Application of aperture dependent model in thermal cracking of rock
LI Mengyi1,2,WU Zhijun1,2,ZHOU Yuan1,2,LIU Quansheng1,2,SHEN Jianqiang3
(1. School of Civil Engineering,Wuhan University,Wuhan,Hubei 430072,China;2. The Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province,Wuhan University,Wuhan,Hubei 430072,China;3. Zhejiang Jiaogongluqiao Construction Co.,Ltd.,Hangzhou,Zhejiang 315101,China)
Abstract:The primary fractures of the rock would hinder heat flux flowing and redistribute temperature field,which in turn affect the thermal stress distribution inside the rock and lead to the cracking of the rock. Therefore,it is of great significance to investigate the mechanism of heat conduction and thermal cracking of multi-fractured rocks under high temperature. In this study,the particle flow code was adopted to simulate the dynamic process of heat transfer-crack inside the rock. Firstly,considering the difference in mineral composition inside the rock,the cluster model was adopted to characterize the meso-structure and composition distribution of the rock,and then the mesoscopic parameters were calibrated. Secondly,to more realistically simulate the influence of internal fractures on heat flux flowing and thermal cracking,the thermodynamic properties of cracks were assumed to be the aperture dependent,and the thermal and meso-mechanical parameters of the fracture were calibrated through the analytical solutions of macroscopic parameters under different fracture aperture conditions. Correspondingly,the aperture dependent models for thermal parameter and meso-mechanical parameter were proposed,respectively. Finally,combined with the random fracture network,the influence of the fracture aperture distribution on the thermal conduction and thermal cracking in multi-fractured rocks were investigated,in which the fracture aperture distribution was controlled by different shape parameters m .The results showed that with the increase of shape parameter m,the time cost for the thermal conduction reaching the steady-state was gradually reduced while the rate of thermal crack initiation increased. The feasibility of the proposed aperture-dependent model in simulating the thermal conduction and thermal cracking in multi-fractured rocks were also verified.
[1] ZHOU X P,YANG H Q. Dynamic damage localization in crack-weakened rock mass:Strain energy density factor approach[J]. Theoretical and Applied Fracture Mechanics,2018,97:289–302.
[2] VIETE DR P G R,CHEN B J,PERERA M S A. Transformation plasticity and the effect of temperature on the mechanical behaviour of Hawkesbury sandstone at atmospheric pressure[J].. Engineering Geology,2012,151:120–127.
[3] CHEN S,YANG C,WANG G. Evolution of thermal damage and permeability of Beishan granite[J]. Applied Thermal Engineering,2017,110:1 533–1 542.
[4] WU Z,MA L,FAN L. Investigation of the characteristics of rock fracture process zone using coupled FEM/DEM method[J]. Engineering Fracture Mechanics,2018,200:355–374.
[5] LEONEL E D,VENTURINI W S,CHATEAUNEUF A. A BEM model applied to failure analysis of multi-fractured structures[J]. Engineering Failure Analysis,2011,18(6):1 538–1 549.
[6] YVONNET J,HE Q C,ZHU Q Z,et al. A general and efficient computational procedure for modelling the Kapitza thermal resistance based on XFEM[J]. Computational Materials Science,2011,50(4):1 220–1 224.
[7] GAO X W,ZHENG B J,YANG K,et al. Radial integration BEM for dynamic coupled thermoelastic analysis under thermal shock loading[J]. Computers and Structures,2015,158:140–147.
[8] TANG S B,TANG C A,LIANG Z Z,et al. Influence of heterogeneity on strength and failure characterization of cement-based composite subjected to uniform thermal loading[J]. Construction and Building Materials,2011,25(8):3 382–3 392.
[9] WU Z,ZHOU Y,FAN L. A fracture aperture dependent thermal-cohesive coupled model for modelling thermal conduction in fractured rock mass[J]. Computers and Geotechnics,2019,114:103–108.
[10] HE J,LIU Q,WU Z,et al. Geothermal-related thermo-elastic fracture analysis by numerical manifold method[J]. Energies,2018,11(6): 1 380.
[11] JING L. A review of techniques,advances and outstanding issues in numerical modelling for rock mechanics and rock engineering[J]. International Journal of Rock Mechanics and Mining Sciences,2003,40(3):283–353.
[12] WANG Y T,ZHOU X P. Peridynamic simulation of thermal failure behaviors in rocks subjected to heating from boreholes[J]. International Journal of Rock Mechanics and Mining Sciences,2019,117:31–48.
[13] WANG X,OUYANG J,SU J,et al. Investigating the role of oriented nucleus in polymer shish-kebab crystal growth via phase-field method[J]. Journal of Chemical Physics,2014,140(11):114102.
[14] ZHANG X P,WONG L N Y. Loading rate effects on cracking behavior of flaw-contained specimens under uniaxial compression[J]. International Journal of Fracture,2013,180(1):93–110.
[15] ZHANG X P,ZHANG Q,WU S. Acoustic emission characteristics of the rock-like material containing a single flaw under different compressive loading rates[J]. Computers and Geotechnics,2017,83:83–97.
[16] ZHAO Z. Thermal influence on mechanical properties of granite:a microcracking perspective[J]. Rock Mechanics and Rock Engineering,2015,49(3):747–762.
[17] YANG S Q,TIAN W L,RANJITH P G. Failure mechanical behavior of australian strathbogie granite at high temperatures: insights from particle flow modeling[J]. Energies,2017,10(6):124–137.
[18] 傅宇方,梁正召,唐春安. 岩石介质细观非均匀性对宏观破裂过程的影响[J]. 岩土工程学报,2000,22(6):705–710.(FU Yufang,LIANG Zhengzhao,TANG Chun'an. Numerical simulation on influence of mesoscopic heterogeneity on macroscopic behavior of rock failure[J]. Chinese Journal of Geotechnical Engineering,2000,22(6):705–710.(in Chinese))
[19] 周小平,张永兴,朱可善. 中低围压下细观非均匀性岩石本构关系研究[J]. 岩土工程学报,2003,25(5):606–610.(ZHOU Xiaoping,ZHANG Yongxing,ZHU Keshan. Study on the complete stress-strain relation for mesoscopic heterogenous rock under triaxial compression with moderate or low lateral compressive stress[J]. Chinese Journal of Geotechnical Engineering,2003,25(5):606–610.(in Chinese))
[20] 冯增朝,赵阳升. 岩石非均质性与冲击倾向的相关规律研究[J]. 岩石力学与工程学报,2003,22(11):1 863–1 865.(FENG Zengchao,ZHAO Yangsheng. Correlativity of rock inhomogeneity and rock bursy trend[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(11):1 863–1 865.(in Chinese))
[21] 周 健,池 永,池毓蔚,等. 颗粒流方法及PFC2D程序[J]. 岩土力学,2000,21(3):271–274.(ZHOU Jian,CHI Yong,CHI Yuwei,et al. The method of particle flow and PFC2D Code[J]. Rock and Soil Mechanics,2000,21(3):271–274.(in Chinese))
[22] WANNE T S,YOUNG R P. Bonded-particle modeling of thermally fractured granite[J]. International Journal of Rock Mechanics and Mining Sciences,2008,45(5):789–799.
[23] 王祥虎. 热力耦合下的煤田火区裂隙演化模拟研究[硕士学位论文][D]. 北京:中国矿业大学,2015.(WANG Xianghu. Study on the fracture evolution of coal-rock mass of coalfield fire with thermo-mechanical coupling effects[M. S. Thesis][D]. Beijing:China University of Mining and Technology,2015.(in Chinese))
[24] 阴红宇. 热–力耦合作用下硬岩力学行为及岩爆发生机制研究[硕士学位论文][D]. 成都:成都理工大学,2013.(YIN Hongyu. Research on the effect of thermal-mechanical coupling of hard rock mechanical behavior and the mechanism of rockburst[M. S. Thesis][D]. Chengdu Chengdu University of Technology,2013.(in Chinese))
[25] SHAO S,RANJITH P G,WASANTHA P L P,et al. Experimental and numerical studies on the mechanical behaviour of Australian Strathbogie granite at high temperatures:An application to geothermal energy[J]. Geothermics,2015,54:96–108.
[26] KUMARI W G P,RANJITH P G,PERERA M S A,et al. Mechanical behaviour of Australian Strathbogie granite under in-situ stress and temperature conditions:An application to geothermal energy extraction[J]. Geothermics,2017,65:44–59.
[27] CARPENTER M A,SALJE E K H,GRAEME-BARBER A. Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals[J]. European Journal of Mineralogy,1998,10(4):621–691.
[28] NASSERI M H B,SCHUBNEL A,YOUNG R P. Coupled evolutions of fracture toughness and elastic wave velocities at high crack density in thermally treated Westerly granite[J]. International Journal of Rock Mechanics and Mining Sciences,2007,44(4):601–616.
[29] YANG S Q,TIAN W L,HUANG Y H. Failure mechanical behavior of pre-holed granite specimens after elevated temperature treatment by particle flow code[J]. Geothermics,2018,72:124–137.
[30] EL-BORGI S,ERDOGAN F,HIDRI L. A partially insulated embedded crack in an infinite functionally graded medium under thermo-mechanical loading[J]. International Journal of Engineering Science,2004,42(3–4):371–393.
[31] 张玉军. 裂隙岩体的热–水–应力耦合模型及二维有限元分析[J]. 岩土工程学报,2006,28(3):288–294.(ZHANG Yujun. Model of thermo-hydro-mechanical coupling for cracked rock mass and its 2D FEM analysis[J]. Chinese Journal of Geotechnical Engineering,2006,28(3):288–294.(in Chinese))
[32] HU W,KWOK C Y,DUAN K,et al. Parametric study of the smooth-joint contact model on the mechanical behavior of jointed rock[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2018,42(2):358–376.
[33] 胡万瑞. 基于光滑节理模型的节理岩体力学特性研究[硕士学位论文][D]. 武汉:武汉大学,2017.(HU Wanrui. Research on mechnical behavior of jointed rock mass based on smooth-joint contact model[M. S. Thesis][D]. Wuhan:Wuhan University,2017.(in Chinese))
[34] 刘良军,曹 智,王俊杰. 基于线性平行黏结接触模型的岩石细观参数选取方法研究[J]. 水利与建筑工程学报,2017,15(5):123–128.(LIU Liangjun,CAO Zhi,WANG Junjie. Selection methods of rock micro-parameters based on the linear parallel bond contact model[J]. Journal of Water Resources amd Architectural Engineering,2017,15(5):123–128.(in Chinese))
[35] 郭奇峰,武 旭,蔡美峰,等. 预制裂隙花岗岩的强度特征与破坏模式试验[J]. 工程科学学报,2019,41(1):43–52.(GUO Qifeng,WU Xu,CAI MEIfeng,et al. Experiment on the strength characteristics and failure modes of granite with pre-existing cracks[J]. Chinese Journal of Engineering,2019,41(1):43–52.(in Chinese))