This paper proposes an analytical model for evaluating the dynamic response of an underground railway tunnel in layered foundation soil with different saturations.The soil is modeled as layered media,and the circular ...This paper proposes an analytical model for evaluating the dynamic response of an underground railway tunnel in layered foundation soil with different saturations.The soil is modeled as layered media,and the circular tunnel lining is modeled as an infinite Flügge cylindrical shell.The separation of variables method is used to solve the motion equation of the shell,and the wave equation of the soil is solved using the Helmholtz decomposition theorem.A dynamic matrix reflecting the wave vectors of soil layers is established using the transfer matrix method.Based on boundary conditions,the tunnel-soil model is coupled using the transformation method of plane wave functions and cylindrical wave functions.The proposed model is validated by comparison with existing tunnel models,and the effects of saturation and the layered properties of soil on the dynamic response of a layered tunnel-soil system is demonstrated via case studies.展开更多
针对非饱和地基土中埋置隧道的三维动力响应计算问题,提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱...针对非饱和地基土中埋置隧道的三维动力响应计算问题,提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱壳的振动控制方程与非饱和土的波动方程.根据隧-土交界面与地表面处的应力、位移以及孔隙流体压力等边界条件,利用平面波与柱面波的转换性质,实现了隧道内作用单位简谐载荷时隧道衬砌与土体系统动力响应的耦合求解.通过与既有单相弹性介质2.5维有限元-边界元法、两相饱和多孔介质2.5维有限元-边界元法以及三相非饱和介质Pip in Pip半解析法的计算结果进行对比,验证了本文计算方法的可靠性.最后,基于该方法,通过算例分析了不同饱和度下非饱和土-隧道系统的动力响应特征.结果表明,饱和度对土体动位移与超孔隙水压力的幅值响应有较大影响.该方法的非饱和地基土参数退化后,也可用来计算和分析饱和地基土或单相弹性地基土与隧道系统的动力响应.展开更多
基金Supported by:National Natural Science Foundation of China under Grant No.51808405。
文摘This paper proposes an analytical model for evaluating the dynamic response of an underground railway tunnel in layered foundation soil with different saturations.The soil is modeled as layered media,and the circular tunnel lining is modeled as an infinite Flügge cylindrical shell.The separation of variables method is used to solve the motion equation of the shell,and the wave equation of the soil is solved using the Helmholtz decomposition theorem.A dynamic matrix reflecting the wave vectors of soil layers is established using the transfer matrix method.Based on boundary conditions,the tunnel-soil model is coupled using the transformation method of plane wave functions and cylindrical wave functions.The proposed model is validated by comparison with existing tunnel models,and the effects of saturation and the layered properties of soil on the dynamic response of a layered tunnel-soil system is demonstrated via case studies.
文摘针对非饱和地基土中埋置隧道的三维动力响应计算问题,提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱壳的振动控制方程与非饱和土的波动方程.根据隧-土交界面与地表面处的应力、位移以及孔隙流体压力等边界条件,利用平面波与柱面波的转换性质,实现了隧道内作用单位简谐载荷时隧道衬砌与土体系统动力响应的耦合求解.通过与既有单相弹性介质2.5维有限元-边界元法、两相饱和多孔介质2.5维有限元-边界元法以及三相非饱和介质Pip in Pip半解析法的计算结果进行对比,验证了本文计算方法的可靠性.最后,基于该方法,通过算例分析了不同饱和度下非饱和土-隧道系统的动力响应特征.结果表明,饱和度对土体动位移与超孔隙水压力的幅值响应有较大影响.该方法的非饱和地基土参数退化后,也可用来计算和分析饱和地基土或单相弹性地基土与隧道系统的动力响应.
