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表位移
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摘要
本文利用复变函数和多极坐标的方法,给出了多个浅埋圆形衬砌结构附近半圆形沉积层的地表位移对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个区域,一个区域为半圆形沉积层,另一区域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.在这两个区域和浅埋圆形衬砌结构内部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,建立求解问题的无穷代数方程组.通过算例的数值分析表明,浅埋圆形衬砌结构的存在对沉积层附近位移有明显的放大作用,且这种作用随着浅埋衬砌圆形结构之间距离的增大而减小.
The ground surface displacement of a semi-cylindrical alluvial valley above multiple subsurface circular structures impacted by incident SH-wave is studied by using complex function and multi-polar coordinates methods in this paper.In the solution process,the whole model is divided into two domains: one domain is the semi-cylindrical alluvial valley and the other one is an elastic half space with a semi-cylindrical canyon above several subsurface circular structures.Wave functions which satisfy zero-stress condition on the horizontal surface are provided in the semi-cylindrical alluvial valley,and the two domains mentioned above,respectively.Displacement and stress continuity are used to build algebra equations on common boundaries between the semi-cylindrical alluvial valley,subsurface circular structures,and the elastic half space.Numerical examples showed that the presence of subsurface circular structures will increase the ground surface displacement of the semi-cylindrical alluvial valley,and the increase effect decreases with the increase of the distance between the subsurface circular structures.
The ground surface displacement of a semi-cylindrical alluvial valley above multiple subsurface circular structures impacted by incident SH-wave is studied by using complex function and multi-polar coordinates methods in this paper.In the solution process,the whole model is divided into two domains: one domain is the semi-cylindrical alluvial valley and the other one is an elastic half space with a semi-cylindrical canyon above several subsurface circular structures.Wave functions which satisfy zero-stress condition on the horizontal surface are provided in the semi-cylindrical alluvial valley,and the two domains mentioned above,respectively.Displacement and stress continuity are used to build algebra equations on common boundaries between the semi-cylindrical alluvial valley,subsurface circular structures,and the elastic half space.Numerical examples showed that the presence of subsurface circular structures will increase the ground surface displacement of the semi-cylindrical alluvial valley,and the increase effect decreases with the increase of the distance between the subsurface circular structures.
引文
[1]M.D.Trifunac.Surface Motion of a Semi-cylindricalAlluvial Valley for Incident Plane SH Waves.Bulletinof the Seismological Society of America.1971,61(6):1755-1770.
[2]H.L.Wong,M.D.Trifunac.Surface Motion of aSemi-elliptical Alluvial Valley for Incident Plane SHWaves.Bulletin of the Seismological Society of Ameri-ca.1974,64(5):1389-1408.
[3]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.23(1)2003.6-12.
[4]Liu D.K.,Wang G.Q.Scattering of SH-wave byMultiple Circular Cavities in Half Space.Earthquakeengineering and Engineering vibration.Vol.1.No.1:36-44.
[5]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射.地震与工程振动,1996,16(2):1-13.
[6]Liu D.K.,Gai B.Z.and Tao G.Y.Applications ofthe Method of Complex Functions to Dynamic StressConcentrations.Wave Motion.1982,4:pp.293-304.
[2]H.L.Wong,M.D.Trifunac.Surface Motion of aSemi-elliptical Alluvial Valley for Incident Plane SHWaves.Bulletin of the Seismological Society of Ameri-ca.1974,64(5):1389-1408.
[3]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.23(1)2003.6-12.
[4]Liu D.K.,Wang G.Q.Scattering of SH-wave byMultiple Circular Cavities in Half Space.Earthquakeengineering and Engineering vibration.Vol.1.No.1:36-44.
[5]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射.地震与工程振动,1996,16(2):1-13.
[6]Liu D.K.,Gai B.Z.and Tao G.Y.Applications ofthe Method of Complex Functions to Dynamic StressConcentrations.Wave Motion.1982,4:pp.293-304.
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