重力坝动态断裂分析
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摘要
地震作用下重力坝的坝踵裂纹及其稳定性是工程界普遍关心的问题。本文基于比例边界有限元法(SBFEM)研究重力坝坝踵裂纹的动态应力强度因子(SIF)的变化规律。SBFEM的优点是可以给出位移场沿径向的解析解,直接按定义求出SIF,而不必对裂尖进行特殊处理。以柯依那(Koyna)重力坝作为算例,进行了频域法和时域法的分析,比较了不同坝踵裂纹长度的应力强度因子,计算了地震应力沿坝基交界面的变化。同时计算了裂纹内水压分布对应力强度因子的影响。计算结果表明随着裂纹长度的延伸,I型应力强度因子的峰值逐渐增大;裂纹内水压力越大,对应力强度因子的影响越大。本文提出的分析方法可应用于对重力坝抗震安全性评价。
Based on the scaled boundary finite element method(SBFEM) the variation of the dynamic stress intensity factors(SIF) at the heel of gravity dams subjected to earthquake excitation is analyzed.The SBFEM has the advantage that the displacement field along the radial direction can be solved analytically and the SIF is determined directly from its definition so that no special crack tip treatment is needed.The Koyna gravity dam is analyzed as an numerical example for demonstration.The time domain and frequency domain analysis are carried out.The SIFs for different length of cracks at dam heel are evaluated and the variations of stress along the dam foundation interface are calculated.In addition,the effect of the water pressure distribution inside the crack is also studied. The results show that the maximum value of K_Ⅰ varies distinctly with the increase of crack length.Furthermore,the SIF tends to increase with higher internal water pressure of crack.The proposed analysis method is useful for aseismic safety evaluation of gravity dam.
Based on the scaled boundary finite element method(SBFEM) the variation of the dynamic stress intensity factors(SIF) at the heel of gravity dams subjected to earthquake excitation is analyzed.The SBFEM has the advantage that the displacement field along the radial direction can be solved analytically and the SIF is determined directly from its definition so that no special crack tip treatment is needed.The Koyna gravity dam is analyzed as an numerical example for demonstration.The time domain and frequency domain analysis are carried out.The SIFs for different length of cracks at dam heel are evaluated and the variations of stress along the dam foundation interface are calculated.In addition,the effect of the water pressure distribution inside the crack is also studied. The results show that the maximum value of K_Ⅰ varies distinctly with the increase of crack length.Furthermore,the SIF tends to increase with higher internal water pressure of crack.The proposed analysis method is useful for aseismic safety evaluation of gravity dam.
引文
[1]潘家铮.断裂力学在水工结构设计中的应用[J].水利学报,1980(1):45-59.
[2]柏承新,赵代深.二次奇性边界元及其在重力坝坝踵断裂分析中的应用[J].土木工程学报,1988(2):43-50.
[3]李庆斌,林皋,周鸿钧.异弹模界面裂缝的边界元分析及其应用[J].大连理工大学学报,1991(2):199-204.
[4]刘光廷,王宗敏,周鸿钧.缝端奇异边界单元和界面裂缝的应力强度因子计算[J].清华大学学报(自然科学版),1996(1):34-40.
[5]贾金生,李新宇,郑璀莹.特高重力坝考虑高压水劈裂影响的初步研究[J].水利学报,2006,37(12):1509-1515.
[6]刘钧玉,林皋,胡志强,等.裂纹内水压分布对重力坝断裂特性的影响[J].土木工程学报,2009,42(4):132-141.
[7]Boriskovsky V G.On the dynamic stress intensity fracture factor in finite cracked bodies under harmonic loading[J].Engineering Fracture Mechanics,1982,16(4):459-465.
[8]周晶,倪汉根,林皋.重力坝坝面水平裂缝的地震应力强度因子[J].水利学报,1982(4):18-26.
[9]胡良明,李宗刊,周鸿钧.重力坝坝踵界面裂缝的地震断裂分析[J].郑州大学学报(工学版),2002,23(3):101-103.
[10]Wolf J P,Song C.Finite-element modelling of unbounded media[M].Wiley:Chichester,1996.
[11]Song C,Wolf J P.The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-forelastodynamics[J].Computer Methods in Applied Mechanics and Engineering,1997,147:3-4.
[12]刘钧玉,林皋,杜建国.基于SBFEM的多裂纹问题的断裂分析[J].大连理工大学学报,2008,48(3):392-397.
[13]Song C.A super-element for crack analysis in the time domain[J].International Journal for Numerical Methods inEngineering,2004,61(8):1332-1357.
[14]Song C,Vrcelj Z.Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finite-elementmethod[J].Engineering Fracture Mechanics,2008,75(8):1960-1980.
[15]Williams M L.The stress around a fault or crack in dissimilar media[J].Bulletin of the Seismological Society,1959,49:199-204.
[16]Sih C G,Paris P C,Irwin G R,et al.On cracks in rectilinearly anisotropic bodies[J].International Journal of Fracture,1965,3:189-203.
[17]Wolf J P.Dynamic soil-structure interaction[M].Prentice-Hall:Englewood Cliffs,NJ,1985.
[18]Murti V,Valliappan S.The use of quarter point element in dynamic crack analysis[J].Engineering Fracture Mechanics,1986,23:585-614.
[19]Chirino F,Gallego R,Saez A,et al.A comparative study of three boundary element approaches to transient dynamiccrack problems[J].Engineering Analysis with Boundary Elements,1994,13:11-19.
[20]Zhu H,Fan T Y,Tian L Q,et al.Composite materials dynamic fracture studies by generalized Shmuely differencealgorithm[J].Engineering Fracture Mechanics,1996,54:869-877.
[21]Chen Y.Numerical computation of dynamic stress intensity factors by a Lagrangian finite-difference method(the HEMPcode)[J].1975,7.
[22]Kobayashi A,Cherepy R D,Kinsel W,et al.T-elements:state of the art and future trends[J].Journal of BasicEngineering,Transactions of the ASME,Series D,1964,86:681-684.
[23]林皋,杜建国.基于SBFEM的坝-库水相互作用分析[J].大连理工大学学报,2005,45(5):723-729.
[24]Hall J F.An FFT algorithm for structural dynamics[J].Earthquake Engineering and Structural Dynamics,1982,10:797-811.
[2]柏承新,赵代深.二次奇性边界元及其在重力坝坝踵断裂分析中的应用[J].土木工程学报,1988(2):43-50.
[3]李庆斌,林皋,周鸿钧.异弹模界面裂缝的边界元分析及其应用[J].大连理工大学学报,1991(2):199-204.
[4]刘光廷,王宗敏,周鸿钧.缝端奇异边界单元和界面裂缝的应力强度因子计算[J].清华大学学报(自然科学版),1996(1):34-40.
[5]贾金生,李新宇,郑璀莹.特高重力坝考虑高压水劈裂影响的初步研究[J].水利学报,2006,37(12):1509-1515.
[6]刘钧玉,林皋,胡志强,等.裂纹内水压分布对重力坝断裂特性的影响[J].土木工程学报,2009,42(4):132-141.
[7]Boriskovsky V G.On the dynamic stress intensity fracture factor in finite cracked bodies under harmonic loading[J].Engineering Fracture Mechanics,1982,16(4):459-465.
[8]周晶,倪汉根,林皋.重力坝坝面水平裂缝的地震应力强度因子[J].水利学报,1982(4):18-26.
[9]胡良明,李宗刊,周鸿钧.重力坝坝踵界面裂缝的地震断裂分析[J].郑州大学学报(工学版),2002,23(3):101-103.
[10]Wolf J P,Song C.Finite-element modelling of unbounded media[M].Wiley:Chichester,1996.
[11]Song C,Wolf J P.The scaled boundary finite-element method-alias consistent infinitesimal finite-element cell method-forelastodynamics[J].Computer Methods in Applied Mechanics and Engineering,1997,147:3-4.
[12]刘钧玉,林皋,杜建国.基于SBFEM的多裂纹问题的断裂分析[J].大连理工大学学报,2008,48(3):392-397.
[13]Song C.A super-element for crack analysis in the time domain[J].International Journal for Numerical Methods inEngineering,2004,61(8):1332-1357.
[14]Song C,Vrcelj Z.Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finite-elementmethod[J].Engineering Fracture Mechanics,2008,75(8):1960-1980.
[15]Williams M L.The stress around a fault or crack in dissimilar media[J].Bulletin of the Seismological Society,1959,49:199-204.
[16]Sih C G,Paris P C,Irwin G R,et al.On cracks in rectilinearly anisotropic bodies[J].International Journal of Fracture,1965,3:189-203.
[17]Wolf J P.Dynamic soil-structure interaction[M].Prentice-Hall:Englewood Cliffs,NJ,1985.
[18]Murti V,Valliappan S.The use of quarter point element in dynamic crack analysis[J].Engineering Fracture Mechanics,1986,23:585-614.
[19]Chirino F,Gallego R,Saez A,et al.A comparative study of three boundary element approaches to transient dynamiccrack problems[J].Engineering Analysis with Boundary Elements,1994,13:11-19.
[20]Zhu H,Fan T Y,Tian L Q,et al.Composite materials dynamic fracture studies by generalized Shmuely differencealgorithm[J].Engineering Fracture Mechanics,1996,54:869-877.
[21]Chen Y.Numerical computation of dynamic stress intensity factors by a Lagrangian finite-difference method(the HEMPcode)[J].1975,7.
[22]Kobayashi A,Cherepy R D,Kinsel W,et al.T-elements:state of the art and future trends[J].Journal of BasicEngineering,Transactions of the ASME,Series D,1964,86:681-684.
[23]林皋,杜建国.基于SBFEM的坝-库水相互作用分析[J].大连理工大学学报,2005,45(5):723-729.
[24]Hall J F.An FFT algorithm for structural dynamics[J].Earthquake Engineering and Structural Dynamics,1982,10:797-811.
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