基于修正系数的岩石本构关系研究
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摘要
为对具有原始微元破坏的工程岩石建立更切合实际的本构关系,通过引入修正系数得到原始损伤部分与岩石整体部分的关系,并基于Weibull随机分布和损伤力学理论,在微元破坏符合摩尔-库仑准则的条件下,采用理论推导与试验验证相结合的方法,建立了基于修正系数的岩石损伤本构关系,并以红砂岩常规力学特性试验验证其合理性。结果表明:通过该本构关系获得的理论曲线与试验曲线较为吻合,能够较好的反映岩石变形破坏阶段的特征;受荷过程中,岩石以原始损伤为基准进一步损伤,最终完全破坏;模型参数m和F0的变化均对岩石损伤关系有一定影响,随着F0变化,弹性阶段、峰值应力和相应应变以及最终达到完全破坏时的应变都呈现一致性变化,影响岩石脆延性;随着m变化,弹性阶段及峰值点有所变化但不明显,峰值应力、峰后损伤程度影响较大;随着修正系数γ变化,峰前峰后同一应变对应的应力均发生变化,但γ的取值对理论曲线的发展趋势及峰值点的大小和位置没有影响。
In order to establish a more realistic constitutive relation to the engineering rocks with original micro-failure,the relationship between the original damage part and the whole part of the rock was obtained by introducing the correction coefficient. Based on the Weibull random distribution and damage mechanics theory,and under the condition of Coulomb criterion,the combination of theoretical derivation and experimental verification were used to establish the damage constitutive relation of rock based on the correction coefficient.The rationality of the red sandstone was verified by the conventional mechanical properties test. The results show that the theoretical curve obtained by the model is in good consistent with the experimental curve,which can better reflect the characteristics of various rock deformation and failure stages. In the process of loading,the rock is further damaged on the basis of original damage,and ultimately completely failed; The changes of the model parameters m and F0 have an effect on the rock damage model. With the change of F0,the elastic phase,the peak stress and the corresponding strain,and the strain just reaching the complete failure show a consistent change,affecting the brittleness and ductilityof the rock.As the change of m,the elastic phase and the peak point change but are not obvious,the peak stress and post-peak damage degree have a greater influence. With the change of correction coefficient,the stress corresponding to the same strain changes before and after the peak changes. However,the value of γ has no effect on the development trend of the theoretical curve,nor does it change the size and position of the peak point.
In order to establish a more realistic constitutive relation to the engineering rocks with original micro-failure,the relationship between the original damage part and the whole part of the rock was obtained by introducing the correction coefficient. Based on the Weibull random distribution and damage mechanics theory,and under the condition of Coulomb criterion,the combination of theoretical derivation and experimental verification were used to establish the damage constitutive relation of rock based on the correction coefficient.The rationality of the red sandstone was verified by the conventional mechanical properties test. The results show that the theoretical curve obtained by the model is in good consistent with the experimental curve,which can better reflect the characteristics of various rock deformation and failure stages. In the process of loading,the rock is further damaged on the basis of original damage,and ultimately completely failed; The changes of the model parameters m and F0 have an effect on the rock damage model. With the change of F0,the elastic phase,the peak stress and the corresponding strain,and the strain just reaching the complete failure show a consistent change,affecting the brittleness and ductilityof the rock.As the change of m,the elastic phase and the peak point change but are not obvious,the peak stress and post-peak damage degree have a greater influence. With the change of correction coefficient,the stress corresponding to the same strain changes before and after the peak changes. However,the value of γ has no effect on the development trend of the theoretical curve,nor does it change the size and position of the peak point.
引文
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[17]熊良宵,虞利军.三种Mohr强度准则的对比分析[J].长江科学院院报,2016,33(4):81-85.XIONG Liangxiao,YU Lijun. Comparative study of three mohr strength criteria[J]. Journal of Yangtze River Scientific Research Institute,2016,33(4):81-85.
[18] ZHOU Shuwei,XIA Cachu,ZHAO Haibin,et al.Statistical damage constitutive model for rocks subjected to cyclic stress and cyclic temperature[J].Acta Geophysica,2017,65(5):893-906.
[19]张慧梅,孟祥振,彭川,等.岩石变形全过程冻融损伤模型及其参数[J].西安科技大学学报,2018,38(2):260-265.ZHANG Huimei,MENG Xiangzhen,PENG Chuan,et al. freezethaw damage model and parameters rock deformation in whole process[J]. Journal of Xian University of Science and Technology,2018,38(2):260-265.
[20] HUANG Shibing,LIU Quansheng,CHENG Aiping,et al.A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application[J]. Cold Regions Science and Technology,2018,145:142-150.
[2]张德,刘恩龙,刘星炎,等.基于修正Mohr-Coulomb屈服准则的冻结砂土损伤本构模型[J].岩石力学与工程学报,2018,37(4):978-986.ZHANG De,LIU Enlong,LIU Xingyan,et al.A damage constitutive model for frozen sandy soils based on modified Mohr-Coulomb yield criterion[J]. Chinese Journal of Rock Mechanics and Engineering,2018,37(4):978-986.
[3]周辉,李震,朱国金,等.基于岩石统一能量屈服准则的硬岩损伤模型[J].岩土力学,2016,37(3):609-624.ZHOU hui,LI zhen,ZHU Guojin,et al. A damage model for hard rock based on unified energy yield criterion of rock[J]. Rock and Soil Mechanics,2016,37(3):609-624.
[4] CHEN Xin,LIAO Zhihong,PENG Xi.Deformability characteristics of jointed rock masses under uniaxial compression[J].International Journal of Mining Sciences and Technology,2012,22(2):213-221.
[5] LI Shuchun,XU Jiang,TAO Yunqi,et al.Study on damage constitutive model of rocks based on lognormal distribution[J].Journal of Coal Science&Engineering,2007,13(4):430-433.
[6]李树春,许江,王鸿,等.岩石损伤统计本构模型及其参数确定的研究[J].矿业研究与开发,2007,27(2):6-8.LI Shuchun,XU Jiang,WANG Hong,et al. Research on statistical damage constitutive model of rock and determination of its parameters[J].Mining Research and Development,2007,27(2):6-8.
[7] ZHOU Hongwei,WANG Chunping,HAN B B,et al.A creep constitutive model for salt rock based on fractional derivatives[J].International Journal of Rock Mechanics&Mining Sciences,2011,48(1):116-121.
[8] WANG Zhiliang,LI Yongchi,WANG Jianguo.A damage-softening statistical constitutive model considering rock residual strength[J].Computers&Geosciences,2007,33(1):1-9.
[9]张慧梅,夏浩峻,杨更社,等.冻融循环和围压对岩石物理力学性质影响的试验研究[J].煤炭学报,2018,43(2):441-448.ZHANG Huimei,XIA Haojun,YANG Gengshe,et al.Experimental research of influences of freeze-thaw cycles and confining pressure on physical-mechanical characteristics of rocks[J]. Journal of China Coal Society,2018,43(2):441-448.
[10]谢祥妙.冻融荷载作用下砂岩损伤特性分析[D].西安,西安科技大学,2015.
[11] LI Hangzhou,LIAO Hongjian,XIONG Guangdong,et al.A threedimensional statistical damage constitutive model for geomaterials[J]. Journal of Mechanical Science and Technology,2015,29(1):71-77.
[12]曹瑞琅,贺少辉,韦京,等.基于残余强度修正的岩石损伤软化统计本构模型研究[J].岩土力学,2013,34(6):1652-1660.CAO Ruilang,HE Shaohui,WEI Jing,et al.Study of modified statistical damage softening constitutive model for rock considering residual strength[J]. Rock and Soil Mechanics,2013,34(6):1652-1660.
[13]李博,吴润江,高为超.岩石损伤软化的修正本构模型[J].地震工程学报,2016,38(5):783-786.LI Bo,WU Runjiang,GAO Weichao.A modified damage softening constitutive model for rock[J]. China Earthquake Engineering Journal,2016,38(5):783-786.
[14]王苏生,徐卫亚,王伟,等.岩石统计损伤本构模型与试验[J].河海大学学报:自然科学版,2017,45(5):464-470.WANG Susheng,XU Weiya,WANG Wei,et al. The statistical damage constitutive model of rocks and its experiment[J].Journal of Hohai University:Natural Sciences,2017,45(5):464-470.
[15]黄海峰,巨能攀,蓝康文,等.岩石统计损伤软化模型及其参数反演[J].长江科学院报,2018,35(6):102-106.HUANG Haifeng,JU Nengpan,LAN Kangwen,et al. Statistical damage softening model for rock and back analysis of its parameters[J]. Journal of Yangtze River Scientific Research Institute,2018,35(6):102-106.
[16]房智恒.基于Mohr-Coulomb准则的岩石损伤本构模型研究[J].矿业工程研究,2017,32(1):7-13.FANG Zhiheng.Rock damage constitutive model based on mohrcoulomb criterion[J]. Mineral Engineering Research,2017,32(1):7-13.
[17]熊良宵,虞利军.三种Mohr强度准则的对比分析[J].长江科学院院报,2016,33(4):81-85.XIONG Liangxiao,YU Lijun. Comparative study of three mohr strength criteria[J]. Journal of Yangtze River Scientific Research Institute,2016,33(4):81-85.
[18] ZHOU Shuwei,XIA Cachu,ZHAO Haibin,et al.Statistical damage constitutive model for rocks subjected to cyclic stress and cyclic temperature[J].Acta Geophysica,2017,65(5):893-906.
[19]张慧梅,孟祥振,彭川,等.岩石变形全过程冻融损伤模型及其参数[J].西安科技大学学报,2018,38(2):260-265.ZHANG Huimei,MENG Xiangzhen,PENG Chuan,et al. freezethaw damage model and parameters rock deformation in whole process[J]. Journal of Xian University of Science and Technology,2018,38(2):260-265.
[20] HUANG Shibing,LIU Quansheng,CHENG Aiping,et al.A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application[J]. Cold Regions Science and Technology,2018,145:142-150.