Strain rate response of damage accumulation of marble under fatigue loading
CAI Yan-yan1, TANG Xin1, LIN Li-hua2, CHEN Hua-long2, GAO Hai-dong3, LI Gang3, YU Jin1
1. Fujian Research Center for Tunneling and Urban Underground Space Engineering, Huaqiao University, Xiamen 361021, China; 2. Xiamen Road & Bridge Engineering Investment and Development Co., Ltd., Xiamen 361026, China;; 3. China Railway 18th Bureau Group Co., Ltd., Tianjin 300222, China
Abstract：The cyclic loading experiments, in which the constant amplitude cyclic loading and unloading are imposed at different stress levels, are carried out on marble samples under various confining pressures to study the effects of fatigue loading conditions on mechanical properties of rock. The results show that: (1) The rock samples are mostly like to be destroyed under high stress ratio or low confining pressure. The elastic modulus of the damaged rock samples decreases rapidly with the increase of the number of fatigue cycles, while the elastic modulus of the undamaged samples fluctuates slightly with the increase of the number of cycles before the final stabilization. (2) The axial strain rate evolution of the rock samples shows a "U" type trend with the strain development during loading. And the volume strain rate shows an inverted "L" type trend with the volume change. Both strain rates increase remarkably when the samples approach failure. During unloading, the axial strain rate evolution shows an inverted "S" shape, and the volume strain rate shows a "U" type trend. (3) At the beginning and ending stages, the strain rate exhibits positive correlation with the residual stress. The initial strain rate reflects the accumulated damage of rock samples under the previous fatigue effect. (4) After the normalization of axial strain rate at the initial stage, there is an obvious linear relationship between the axial strain rate and the damage factor, and the coefficient K decreases with the increase of confining pressure or the decrease of stress ratio. The evolution of the cyclic normalized axial strain rate and damage factor of the undamaged rock samples retracts as a hook type.
[1] 张传庆, 张洋, 周辉, 等. 深埋软岩隧洞围岩变形控制方法[J]. 现代隧道技术, 2018, 55(2): 28-35. (ZHANG Chuan-qing, ZHANG Yang, ZHOU Hui, et al.Surrounding rock deformation control for deep-buried soft-rock tunnels[J]. Modern Tunnelling Technology, 2018, 55(2): 28-35. (in Chinese)) [2] LI M, MAO X B, YU Y L, et al.Stress and deformation analysis on deep surrounding rock at different time stages and its application[J]. International Journal of Mining Science and Technology, 2012, 22: 301-306. [3] 曹海静, 刘志强, 吴剑, 等. 铁路黄土隧道施工变形规律及预留变形量研究[J]. 铁道标准设计, 2018, 62(3): 85-88. (CAO Hai-jing, LIU Zhi-qiang, WU Jian, et al.Study on deformation law and preset deformation of railway tunnels in loess[J]. Railway Standard Design, 2018, 62(3): 85-88. (in Chinese)) [4] 张民庆, 黄鸿健, 吴川. 铁路隧道施工围岩变形安全等级的研究与应用[J].铁路工程学报, 2014(11): 87-93. (ZHANG Min-qing, HUANG Hong-jian, WU Chuan.Study and application of safety grade of surrounding rock deformation in construction of railing tunnel[J]. Journal of Railway Engineering Society, 2014(11): 87-93. (in Chinese)) [5] 王学滨. 煤岩两体模型变形破坏数值模拟[J]. 岩土力学, 2006, 27(7): 1066-1070. (WANG Xue-bin.Numerical simulation of deformation and failure for two bodies model composed of rock and coal[J]. Rock and Soil Mechanics, 2006, 27(7): 1066-1070. (in Chinese)) [6] ROSEA N D, HUNGRB O.Forecasting potential rock slope failure in open pit minesusing the inverse-velocity method[J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44: 308-320. [7] 王延平, 许强, 郑光, 等. 速度倒数法滑坡预警模型流变试验研[J]. 岩土力学, 2015, 36(6): 1606-1614. (WANG Yan-ping, XU Qiang, ZHENG Guang, et al.A rheology experimental investigation on early warning model for landslide based on inverse-velocity method[J]. Rock and Soil Mechanics, 2015, 36(6): 1606-1614. (in Chinese)) [8] 公路隧道施工技术规范: JTGF60—2009[S]. 2009. (Technical Specications for Constraction of Highway Tunnel: JTGF60—2009[S]. 2009. (in Chinese)) [9] 铁路隧道设计规范: TB10003—2016[S]. 2016. (Code for Design of Railway Tunnel: TB10003—2016[S]. 2016. (in Chinese)) [10] YAMAMOTO Kiyohiko.A theory of rock core-based methods for in-situ stress measurement[J]. Earth Planets Space, 2009, 61: 1143-1161. [11] 谢强, 邱鹏, 余贤斌, 等. 利用声发射法和变形率变化法联合测定地应力[J]. 煤炭学报, 2010, 35(4): 559-564. (ZHANG Qiang, QIU Peng, YU Xian-bin, et al.Initial stress measurements with AE and DRA combined technique[J]. Journal of Coal Science, 2010, 35(4): 559-564. (in Chinese)) [12] 王海军, 任旭华, 陶冉冉, 等. 基于摩擦滑动的低应力区岩石变形记忆性机理[J]. 中南大学学报, 2012, 43(11): 4464-4472. (WANG Hai-jun, REN Xu-hua, TAO Ran-ran, et al.Mechanism of rock deformation memory effect in low stress region based on frictional sliding[J]. Journal of Central South University, 2012, 43(11): 4464-4472. (in Chinese)) [13] HSIEH Ariel, DIGHT Phil. The desirable and undesirable effects on stress reconstruction using the deformation rate analysis (DRA)[C]// 7th International Symposiurn of In-situ Rock Stress (RS2016), 2016, Tampere: 212-224. [14] 葛伟凤, 张飞, 陈勉, 等. 盐膏岩DRA-Kaiser地应力测试方法测试[J]. 岩石力学与工程学报, 2015, 34(增刊1): 3138-3142. (GE Wei-feng, ZHANG Fei, CHEN Mian, et al.Research on geostress measurement using DRA-Kaiser method in salt gypsum formation[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(S1): 3138-3142. (in Chinese)) [15] 葛修润, 蒋宇, 卢允德, 等. 周期荷载作用下岩石疲劳变形特性试验研究[J]. 岩石力学与工程学报, 2003, 22(10): 1581-1585. (GE Xiu-run, JIANG Yu, LU Yun-de, et al.Testing study on fatigue deformation law of rock under cyclic loading[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(10): 1581-1585. (in Chinese)) [16] SHAHNAZARI H, DEHNAVI Y, ALAVI A H.Numerical modeling of stress-strain behavior of sand under cyclic loading[J]. Engineering Geology, 2010, 116(1/2): 53-72. [17] LIU E L, HE S M.Effects of cyclic dynamic loading on the mechanical properties of intact rock samples under confining pressure conditions[J]. Engineering Geology, 2012, 125: 81-91. [18] LIU E L, HUANG R Q, HE S M .Effects of frequency on the dynamic properties of intact rock samples subjected to cyclic loading under confining pressure conditions[J]. Rock Mechanics and Rock Engineering, 2012, 45(1): 89-102. [19] 孙红伟. 循环载荷作用下岩石与孔隙水耦合作用机理研究[D]. 重庆: 重庆大学, 2011. (SUN Hong-wei.Study on Coupling Mechanism of Rock and Pore Water under Cyclic Loading[D]. Chongqing: The Chongqing University, 2011. (in Chinese)) [20] 席道瑛, 刘小燕, 张程远. 应力控制疲劳载荷作用下循环硬化的应变响应[J]. 岩石力学与工程学报, 2003, 22(11): 1807-1807. (XI Dao-ying, LIU Xiao-yan, ZHANG Cheng-yuan.Strain response of cyclic hardening under fatigue loading on saturated rock[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(11): 1807-1807. (in Chinese)) [21] 蔡燕燕, 孙启超, 俞缙, 等. 蠕变作用后大理岩强度与变形特性试验研究[J]. 岩石力学与工程学报, 2017, 36(11): 2767-2777. (CAI Yan-yan, SUN Qi-chao, YU Jin, et al.Experimental study on strength and deformation characteristics of marble after creep[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(11): 2767-2777. (in Chinese)) [22] 张世殊, 刘恩龙, 张建海. 砂岩在低频循环荷载作用下的疲劳和损伤特性试验研究[J]. 岩石力学与工程学报, 2014, 33(1): 3212-3218. (ZHANG Shi-shu, LIU En-long, ZHANG Jian-hai.Experimental study of fatigue damage properties of sandstone samples under cyclic loading with low frequencies[J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(1): 3212-3218. (in Chinese))
