连续损伤力学基临界奇异指数与破坏时间预测

周孙基; 程磊; 王立伟; 王鼎; 郝圣旺

doi:10.6052/0459-1879-19-120

连续损伤力学基临界奇异指数与破坏时间预测

doi: 10.6052/0459-1879-19-120

燕山大学建筑工程与力学学院,河北秦皇岛 066004

基金项目: 1)国家自然科学基金资助项目(11672258)

详细信息

通讯作者:
郝圣旺

中图分类号: O341
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出版历程
- 收稿日期: 2019-05-11
- 刊出日期: 2019-09-18

CONTINUUM DAMAGE MECHANICS-BASED CRITICAL SINGULARITY EXPONENT AND FAILURE TIME PREDICTION

School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004,Hebei,China

摘要

摘要: 响应量在临近破坏时呈现出临界幂律奇异性加速特征,是一种被广泛证实的灾变破坏前兆,并被火山、滑坡和岩石破坏实验等后验预测结果证实为一种对破坏时间进行短临期预测的可行方法.但是,奇异性指数测量值的较大分散性导致了对其具体取值的争议和预测效果的不确定性.因此,理解奇异性指数取值特征及其内在物理控制因素,成为了一个核心问题.本文基于连续介质损伤力学和材料时间相关失效特征,构建了刻画损伤加速发展通向破坏过程的力学模型.导出了恒名义应力蠕变加载和控制名义应力随时间线性增大两种典型加载方式下,损伤和应变率加速发展通向破坏的临界幂律奇异性前兆特征.阐明了临界幂律奇异性指数取值依赖于材料损伤与承受真应力之间的非线性关系这一内在物理根源,表明了实际测量中奇异性指数的分散性不完全归结于测量数据误差,而是有着内在物理控制因素.针对破坏前奇异性指数的不确定性,建议了在未知奇异性指数条件下预测破坏时间的方法,并基于花岗岩脆性蠕变破坏实验进行了验证和说明.
- 加速破坏 /
- 幂律奇异性 /
- 指数 /
- 破坏时间 /
- 预测
Abstract: The accelerating increase of response quantities, such as strain and acoustic emission signals in the vicinity of failure time, has been revealed as a precursor of catastrophic failure. This critical precursor has been widely validated as a valid way to predict failure time by the retrospective prediction of volcanic eruptions, landslides and laboratory experiments of rock failures. But the scatter of exponents in the critical power law singularity relationship that describes acceleration in precursory signals leads to a debate on the actual value of critical exponent and the uncertainty of failure time prediction. Consequently, the uncertainty resulting from the scatter of exponents is a key difficulty in using such methods for prediction of the failure time through the use of acceleration precursors. Thus understanding the underlying mechanisms for the magnitude and variation of critical power-law exponents becomes a central problem for understanding the process of failure and failure time prediction. This paper presents a multi-scale damage mechanic model describing the accelerating process of time dependent failure. Theoretic derivations and demonstrations of critical power law relationship are presented for two typical load process, i.e. brittle creep failure under constant nominal stress and the load process of linearly increasing the nominal stress with time. It is found that values of the singularity exponents have a relationship with the parameter that defines the nonlinear level of damage evolution rate depending on to the local true stress. The physical expressions of critical parameters are deduced and the physical meanings of these critical parameters are explained. It is declared that the observed variation of the critical power law exponents not only due to the fluctuation in the measurement data, but has its intrinsic physical controls. Then a method is suggested to predict the failure time when the critical singularity exponent is unknown. This proposed methodology is validated through granite creep failure experiments in laboratory and the challenges for practical applications are demonstrated.
- failure acceleration /
- power law singularity /
- exponent /
- failure time /
- prediction

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参考文献(1)

[1]	Xia MF, Song ZQ, Xu JB , et al. Sample-specific behavior in failure models of disordered media. Communications in Theoretical Physics, 1996,25:49-54
[2]	Bai YL, Wang HY, Xia MF , et al. Statistical mesomechanics of solid, liking coupled multiple space and time scales. Applied Mechanics Review, 2005,58:372-388
[3]	Yin XC, Chen XZ, Song ZP , et al. A new approach to earthquake prediction: The load/unload response ratio (LURR) theory. Pure and Applied Geophysics, 1995,145:701-715
[4]	尹祥础, 刘月 . 加卸载响应比------地震预测与力学的交叉. 力学进展, 2013,43(6):555-580
[4]	( Yin Xiangchu, Liu Yue . Load-unload response ratio --- An interplay between earthquake prediction and mechanics. Advances of Mechanics, 2013,43(6):555-580 (in Chinese))
[5]	尹祥础, 刘月, 张浪平等. "泛西南"地区加卸载响应比异常及大震活动预测与追踪. 地震, 2017,37(4):37-49
[5]	( Yin Xiangchu, Liu Yue, Zhang Langping , et al. LURR anomaly, prediction and tracking of large earthquakes in the Pan-southwestern region. Earthquake, 2017,37(4):37-49 (in Chinese))
[6]	Xia MF, Wei YJ, Ke FJ , et al. Critical sensitivity and trans-scale fluctuations in catastrophic rupture. Pure and Applied Geophysics, 2002,159:2491-2509
[7]	李雪艳, 张惠民 . 基于应变脉冲响应协方差的损伤识别方法研究. 力学学报, 2017,49(5):1081-1090
[7]	( Li Xueyan, Zhang Huimin . Study of damage identification method based on the covariance of strain impulse response function. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(5):1081-1090 (in Chinese))
[8]	马瑾 . 从"是否存在有助于预报的地震先兆"说起. 科学通报, 2016,61:409-414
[8]	( Ma Jin . On "whether earthquake precursors help for prediction do exist". Chinese Science Bulletin, 2016,61:409-414 (in Chinese))
[9]	许强, 黄润秋 . 非线性科学理论在地质灾害评价预测中的应用------地质灾害系统分析原理. 山地学报, 2000,18(3):272-277
[9]	( Xu Qiang, Huang Runqiu . Systematic analysis principles of geological hazards. Journal of Mountain Science, 2000,18(3):272-277(in Chinese))
[10]	张琰, 吴忠良, 李佳威 . 地震预测预报研究议程的演变: 文献计量分析的启示. 物理, 2019,39(2):159-173
[10]	( Zhang Yan, Wu Zhongliang, Li Jiawei . Agenda evolution of earthquake forecast/prediction research: Inspiration from bibliometric analysis. Physics, 2019,39(2):159-173 (in Chinese))
[11]	Xue J, Hao SW, Wang J , et al. The changeable power law singularity and its application to prediction of catastrophic rupture in uniaxial compressive tests of geomedia. Journal of Geophysical Research: Solid Earth, 2018,123:2645-2657
[12]	Long H, Liang LH, Wei YG . Failure characterization of solid structures based on an equivalence of cohesive zone model. International Journal of Solids and Structures, 2019,163:194-210
[13]	Liang LH, Li XN, Liu HY , et al. Power-law characteristics of damage and failure of ceramic coating systems under three-point bending. Surface and Coatings Technology, 2016,285:113-119
[14]	Wang XG, Yin YP, Wang JD , et al. A nonstationary parameter model for the sandstone creep tests. Landslides, 2018,15:1377-1389
[15]	郝圣旺 . 非均匀介质的变形局部化、灾变破坏及临界奇异性. [博士论文]. 北京:中国科学院力学研究所, 2007
[15]	( Hao Shengwang . Localization, catastrophic rupture and critical singularity of heterogeneous brittle media. [PhD Thesis]. Beijing: Institute of Mechanics, Chinese Academy of Sciences, 2007 (in Chinese))
[16]	Hao SW, Rong F, Lu MF , et al. Power-law singularity as a possible catastrophe warning observed in rock experiments. International Journal of Rock Mechanics and Mining Sciences, 2013,60:253-262
[17]	Heap MJ, Baud P, Meredith PG , et al. Brittle creep in basalt and its application to time-dependent volcano deformation. Earth and Planetary Science Letters, 2011,307:71-82
[18]	Hao SW, Zhang BJ, Tian JF , et al. Predicting time-to-failure in rock extrapolated from secondary creep. Journal of Geophysical Research: Solid Earth, 2014,119:1942-1953
[19]	陆明富 . 双轴加载下非均匀介质的损伤演化与灾变. [博士论文]. 北京:中国科学院力学研究所, 2011
[19]	( Lu Mingfu . Damage induced catastrophic rupture in heterogeneous media under biaxial loading. [PhD Thesis]. Beijing: Institute of Mechanics, Chinese Academy of Sciences, 2011 (in Chinese))
[20]	徐海元 . 地壳变形的非均匀演化重构及灾变前兆分析. [博士论文]. 北京:中国科学院力学研究所, 2015
[20]	( Xu Haiyuan . Reconstruction of heterogeneous evolution of crustal deformation and analysis of precursors to catastrophic rupture. [PhD Thesis]. Beijing: Institute of Mechanics, Chinese Academy of Sciences, 2015 (in Chinese))
[21]	薛健 . 非均匀介质在压缩载荷下灾变破坏的幂律奇异性前兆及灾变预测. [博士论文]. 北京: 中国科学院力学研究所, 2018
[21]	( Xue Jian . Power-law singularity precursor and prediction of catastrophic rupture in heterogeneous media under compression. [PhD Thesis]. Beijing: Institute of Mechanics, Chinese Academy of Sciences, 2018 (in Chinese))
[22]	Voight B, Cornelius RR . Prospects for eruption prediction in near real-time. Nature, 1991,350:695-698
[23]	Kilburn CRJ, Petley DN . Forecasting giant, catastrophic slope collapse: Lessons from Vajont, northern Italy. Geomorphology, 2003,54(1-2):21-32
[24]	Voight B . A method for prediction of volcanic eruptions. Nature, 1988,332:125-130
[25]	Hao SW, Yang H, Elsworth D . An accelerating precursor to predict "time-to-failure" in creep and volcanic eruptions. Journal of Volcanology and Geothermal Research, 2017,343:252-262
[26]	Tommaso C, Emanuele I, Federico DT , et al. Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses. Landslides, 2017,14:517-534
[27]	Bell AF . Predictability of landslide timing from quasi-periodic precursory earthquakes. Geophysical Research Letters, 2018,45:1860-1869
[28]	Vasseur J, Wadsworth FB, Heap MJ , et al. Does an inter-flaw length control the accuracy of rupture forecasting in geological materials? Earth and Planetary Science Letters, 2017,475:181-189
[29]	荣峰 . 非均匀脆性介质损伤演化的多尺度数值模拟. [博士论文]. 北京:中国科学院力学研究所, 2006
[29]	( Rong Feng . Multiscale simulations of damage evolution in heterogeneous brittle media. [PhD Thesis]. Beijing: Institute of Mechanics, Chinese Academy of Sciences, 2006 (in Chinese))
[30]	Voight B . A relation to describe rate-dependent material failure. Science, 1989,243:200-203
[31]	Zhou SJ, Hao SW, Elsworth D . Magnitude and variation of the critical power law exponent and its physical controls. Physica A, 2018,510:552-557
[32]	Krajcinovic D, Rinaldi A . Statistical damage mechanics-Part I: Theory. Journal of Applied Mechanics, 2005,72:76-85
[33]	余寿文, 冯西桥 . 损伤力学 . 北京:清华大学出版社, 1997
[33]	( Yu Shouwen, Feng Xiqiao . Damage Mehcanics. Beijing: Tsinghua University Press, 1997 (in Chinese))
[34]	卡恰诺夫. 连续介质损伤力学引论. 杜善义, 王殿富译. 哈尔滨: 哈尔滨工业大学出版社, 1989
[34]	( Kachanov LM. Introduction to Continuum Damage Mechanics. Du Shanyi, Wang Dianfu (Translation). Harbin: Harbin Institute of Technology Press, 1989 (in Chinese))
[35]	Kachanov LM . Rupture time under creep conditions. International Journal of Fracture, 1999,97:11-18
[36]	冯西桥, 余寿文 . 准脆性材料细观损伤力学. 北京: 高等教育出版社, 2002
[36]	( Feng Xiqiao, Yu Shouwen. Damage Micromehcanics of Quasi-Brittle Materials. Beijing: Higher Education Press, 2002 (in Chinese))
[37]	Newman WI, Phoenix SL . Time-dependent fiber bundles with local load sharing. Physical Review E, 2001,63:021507
[38]	Bozzano F, Mazzanti P, Moretto S . Discussion to: `Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses' by T. Carlà, E. Intrieri, F. Di Traglia, T. Nolesini, G. Gigli and N. Casagli. Landslides, 2018,15:1437-1441
[39]	Tommaso C, Emanuele I, Federico DT , et al. Reply to discussion on "Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses" by F. Bozzano, P. Mazzanti, and S. Moretto. Landslides, 2018,15:1443-1444
[40]	Bell AF, Naylor M, Hernandez S , et al. Volcanic eruption forecasts from accelerating rates of drumbeat long-period earthquakes. Geophysical Research Letters, 2018,45(3):1339-1348
[41]	Kilburn CRJ, Natale GD, Carlino S . Progressive approach to eruption at Campi Flegrei caldera in southern Italy. Nature Communications, 2017,8:15312
[42]	卢梦凯, 张洪武, 郑勇刚 . 应变局部化分析的嵌入强间断多尺度有限元法. 力学学报, 2017,49(3):649-658
[42]	( Lu Mengkai, Zhang Hongwu, Zheng Yonggang . Embedded strong discontinuity model based multiscale finite element method for strain localization analysis. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(3):649-658 (in Chinese))
[43]	王增会, 李锡夔 . 基于介观力学信息的颗粒材料损伤$\!$-$\!$-$\!$愈合与塑性宏观表征. 力学学报, 2018,50(2):284-296
[43]	( Wang Zenghui, Li Xikui . Meso-mechanically informed macroscopic characterization of damage-healing-plasticity for granular materials. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):284-296 (in Chinese))