摘要
天然地基通常含有不规则的分层界面。对此,提出了一种计算具有不规则界面的层状地基三维动力响应的薄层法,推导了简谐点源作用下不规则分层半空间三维动力问题的基本解。基于双重Fourier变换,获得弹性介质在频域-波数域内的薄层单元系统控制方程;利用模态叠加原理,推导了半无限长和有限长薄层单元的刚度矩阵,引入完美匹配层模拟波向底层半无限空间的传播,从而构建可考虑土层界面沿横向不规则分布的三维层状地基计算模型,获得了简谐点源作用下不规则分层地基三维动力问题的基本解;通过与既有方法的对比分析,验证了新方法的正确性。最后,利用该方法计算了具有倾斜分层界面的双层地基在简谐荷载作用下的动力响应,结果表明:界面倾斜导致的动力响应差异大,且随着倾斜度以及荷载频率的增加而变大。在进行天然地基的动力分析时,需考虑地基的不规则分层特性导致的振动响应差异。
Natural foundation usually contains irregular interfaces between the soil layers.Therefore,this paper proposes a thin layer method to calculate the three-dimensional(3D)dynamic response of stratified soils with irregular interfaces.Based on the double Fourier transform,the system of equations in terms of thin layer elements for the elastic medium are obtained in the frequency-wavenumber domain.The stiffness matrices of the semi-infinite thin-layer elements and the finite-length thin-layer elements are derived through the modal superposition principle.The perfectly matched layers(PMLs)are subsequently introduced to simulate the wave propagation in the bottom half-space.By using the semi-infinite and the finite-length thin-layer elements as well as the PMLs,a calculation model is finally developed to obtain the 3D fundamental solution for a harmonic point load acting on a layered half-space with irregular interfaces.The accuracy of the proposed method is verified by comparing with the existing methods.Finally,the dynamic responses induced by a harmonic load acting on a two-layer foundation with an inclined interface are investigated.The results show that the inclination of the inclined interface exhibits a significant influence on the dynamic response.The difference in the vibration level increases as the inclination and the load frequency increase.The irregular interface needs to be considered in the evaluation of dynamic response of natural foundation.
作者
李小信
何超
周顺华
李晖
LI Xiao-xin;HE Chao;ZHOU Shun-hua;LI Hui(Key Laboratory of Road and Traffic Engineering of the Ministry of Education,Tongji University,Shanghai 201804,China;Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety,Tongji University,Shanghai 201804,China)
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2023年第S01期655-668,共14页
Rock and Soil Mechanics
基金
国家自然科学基金(No.52208442)
青年人才托举工程(No.2020QNRC013)
上海市青年科技英才扬帆计划(No.22YF1450800)
中央高校基本科研业务费专项资金。
关键词
动力响应
层状地基
基本解
薄层法
完美匹配层
dynamic response
layered foundation
fundamental solution
thin layer method
perfectly matched layer
