P-SV波斜入射时有阻尼成层介质自由波场的一维化时域算法  

A 1D Time-Domain Method for in-plane Wave Motion of Free Field in Layered Media with Damping under Obliquely Incident P-SV Waves

作　　者：卓卫东[1,2] 高智能[1] 谷音[1,2] 

机构地区：[1]福州大学土木工程学院,福建福州350116 [2]福州大学福建省土木工程多灾害防治重点实验室,福建福州350116

出　　处：《水利与建筑工程学报》2016年第6期18-24,34,共8页Journal of Water Resources and Architectural Engineering

基　　金：国家自然科学基金资助项目(51108088)

摘　　要：为了研究土层介质阻尼对自由波场计算的影响,在一维化时域算法基础上,采用有限差分方法,推导建立了考虑阻尼影响的水平成层弹性介质平面内自由波场求解的显式的数值逐步法公式,并采用MATLAB程序语言编制了相应的数值计算程序,进行平面内P-SV波斜入射情形下均匀弹性土层的算例分析。结果表明:阻尼对水平成层弹性介质平面内的自由波场有着重要的影响,与无阻尼均匀土层相比,P波斜入射下有阻尼均匀土层的水平和竖向位移幅值分别可减小53.1%和26.5%,SV波斜入射下水平和竖向位移幅值分别可减小48.2%和31.7%;阻尼使均匀土层自由表面的位移幅值明显减小,而中、下部节点的位移幅值减小相对较小。由此可见,土层介质阻尼对成层半空间平面内自由波场一维化计算的影响不可忽视。In order to study the influence of layered-soil damping on the free field algorithm,based on a 1D timedomain method for in-plane wave motion of free field in layered media proposed by Liu and Wang,formulas of explicit time-stepping method to solve the in-plane wave motion of free field in layered media with damping are established by using finite difference method,and its numerical program has been developed with Matlab programming language. A case study of in-plane wave motion of free field in layered soil with damping under obliquely incident P wave and SV wave was carried out respectively. The results show that： the peak horizontal and vertical displacements in layered soil with damping can be reduced by 53. 1% and 26. 5%,respectively,under incident P wave,and the peak horizontal and vertical displacements can be reduced by 48. 2% and 31. 7%,respectively,under incident SV wave,comparing with layered soil without damping. The case study indicates that soil damping has significant influence on in-plane wave motion of free field in layered soil,and it can reduce greatly with the displacement amplitude of the free surface of the layered soil,and reduce slightly with the displacement amplitudes of the middle and lower nodes. Thus it can be seen that the influence of layered-soil damping on 1D time-domain method for the free field algorithm in layered half space by incident in-plane wave can not be ignored.

关 键 词：成层介质 自由波场 一维化时域算法 土层介质阻尼 逐步法 

分 类 号：P315[天文地球—地震学] TU311[天文地球—固体地球物理学]