基于四维离散数值方法的岩石圆环试样动态破坏及耗能规律
|
摘要
利用最新提出的四维离散弹簧元法(4D-LSM)对岩石圆环的动态抗变形及耗能特性进行研究。首先对4D-LSM用于描述岩石圆环试样破坏的适用性进行了验证,发现4D-LSM可以较好地再现岩石试样的孔径比与破坏形态和强度间的影响规律。在此基础上,对孔隙率、非均质性、厚径比等因素与抗变形及耗能间的规律进行研究,得到了对应的数学公式。利用4D-LSM模拟大变形方面的优势,发现当岩石材料的变形抵抗能力较大时,岩石圆环将表现出与传统仅考虑小变形情况下实验和数值计算不同的破坏形态,岩石圆环的材料抗拉强度与抗变形能力也分别呈现非线性关系。通过建立圆环阵列模型,研究了由多个岩环构成的组合结构的抗变形和能量抵抗能力以及对应的破坏形态。结果表明,组合结构中的圆环单元与单圆环受力的破裂形态有所不同,但单圆环的抗变形及耗能规律仍适用于岩环阵列结构的分析。
In this work,the deformation resistance and energy dissipation of rock rings were investigated by using the 4 D lattice spring model(4 D-LSM).Firstly,the 4 D-LSM was verified against existing experimental and numerical simulation results in terms of the influence of rock ring size on the failure pattern and strength.On this basis,empirical relationships of the influence of various factors,e.g.the porosity,heterogeneity,and thickness-diameter ratio,on the deformation resistance and energy dissipation of the rock ring were derived from numerical tests with the 4 D-LSM. When considering the large deformation,it was found that the failure pattern of the rock ring would be different from the classical experimental and numerical observations. Moreover,different empirical relationships between thedeformation resistance and energy dissipation as well as the material ultimate deformation were derived compared to these numerical tests considering small deformation only.Finally,the failure pattern,deformation resistance and energy dissipation of a composed structure made up from an array of rock rings were studied.Numerical results reveal that these relationships obtained for the single rock ring are also applicable to the composed structure.
In this work,the deformation resistance and energy dissipation of rock rings were investigated by using the 4 D lattice spring model(4 D-LSM).Firstly,the 4 D-LSM was verified against existing experimental and numerical simulation results in terms of the influence of rock ring size on the failure pattern and strength.On this basis,empirical relationships of the influence of various factors,e.g.the porosity,heterogeneity,and thickness-diameter ratio,on the deformation resistance and energy dissipation of the rock ring were derived from numerical tests with the 4 D-LSM. When considering the large deformation,it was found that the failure pattern of the rock ring would be different from the classical experimental and numerical observations. Moreover,different empirical relationships between thedeformation resistance and energy dissipation as well as the material ultimate deformation were derived compared to these numerical tests considering small deformation only.Finally,the failure pattern,deformation resistance and energy dissipation of a composed structure made up from an array of rock rings were studied.Numerical results reveal that these relationships obtained for the single rock ring are also applicable to the composed structure.
引文
[1]陈国兴,陈苏,杜修力,等.城市地下结构抗震研究进展[J].防灾减灾工程学报,2016,36(1):1-23.CHEN G X,CHEN S,DU X L,et al.Review of seismic damage,model test,available design and analysis methods of urban underground structures:Retrospect and prospect[J].Journal of Disaster Prevention and Mitigation Engineering,2016,36(1):1-23.(in Chinese)
[2]吴畏,蒋美蓉,石磊,等.地下工程隔震技术应用探讨[J].地下空间与工程学报,2007,3(Sup2):1583-1586.WU W,JIANG M R,SHI L,et al.Discussion on application of shock-isolation technology in underground engineering[J].Chinese Journal of Underground Space Engineering,2007,3(Sup2):1583-1586.(in Chinese)
[3]孙铁成,高波,叶朝良.地下结构抗震减震措施与研究方法探讨[J].现代隧道技术,2007,44(3):1-5.SUN T C,GAO B,YE C L.Discussion on antiseismic and seismic-relieving measures and corresponding research methods for underground structures[J].Modern Tunnelling Technology,2007,44(3):1-5.(in Chinese)
[4]喻寅,贺红亮,王文强,等.多孔脆性材料对高能量密度脉冲的吸收和抵抗能力[J].物理学报,2015,64(12):263-271.YU Y,HE H L,WANG W Q,et al.The ability of porous brittle materials to absorb and withstand high energy density pulse[J].Acta Physica Sinica,2015,64(12):263-271.(in Chinese)
[5]HANSSEN A G,ENSTOCK L,LANGSETH M.Close-range blast loading of aluminium foam panels[J].International Journal of Impact Engineering,2002,27(6):593-618.
[6]RATHBUN H J,RADFORD D D,XUE Z,et al.Performance of metallic honeycomb-core sandwich beams under shock loading[J].International Journal of Solids and Structures,2006,43(6):1746-1763.
[7]RADFORD D D,MCSHANE G J,DESHPANDE VS,et al.The response of clamped sandwich plates with metallic foam cores to simulated blast loading[J].International Journal of Solids and Structures,2006,43(7/8):2243-2259.
[8]王建军,郭伟国,赵融,等.轻质泡沫混凝土吸能特性及其压溃流动应力方程[J].土木建筑与环境工程,2013,35(6):96-102.WANG J J,GUO W G,ZHAO R,et al.Energyabsorbing properties and crushing flow stress equation of lightweight foamed concrete[J].Journal of Civil,Architectural&Environmental Engineering,2013,35(6):96-102.(in Chinese)
[9]王智,钱觉时,张朝辉,等.多孔混凝土配合比设计方法初探[J].重庆建筑大学学报,2008,30(3):121-124.WANG Z,QIAN J S,ZHANG Z H,et al.Preliminary discussion on mixing design of porous concrete[J].Journal of Chongqing Jianzhu University,2008,30(3):121-124.(in Chinese)
[10]黄胜,陈卫忠,杨建平,等.地下工程地震动力响应及抗震研究[J].岩石力学与工程学报,2009,28(3):483-490.HUANG S,CHEN W Z,YANG J P,et al.Research on earthquake-induced dynamic responses and aseismic measures for underground engineering[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):483-490.(in Chinese)
[11]赵武胜,陈卫忠,谭贤君,等.高性能泡沫混凝土隧道隔震材料研究[J].岩土工程学报,2013,35(8):1544-1552.ZHAO W S,CHEN W Z,TAN X J,et al.Highperformance foam concrete for seismic-isolation materials of tunnels[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1544-1552.(in Chinese)
[12]王代华,刘殿书,杜玉兰,等.含泡沫吸能层防护结构爆炸能量分布的数值模拟研究[J].爆炸与冲击,2006,26(6):562-567.WANG D H,LIU D S,DU Y L,et al.Numerical simulation of anti-blasting mechanism and energy distribution of composite protective structure with foam concrete[J].Explosion and Shock Waves,2006,26(6):562-567.(in Chinese)
[13]刘海燕,李然.泡沫混凝土吸能机理试验研究[J].成都大学学报(自然科学版),2010,29(2):166-167,180.LIU H Y,LI R.Experimental study on endergonic mechanism of foam concrete[J].Journal of Chengdu University(Natural Science Edition),2010,29(2):166-167,180.(in Chinese)
[14]叶燕华,李利群,孙伟民,等.内注泡沫混凝土空心砌块墙体抗震性能的试验研究[J].地震工程与工程振动,2004,24(5):154-158.YE Y H,LI L Q,SUN W M,et al.Experimental study on seismic behaviors of hollow block wall filled with foaming concrete[J].Earthquake Engineering and Engineering Vibration,2004,24(5):154-158.(in Chinese)
[15]ZHAO G F.Developing a four-dimensional lattice spring model for mechanical responses of solids[J].Computer Methods in Applied Mechanics and Engineering,2017,315:881-895.
[16]ZHAO G F.Development of micro-macro continuumdiscontinuum coupled numerical method[D].EPFL,Switzerland,2010.
[17]WANG Q Z,XING L.Determination of fracture toughness KIC by using the flattened Brazilian disk specimen for rocks[J].Engineering Fracture Mechanics,1999,64(2):193-201.
[18]LI D Y,WANG T,CHENG T J,et al.Static and dynamic tensile failure characteristics of rock based on splitting test of circular ring[J].Transactions of Nonferrous Metals Society of China,2016,26(7):1912-1918.
[19]MELLOR M,HAWKES I.Measurement of tensile strength by diametral compression of discs and annuli[J].Engineering Geology,1971,5(3):173-225.
[20]LI X,FENG F,LI D.Numerical simulation of rock failure under static and dynamic loading by splitting test of circular ring[J].Engineering Fracture Mechanics,2018,188:184-201.
[21]尤明庆,陈向雷,苏承东.干燥及饱水岩石圆盘和圆环的巴西劈裂强度[J].岩石力学与工程学报,2011,30(3):464-472.YOU M Q,CHEN X L,SU C D.Brazilian splitting strengths of discs and rings of rocks in dry and saturated conditions[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(3):464-472.(in Chinese)
[22]王作棠,周华强,谢耀社.矿山岩体力学[M].江苏徐州:中国矿业大学出版社,2007.WANG Z T,ZHOU H Q,XIE Y S.Mine rock mechanics[M].Xuzhou,Jiangsu:China University of Mining and Technology Press,2007.(in Chinese)
[23]LI X B,WU Q H,TAO M,et al.Dynamic Brazilian splitting test of ring-shaped specimens with different hole diameters[J].Rock Mechanics and Rock Engineering,2016,49(10):4143-4151.
[2]吴畏,蒋美蓉,石磊,等.地下工程隔震技术应用探讨[J].地下空间与工程学报,2007,3(Sup2):1583-1586.WU W,JIANG M R,SHI L,et al.Discussion on application of shock-isolation technology in underground engineering[J].Chinese Journal of Underground Space Engineering,2007,3(Sup2):1583-1586.(in Chinese)
[3]孙铁成,高波,叶朝良.地下结构抗震减震措施与研究方法探讨[J].现代隧道技术,2007,44(3):1-5.SUN T C,GAO B,YE C L.Discussion on antiseismic and seismic-relieving measures and corresponding research methods for underground structures[J].Modern Tunnelling Technology,2007,44(3):1-5.(in Chinese)
[4]喻寅,贺红亮,王文强,等.多孔脆性材料对高能量密度脉冲的吸收和抵抗能力[J].物理学报,2015,64(12):263-271.YU Y,HE H L,WANG W Q,et al.The ability of porous brittle materials to absorb and withstand high energy density pulse[J].Acta Physica Sinica,2015,64(12):263-271.(in Chinese)
[5]HANSSEN A G,ENSTOCK L,LANGSETH M.Close-range blast loading of aluminium foam panels[J].International Journal of Impact Engineering,2002,27(6):593-618.
[6]RATHBUN H J,RADFORD D D,XUE Z,et al.Performance of metallic honeycomb-core sandwich beams under shock loading[J].International Journal of Solids and Structures,2006,43(6):1746-1763.
[7]RADFORD D D,MCSHANE G J,DESHPANDE VS,et al.The response of clamped sandwich plates with metallic foam cores to simulated blast loading[J].International Journal of Solids and Structures,2006,43(7/8):2243-2259.
[8]王建军,郭伟国,赵融,等.轻质泡沫混凝土吸能特性及其压溃流动应力方程[J].土木建筑与环境工程,2013,35(6):96-102.WANG J J,GUO W G,ZHAO R,et al.Energyabsorbing properties and crushing flow stress equation of lightweight foamed concrete[J].Journal of Civil,Architectural&Environmental Engineering,2013,35(6):96-102.(in Chinese)
[9]王智,钱觉时,张朝辉,等.多孔混凝土配合比设计方法初探[J].重庆建筑大学学报,2008,30(3):121-124.WANG Z,QIAN J S,ZHANG Z H,et al.Preliminary discussion on mixing design of porous concrete[J].Journal of Chongqing Jianzhu University,2008,30(3):121-124.(in Chinese)
[10]黄胜,陈卫忠,杨建平,等.地下工程地震动力响应及抗震研究[J].岩石力学与工程学报,2009,28(3):483-490.HUANG S,CHEN W Z,YANG J P,et al.Research on earthquake-induced dynamic responses and aseismic measures for underground engineering[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):483-490.(in Chinese)
[11]赵武胜,陈卫忠,谭贤君,等.高性能泡沫混凝土隧道隔震材料研究[J].岩土工程学报,2013,35(8):1544-1552.ZHAO W S,CHEN W Z,TAN X J,et al.Highperformance foam concrete for seismic-isolation materials of tunnels[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1544-1552.(in Chinese)
[12]王代华,刘殿书,杜玉兰,等.含泡沫吸能层防护结构爆炸能量分布的数值模拟研究[J].爆炸与冲击,2006,26(6):562-567.WANG D H,LIU D S,DU Y L,et al.Numerical simulation of anti-blasting mechanism and energy distribution of composite protective structure with foam concrete[J].Explosion and Shock Waves,2006,26(6):562-567.(in Chinese)
[13]刘海燕,李然.泡沫混凝土吸能机理试验研究[J].成都大学学报(自然科学版),2010,29(2):166-167,180.LIU H Y,LI R.Experimental study on endergonic mechanism of foam concrete[J].Journal of Chengdu University(Natural Science Edition),2010,29(2):166-167,180.(in Chinese)
[14]叶燕华,李利群,孙伟民,等.内注泡沫混凝土空心砌块墙体抗震性能的试验研究[J].地震工程与工程振动,2004,24(5):154-158.YE Y H,LI L Q,SUN W M,et al.Experimental study on seismic behaviors of hollow block wall filled with foaming concrete[J].Earthquake Engineering and Engineering Vibration,2004,24(5):154-158.(in Chinese)
[15]ZHAO G F.Developing a four-dimensional lattice spring model for mechanical responses of solids[J].Computer Methods in Applied Mechanics and Engineering,2017,315:881-895.
[16]ZHAO G F.Development of micro-macro continuumdiscontinuum coupled numerical method[D].EPFL,Switzerland,2010.
[17]WANG Q Z,XING L.Determination of fracture toughness KIC by using the flattened Brazilian disk specimen for rocks[J].Engineering Fracture Mechanics,1999,64(2):193-201.
[18]LI D Y,WANG T,CHENG T J,et al.Static and dynamic tensile failure characteristics of rock based on splitting test of circular ring[J].Transactions of Nonferrous Metals Society of China,2016,26(7):1912-1918.
[19]MELLOR M,HAWKES I.Measurement of tensile strength by diametral compression of discs and annuli[J].Engineering Geology,1971,5(3):173-225.
[20]LI X,FENG F,LI D.Numerical simulation of rock failure under static and dynamic loading by splitting test of circular ring[J].Engineering Fracture Mechanics,2018,188:184-201.
[21]尤明庆,陈向雷,苏承东.干燥及饱水岩石圆盘和圆环的巴西劈裂强度[J].岩石力学与工程学报,2011,30(3):464-472.YOU M Q,CHEN X L,SU C D.Brazilian splitting strengths of discs and rings of rocks in dry and saturated conditions[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(3):464-472.(in Chinese)
[22]王作棠,周华强,谢耀社.矿山岩体力学[M].江苏徐州:中国矿业大学出版社,2007.WANG Z T,ZHOU H Q,XIE Y S.Mine rock mechanics[M].Xuzhou,Jiangsu:China University of Mining and Technology Press,2007.(in Chinese)
[23]LI X B,WU Q H,TAO M,et al.Dynamic Brazilian splitting test of ring-shaped specimens with different hole diameters[J].Rock Mechanics and Rock Engineering,2016,49(10):4143-4151.