Anelastic attenuation and damage of saturated sandstone under cyclic loading
XI Jun1，WAN Xinlin2，XI Daoying3，4
(1. School of Mechanical Engineering，Beijing Institute of Petrochemical Technology，Beijing102617，China；
2. Civil Engineering College，Anhui Jianzhu University，Hefei，Anhui 230023，China；3. Mengcheng Geophysical National Field Station，University of Science and Technology of China，Hefei，Anhui 230026，China；4. School of Earth and Space Sciences，University of Science and Technology of China，Hefei，Anhui 230026，China)
Abstract：To investigate the relationship between anelastic attenuation and damage of saturated sandstone in the elastic range，the forced resonance and uniaxial cyclic loading experiments were carried out in the frequency range of 0.01–1 000 Hz and the temperature range of −60 ℃–190 ℃. The experimental results show that the response curve of the rock exhibits a relaxation attenuation peak，and the dispersion effect in the rock becomes more apparent with the increase of temperature and frequency. The research results indicate that stress induces micro damage movement and interaction within rocks. The increase in vibration frequency promotes the growth of rock microcracks. The rise of temperature and small activation energy contribute to the initiation and propagation of microcracks. Cyclic stress also generates new fatigue micro damage in the uneven microstructure inside the rock. Although the anelastic micro damage that decreases the rock quality occurs within the elastic range，its cumulative effect will accelerate development under dynamic and high-frequency loads，which is worthy of concern.
[1] YOSHINAKA R，KIKUCHI K. Rock Foundation[C]// Proceedings of the International Workshop on Rock Foundation. Tokyo，Japan：[S. n.]，1995：457–463.
[2] FUJIWARA H，UE S，YASUHARA K. Consolidation of alluvial clay under repeated loading[J]. Soils and Foundations，1985，25(3)：19–30.
[3] HYODO M，YASUHARA K. Analytical procedure for evaluating pore-water pressure and deformation of saturated clay ground subjected to traffic load[C]//Proceeding of the 6th International Conference on Numerical Methods in Geomechanics. Rotterdam，Holland：1988，653–658.
[4] 王常晶，陈云敏. 移动荷载引起的地基应力状态变化及主应力轴旋转[J]. 岩石力学与工程学报，2007，26(8)：1 698–1 704.(WANG Changjing，CHEN Yinmin. Stress state variation and principal stress axes rotation of ground induced by moving loads[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(8)：1 698–1 704.(in Chinese))
[5] 边学成. 高速列车荷载作用下高架桥和地基振动分析[J]. 振动工程学报，2006，19(4)：438–445.(BIAN Xuecheng. Analysis of viaduct-ground vibrations due to high-speed train moving loads[J]. Journal of Vibration Engineering，2006，19(4)：438–445.(in Chinese))
[6] 边学成，陈云敏. 列车荷载作用下分层地基响应特性[J]. 岩石力学与工程学报，2007，26(1)：182–189.(BIAN Xuecheng，CHEN Yunmin. Characteristics of layered ground responses under train moving loads[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(1)：182–189.(in Chinese))
[7] 席道瑛，刘 斌，刘 卫，等. 饱和多孔岩石弛豫衰减对时间和温度的依赖性[J]. 地球物理学报，2000，43(6)：827–834.(XI Daoying，LIU Bin，LIU Wei，et al. The dependence relationship of relaxation attenuation on time and temperature of saturated rocks[J]. Chinese Journal of Geophysics，2000，43(6)：827–834.(in Chinese))
[8] XI D Y，XU S L，DU Y，et al. Wave propagation analysis of porous rocks with thermal activated relaxation mechanism[J]. Journal of Applied Geophysics，2011，73(3)：289–303.
[9] 席道瑛，徐松林，杜 赟. 泵油饱和砂岩黏弹行为的实验研究[J]. 物理学报，2012，61(11)：119102–1–7.(XI Daoying，XU Songlin，DU Yun. Experimental Research of viscoelastic behavior for saturated rocks[J]. ACTA Physica Sinica，2012，61(11)：119102–1–7.(in Chinese))
[10] 蒋 军，陈龙珠. 长期循环荷载作用下黏土的一维沉降[J]. 岩土工程学报，2001，23(3)：366–369.(JIANG Jun，CHEN Longzhu. One-dimensional settlement due to long-term cyclic loading[J]. Chines Journal of Geotechnical Engineering，2001，23(3)：366–369.(in Chinese))
[11] 李树春，许 江，陶云奇，等. 岩石低周疲劳损伤模型与损伤变量表达方法[J]. 岩土力学，2009，30(6)：1 611–1 614.(LI Shuchun，XU Jiang，TAO Yunqi，et al. Low cycle fatigue damage model and damage variable expression of rock[J]. Rock and Soil Mechanics，2009，30(6)：1 611–1 614.(in Chinese))
[12] 杨国香，伍法权，董金玉，等. 地震作用下岩质边坡动力响应特性及变形破坏机制研究[J]. 岩石力学与工程学报，2012，31(4)：696–702.(YANG Guoxinag，WU Faquan，DONG Jinyu，et al. Study of dynamic response characters and failure mechanism of rock slope under earthquake[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(4)：696–702.(in Chinese))
[13] 王志伟，符力耘，韩同城，等. 岩石热弹性理论及其在地球物理中的应用[J]. 地球与行星物理论评，2021，52(6)：623–633.(WANG Zhiwei，FU Liyun，HAN Tongcheng，et al. Review of thermoelastie theory in rocks and its applications[J]. Reviews of Geophysics and Planetary Physics，2021，52(6)：623–633.(in Chinese))
[14] GUO S F，QI S W，ZHAN Z F，et al. Plastic-strain-dependent strength model to simulate the cracking process of brittle rocks with an existing non-persistent joint[J]. Engineering Geology，2017，231：114–125.
[15] QI S W，LAN H X，DEREK M，et al. Factors controlling the difference in brazilian and direct tensile strengths of the Lac du Bonnet granite[J]. Rock Mechanics and Rock Engineering，2020，53(3)：1 005–1 019.
[16] 席道瑛，徐松林，刘永贵，等. 饱和砂岩的滞弹性弛豫衰减特征及微观机制的探索[J]. 物理学报，2012，61(14)：515–522.(XI Daoying XU Songlin，LIU Yonggui，et al. Viscoelastic relaxation attenuation property for saturated sandstones and corresponding investigation on micro-scale mechanism[J]. Acta Physica Sinica，2012，61(14)：515–522.(in Chinese))
[17] 席 军，杜 赟，徐松林，等. 饱和岩石滞弹性弛豫机制的实验研究[J]. 实验力学，2011，26(3)：316–321.(XI Jun，DU Yun，XU Songlin，et al. Experimental research on anelastic mechanism of saturated rocks[J]. Journal of Experimental Mechanics，2011，26(3)：316–321.(in Chinese))
[18] RENARD F. Critical evolution of damage toward system-size failure in crystalline rock[J]. Journal of Geophysical Research，2018：1 231 969–1 231 986.
[19] RENARD F，MCBECK J，KANDULA N，et al. Volumetric and shear processes in crystalline rock approaching faulting[J]. PNAS，2019，116(33)：16 234–16 239.
[20] 樊秀峰，简文彬. 砂岩疲劳特性的超声波速法试验研究[J]. 岩石力学与工程学报，2008，27(3)：557–563.(FAN Xiufeng，JIAN Wenbin. Experimental research on fatigue characteristics of sandstone using ultrasonic wave velocity method[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(3)：557–563.(in Chinese))
[21] ZENER C. Elasticity and anelasticity of metals[M]. Chicage：University of Chicago Press，1948：23–25.
[22] 席道瑛，杜 赟，席 军，等. 饱和砂岩在疲劳载荷作用下的黏弹性性质，岩石力学与工程学报，2011，30(5)：865–870.(XI Daoying，DU Yun，XI Jun，et al. Viscoelastic properties of saturated sandstones under fatigue loading[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(5)：865–870.(in Chinese))
[23] 席道瑛，徐松林，周城光，等. 用非强迫共振法研究饱和岩石的黏弹性响应[J]. 岩石力学与工程学报，2012，31(4)：688–695.(XI Daoying，XU Songlin，ZHOU Chengguang，et al. Study of viscoelastic behavior of staturated rocks by using non-forced resonance method[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(4)：688–695.(in Chinese))
[24] 席道瑛，徐松林. 岩石物理学基础[M]. 合肥：中国科学技术大学出版社，2012：340–342.(XI Daoying，XU Songlin. Foundations of rock physics[M]. Hefei：University of Science and Technology of China Press，2012：340–342.(in Chinese))
[25] XI D Y，LIU X Y，ZHANG C Y. The frequency(or time) -temperature equivalence of relaxation in saturated rocks[J]. Pure and Applied Geophysics，2007，164：2 157–2 173.
[26] 席道瑛，徐松林，席 军，等. 饱和砂岩的黏弹行为的实验研究[J]. 地球物理学报，2011，54(9)：2 302–2 308.(XI Daoying，XU Songlin，XI Jun，et al. Experimental research on viscoelastic behavior for saturated rocks[J]. Chinese Journal of Geophysics，2011，54(9)：2 302–2 308.(in Chinese))
[27] 葛庭燧. 固体内耗理论基础-晶界弛豫与晶界结构[M]. 北京：科学出版社，2000：23–30.(GE Tingsui. Theoretical basis of solid： internal friction grain boundary relaxation and grain boundary structure[M]. Beijing： Science Press，2000：23–30.(in Chinese))
[28] 席 军，宛新林，周城光，等. 饱和砂岩在温度域和频率域的衰减和速度频散[J]. 地震学报，2013，35(6)：914–922.(XI Jun，WAN Xinlin ZHOU Chengguang，et al. Attenuation and dispersion of Saturated rocks in temperature and frequency domains[J]. Acta Seismologica Sinica，2013，35(6)：914–922.(in Chinese))
[29] BATZLE M L，HOFMANN R. Fluids and frequency dependent seismic velocity of rocks[J]. The Leading Edge，2001，20：168–171.
[30] WHITE J E. Biot-Gardner theory of extensional waves in porous rods[J]. Geophys，1986，51：742–745.
[31] BIOT M A. Theory of propagation of elastic waves in a fluid saturated porous solid. I. Low-frequency range[J]. Journal of the Acoustical Society of America，1956，28：168–178.
[32] BIOT M A. Theory of propagation of elastic waves in a fluid saturated porous solid. II. Higher frequency range[J]. Journal of the Acoustical Society of America，1956，28：179–191.
[33] 刘小燕. 二氧化碳深含水层隔离的二相渗流模拟与岩石物理学研究[博士学位论文][D]. 合肥：中国科学技术大学，2005.(LIU Xiaoyan. Study of two-phase flow simulation and rock physics model for carbon dioxide sequestration in deep aquifers[Ph. D Thesis][D]. Hefei：University of Science and Technology of China，2005.(in Chinese))
[34] B. I. 桑多尔. 循环应力与循环应变的基本原理[M]. 俞炯亮，译. 北京：科学出版社，1985：171–182.(SANDOR B I. Fundamentals of cyclic stress and strain[M]. Translated by YU Jiongliang. Beijing：Science Press，1985：171–182.(in Chinese))
[35] 中国大百科全书总编辑委员会. 中国大百科全书[M]. 北京：中国大百科全书出版社，1985：2 118–2 119.(China Encyclopedia Editorial Board. Encyclopedia of China[M]. Beijing：China Encyclopedia Press，1985：2 118–2 119.(in Chinese))
[36] LI Y. New research on the stress field of elastic-plastic small deformation problems[J]. Journal Materials Processing Technology 2003，138：508–512.
2023, Vol. 42 
