考虑非贯通节理损伤演化岩体复合本构模型
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摘要
非贯通节理岩体的力学特征与完整岩石相比有较大差异.为推导非贯通节理岩体在单轴压缩下的复合损伤本构模型,采用修正自洽方法考虑不同损伤变量之间的复合.从附加应变能增量和损伤应变能释放量相关联的思路出发,采用等效直线裂纹作为节理裂隙损伤演化轨迹,分别计算细观损伤、初始节理和节理裂隙损伤演化引起的附加应变能;基于Betti能量互易定理,引入自洽方法考虑节理裂隙之间的相互作用,并采用逐条添加节理的方法对传统自洽方法进行修正,得出岩体不同受力阶段细观、初始节理和节理裂隙损伤演化的复合损伤本构模型;将本构模型的理论计算结果与现有文献的室内试验结果进行对比分析,结果显示:本构模型的理论计算结果与室内试验结果规律一致,随着节理个数增加,初始弹性模量和荷载峰值均呈下降趋势,下降幅度较为一致;节理裂隙的损伤演化对岩体的力学特性有重要影响,考虑节理裂隙损伤演化的理论应力应变曲线和荷载峰值与室内试验结果更为吻合,有效验证了复合损伤本构模型的正确性与合理性.
Comparing with intact rock,the mechanical characteristics of non-persistent closed jointed rock mass have relatively large differences. A revised self-consistent method was used to consider the coupling between different damages,as a result,the compound constitutive model was deduced for non-persistent closed jointed rock mass under uniaxial compression. Based on the correlation between additional strain energy increment and damage strain energy release,the equivalent linear crack as jointed crack damage evolution trajectories was adopted,and then the additional strain energy for micromechanical damage,initial joints and jointed crack damage evolution was respectively calculated. In accordance to the Betti energy reciprocity theorem, a self-consistent method was introduced to account for the correlation among cracks,moreover,an approach for adding joints one by one was utilized to correct the traditional self-consistent method,in which the compound damage constitutive model was deduced in regard to different stages during uniaxial compression. The theoretical calculation results of the proposed model were compared with in-house experimental results in existing literature. The results show that: the theoretical calculation results are consistent with the experimental results. With the increase the number of joints,the initial elastic modulus and peak load show a downward trend,and the reducing value is in the same extent; there are significant impacts for the damage evolution of joints crack damage on the mechanical characteristics of the rock mass. The theoretical stress-strain curve and peak load for joint fissure damage evolution are consistent with inhouse experimental results,which apparently verify the correctness and reasonability of the compound damage constitutive model.
Comparing with intact rock,the mechanical characteristics of non-persistent closed jointed rock mass have relatively large differences. A revised self-consistent method was used to consider the coupling between different damages,as a result,the compound constitutive model was deduced for non-persistent closed jointed rock mass under uniaxial compression. Based on the correlation between additional strain energy increment and damage strain energy release,the equivalent linear crack as jointed crack damage evolution trajectories was adopted,and then the additional strain energy for micromechanical damage,initial joints and jointed crack damage evolution was respectively calculated. In accordance to the Betti energy reciprocity theorem, a self-consistent method was introduced to account for the correlation among cracks,moreover,an approach for adding joints one by one was utilized to correct the traditional self-consistent method,in which the compound damage constitutive model was deduced in regard to different stages during uniaxial compression. The theoretical calculation results of the proposed model were compared with in-house experimental results in existing literature. The results show that: the theoretical calculation results are consistent with the experimental results. With the increase the number of joints,the initial elastic modulus and peak load show a downward trend,and the reducing value is in the same extent; there are significant impacts for the damage evolution of joints crack damage on the mechanical characteristics of the rock mass. The theoretical stress-strain curve and peak load for joint fissure damage evolution are consistent with inhouse experimental results,which apparently verify the correctness and reasonability of the compound damage constitutive model.
引文
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[11]袁小清,刘红岩,刘京平.基于宏细观损伤耦合的非贯通裂隙岩体本构模型[J].岩土力学,2015,36(10):2804-2813.DOI:10.16285/j.rsm.2015.10.009.YUAN Xiaoqing,LIU Hongyan,LIU Jingping.Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2804-2813.DOI:10.16285/j.rsm.2015.10.009.
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[15]HORII S,NEMAT N.Brittle failure in compression:splitting,faulting and brittle-ductile transition[J].Phil.Mathematical and Physical Sciences,1986,319(1549):319,337-374.
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[18]TOSHIKAZU K,YASUAKI I,TAKASHI K.Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory[J].International Journal for Numerical and Analytical Method in Geomechanics,1988,12(1):1-30.
[19]杨圣奇,戴永浩,韩立军,等.断续预制裂隙脆性大理岩变形破坏特性单轴压缩试验研究[J].岩石力学与工程学报,2009,28(12):2391-2404.YANG Shengqi,DAI Yonghao,HAN Lijun,et al.Uniaxial compression experimental research on deformation and failure properties of brittle marble specimen with pre-existing fissures[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(12):2391-2404.
[20]杨圣奇.断续三裂隙砂岩强度破坏和裂纹扩展特征研究[J].岩土力学,2013,34(1):31-39.DOI:10.16285/j.rsm.2013.01.009.YANG Shengqi.Study of strength failure and crack coalescence behavior of sandstone containing three pre-existing fissures[J].Rock and Soil Mechanics,2013,34(1):31-39.DOI:10.16285/j.rsm.2013.01.009.
[21]崔智丽.岩石类材料中心裂纹圆盘试件动态断裂韧性测试系统的动力学有限元分析及测试方法的研究[D].安徽:安徽理工大学,2011.CUI Zhili.Research on dynamics finite element analysis and testing methods of dynamic fracture toughness test system of central cracked circular disk specimen of rock[D].Anhui:Anhui University of Science and Technology,2011.
[2]WEIBULL W.A statistical distribution function of wide applicability.Journal of Applied Mechanics[J].1951,18:293-297.
[3]WANG Zhiliang,LI Yongchi,WANG J G.A damage-softening statistical constitutive model considering rock residual strength[J].Computers&Geosciences,2007,3:1-9.
[4]曹文贵,张升,赵明华.软化与硬化特性转化的岩石损伤统计本构模型之研究[J].工程力学,2006,23(11):110-115.CAO Wengui,ZHANG Sheng,ZHAO Minghua.Study on a statistical damage constitutive model with conversion between softening and hardening properties of rock[J].Engineering Mechanics,2006,23(11):110-115.
[5]KYOYA T,ICHIKAWA Y,KAWAMOTO T A.Damage mechanics theory for discontinuous rock mass[C]//5th International Conference on Numerical Methods in Geomechanics.Innsbruck:[s.n.],1985:469-480.
[6]CHEN Xin,ZDENEK P B.Microplane damage model for jointed rock masses[J].International journal for numerical and analytical methods in geomechanics,2014,38(14):1431-1452.
[7]陈文玲,李宁.含非贯通裂隙岩体介质的损伤模型[J].岩土工程学报,2000,22(4):430-434CHEN Wenling,LI Ning.Damage model of the rock mass medium with intermittent cracks[J].Chinese Journal of Geotechnical Engineering,2000,22(4):430-434.
[8]KEMENY J.Effective moduli,non-linear deformation and strength of a cracked elastic solid[J].Int.J.Rock.Mech.Min,1986,23(2):107-118.
[9]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.DOI:10.16285/j.rsm.2013.06.018.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.DOI:10.16285/j.rsm.2013.06.018.
[10]张明,王菲,杨强.基于三轴压缩试验的岩石统计损伤本构模型[J].岩土工程学报,2013,35(11):1965-1971.ZHANG Ming,WANG Fei,YANG Qiang.Statistical damage constitutive model for rocks based on triaxial compression tests[J].Chinese Journal of Geotechnical Engineering,2013,35(11):1965-1971.
[11]袁小清,刘红岩,刘京平.基于宏细观损伤耦合的非贯通裂隙岩体本构模型[J].岩土力学,2015,36(10):2804-2813.DOI:10.16285/j.rsm.2015.10.009.YUAN Xiaoqing,LIU Hongyan,LIU Jingping.Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2804-2813.DOI:10.16285/j.rsm.2015.10.009.
[12]ISIDA M.On the tension of a strip with a central elliptical hole[J].Transactions of the Japan Society of Mechanical Engineering,1955,21(107):507-518.
[13]KEMENY J M,COOK N G W.Micromechanics of deformation in rocks[J].Toughening Mechanisms in Quasi-Brittle Materials,1991,195:155-188.
[14]HORII S,NEMAT N.Estimate of stress intensity factor for interacting cracks[J].In Advances in Aerospace Structures,materials and dynamics,1983,6:111-117.
[15]HORII S,NEMAT N.Brittle failure in compression:splitting,faulting and brittle-ductile transition[J].Phil.Mathematical and Physical Sciences,1986,319(1549):319,337-374.
[16]PAUL S.Crack extension under compressive loading[J].Engineering Fracture Mechanics.1984,3:463-473.
[17]BRUNER W M.Comment on seismic velocities in dry and statured cracked solids by Oconnell budiansky[J].Geophys Res,1976,81:2573-2576.
[18]TOSHIKAZU K,YASUAKI I,TAKASHI K.Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory[J].International Journal for Numerical and Analytical Method in Geomechanics,1988,12(1):1-30.
[19]杨圣奇,戴永浩,韩立军,等.断续预制裂隙脆性大理岩变形破坏特性单轴压缩试验研究[J].岩石力学与工程学报,2009,28(12):2391-2404.YANG Shengqi,DAI Yonghao,HAN Lijun,et al.Uniaxial compression experimental research on deformation and failure properties of brittle marble specimen with pre-existing fissures[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(12):2391-2404.
[20]杨圣奇.断续三裂隙砂岩强度破坏和裂纹扩展特征研究[J].岩土力学,2013,34(1):31-39.DOI:10.16285/j.rsm.2013.01.009.YANG Shengqi.Study of strength failure and crack coalescence behavior of sandstone containing three pre-existing fissures[J].Rock and Soil Mechanics,2013,34(1):31-39.DOI:10.16285/j.rsm.2013.01.009.
[21]崔智丽.岩石类材料中心裂纹圆盘试件动态断裂韧性测试系统的动力学有限元分析及测试方法的研究[D].安徽:安徽理工大学,2011.CUI Zhili.Research on dynamics finite element analysis and testing methods of dynamic fracture toughness test system of central cracked circular disk specimen of rock[D].Anhui:Anhui University of Science and Technology,2011.