高应力泥质粉砂岩黏弹塑性蠕变模型
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摘要
为揭示高应力作用下深埋硐室围岩的流变特性,采用分级增量加载方式对泥质粉砂岩进行三轴压缩蠕变实验,根据稳态蠕变速率与应力的关系,利用给定蠕变速率阈值确定岩石的长期强度;结合蠕变曲线特征,将瞬弹性、黏弹性、黏塑性应变分离,建立模型各参数与应力和时间的函数关系;根据损伤定义确定瞬弹性、黏弹性元件的损伤变量,并引入瞬弹性、黏弹性损伤变量和黏塑性修正系数对西原模型进行优化,提出一种可以描述高应力作用下岩石蠕变全过程的变参数模型。研究结果表明:稳态蠕变速率随应力增大呈指数增大,采用给定蠕变速率阈值求得岩石的长期强度为68.82 MPa,为单轴抗压强度的74.80%;基于黏弹塑性应变分离建立的蠕变模型能够很好地描述岩石蠕变全过程的非线性特征,且优化模型与实验数据拟合较好,证明了该蠕变模型的合理性。
In order to reveal the rheological characteristics of deep buried underground chamber surrounding rock under high stress, triaxial compression creep test was carried out on argillaceous siltstone by incremental loading method.According to the relationship between steady-state creep rate and stress, the long-term strength of rock was determined by using a given creep rate threshold. Considering the characteristics of creep curve, the function relationship among the parameters of model, stress level and time was established based on separation of instantaneous elasticity viscoelastic,and viscoplastic strain from creep curves. According to the damage definition, the damage variables of instantaneous elastic element and viscoelastic element were determined, and the Nishihara model was optimized by introducing instantaneous elasticity, viscoelastic damage variable and viscoplastic correction coefficient, which could describe the whole process of rock creep under high stress. The results show that the steady creep rate increases exponentially with the increase of stress. The long-term strength of rock obtained by the given creep rate threshold is 68.82 MPa, which is 74.80% of the uniaxial compressive strength. The creep model established based on strain viscoelastic-plastic separation can well describe the nonlinear characteristics of the whole process of rock creep, and the fitting between the optimized model and the experimental data is good, which proves the rationality of the creep model.
In order to reveal the rheological characteristics of deep buried underground chamber surrounding rock under high stress, triaxial compression creep test was carried out on argillaceous siltstone by incremental loading method.According to the relationship between steady-state creep rate and stress, the long-term strength of rock was determined by using a given creep rate threshold. Considering the characteristics of creep curve, the function relationship among the parameters of model, stress level and time was established based on separation of instantaneous elasticity viscoelastic,and viscoplastic strain from creep curves. According to the damage definition, the damage variables of instantaneous elastic element and viscoelastic element were determined, and the Nishihara model was optimized by introducing instantaneous elasticity, viscoelastic damage variable and viscoplastic correction coefficient, which could describe the whole process of rock creep under high stress. The results show that the steady creep rate increases exponentially with the increase of stress. The long-term strength of rock obtained by the given creep rate threshold is 68.82 MPa, which is 74.80% of the uniaxial compressive strength. The creep model established based on strain viscoelastic-plastic separation can well describe the nonlinear characteristics of the whole process of rock creep, and the fitting between the optimized model and the experimental data is good, which proves the rationality of the creep model.
引文
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[12]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.The improvement of the three-dimensional creep constitutive equation and its parameter identification of the Xiyuan model[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(2):347-355.
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[14]蒋海飞,刘东燕,赵宝云,等.高围压高水压条件下岩石非线性蠕变本构模型[J].采矿与安全工程学报,2014,31(2):284-291.JIANG Haifei,LIU Dongyan,ZHAO Baoyun,et al.Nonlinear creep constitutive model of rock under high confining pressure and high water pressure[J].Journal of Mining&Safety Engineering,2014,31(2):284-291.
[15]赵宝云,刘东燕,郑志明,等.基于短时三轴蠕变实验的岩石非线性黏弹塑性蠕变模型研究[J].采矿与安全工程学报,2011,28(3):446-451.ZHAO Baoyun,LIU Dongyan,ZHENG Zhiming,et al.Study on nonlinear viscoelastic-plastic creep model of rock based on short time triaxial creep test[J].Proceedings of Mining&Safety Engineering,2011,28(3):446-451.
[16]刘新喜,童庆闯,侯勇,等.高应力泥质粉砂岩非线性蠕变损伤模型研究[J].中国公路学报,2018,31(2):280-288.LIU Xinxi,TONG Qingchuang,HOU Yong,et al.Research on nonlinear creep damage model of high stress argillaceous siltstone[J].Acta Sinica Sinica de Highway,2018,31(2):280-288.
[17]沈明荣,谌洪菊.红砂岩长期强度特性的实验研究[J].岩土力学,2011,32(11):3301-3305.SHEN Mingrong,CHEN Hongju.Testing study of long-term strength characteristics of red sandstone[J].Rock and Soil Mechanics,2011,32(11):3301-3305.
[18]崔旋,佘成学.推断岩石长期强度的黏塑性应变率法研究[J].岩石力学与工程学报,2011,30(S2):3899-3904.CUI Xuan,SHE Chengxue.Study of viscoplastic strain rate method to quickly determine long-term strength of rock.Chinese Journal of Rock Mechanics and Engineering,2011,30(S2):3899-3904.
[19]李良权,徐卫亚,王伟,等.基于流变实验的向家坝砂岩长期强度评价[J].工程力学,2010,27(11):127-136,143.LI Liangquan,XU Weiya,WANG Wei,et al.Estimation of long term strength of Xiangjiaba sandstone based on rheological test[J].Engineering Mechanics,2010,27(11):127-136,143.
[20]SZCZEPANIK Z,MILNE D,KOSTAKIS K,et al.Long term laboratory strength tests in hard rock[C]//ISRM 2003-Technology Roadmap for Rock Mechanics.Johannesburg:South African Institute of Mining and Metallurgy,2003:1179-1184.
[21]范秋雁,阳克青,王渭明.泥质软岩蠕变机制研究[J].岩石力学与工程学报,2010,29(8):1555-1561.FAN Qiuyan,YANG Keqing,WANG Weiming.Study on creep mechanism of muddy soft rock[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(8):1555-1561.
[22]赵延林,曹平,文有道,等.岩石弹黏塑性流变实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 al.Study on elasto-viscoplastic rheological test and nonlinear rheological model of rock[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(3):477-486.
[2]王更峰.炭质板岩蠕变特性研究及其在隧道变形控制中的应用[D].重庆:重庆大学土木工程学院,2012:6-8.WANG Gengfeng.Creep characteristics of carbonaceous slate and its application in tunnel deformation control[D].Chongqing:Chongqing University.School of Civil Engineering,2012:6-8.
[3]汪斌,朱杰兵,邬爱清,等.高应力下岩石非线性强度特性的实验验证[J].岩石力学与工程学报,2010,29(3):542-548.WANG Bin,ZHU Jiebing,WU Aiqing,et al.Experimental verification of rock nonlinear strength characteristics under high stress[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(3):542-548.
[4]朱杰兵.高应力下岩石卸荷及其流变特性研究[D].武汉:中国科学院研究生院(武汉岩土力学研究所),2009:84-88.ZHU Jiebing.Study on unloading and rheological properties of rock under high stress[D].Wuhan:Graduate School of Chinese Academy of Sciences(Wuhan Institute of Geotechnical Mechanics),2009:84-88.
[5]昝月稳,俞茂宏,赵坚,等.高应力状态下岩石非线性统一强度理论[J].岩石力学与工程学报,2004,23(13):2143-2148.ZAN Yuewen,YU Maohong,ZHAO Jian,et al.Rock nonlinear unified strength theory under high stress state[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(13):2143-2148.
[6]杨文东,张强勇,陈芳,等.辉绿岩非线性流变模型及蠕变加载历史的处理方法研究[J].岩石力学与工程学报,2011,30(7):1405-1413.YANG Wendong,ZHANG Qiangyong,CHEN Fang,et al.Research on nonlinear rheological model of diabase and treatment for creep loading history[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(7):1405-1413.
[7]宋勇军,雷胜友,韩铁林.一种新的岩石非线性黏弹塑性流变模型[J].岩土力学,2012,33(7):2076-2080.SONG Yongjun,LEI Shengyou,HAN Tielin.A new nonlinear viscoelasto-plastic rheological model for rocks[J].Rock and Soil Mechanics,2012,33(7):2076-2080.
[8]王军保,刘新荣,王铁行.基于改进分数阶黏滞体的岩石非线性蠕变模型[J].中南大学学报(自然科学版),2015,46(4):1461-1467.WANG Junbao,LIU Xinrong,WANG Tiehang.A nonlinear creep model for rocks based on modified fractional viscous body[J].Journal of Central South University(Science and Technology),2015,46(4):1461-1467.
[9]张治亮,徐卫亚,王伟.向家坝水电站坝基挤压带岩石三轴蠕变实验及非线性黏弹塑性蠕变模型研究[J].岩石力学与工程学报,2011,30(1):132-140.ZHANG Zhiliang,XU Weiya,WANG Wei.Triaxial creep test and nonlinear viscoelastic-plastic creep model of rock in compression zone of Xiangjiaba Hydropower Station[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(1):132-140.
[10]高赛红,曹平,汪胜莲,等.改进的岩石非线性黏弹塑性蠕变模型及其硬化黏滞系数的修正[J].煤炭学报,2012,37(6):936-943.GAO Saihong,CAO Ping,WANG Shenglian,et al.Improved rock nonlinear viscoelastic plastic creep model and correction of hardening viscosity coefficient[J].Journal of China Coal Society,2012,37(6):936-943.
[11]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):1049-1055.KANG Yonggang,ZHANG Xiue.An improved constitutive model of rock creep[J].Rock and Soil Mechanical,2014,35(4):1049-1055.
[12]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.The improvement of the three-dimensional creep constitutive equation and its parameter identification of the Xiyuan model[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(2):347-355.
[13]LI Wenquan,LI Xiangdong,HAN Bing,et al.Recognition of creep model of layer composite rock mass and its application[J].Journal of Central South University of Technology,2007,14(1):329-331.
[14]蒋海飞,刘东燕,赵宝云,等.高围压高水压条件下岩石非线性蠕变本构模型[J].采矿与安全工程学报,2014,31(2):284-291.JIANG Haifei,LIU Dongyan,ZHAO Baoyun,et al.Nonlinear creep constitutive model of rock under high confining pressure and high water pressure[J].Journal of Mining&Safety Engineering,2014,31(2):284-291.
[15]赵宝云,刘东燕,郑志明,等.基于短时三轴蠕变实验的岩石非线性黏弹塑性蠕变模型研究[J].采矿与安全工程学报,2011,28(3):446-451.ZHAO Baoyun,LIU Dongyan,ZHENG Zhiming,et al.Study on nonlinear viscoelastic-plastic creep model of rock based on short time triaxial creep test[J].Proceedings of Mining&Safety Engineering,2011,28(3):446-451.
[16]刘新喜,童庆闯,侯勇,等.高应力泥质粉砂岩非线性蠕变损伤模型研究[J].中国公路学报,2018,31(2):280-288.LIU Xinxi,TONG Qingchuang,HOU Yong,et al.Research on nonlinear creep damage model of high stress argillaceous siltstone[J].Acta Sinica Sinica de Highway,2018,31(2):280-288.
[17]沈明荣,谌洪菊.红砂岩长期强度特性的实验研究[J].岩土力学,2011,32(11):3301-3305.SHEN Mingrong,CHEN Hongju.Testing study of long-term strength characteristics of red sandstone[J].Rock and Soil Mechanics,2011,32(11):3301-3305.
[18]崔旋,佘成学.推断岩石长期强度的黏塑性应变率法研究[J].岩石力学与工程学报,2011,30(S2):3899-3904.CUI Xuan,SHE Chengxue.Study of viscoplastic strain rate method to quickly determine long-term strength of rock.Chinese Journal of Rock Mechanics and Engineering,2011,30(S2):3899-3904.
[19]李良权,徐卫亚,王伟,等.基于流变实验的向家坝砂岩长期强度评价[J].工程力学,2010,27(11):127-136,143.LI Liangquan,XU Weiya,WANG Wei,et al.Estimation of long term strength of Xiangjiaba sandstone based on rheological test[J].Engineering Mechanics,2010,27(11):127-136,143.
[20]SZCZEPANIK Z,MILNE D,KOSTAKIS K,et al.Long term laboratory strength tests in hard rock[C]//ISRM 2003-Technology Roadmap for Rock Mechanics.Johannesburg:South African Institute of Mining and Metallurgy,2003:1179-1184.
[21]范秋雁,阳克青,王渭明.泥质软岩蠕变机制研究[J].岩石力学与工程学报,2010,29(8):1555-1561.FAN Qiuyan,YANG Keqing,WANG Weiming.Study on creep mechanism of muddy soft rock[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(8):1555-1561.
[22]赵延林,曹平,文有道,等.岩石弹黏塑性流变实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 al.Study on elasto-viscoplastic rheological test and nonlinear rheological model of rock[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(3):477-486.