含贯通-非贯通交叉节理岩体等效弹性模型及强度特性
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摘要
基于等效弹性模型的方法,构建综合考虑含贯通—非贯通交叉节理岩体宏细观缺陷的复合损伤模型。首先,将贯通节理部分看成一定厚度的独立材料,其主要产生闭合变形及沿节理面的剪切变形,其储存弹性应变能及剪切应变能;其次,基于断裂力学及应变能理论相结合,将交叉节理中的非贯通节理岩体部分看成岩体内部宏观损伤,对节理尖端的应力强度因子进行了计算,推导得出了储存在非贯通节理中的应变能计算公式,并将岩体内部的细观损伤按Weibull分布描述,建立综合考虑宏细观缺陷的节理岩体复合损伤模型;再次,对交叉节理岩体的强度准则进行了讨论,构建考虑交叉节理不同强度准则的等效弹性模型;最后,将计算结果与试验结果进行了比较分析,模型计算结果与试验结果吻合较好,证明了模型的合理性,同时讨论了贯通节理倾角、非贯通节理倾角对岩体峰值强度及破坏准则的影响,以及非贯通节理贯通率对初始损伤变量影响规律。
Based on the method of the equivalent elastic model,the composite damage model was constructed to consider comprehensively the mac-roscopic and microscopic defects of the rock mass containing persistent and non-persistent joints.Firstly,the part of persistent joint was considered as an independent material with a certain thickness,which mainly produces closed deformation and shear deformation along the joint surface,which can store elastic strain energy and shear strain energy.Secondly,based on the combination of fracture mechanic and strain energy theory,the non-persistent joint rock part of the cross joint was regarded as the internal macro damage of rock mass. Therefore,the joint point of stress intensity factor was calculated,and the formula of strain energy stored in non-persistent joint was derived.The microscopic damage was described according to the Weibull distribution within the rock mass,and the comprehensive consideration macro and micro defects of joint rock damage model was established.Thirdly,the strength criterion of cross jointed rock mass was discussed,and the equivalent elastic model of different strength criterion was constructed.Finally,the calculated results were compared with the test results,the model calculation results are in good a-greement with the experiment results,which proves the rationality of the model.In addition,the influence of persistent joint angle and non-persistent joint angle on the peak strength and failure criterion of rock mass,and the influence law of initial damage variables affected by penetration rate of non-persistent joint were discussed.
Based on the method of the equivalent elastic model,the composite damage model was constructed to consider comprehensively the mac-roscopic and microscopic defects of the rock mass containing persistent and non-persistent joints.Firstly,the part of persistent joint was considered as an independent material with a certain thickness,which mainly produces closed deformation and shear deformation along the joint surface,which can store elastic strain energy and shear strain energy.Secondly,based on the combination of fracture mechanic and strain energy theory,the non-persistent joint rock part of the cross joint was regarded as the internal macro damage of rock mass. Therefore,the joint point of stress intensity factor was calculated,and the formula of strain energy stored in non-persistent joint was derived.The microscopic damage was described according to the Weibull distribution within the rock mass,and the comprehensive consideration macro and micro defects of joint rock damage model was established.Thirdly,the strength criterion of cross jointed rock mass was discussed,and the equivalent elastic model of different strength criterion was constructed.Finally,the calculated results were compared with the test results,the model calculation results are in good a-greement with the experiment results,which proves the rationality of the model.In addition,the influence of persistent joint angle and non-persistent joint angle on the peak strength and failure criterion of rock mass,and the influence law of initial damage variables affected by penetration rate of non-persistent joint were discussed.
引文
[1]熊飞,靖洪文,苏海健.尖端相交裂隙砂岩强度与破裂演化特征试验研究[J].煤炭学报,2017,42(4):886-895.XIONG Fei,JING Hongwen,SU Haijian,et al. Strength and fracture behaviors of sandstone samples containing intersect fissures under uniaxial compression[J]. Journal of China Coal Society,2017,42(4):886-895.
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[4] ZHAO D,SWOBODA G,LAABMAYR F.Damage mechanics and its application for the design for an underground theater[J].Tunnelling and Underground Space Technology,2004,19:567-575.
[5] WANG T T,HUANG T H.A constitutive model for the deformation of a rock mass containing sets of ubiquitous joints[J]. International Journal of Rock Mechanics&Mining Sciences,2009,46(3):521-530.
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[7]刘东燕,朱可善,范景伟.双向应力作用下X型断续节理岩体的强度特性研究[J].重庆建筑工程学院学报,1991,13(4):40-46.LIU Dongyan,ZHU Keshan,FAN Jingwei. Strength properties of rock mass joints[J]. Journal of Chongqing Institute of Architecture and Engineering,1991,13(4):40-46.
[8]张波,李术才,杨学英,等.含交叉裂隙岩体相似材料试件力学性能单轴压缩试验[J].岩土力学,2012,33(12):3674-3679.ZHANG Bo,LI Shucai,YANG Xueying,et al. Uniaxial compression tests on mechanical properties of rock mass similar material with cross-cracks[J]. Rock and Soil Mechanics,2012,33(12):3674-3679.
[9]张波,李术才,杨学英,等.含交叉多裂隙类岩石材料单轴压缩力学性能研究[J].岩石力学与工程学报,2015,34(9):1777-1785.ZHANG Bo,LI Shucai,YANG Xueying,et al.Mechanical property of rock-link material with intersecting multi flaws under uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(9):1777-1785.
[10]刘学伟,刘泉声,陈元,等.裂隙形式对岩体强度特征及破坏模式影响的试验研究[J].岩土力学,2015,36(S2):208-214.LIU Xuewei,LIU Quansheng,CHEN Yuan,et al. Experimental study of effects of fracture type on strength characteristics and failure modes of fractured rockmass[J]. Rock and Soil Mechanics,2015,36(S2):208-214.
[11]刘红岩,张力民,苏天明,等.节理岩体损伤本构模型及工程应用[M].北京:冶金工业出版社,2016.
[12]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):2804-2814.YUAN Xiaoqing,LIU Hongyan,LIU Jingping,et al. Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2804-2814.
[13]孙广忠,孙毅.岩体力学原理[M].北京:科学出版社,2011:44-50.
[14]夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002:133-140.
[15]刘红岩,王新生,张力民,等.非贯通节理岩体单轴压缩动态损伤本构模型[J].岩土工程学报,2016,38(3):426-436.LIU Hongyan,WANG Xinsheng,ZHANG limin,et al. A dynamic damage constitutive model for rock mass with nonpersistent joints under uniaxial compression[J]. Chinese Journal of Geotechnical Engineering,2016,38(3):426-436.
[16]郑安兴,罗先启.压剪应力状态下岩石复合型断裂判据的研究[J].岩土力学,2015,36(7):1892-1898.ZHENG Anxing,LUO Xianqi.Research on combined fracture criterion of rock under compression-shear stress[J].Rock and Soil Mechanics,2015,36(7):1892-1898.
[17] BANDIS S C.Experimental studies of scale effect on the shear behaviour of rock joint[J]. International Journal of Rock Mechanics&Mining Sciences&Geomechanics Abstracts,1981,18(1):1-21.
[18] BARTON N.Review of a new shear strength criterion for rock joints[J].Eng.Geol.,1973,7:287-332.
[19]夏才初,肖维民,丁增志.非贯通节理Jennings强度准则的岩桥弱化和节理面起伏角修正[J].岩石力学与工程学报,2010,29(3):485-493.XIA Caichu,XIAO Weimin,DING Zengzhi.Modification of Jennings strength criterion for intermittent joints considering rock bridge weakening and joint surface undulating angle[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(3):485-493.
[20]刘红岩,黄妤诗,李楷兵,等.预制节理岩体试件强度及破坏模式的试验研究[J].岩土力学,2013,34(5):1235-1243.LIU Hongyan,HUANG Yushi,LI Kaibing,et al. Test study of strength and failure mode of pre-existing jointed rock mass[J].Rock and Soil Mechanics,2013,34(5):1235-1243.
[21]邓正定,王桢,刘红岩.基于复合损伤的节理岩体动态本构模型研究[J].岩土力学,2015,36(5):1368-1374.DENG Zhengding,WANG Zhen,LIU Hongyan. Dynamic constitutive model of jointed rock mass based on the theory of composite damage[J]. Rock and Soil Mechanics,2015,36(5):1368-1374.
[22]陈新,廖志红,李德建.节理倾角及连通率对岩体强度、变形影响的单轴压缩试验研究[J].岩石力学与工程学报,2011,30(4):781-789.CHEN Xin,LIAO Zhihong,LI Dejian.Experimental study of effects of joint inclination angle and connectivity rate on strength and deformation properties of rock masses under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineeing,2011,30(4):781-789.
[23]张波,杨学英,李术才,等.含两组叠置X型裂隙类岩石材料单轴拉伸破坏特征[J].煤炭学报,2017,42(8):1987-1993.ZHANG Bo,YANG Xueying,LI Shucai,et al. Uniaxial tensile failure properties of rock-like specimens with two overlapped X-type flaws[J].Journal of China Coal Society,2017,42(8):1987-1993.
[24] XUE Junhua,WANG Hanpeng,ZHOU Wei,et al.Experimental research on overlying strata movement and fracture evolution in pillarless stress-relief mining[J].International Journal of Coal Science&Technology,2015,2(1):38-45.
[2]刘红岩,邓正定,王新生.节理岩体动态破坏的SHPB相似材料试验研究[J].岩土力学,2014,35(3):659-665.LIU Hongyan,DENG Zhengding,WANG Xinsheng. Similar material test study of dynamic failure of jointed rock mass with SHPB[J].Rock and Soil Mechanics,2014,35(3):659-665.
[3]张平,李宁,李贺兰.动载下3条断续裂隙岩样的裂缝贯通机制[J].岩土力学,2006,27(9):1457-1464.ZHANG Ping,LI Ning,LI Helan. Fracture coalescence mechanism of three-intermittent-flaws rock specimen under dynamic loading[J].Rock and Soil Mechanics,2006,27(9):1457-1464.
[4] ZHAO D,SWOBODA G,LAABMAYR F.Damage mechanics and its application for the design for an underground theater[J].Tunnelling and Underground Space Technology,2004,19:567-575.
[5] WANG T T,HUANG T H.A constitutive model for the deformation of a rock mass containing sets of ubiquitous joints[J]. International Journal of Rock Mechanics&Mining Sciences,2009,46(3):521-530.
[6]张力民,张慧,刘红岩.单轴压缩荷载下非贯通闭合节理岩体损伤本构模型[J].煤田地质与勘探,2016,44(1):79-84.ZHANG Limin,ZHANG Hui,LIU Hongyan. A damage constitutive model for rock mass with non-persistently closed joints under uniaxial compression load[J]. Coal Geology&Exploration,2016,44(1):79-84.
[7]刘东燕,朱可善,范景伟.双向应力作用下X型断续节理岩体的强度特性研究[J].重庆建筑工程学院学报,1991,13(4):40-46.LIU Dongyan,ZHU Keshan,FAN Jingwei. Strength properties of rock mass joints[J]. Journal of Chongqing Institute of Architecture and Engineering,1991,13(4):40-46.
[8]张波,李术才,杨学英,等.含交叉裂隙岩体相似材料试件力学性能单轴压缩试验[J].岩土力学,2012,33(12):3674-3679.ZHANG Bo,LI Shucai,YANG Xueying,et al. Uniaxial compression tests on mechanical properties of rock mass similar material with cross-cracks[J]. Rock and Soil Mechanics,2012,33(12):3674-3679.
[9]张波,李术才,杨学英,等.含交叉多裂隙类岩石材料单轴压缩力学性能研究[J].岩石力学与工程学报,2015,34(9):1777-1785.ZHANG Bo,LI Shucai,YANG Xueying,et al.Mechanical property of rock-link material with intersecting multi flaws under uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(9):1777-1785.
[10]刘学伟,刘泉声,陈元,等.裂隙形式对岩体强度特征及破坏模式影响的试验研究[J].岩土力学,2015,36(S2):208-214.LIU Xuewei,LIU Quansheng,CHEN Yuan,et al. Experimental study of effects of fracture type on strength characteristics and failure modes of fractured rockmass[J]. Rock and Soil Mechanics,2015,36(S2):208-214.
[11]刘红岩,张力民,苏天明,等.节理岩体损伤本构模型及工程应用[M].北京:冶金工业出版社,2016.
[12]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):2804-2814.YUAN Xiaoqing,LIU Hongyan,LIU Jingping,et al. Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2804-2814.
[13]孙广忠,孙毅.岩体力学原理[M].北京:科学出版社,2011:44-50.
[14]夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002:133-140.
[15]刘红岩,王新生,张力民,等.非贯通节理岩体单轴压缩动态损伤本构模型[J].岩土工程学报,2016,38(3):426-436.LIU Hongyan,WANG Xinsheng,ZHANG limin,et al. A dynamic damage constitutive model for rock mass with nonpersistent joints under uniaxial compression[J]. Chinese Journal of Geotechnical Engineering,2016,38(3):426-436.
[16]郑安兴,罗先启.压剪应力状态下岩石复合型断裂判据的研究[J].岩土力学,2015,36(7):1892-1898.ZHENG Anxing,LUO Xianqi.Research on combined fracture criterion of rock under compression-shear stress[J].Rock and Soil Mechanics,2015,36(7):1892-1898.
[17] BANDIS S C.Experimental studies of scale effect on the shear behaviour of rock joint[J]. International Journal of Rock Mechanics&Mining Sciences&Geomechanics Abstracts,1981,18(1):1-21.
[18] BARTON N.Review of a new shear strength criterion for rock joints[J].Eng.Geol.,1973,7:287-332.
[19]夏才初,肖维民,丁增志.非贯通节理Jennings强度准则的岩桥弱化和节理面起伏角修正[J].岩石力学与工程学报,2010,29(3):485-493.XIA Caichu,XIAO Weimin,DING Zengzhi.Modification of Jennings strength criterion for intermittent joints considering rock bridge weakening and joint surface undulating angle[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(3):485-493.
[20]刘红岩,黄妤诗,李楷兵,等.预制节理岩体试件强度及破坏模式的试验研究[J].岩土力学,2013,34(5):1235-1243.LIU Hongyan,HUANG Yushi,LI Kaibing,et al. Test study of strength and failure mode of pre-existing jointed rock mass[J].Rock and Soil Mechanics,2013,34(5):1235-1243.
[21]邓正定,王桢,刘红岩.基于复合损伤的节理岩体动态本构模型研究[J].岩土力学,2015,36(5):1368-1374.DENG Zhengding,WANG Zhen,LIU Hongyan. Dynamic constitutive model of jointed rock mass based on the theory of composite damage[J]. Rock and Soil Mechanics,2015,36(5):1368-1374.
[22]陈新,廖志红,李德建.节理倾角及连通率对岩体强度、变形影响的单轴压缩试验研究[J].岩石力学与工程学报,2011,30(4):781-789.CHEN Xin,LIAO Zhihong,LI Dejian.Experimental study of effects of joint inclination angle and connectivity rate on strength and deformation properties of rock masses under uniaxial compression[J].Chinese Journal of Rock Mechanics and Engineeing,2011,30(4):781-789.
[23]张波,杨学英,李术才,等.含两组叠置X型裂隙类岩石材料单轴拉伸破坏特征[J].煤炭学报,2017,42(8):1987-1993.ZHANG Bo,YANG Xueying,LI Shucai,et al. Uniaxial tensile failure properties of rock-like specimens with two overlapped X-type flaws[J].Journal of China Coal Society,2017,42(8):1987-1993.
[24] XUE Junhua,WANG Hanpeng,ZHOU Wei,et al.Experimental research on overlying strata movement and fracture evolution in pillarless stress-relief mining[J].International Journal of Coal Science&Technology,2015,2(1):38-45.