层状场地中局部不均体对平面P波的散射
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摘要
利用间接边界元方法,在频域内求解了层状场地中局部不均体对平面P波的散射。利用精确的土层动力刚度矩阵进行自由场反应分析,求得位移和应力响应。通过计算虚拟分布荷载的格林影响函数,求得相应位移和应力;根据边界条件确定虚拟分布荷载,最终得到问题的解答。研究了入射P波时,不均体宽度、埋深、厚度、入射角、入射频率度等参数对地表位移幅值的影响,并与相应自由场的结果进行了比较。不均体对P波散射有重要影响,在工程场地地震安全性评价中,应合理考虑局部不均体对场地设计地震动参数确定的影响。
The scattering of P waves by a local nonhomogeneous body of arbitrary shape in a layered half-space is modeled using the indirect boundary element method (IBEM) in the frequency domain. The free-field responses are calculated by using the exact dynamic-stiffness matrix of soil layers to determine the displacements and stresses at the interface of the local nonhomogeneous body; and fictitious distributed loads are then applied at the interface in the free field to calculate the Green’s functions for displacements and stresses. The amplitudes of the fictitious distributed loads are determined from the boundary conditions; and the displacements arising from the waves in the free field and from the fictitious distributed loads are summed to obtain the solution. The effects of width and thickness of the local nonhomogeneous body, and the incident angle and frequency on the surface displacements for P waves are studied. These results are compared with that of one-dimensional model. The local nonhomogeneous body has important influence on the scattering of P waves. The influence of local nonhomogeneous body on determination of design earthquake ground motion parameters should be considered reasonably in evaluation of seismic safety for engineering site.
The scattering of P waves by a local nonhomogeneous body of arbitrary shape in a layered half-space is modeled using the indirect boundary element method (IBEM) in the frequency domain. The free-field responses are calculated by using the exact dynamic-stiffness matrix of soil layers to determine the displacements and stresses at the interface of the local nonhomogeneous body; and fictitious distributed loads are then applied at the interface in the free field to calculate the Green’s functions for displacements and stresses. The amplitudes of the fictitious distributed loads are determined from the boundary conditions; and the displacements arising from the waves in the free field and from the fictitious distributed loads are summed to obtain the solution. The effects of width and thickness of the local nonhomogeneous body, and the incident angle and frequency on the surface displacements for P waves are studied. These results are compared with that of one-dimensional model. The local nonhomogeneous body has important influence on the scattering of P waves. The influence of local nonhomogeneous body on determination of design earthquake ground motion parameters should be considered reasonably in evaluation of seismic safety for engineering site.
引文
[1]胡聿贤.地震工程学(第二版)[M].北京:地震出版社,2006.
[2]李小军.工程场地地震安全性评价工作及相关技术问题[J].震灾防御技术,2006,1(1):15-24.LI Xiao-jun.Evaluation of seismic safety for engineering sites and relevant technical problems[J].Technology for Earthquake Disaster Prevention,2006,1(1):15-24.
[3]WONG Y L,et al.Assessing seismic response of soft soil site in Hong Kong using microtremor records[J].Hong Kong Institute of Engineering,Transactions,1998,5(3):70-79.
[4]MANOOGIAN M E,LEE V W.Diffraction of SH-waves by subsurface inclusions of arbitrary shape[J].Journal of Engineering Mechanics,1996,122(2):123-129.
[5]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.LIANG Jian-wen,YAN Lin-jun,LI Jun-wei1,et al.Response of circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,22(2):138-143.
[6]梁建文,张浩,LEE V W.平面P波入射下地下洞室群动应力集中问题解析解[J].岩土工程学报,2004,26(6):815-819.LIANG Jian-wen,ZHANG Hao,LRR V W.An analytical solution for dynamic stress concentration of underground cavities under incident plane P waves[J].Chinese Journal of Geotechnical Engineering,2004,26(6):815-819.
[7]李伟华,赵成刚.饱和土半空间中圆柱形孔洞对平面P波的散射[J].岩土力学,2004,25(12):1867-1872.LI Wei-hua,ZHAO Cheng-gang.An analytical solution for diffraction of plane P-waves by cylindrical cavity in a fluid-saturated porous media semi-space[J].Rock and Soil Mechanics,2004,25(12):1867-1872.
[8]DRAVINSKI M,MOSSESSIAN T K.Scattering of planeharmonic P,SV and Rayleigh waves by dipping layers of arbitrary shape[J].Bull Seism Soc Am,1987,77(1):212-235.
[9]FISHMAN K L,ALIMAD S.Seismic response for alluvial valleys subjected to SH,P and SV waves[J].Soil Dynamics and Earthquake Engineering,1995,14:249-258.
[10]梁建文,尤红兵.层状半空间中洞室对入射平面P波的放大作用[J].地震工程与工程振动,2005,25(2):16-24.
[11]LIANG Jian-wen,YOU Hong-bing,Amplification of plane P waves by a cavity in a layered half-space[J].Earthquake Engineering and Engineering Vibration,2005,25(2):16-24.
[12]尤红兵,梁建文,层状半空间中洞室对入射平面SV波的散射[J].岩土力学,2006,27(3):383-388.YOU Hong-bing,LIANG Jian-wen.Scattering of plane SV waves by a cavity in a layered half-space[J].Rock and Soil Mechanics,2006,27(3):383-388.
[13]WOLF J P.Dynamic soil-structure interaction[M].Englewood Cliffs:Prentice-Hall,1985.
[2]李小军.工程场地地震安全性评价工作及相关技术问题[J].震灾防御技术,2006,1(1):15-24.LI Xiao-jun.Evaluation of seismic safety for engineering sites and relevant technical problems[J].Technology for Earthquake Disaster Prevention,2006,1(1):15-24.
[3]WONG Y L,et al.Assessing seismic response of soft soil site in Hong Kong using microtremor records[J].Hong Kong Institute of Engineering,Transactions,1998,5(3):70-79.
[4]MANOOGIAN M E,LEE V W.Diffraction of SH-waves by subsurface inclusions of arbitrary shape[J].Journal of Engineering Mechanics,1996,122(2):123-129.
[5]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.LIANG Jian-wen,YAN Lin-jun,LI Jun-wei1,et al.Response of circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,22(2):138-143.
[6]梁建文,张浩,LEE V W.平面P波入射下地下洞室群动应力集中问题解析解[J].岩土工程学报,2004,26(6):815-819.LIANG Jian-wen,ZHANG Hao,LRR V W.An analytical solution for dynamic stress concentration of underground cavities under incident plane P waves[J].Chinese Journal of Geotechnical Engineering,2004,26(6):815-819.
[7]李伟华,赵成刚.饱和土半空间中圆柱形孔洞对平面P波的散射[J].岩土力学,2004,25(12):1867-1872.LI Wei-hua,ZHAO Cheng-gang.An analytical solution for diffraction of plane P-waves by cylindrical cavity in a fluid-saturated porous media semi-space[J].Rock and Soil Mechanics,2004,25(12):1867-1872.
[8]DRAVINSKI M,MOSSESSIAN T K.Scattering of planeharmonic P,SV and Rayleigh waves by dipping layers of arbitrary shape[J].Bull Seism Soc Am,1987,77(1):212-235.
[9]FISHMAN K L,ALIMAD S.Seismic response for alluvial valleys subjected to SH,P and SV waves[J].Soil Dynamics and Earthquake Engineering,1995,14:249-258.
[10]梁建文,尤红兵.层状半空间中洞室对入射平面P波的放大作用[J].地震工程与工程振动,2005,25(2):16-24.
[11]LIANG Jian-wen,YOU Hong-bing,Amplification of plane P waves by a cavity in a layered half-space[J].Earthquake Engineering and Engineering Vibration,2005,25(2):16-24.
[12]尤红兵,梁建文,层状半空间中洞室对入射平面SV波的散射[J].岩土力学,2006,27(3):383-388.YOU Hong-bing,LIANG Jian-wen.Scattering of plane SV waves by a cavity in a layered half-space[J].Rock and Soil Mechanics,2006,27(3):383-388.
[13]WOLF J P.Dynamic soil-structure interaction[M].Englewood Cliffs:Prentice-Hall,1985.
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