building Press,1999. (in Chinese))
[34] Zhou H W,Wang C P,Mishaevsky L J,et al. A fractional derivative approach to full creep regions in salt rock[J]. Mechanics of Time-dependent Materials,2013,17(3):413-425.
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