DDA方法在波动问题计算中的初步研究
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摘要
采用DDA方法验证了1维应力波在不同边界的响应情况;在此基础上,实现了位移和应力2种地震波输入方式,并对2种方法进行了比较。基于DDA的1维计算模型,研究了在计算波动问题时块体单元尺寸和节理刚度的取值问题。研究结果表明:DDA模型网格在波传播方向的尺寸取最短波长的1/15～1/20;随着法向刚度的降低,节理对弹性纵波的衰减作用增大;当节理标准强度大于0.5时,DDA计算的节理面透射系数与理论透射系数的误差在5%以内。此外,基于DDA方法中波动问题的初步研究成果,对某地下厂房在正弦波作用下的动力响应情况进行了简单的分析,分析成果与有限元计算结果基本一致,这为DDA方法用于工程实例的动力响应分析奠定了基础。
The responses of one-dimensional stress wave with different boundaries were verified using DDA method.On this basis,both the displacement and stress way to input seismic wave were achieved and compared.Based on the one-dimensional DDA model,the block element size and joint stiffness in wave calculation were studied.The results showed that the DDA model grid in the direction of wave propagation should take 1/15~1/20 of the shortest wavelength.The lower the joint stiffness is,the more observable the attenuation of elastic P-wave is.When the joint standard strength is greater than 0.5,the difference between DDA calculation and theoretical solution of transmission coefficient of joint surface is less than 5%.Based on the preliminary research results of wave problem in DDA method,the dynamic response of an underground house under sine wave was analyzed simply.The DDA result is consistent with the finite element solution,and it lays the foundation for dynamic response analysis of engineering case using DDA method.
The responses of one-dimensional stress wave with different boundaries were verified using DDA method.On this basis,both the displacement and stress way to input seismic wave were achieved and compared.Based on the one-dimensional DDA model,the block element size and joint stiffness in wave calculation were studied.The results showed that the DDA model grid in the direction of wave propagation should take 1/15~1/20 of the shortest wavelength.The lower the joint stiffness is,the more observable the attenuation of elastic P-wave is.When the joint standard strength is greater than 0.5,the difference between DDA calculation and theoretical solution of transmission coefficient of joint surface is less than 5%.Based on the preliminary research results of wave problem in DDA method,the dynamic response of an underground house under sine wave was analyzed simply.The DDA result is consistent with the finite element solution,and it lays the foundation for dynamic response analysis of engineering case using DDA method.
引文
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[4]Cheng Y M,Zhang Y H.Rigid body rotation and block inter-nal discretization in DDA analysis[J].Int J Numer Anal Meth Geomech,2000,24:567-578.
[5]Jiao Y Y,Zhang X L,Zhao J,et al.Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J].International Journal of Rock Mechanics and Mining Sciences,2007,47:1070-1076.
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[7]Hatzor Y H,Arzi A A,Zaslavskyc Y,et al.Dynamic stability analysis of jointed rock slopes using the DDA method:King Herod’s Palace,Masada,Israel[J].International Journal of Rock Mechanics&Mining Sciences,2004,41:813-832.
[8]Wu J H.Seismic landslide simulations in discontinuous de-formation analysis[J].Computers and Geotechnics,2010,37(5):594-601.
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[12]Wang Weihua,Li Xibing,Hu Shengbin.Effect of model pa-rameters on3DEC dynamic modeling[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(Supp1):4390-4397.[王卫华,李夕兵,胡盛斌.模型参数对3DEC动态建模的影响[J].岩石力学与工程学报,2005,24(增1):4390-4397.]
[13]Liu Jingbo,Liao Zhenpeng.Elastic wave motion in discrete grids(Ⅲ)—the effect of discretization in time domain on wave motior[J].Earthquake Engineering and Engineering Vibration,1990,10(2):1-10.[刘晶波,廖振鹏.离散网格中的弹性波动(Ⅲ)———时域离散化对波传播规律的影响[J].地震工程与工程振动,1990,10(2):1-10.]
[14]Chinese Earthquake Administration.GB17741—2005E-valuation of seismic safety for engineering sites[S].Beijing:Standards press of China,2005.[中国地震局.GB17741—2005工程场地地震安全性评价技术规范[S].北京:中国标准出版社,2005.]
[15]Schoenberg M.Elastic wave behavior across linear slip in-terfaces[J].Journal of Acoustics Society of America,1980,68(5):1516-1521.
[2]石根华.数值流形方法与非连续变形分析[M].裴觉民,译.北京:清华大学出版社,1997.
[3]MacLaughlin M M,Doolin D M.Review of validation of the discontinuous deformation analysis(DDA)method[J].Inter National Journal for Numerical and Analytical Methods in Geomechanics,2006,30(4):271-305.
[4]Cheng Y M,Zhang Y H.Rigid body rotation and block inter-nal discretization in DDA analysis[J].Int J Numer Anal Meth Geomech,2000,24:567-578.
[5]Jiao Y Y,Zhang X L,Zhao J,et al.Viscous boundary of DDA for modeling stress wave propagation in jointed rock[J].International Journal of Rock Mechanics and Mining Sciences,2007,47:1070-1076.
[6]Zheng Hong,Jiang Wei.Discontinuous deformation analysis based on complementary theory[J].Sci in China Ser E:Tech Sci,2009,39(10):1702-1708.[郑宏,江巍.基于互补理论的非连续变形分析方法[J].中国科学E辑:技术科学,2009,39(10):1702-1708.]
[7]Hatzor Y H,Arzi A A,Zaslavskyc Y,et al.Dynamic stability analysis of jointed rock slopes using the DDA method:King Herod’s Palace,Masada,Israel[J].International Journal of Rock Mechanics&Mining Sciences,2004,41:813-832.
[8]Wu J H.Seismic landslide simulations in discontinuous de-formation analysis[J].Computers and Geotechnics,2010,37(5):594-601.
[9]廖振鹏.工程波动理论导论[M].第2版.北京:科学出版社,2002.
[10]Gu Jiong,Zhao Zhiye.Considerations of the discontinuous deformation analysis on wave propagation problems[J].In-ternational Journal for Numerical and Analytical Methods in Geomechanic,2009,33:1449-1465.
[11]Lysmer J,Kuhlemeyer R L.Finite dynamic model for in fi-nite media[J].Journal of the Engineering Mechanics Divi-sion(ASCE),1969,95:859-877.
[12]Wang Weihua,Li Xibing,Hu Shengbin.Effect of model pa-rameters on3DEC dynamic modeling[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(Supp1):4390-4397.[王卫华,李夕兵,胡盛斌.模型参数对3DEC动态建模的影响[J].岩石力学与工程学报,2005,24(增1):4390-4397.]
[13]Liu Jingbo,Liao Zhenpeng.Elastic wave motion in discrete grids(Ⅲ)—the effect of discretization in time domain on wave motior[J].Earthquake Engineering and Engineering Vibration,1990,10(2):1-10.[刘晶波,廖振鹏.离散网格中的弹性波动(Ⅲ)———时域离散化对波传播规律的影响[J].地震工程与工程振动,1990,10(2):1-10.]
[14]Chinese Earthquake Administration.GB17741—2005E-valuation of seismic safety for engineering sites[S].Beijing:Standards press of China,2005.[中国地震局.GB17741—2005工程场地地震安全性评价技术规范[S].北京:中国标准出版社,2005.]
[15]Schoenberg M.Elastic wave behavior across linear slip in-terfaces[J].Journal of Acoustics Society of America,1980,68(5):1516-1521.
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