Scattering of elastic waves by mountain cracks in elastic half space
SUN Xiaojian1, LIU Zhongxian1,2, ZHANG Hai1
1. Tianjin Municipal Key Lab of Civil Structure Protection and Reinforcement, Tianjin Chengjian University, Tianjin 300384, China;
2. Tianjin Institute of Earthquake Engineering, Tianjin 300384, China
Abstract：The indirect boundary element method (IBEM) was used to solve scattering of elastic waves by mountain cracks in elastic half space. Taking a semi-circular mountain with cracks as an example, effects of incident wave frequency, crack angle, crack location and crack number on plane elastic wave scattering were analyzed, anddisplacementamplitudes of the mountain surfaceand the surface on both sides were calculated. Results showed thatcracks have obviousscaling effect on mountain surface displacement; with increase in frequency, effects of crack angle decrease, while effects of crack number increase gradually; when P wave is vertically incident, the amplification effect is the most obvious at the mountainside; compared with the mountain without crack, the peak value of horizontal displacement at the mountainside in the frequency range of 3 to 5 is about 2 times largerthan that in case of the mountain without crack; when SV wave is vertically incident, change at the mountain foot is the most obvious, the maximum peak value reaches 1.8, nearly 27% higher than that in case of the mountain without crack.
孙晓剑1，刘中宪1,2，张海1. 弹性半空间山体裂纹对弹性波的散射[J]. 振动与冲击, 2020, 39(19): 195-203.
SUN Xiaojian1, LIU Zhongxian1,2, ZHANG Hai1. Scattering of elastic waves by mountain cracks in elastic half space. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(19): 195-203.
[1] 刘中宪,张雪,孙帅杰,等.邻近山体地形地震动力相互作用边界元法模拟[J].应用力学学报,2018,35(4):722-729.LIU Zhongxian, ZHANG Xue, SUN Shuaijie, et al.Boundary element method for dynamic interaction of terrain and earthquake in adjacent mountains[J].Chinese Journal of ChineseJournalof Applied Mechanics.2018,35(04):722-729.AppliedMechanics .2018,35(04):722-729.
[2] 巴振宁,黄棣旸,梁建文,等.层状半空间中周期分布凸起地形对平面 SH 波的散射[J].地球物理学报，2017,60(3):1039-1052.BA Zhenning, HUANG Diyang, LIANG Jianwen,et al. Scattering and diffraction of plane SH-waves by periodically distributed hill topographies [J].
Chinese journal of geophysics,2017,60(3):1039-1052.
[3] 韩峰,王光政,陈翰.SH波对多个凸起与凹陷相连地形的散射问题研究[J].应用数学和力学,2013,34(4): 355-363.
HAN Feng, WANG Guangzheng, CHEN Han. Research on Scattering of SH-Waves on Multiple Hills and Canyons. [J].Applied mathematics and mechanics,2013,34(4:)355-
363.
[4] 张吉晗.地震动山体地形效应数值模拟研究[D].浙江大学,2018.ZHANG Jihan. Study on numerical simulation of topographic effect of ground motion mountain[D]. Zhejiang University.2018.
[5] 韩开锋,尹梓安,曾新吾.间接边界元法模拟含裂纹介质中弹性波的传播[J].国防科技大学学报,2005(3):92-95.HAN Kaifeng,YIN Zian,ZENG Xinwu. Numerical modeling of elastic waves propagating in cracked media by the indirect BEM [J].Journal of national university of defense technology.2005(03):92-95.
[6] 韩开锋,曾新吾.边界元法模拟含随机分布裂纹介质中波的传播[J].岩土工程学报2006, 28(7) :922-925.HAN Kaifeng, ZENG Xinwu . Boundary element Modeling of elastic waves propagating in the media with randomly distributed cracks [J].Chinese Journal of Geotechnical Engineering.200628(07):922-925.
[7] 杨在林,闫培雷,刘殿魁.SH波对浅埋弹性圆柱及裂隙的散射与地震动[J]. 力学学报, 2009,41(2) : 229-235.
YANG Zailin, YAN Peilei, LIU Diankui. Scattering and ground motion of SH waves on shallow buried elastic cylinder and crack [J].Chinese Journal of Theoretical and Applied Mechanics.2009,41(02):229-235.
[8] 雷钧.裂纹动态扩展的边界元模拟[J].北京工业大学学报,2013 (6):806-810.LEI Jun.Boundary element simulation of crack dynamic propagation[J].Journal of Beijing University of Technology.2013,(06):806-810.
[9] 李竟艳,高文学,宋肖龙.岩石材料动载下泛形裂纹扩展数值模拟[J].振动与冲击,2018,37(22):88-91. LI Jingyan,GAO Wenxue,SONG Xiaolong.Numerical simulation on the extension of a ubiquitiformal crack
of rock materials under dynamic loading[J].Journal of Vibration and Shock.2018,37(22):88-91.
[10] 杨仁树,左进京,宋俊生,等.爆炸应力波作用下空孔周围裂纹群的扩展规律[J].振动与冲击,2018,37(14):806-810.YANG Renshu,ZUO Jinjing,
SONG Junsheng ,et al. Experimental study on the extension rule of crack group around a hole under explosive stress wave[J]. Journal of Vibration and Shock.2018,37(14):74-78.
[11] 钟伟芳,钱维平.各向异性体内含任意孔洞对反平面波散射的边界元方法[J]. 固体力学报,1990,12(4):285-297. ZHONG Weifang, QIAN Weiping. Boundary element method for scattering of antiplane wave with arbitrary holes in anisotropic body [J].Journal of Solid Mechanics. 1990,12(04):285-297.
[12] 刘中宪,齐欣,王冬.沉积河谷-建筑群地震动力相互作用的二维IBEM模拟[J].岩土力学,2018,39(10):3803-
3811.LIU Zhongxian, QI Xin,WANG Dong. LIANG Jianwen. Dynamic response of a mountain tunnel under
plane P-SV waves[J].Rock and Soil Mechanics. 2018,39(10):3803-3811.
[13] 巴振宁,喻志颖,梁建文.山岭隧洞在平面P-SV波入射下的地震动力响应[J]. 地震工程与工程振动, 2018, 38(5):
50-58. BA Zhenning, YU Zhiying. LIANG Jianwen.
Dynamic response of a mountain tunnel underplane P-SV waves[J].Earthquake Engineering andEngineering Vibrations. 2018,38(05):50-58.
[14] Sanchez Sesma F J, Campillo M. Diffraction of P, SV and rayleigh waves by topographic features: a boundary integral formulation[J]. Bull.seism.soc.am, 81(6), 2234-
2253.
[15] Rodríguez-Castellanos. A, Luzón.F, Sanchez Sesma F J. Diffraction of seismic waves in an elastic, cracked halfplane using a boundary integral formulation[J]. Soil Dynamics & Earthquake Engineering, 2005, 25
(11):827-837.
