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
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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.
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.
引文
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[18]潘旦光,楼梦麟,董聪.土层地震行波反应分析中侧向人工边界的影响[J].岩土工程学报,2005,27(3):308-312.
[19]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1070-1075.
[20]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.
[21]卢华喜,梁平英,尚守平.地基非线性波动问题中黏-弹性人工边界研究[J].岩土力学,2008,29(7):1911-1916.
[22]张波,李术才,杨学英,等.三维黏弹性介质人工边界研究[J].岩土力学,2009,30(11):3469-3475.
[2]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.
[3]Wolf J P,Obernhuber P.Effects of horizontally traveling waves in soil-structure interaction[J].Nuclear Engineering and Design,1979,57(2):221-244.
[4]李山有,廖振鹏,周正华.大型结构地震反应数值模拟中的波动输入[J].地震工程与工程振动,2001,6(2):1-5.
[5]潘旦光,楼梦麟,范立础.多点输入下大跨度结构地震反应分析研究现状[J].同济大学学报,2001,29(10):1213-1219.
[6]杜修力,陈维,李亮,等.斜入射条件下地下结构时域地震反应分析初探[J].震灾防御技术,2007,2(3):290-296.
[7]傅淑芳,刘宝诚.地震学教程[M].北京:地震出版社,1991.
[8]李山有,王学良,周正华.地震波斜入射情形下水平成层半空间自由场的时域计算[J].吉林大学学报(地球科学版),2003,33(3):372-376.
[9]刘晶波,王艳.成层半空间出平面自由波场的一维化时域算法[J].力学学报,2006,38(2):219-225.
[10]刘晶波,王艳.成层介质中平面内自由波场的一维化时域算法[J].工程力学,2007,24(7):16-22.
[11]Liu Jing-bo,Wang Yan.A 1D time-domain method for inplane wave motions in a layered half-space[J].Acta Mechanica Sinica,2007,23(6):673-680.
[12]赵密,杜修力,刘晶波,等.P-SV波斜入射时成层半空间自由场的时域算法[J].地震工程学报,2013,35(1):84-90.
[13]Lysmer J,Kulemeyer R L.Finite dynamic model for infinite media[J].Journal of Engineering Mechanics,ASCE,1969,95(4):859-877.
[14]Wolf P J.A comparison of time-domain transmitting boundaries[J].Earthquake Engineering and Structure Dynamics,1986,14(14):655-673.
[15]Deeks A J,Randolph M F.Axisymmetric time-domain transmitting boundaries[J].Journal of Engineering Mechanics,ASCE,1994,120(1):25-42.
[16]王振宇,刘晶波.成层地基非线性波动问题人工边界与波动输入研究[J].岩石力学与工程学报,2004,23(7):1169-1173.
[17]刘晶波,王振宇,杜修力,等.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46-51.
[18]潘旦光,楼梦麟,董聪.土层地震行波反应分析中侧向人工边界的影响[J].岩土工程学报,2005,27(3):308-312.
[19]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1070-1075.
[20]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.
[21]卢华喜,梁平英,尚守平.地基非线性波动问题中黏-弹性人工边界研究[J].岩土力学,2008,29(7):1911-1916.
[22]张波,李术才,杨学英,等.三维黏弹性介质人工边界研究[J].岩土力学,2009,30(11):3469-3475.