冻融荷载下节理岩体的复合损伤模型
|
摘要
针对工程实际中的冻融受荷岩体,以岩石初始损伤状态为参考状态,将冻融与荷载作用引起的损伤视为细观损伤,节理引起的损伤视为宏观损伤,根据Lemaitre应变等效性假设,推导建立考虑宏细观缺陷的节理岩体复合损伤模型.应用该模型分析贯通率和冻融次数分别对岩体力学性质劣化的影响,结果表明:在贯通率一定时,损伤演化曲线随冻融次数的增加而增加,试验与理论峰值强度(或弹性模量)曲线随冻融循环次数增加而降低;在冻融次数一定时,损伤演化曲线与贯通率呈正相关关系,试验与理论峰值强度(或弹性模量)与贯通率呈负相关关系.说明贯通率与冻融次数对岩体的劣化产生一定影响,且饱和试验组受冻融效应较天然试验组力学性能劣化严重.将所建模型计算结果与试验值进行比较,理论曲线与试验曲线吻合良好,验证了所建模型的合理性与有效性.
For the frozen thawing rock mass in the engineering practice,taking the initial damage state of rock as the baseline state,the damage caused by freezing thawing and loading is considered as meso damage,and the damage caused by joints is regarded as macroscopic damage. According to the hypothesis of Lemaitre strain equivalence,a composite damage model of jointed rock mass considering macro and micro defects was derived. The effect of the penetration rate and the number of freezing and thawing on the deterioration of mechanical properties of rock mass was analyzed by this model. The results show that when the penetration rate was constant,the damage evolution curve increased with the increase of freeze-thaw times,and the experimental and theoretical peak strength(or modulus of elasticity) curves decreased with the increase of freeze-thaw times. When the freeze-thaw times were constant,the damage evolution curve was positively correlated with the penetration rate,and the experimental and theoretical peak strength( or modulus of elasticity) were negatively correlated with the penetration rate. It indicates that the penetration rate and the freezing thawing times have a certain effect on the deterioration of the rock mass,and the freezing thawing effect of the saturated test group is worse than the natural test group. The calculated results of the model were compared with the experimental values,and the theoretical curves are in good agreement with the experimental curves,which verified the rationality and validity of the model.
For the frozen thawing rock mass in the engineering practice,taking the initial damage state of rock as the baseline state,the damage caused by freezing thawing and loading is considered as meso damage,and the damage caused by joints is regarded as macroscopic damage. According to the hypothesis of Lemaitre strain equivalence,a composite damage model of jointed rock mass considering macro and micro defects was derived. The effect of the penetration rate and the number of freezing and thawing on the deterioration of mechanical properties of rock mass was analyzed by this model. The results show that when the penetration rate was constant,the damage evolution curve increased with the increase of freeze-thaw times,and the experimental and theoretical peak strength(or modulus of elasticity) curves decreased with the increase of freeze-thaw times. When the freeze-thaw times were constant,the damage evolution curve was positively correlated with the penetration rate,and the experimental and theoretical peak strength( or modulus of elasticity) were negatively correlated with the penetration rate. It indicates that the penetration rate and the freezing thawing times have a certain effect on the deterioration of the rock mass,and the freezing thawing effect of the saturated test group is worse than the natural test group. The calculated results of the model were compared with the experimental values,and the theoretical curves are in good agreement with the experimental curves,which verified the rationality and validity of the model.
引文
[1]刘泉声,黄诗冰,康永水,等.裂隙岩体冻融损伤研究进展与思考[J].岩石力学与工程学报,2015,34(3):452LIU Quansheng,HUANG Shibing,KANG Yongshui,et al. Advance and review on freezing-thawing damage of fractured rock[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(3):452.DOI:10. 13722/j. cnki. jrme. 2015. 03. 003
[2]LAI Y,XU X,DONG Y,et al. Present situation and prospect of mechanical research on frozen soils in China[J]. Cold Regions Science and Technology,2013,87(1):6. DOI:10. 1016/j.coldregions. 2012. 12. 001
[3]申艳军,杨更社,荣腾龙,等.冻融循环作用下单裂隙类砂岩局部化损伤效应及端部断裂特性分析[J].岩石力学与工程学报,2017,36(3):562SHEN Yanjun,YANG Gengshe,RONG Tenglong,et al. Localized damage effects of quasi-sandstone with single fracture and fracture behaviors of joint end under cyclic freezing and thawing[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(3):562.DOI:10. 13722/j. cnki. jrme. 2016. 0122
[4]PARK J,HYUN C U,PARK H D. Changes in microstructure and physical properties of rocks caused by artificial freeze-thaw action[J]. Bulletin of Engineering Geology and the Environment,2015,74(2):555. DOI:10. 1007/s10064-014-0630-8
[5]CHEN T C,YEUNG M R,MORIC N. Effect of water saturation on deterioration of welded tuff due to freeze-thaw action[J]. Cold Regions Science and Technology,2004,38(1):127. DOI:10.1016/j. coldregions. 2003. 10. 001
[6]LUO X,JIANG N,ZUO C,et al. Damage characteristics of altered and unaltered diabases subjected to extremely cold freeze-thaw cycles[J]. Rock Mechanics&Rock Engineering,2014,47(6):1997.DOI:10. 1007/s00603-013-0516-2
[7] YAMABE T, NEAUPANE K M. Determination of some thermomechanical properties of Sirahama sandstone under subzero temperature condition[J]. International Journal of Rock Mechanics and Mining Sciences,2001,38(7):1209. DOI:10. 1016/S1365-1609(1)00067-3
[8]KANG Y,LIU Q,HUANG S. A fully coupled thermo-hydromechanical model for rock mass under freezing/thawing condition[J]. Cold Regions Science&Technology,2013,95(11):19.DOI:10. 1016/j. coldregions. 2013. 08. 002
[9]KHANLARI G,SAHAMIEH R Z,ABDILOR Y. The effect of freeze–thaw cycles on physical and mechanical properties of upper red formation sandstones,central part of Iran[J]. Arabian Journal of Geosciences,2014:1. DOI:10. 1007/s12517-014-1653-y
[10]QIN L,ZHAI C,LIU S,et al. Changes in the petrophysical properties of coal subjected to liquid nitrogen freeze-thaw-A nuclear magnetic resonance investigation[J]. Fuel,2017,194:102.DOI:10. 1016/j. fuel. 2017. 01. 005
[11]MATSUOKA N. Mechanics of rock breakdown by frost action:An experimental approach[J]. Cold Regions Science and Technology,1990,17(3):253. DOI:10. 1016/S0165-232X(05)80005-9
[12]NICHOLSON D T,NICHOLSON F H. Physical deterioration of sedimentary rocks subjected to experimental freeze-thaw weathering[J]. Earth Surface Processes and Landforms,2015,25(12):1295
[13]PRICK A. Dilatometrical behaviour of porous calcareous rock samples subjected to freeze-thaw cycles[J]. Catena,1995,25(1-4):7. DOI:10. 1016/0341-8162(94)00038-G
[14]RUIZ V G,REY R A,CELORIO C,et al. Characterization by computed X-ray tomography of the evolution of the pore structure of a dolomite rock during freeze-thaw cyclic tests[J]. Physics and Chemistry of the Earth,1999,24(7):633. DOI:10. 1016/S1464-1895(99)00092-7
[15]BAYRAM F. Predicting mechanical strength loss of natural stones after freeze-thaw in cold regions[J]. Cold Regions Science and Technology, 2012, 83/84(12):98. DOI:10. 1016/j.coldregions. 2012. 07. 003
[16]HUANG S,LIU Q,LIU Y,et al. Frost heaving and frost cracking of elliptical cavities(fractures)in low-permeability rock[J].Engineering Geology,2018:1. DOI:10. 1016/j. enggeo. 2017. 12.024
[17]徐光苗,刘泉声.岩石冻融破坏机理分析及冻融力学试验研究[J].岩石力学与工程学报,2005,24(17):3076XU Guangmiao,LIU Quansheng. Analysis of mechanism of rock failure due to freezing-thawing cycling and mechanical testing study on frozenthawed rocks[J]. Chinese Journal of Rock Mechanics and Engineering,2005,24(17):3076. DOI:10. 3321/j. issn:1000-6915. 2005. 17. 012
[18]张继周,缪林昌,杨振峰.冻融条件下岩石损伤劣化机制和力学特性研究[J].岩石力学与工程学报,2008,27(8):1688ZHANG Jizhou,MIAO Linchang,YANG Zhenfeng. Research on rock degradation and deterioration mechanisms and mechanical characteristics under cyclic freezing-thawing[J]. Chinese Journal of Rock Mechanics and Engineering,2008,27(8):1688. DOI:10.3321/j. issn:1000-6915. 2008. 08. 020
[19]刘慧,杨更社,叶万军,等.基于CT图像的冻结岩石冰含量及损伤特性分析[J].地下空间与工程学报,2016,12(4):912LIU Hui,YANG Gengshe,YE Wanjun,et al. Analysis of ice content and damage characteristics of frozen rock based on pseudocolor enhanced CT image[J]. Chinese Journal of Underground Space and Engineering,2016,12(4):912
[20]葛修润,任建喜,蒲毅彬,等.岩石细观损伤扩展规律的CT实时试验[J].中国科学,2000,30(2):104GE Xiurun,REN Jianxi,PU Yibin. et al. Primary study of CT real-time testing of fatigue meso-damage propagation law of rock[J]. Chinese Journal of Geotechnical Engineering,2000,30(2):104. DOI:10. 3321/j. issn:1006-9275. 2000. 02. 002
[21]赖远明,吴紫汪,朱元林,等.大坂山隧道围岩冻融损伤的CT分析[J].冰川冻土,2000,22(3):206LAI Yuanming,WU Ziwang,ZHU Yuanlin,et al. CT analysis of frost damage of the surrounding rocks of a tunnel in the Daban Mountain[J]. Journal of Glaciology and Geocryology,2000,22(3):206. DOI:10. 3969/j. issn. 1000-0240. 2000. 03. 003
[22]张慧梅,杨更社.冻融与荷载耦合作用下岩石损伤模型的研究[J].岩石力学与工程学报,2010,29(3):471ZHANG Huimei,YANG Gengshe. Research on damage model of rock under coupling action of freeze-thaw and load[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(3):471
[23]袁小清,刘红岩,刘京平.冻融荷载耦合作用下节理岩体损伤本构模型[J].岩石力学与工程学报,2015,34(8):1602YUAN Xiaoqing,LIU Hongyan,LIU Jingping. A damaging model of jointed rock under coupled action of freezing and thawing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1602. DOI:10. 13722/j. cnki. jrme. 2014. 1342
[24]刘红岩,刘冶,邢闯锋,等.循环冻融条件下节理岩体损伤破坏试验研究[J].岩土力学,2014,35(6):1547LIU Hongyan,LIU Ye,XING Chuangfeng,et al. Test study of damage failure of jointed rock mass under freezing-thawing cycles[J]. Rock and Soil Mechanics,2014,35(6):1547
[25]路亚妮,李新平,肖家双.单裂隙岩体冻融力学特性试验分析[J].地下空间与工程学报,2014,10(3):594LU Yani,LI Xinping,XIAO Jiashuang. Experimental analysis on mechanical characteristic of single cracked rock mass under freezethaw condition[J]. Chinese Journal of Underground Space and Engineering,2014,10(3):594
[26]陈有亮,代明星,刘明亮,等.含初始损伤岩石的冻融损伤试验研究[J].力学季刊,2013,34(1):74CHEN Youliang, DAI Mingxing, LIU Mingliang, et al.Experimental investigation on freezing damage characteristics of granite with initial damage[J]. Chinese Quarterly of Mechanics,2013,34(1):74. DOI:10. 3969/j. issn. 0254-0053. 2013. 01. 010
[27]刘松明,陈有亮,杜曦,等.酸侵蚀区白砂岩冻融损伤的影响因素研究[J].水资源与水工程学报,2014,25(5):127LIU Songming,CHEN Youliang,DU Xi,et al. Study on influences factor of freezing-thawing damage of white sandstone in acid erosion area[J]. Journal of Water Resources and Water Engineering,2014,25(5):127. DOI:10. 11705/j. issn. 1672-643X. 2014.05. 028
[28]李新平,路亚妮,王仰君.冻融荷载耦合作用下单裂隙岩体损伤模型研究[J].岩石力学与工程学报,2013,32(11):2307LI Xinping,LU Yani,WANG Yangjun. Research on damage model of single jointed rock masses under coupling action of freeze-thaw and loading[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(11):2307
[29]曹文贵,方祖烈,唐学军.岩石损伤软化统计本构模型之研究[J].岩石力学与工程学报,1998,17(6):628CAO Wengui,FANG Zulie,TANG Xuejun. A study of statistical constitutive model for soft and damage rock[J]. Chinese Journal of Rock Mechanics and Engineering,1998,17(6):628
[30]KRAJCINOVIC D,SILVA M A G. Statistical aspects of the continuous damage theory[J]. International Journal of Solids and Structures,1982,18(7):551. DOI:10. 1016/0020-7683(82)90039-7
[31]张慧梅,雷利娜,杨更社.温度与荷载作用下岩石损伤模型[J].岩石力学与工程学报,2014(s2):3391ZHANG Huimei,LEI Lina,YANG Gengshe. Damage model of rock under temperature and load[J]. Chinese Journal of Rock Mechanics and Engineering,2014(s2):3391. DOI:10. 13722/j.cnki. jrme. 2014. s2. 001
[32]张全胜,杨更社,任建喜.岩石损伤变量及本构方程的新探讨[J].岩石力学与工程学报,2003,22(1):30ZHANG Quansheng,YANG Gengshe,REN Jianxi. New study of damage variable and constitutive equation of rock[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(1):30.DOI:10. 3321/j. issn:1000-6915. 2003. 01. 005
[33]杨更社,谢定义.岩体宏观细观损伤的耦合计算分析[C]//第六次全国岩石力学与工程学术大会论文集.武汉:[s. n.],2000:327YANG Gengshe,XIE Dingyi. Coupling analysis on the macrodamage and meso-damage of rock masses[C]//Symposium on the Sixth National Rock Mechanics and Engineering Academic Conference. Wuhan:[s. n.],2000:327
[34]张力民,吕淑然,刘红岩.综合考虑宏细观缺陷的岩体动态损伤本构模型[J].爆炸与冲击,2015,35(3):428ZHANG Limin,LV Shuran,LIU Hongyan. A dynamic damage constitutive model of rock mass by comprehensively considering macroscopic and mesoscopic flaws[J]. Explosion and Shock Waves,2015,35(3):428
[35]王乐华,陈招军,金晶,等.节理岩体冻融力学特性试验研究[J].水利水电技术,2016(5):149WANG Lehua,CHEN Zhaojun,JIN Jing,et al. Experimental study on mechanic characteristics of jointed rock under freeze-thaw condition[J]. Water Resources and Hydropower Engineering,2016(5):149. DOI:10. 13928/j. cnki. wrahe. 2016. 05. 035
[2]LAI Y,XU X,DONG Y,et al. Present situation and prospect of mechanical research on frozen soils in China[J]. Cold Regions Science and Technology,2013,87(1):6. DOI:10. 1016/j.coldregions. 2012. 12. 001
[3]申艳军,杨更社,荣腾龙,等.冻融循环作用下单裂隙类砂岩局部化损伤效应及端部断裂特性分析[J].岩石力学与工程学报,2017,36(3):562SHEN Yanjun,YANG Gengshe,RONG Tenglong,et al. Localized damage effects of quasi-sandstone with single fracture and fracture behaviors of joint end under cyclic freezing and thawing[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(3):562.DOI:10. 13722/j. cnki. jrme. 2016. 0122
[4]PARK J,HYUN C U,PARK H D. Changes in microstructure and physical properties of rocks caused by artificial freeze-thaw action[J]. Bulletin of Engineering Geology and the Environment,2015,74(2):555. DOI:10. 1007/s10064-014-0630-8
[5]CHEN T C,YEUNG M R,MORIC N. Effect of water saturation on deterioration of welded tuff due to freeze-thaw action[J]. Cold Regions Science and Technology,2004,38(1):127. DOI:10.1016/j. coldregions. 2003. 10. 001
[6]LUO X,JIANG N,ZUO C,et al. Damage characteristics of altered and unaltered diabases subjected to extremely cold freeze-thaw cycles[J]. Rock Mechanics&Rock Engineering,2014,47(6):1997.DOI:10. 1007/s00603-013-0516-2
[7] YAMABE T, NEAUPANE K M. Determination of some thermomechanical properties of Sirahama sandstone under subzero temperature condition[J]. International Journal of Rock Mechanics and Mining Sciences,2001,38(7):1209. DOI:10. 1016/S1365-1609(1)00067-3
[8]KANG Y,LIU Q,HUANG S. A fully coupled thermo-hydromechanical model for rock mass under freezing/thawing condition[J]. Cold Regions Science&Technology,2013,95(11):19.DOI:10. 1016/j. coldregions. 2013. 08. 002
[9]KHANLARI G,SAHAMIEH R Z,ABDILOR Y. The effect of freeze–thaw cycles on physical and mechanical properties of upper red formation sandstones,central part of Iran[J]. Arabian Journal of Geosciences,2014:1. DOI:10. 1007/s12517-014-1653-y
[10]QIN L,ZHAI C,LIU S,et al. Changes in the petrophysical properties of coal subjected to liquid nitrogen freeze-thaw-A nuclear magnetic resonance investigation[J]. Fuel,2017,194:102.DOI:10. 1016/j. fuel. 2017. 01. 005
[11]MATSUOKA N. Mechanics of rock breakdown by frost action:An experimental approach[J]. Cold Regions Science and Technology,1990,17(3):253. DOI:10. 1016/S0165-232X(05)80005-9
[12]NICHOLSON D T,NICHOLSON F H. Physical deterioration of sedimentary rocks subjected to experimental freeze-thaw weathering[J]. Earth Surface Processes and Landforms,2015,25(12):1295
[13]PRICK A. Dilatometrical behaviour of porous calcareous rock samples subjected to freeze-thaw cycles[J]. Catena,1995,25(1-4):7. DOI:10. 1016/0341-8162(94)00038-G
[14]RUIZ V G,REY R A,CELORIO C,et al. Characterization by computed X-ray tomography of the evolution of the pore structure of a dolomite rock during freeze-thaw cyclic tests[J]. Physics and Chemistry of the Earth,1999,24(7):633. DOI:10. 1016/S1464-1895(99)00092-7
[15]BAYRAM F. Predicting mechanical strength loss of natural stones after freeze-thaw in cold regions[J]. Cold Regions Science and Technology, 2012, 83/84(12):98. DOI:10. 1016/j.coldregions. 2012. 07. 003
[16]HUANG S,LIU Q,LIU Y,et al. Frost heaving and frost cracking of elliptical cavities(fractures)in low-permeability rock[J].Engineering Geology,2018:1. DOI:10. 1016/j. enggeo. 2017. 12.024
[17]徐光苗,刘泉声.岩石冻融破坏机理分析及冻融力学试验研究[J].岩石力学与工程学报,2005,24(17):3076XU Guangmiao,LIU Quansheng. Analysis of mechanism of rock failure due to freezing-thawing cycling and mechanical testing study on frozenthawed rocks[J]. Chinese Journal of Rock Mechanics and Engineering,2005,24(17):3076. DOI:10. 3321/j. issn:1000-6915. 2005. 17. 012
[18]张继周,缪林昌,杨振峰.冻融条件下岩石损伤劣化机制和力学特性研究[J].岩石力学与工程学报,2008,27(8):1688ZHANG Jizhou,MIAO Linchang,YANG Zhenfeng. Research on rock degradation and deterioration mechanisms and mechanical characteristics under cyclic freezing-thawing[J]. Chinese Journal of Rock Mechanics and Engineering,2008,27(8):1688. DOI:10.3321/j. issn:1000-6915. 2008. 08. 020
[19]刘慧,杨更社,叶万军,等.基于CT图像的冻结岩石冰含量及损伤特性分析[J].地下空间与工程学报,2016,12(4):912LIU Hui,YANG Gengshe,YE Wanjun,et al. Analysis of ice content and damage characteristics of frozen rock based on pseudocolor enhanced CT image[J]. Chinese Journal of Underground Space and Engineering,2016,12(4):912
[20]葛修润,任建喜,蒲毅彬,等.岩石细观损伤扩展规律的CT实时试验[J].中国科学,2000,30(2):104GE Xiurun,REN Jianxi,PU Yibin. et al. Primary study of CT real-time testing of fatigue meso-damage propagation law of rock[J]. Chinese Journal of Geotechnical Engineering,2000,30(2):104. DOI:10. 3321/j. issn:1006-9275. 2000. 02. 002
[21]赖远明,吴紫汪,朱元林,等.大坂山隧道围岩冻融损伤的CT分析[J].冰川冻土,2000,22(3):206LAI Yuanming,WU Ziwang,ZHU Yuanlin,et al. CT analysis of frost damage of the surrounding rocks of a tunnel in the Daban Mountain[J]. Journal of Glaciology and Geocryology,2000,22(3):206. DOI:10. 3969/j. issn. 1000-0240. 2000. 03. 003
[22]张慧梅,杨更社.冻融与荷载耦合作用下岩石损伤模型的研究[J].岩石力学与工程学报,2010,29(3):471ZHANG Huimei,YANG Gengshe. Research on damage model of rock under coupling action of freeze-thaw and load[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(3):471
[23]袁小清,刘红岩,刘京平.冻融荷载耦合作用下节理岩体损伤本构模型[J].岩石力学与工程学报,2015,34(8):1602YUAN Xiaoqing,LIU Hongyan,LIU Jingping. A damaging model of jointed rock under coupled action of freezing and thawing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1602. DOI:10. 13722/j. cnki. jrme. 2014. 1342
[24]刘红岩,刘冶,邢闯锋,等.循环冻融条件下节理岩体损伤破坏试验研究[J].岩土力学,2014,35(6):1547LIU Hongyan,LIU Ye,XING Chuangfeng,et al. Test study of damage failure of jointed rock mass under freezing-thawing cycles[J]. Rock and Soil Mechanics,2014,35(6):1547
[25]路亚妮,李新平,肖家双.单裂隙岩体冻融力学特性试验分析[J].地下空间与工程学报,2014,10(3):594LU Yani,LI Xinping,XIAO Jiashuang. Experimental analysis on mechanical characteristic of single cracked rock mass under freezethaw condition[J]. Chinese Journal of Underground Space and Engineering,2014,10(3):594
[26]陈有亮,代明星,刘明亮,等.含初始损伤岩石的冻融损伤试验研究[J].力学季刊,2013,34(1):74CHEN Youliang, DAI Mingxing, LIU Mingliang, et al.Experimental investigation on freezing damage characteristics of granite with initial damage[J]. Chinese Quarterly of Mechanics,2013,34(1):74. DOI:10. 3969/j. issn. 0254-0053. 2013. 01. 010
[27]刘松明,陈有亮,杜曦,等.酸侵蚀区白砂岩冻融损伤的影响因素研究[J].水资源与水工程学报,2014,25(5):127LIU Songming,CHEN Youliang,DU Xi,et al. Study on influences factor of freezing-thawing damage of white sandstone in acid erosion area[J]. Journal of Water Resources and Water Engineering,2014,25(5):127. DOI:10. 11705/j. issn. 1672-643X. 2014.05. 028
[28]李新平,路亚妮,王仰君.冻融荷载耦合作用下单裂隙岩体损伤模型研究[J].岩石力学与工程学报,2013,32(11):2307LI Xinping,LU Yani,WANG Yangjun. Research on damage model of single jointed rock masses under coupling action of freeze-thaw and loading[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(11):2307
[29]曹文贵,方祖烈,唐学军.岩石损伤软化统计本构模型之研究[J].岩石力学与工程学报,1998,17(6):628CAO Wengui,FANG Zulie,TANG Xuejun. A study of statistical constitutive model for soft and damage rock[J]. Chinese Journal of Rock Mechanics and Engineering,1998,17(6):628
[30]KRAJCINOVIC D,SILVA M A G. Statistical aspects of the continuous damage theory[J]. International Journal of Solids and Structures,1982,18(7):551. DOI:10. 1016/0020-7683(82)90039-7
[31]张慧梅,雷利娜,杨更社.温度与荷载作用下岩石损伤模型[J].岩石力学与工程学报,2014(s2):3391ZHANG Huimei,LEI Lina,YANG Gengshe. Damage model of rock under temperature and load[J]. Chinese Journal of Rock Mechanics and Engineering,2014(s2):3391. DOI:10. 13722/j.cnki. jrme. 2014. s2. 001
[32]张全胜,杨更社,任建喜.岩石损伤变量及本构方程的新探讨[J].岩石力学与工程学报,2003,22(1):30ZHANG Quansheng,YANG Gengshe,REN Jianxi. New study of damage variable and constitutive equation of rock[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(1):30.DOI:10. 3321/j. issn:1000-6915. 2003. 01. 005
[33]杨更社,谢定义.岩体宏观细观损伤的耦合计算分析[C]//第六次全国岩石力学与工程学术大会论文集.武汉:[s. n.],2000:327YANG Gengshe,XIE Dingyi. Coupling analysis on the macrodamage and meso-damage of rock masses[C]//Symposium on the Sixth National Rock Mechanics and Engineering Academic Conference. Wuhan:[s. n.],2000:327
[34]张力民,吕淑然,刘红岩.综合考虑宏细观缺陷的岩体动态损伤本构模型[J].爆炸与冲击,2015,35(3):428ZHANG Limin,LV Shuran,LIU Hongyan. A dynamic damage constitutive model of rock mass by comprehensively considering macroscopic and mesoscopic flaws[J]. Explosion and Shock Waves,2015,35(3):428
[35]王乐华,陈招军,金晶,等.节理岩体冻融力学特性试验研究[J].水利水电技术,2016(5):149WANG Lehua,CHEN Zhaojun,JIN Jing,et al. Experimental study on mechanic characteristics of jointed rock under freeze-thaw condition[J]. Water Resources and Hydropower Engineering,2016(5):149. DOI:10. 13928/j. cnki. wrahe. 2016. 05. 035
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |