SH波入射时多个浅埋圆形衬砌结构附近半圆形沉积层的地震动
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摘要
采用辅助函数思想,利用复变函数和多极坐标的方法给出了地下多个浅埋圆形衬砌结构与地面上半圆形沉积层对SH波散射问题的解答。在求解过程中,将整个求解区域分割成两部分来处理,区域I为半圆形沉积层,区域II为多个浅埋圆形衬砌结构附近带半圆形凹陷的半无限弹性空间。在区域I、II和浅埋圆形结构内部中分别构造满足水平界面上应力为零的位移解,并在半无限弹性空间和半圆形沉积层及浅埋圆形结构的“公共边界”上分别实施位移和应力连续条件,建立起求解该问题的无穷代数方程组。最后,给出了分析例题和数值结果,并对其进行讨论。
Methods of auxiliary function, complex function and multi-polar coordinate were used to study effects of SH wave’s dispersion on multiple subsurface circular structures and semi-cylindrical sedimentary stratum above the ground. The whole solving domain was divided into two parts: domain I is the semi-cylindrical sedimentary stratum; domain II is a half infinite space with a semi-cylindrical canyon nearby several subsurface circular structures. Displacement solutions satisfying zero-stress condition on the horizontal surface were constructed in domain I, II and the subsurface circular structures, respectively. The continuity conditions for displacement and stress were used to build algebra equations in the valley-half space, subsurface structures-half space common boundaries. Numerical examples and results were discussed.
Methods of auxiliary function, complex function and multi-polar coordinate were used to study effects of SH wave’s dispersion on multiple subsurface circular structures and semi-cylindrical sedimentary stratum above the ground. The whole solving domain was divided into two parts: domain I is the semi-cylindrical sedimentary stratum; domain II is a half infinite space with a semi-cylindrical canyon nearby several subsurface circular structures. Displacement solutions satisfying zero-stress condition on the horizontal surface were constructed in domain I, II and the subsurface circular structures, respectively. The continuity conditions for displacement and stress were used to build algebra equations in the valley-half space, subsurface structures-half space common boundaries. Numerical examples and results were discussed.
引文
1Trifunac M D.Surface Motion of a Semi-cylindrical Alluvial Valley for Incident Plane SH Waves.Bulletin of the Seismological Society of America,1971,61(6):1755~1770
2Wong HL,Trifunac MD.Surface Motion of a Semi-elliptical Alluvi-al Valley for Incident Plane SH Waves.Bulletin of the Seismological Society of America,1974,64(5):1389~1408
3Tordovoska M,Lee VW.Surface Motion of a ShallowCircular Alluvial Valleys for Incident Plane SHWaves:Analytical Solution.Soil Dynam Earthq Eng,1991(4):192~200
4Yuan Xiaoming,Liao Zhenpeng.Scattering of Plane SH Waves by a Cylindrical Alluvial Valley of Circular Arc Cross Section.Earthq Eng Struc Dynam,1995(24):1303~1313
5林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动,2002,22(2):9~16
6刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动.爆炸与冲击,2003,23(1):6~12
7Liu D K,Gai B Z,Tao G Y.Applications of the Method of Complex Functions to Dynamic Stress Concentrations.Wave Motion,1982(4):293~304
8Yuan X M,Liao Z P.Surface motion of a Cylindrical hill of circular arc cross-section for incident plane SHwaves.Soil Dyn and Ear Eng,1996(15):189~199
2Wong HL,Trifunac MD.Surface Motion of a Semi-elliptical Alluvi-al Valley for Incident Plane SH Waves.Bulletin of the Seismological Society of America,1974,64(5):1389~1408
3Tordovoska M,Lee VW.Surface Motion of a ShallowCircular Alluvial Valleys for Incident Plane SHWaves:Analytical Solution.Soil Dynam Earthq Eng,1991(4):192~200
4Yuan Xiaoming,Liao Zhenpeng.Scattering of Plane SH Waves by a Cylindrical Alluvial Valley of Circular Arc Cross Section.Earthq Eng Struc Dynam,1995(24):1303~1313
5林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动,2002,22(2):9~16
6刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动.爆炸与冲击,2003,23(1):6~12
7Liu D K,Gai B Z,Tao G Y.Applications of the Method of Complex Functions to Dynamic Stress Concentrations.Wave Motion,1982(4):293~304
8Yuan X M,Liao Z P.Surface motion of a Cylindrical hill of circular arc cross-section for incident plane SHwaves.Soil Dyn and Ear Eng,1996(15):189~199
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