基于谱元法的Rayleigh波频散特征计算与模态叠加耦合机理研究  

Study on dispersion characteristics calculation and coupling mechanism of multi-modes superposition of Rayleigh wave based on spectral element method

作　　者：杨博 张萌[1] 夏江海 龙友明 吴忧 YANG Bo;ZHANG Meng;XIA Jianghai;LONG Youming;WU You(School of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China;School of Earth Sciences,Zhejiang University,Hangzhou 310027,China;National and Local Joint Laboratory of Transportation and Civil Engineering Materials,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学土木工程学院,重庆400074 [2]浙江大学地球科学学院,浙江杭州310027 [3]重庆交通大学交通土建工程材料国家地方联合工程实验室,重庆400074

出　　处：《地震工程与工程振动》2024年第1期205-213,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(51708071,41830103);国家重大科研仪器研制项目(51927814);重庆市自然科学基金项目(CSTB2023NSCQ-MSX1024);重庆交通大学自然科学类揭榜桂帅项目(XJ2023000201);重庆市研究生教育项目(YKCSZ23123)。

摘　　要：为了提升Rayleigh波勘探成层结构力学参数的精细化水平,基于谱元法,构建了弹性层状半无限结构的Rayleigh波频散方程。针对半无限土基和“上软下硬”这2种规则成层结构,运用谱元法与快速矢量传递法对比计算了Rayleigh波多阶模态的频散曲线。结果表明:谱元法与解析法计算结果之间的相对误差在0.05%以下,具有较高的计算精度。在此基础上,进一步针对“上硬下软”的典型路面结构、含“软夹层”和含“硬夹层”的复杂成层结构,结合谱元法,推导了表面位移的计算方法,通过分解Rayleigh波各模态相速度对表面位移能量的贡献,建立了一种基于谱元法确定复杂成层结构中Rayleigh波多模态叠加耦合机理的半解析方法,此方法确定的Rayleigh各阶模态叠加耦合频散特征与速度-应力有限差分方法仿真结果之间具有很好的吻合度,表明基于谱元法计算Rayleigh波频散曲线并以此揭示成层结构中Rayleigh波模态叠加耦合机理是合理、可行的。In order to improve the refinement level of mechanical parameters of layered structures explored by Rayleigh wave,this study constructed the Rayleigh wave dispersion equation in layered elastic semi-infinite stratum based on the spectral element method.For the two stratum structures of semi-infinite and“upper soft and lower hard”,compared and calculated the dispersion curves of multi-modes Rayleigh wave with spectral element method and fast vector-transfer algorithm.The results show that the relative error between the calculation results of spectral element method and the corresponding results of fast vector-transfer algorithm is under 0.05%,which has high calculation accuracy.On this basis,for the three complex layered structures of“upper hard and lower soft”pavement structure,containing“soft interlayer”and containing“hard interlayer”,this study derived the calculation method of surface displacement based on spectral element method,and established an semi-analytical method to determine the superposition coupling mechanism of multi-modes Rayleigh wave in complex stratum structure by analyzing the contribution of each mode phase velocity of Rayleigh wave to surface displacement energy,which are in good agreement with the corresponding simulation results of velocity-stress finite element method,indicating that it is reasonable and feasible to calculate the dispersion curves of Rayleigh wave and reveal the superposition coupling mechanism of multi-modal Rayleigh wave based on spectral element method.

关 键 词：谱元法 Rayleigh波频散曲线 模态叠加耦合 成层结构 面波勘探 

分 类 号：TU435[建筑科学—岩土工程]