Analytical solution of ground-borne vibration due to a spatially periodic harmonic moving load in a tunnel embedded in layered soil

目的 地铁列车运行时诱发的振动会对周围环境造成不利影响。本文旨在提出适用于振动预测的周期性隧道-地层耦合解析模型, 探讨各种参数(地层参数、隧道参数、荷载参数等)对振动响应的影响, 研究振动的传播规律, 为减振设计提供理论依据。 创新点 1. 根据平面波与柱面波之间的转换关系, 推导适用于环境振动预测的周期性隧道-地层耦合解析模型; 2. 通过参数分析, 明确移动周期简谐荷载下振动响应的规律及各种参数的影响。 方法 1. 通过理论推导和考虑隧道结构与层状土间的动力相互作用, 获得移动周期简谐荷载下动力响应的计算方法(公式(19)); 2. 通过对比验证, 以及根据现有移动常力及移动简谐荷载的动力响应结果, 验证所提模型的准确性及高效性(图4~6); 3. 通过参数分析, 设置工程常见的参数(地层参数、隧道参数和荷载参数等), 得到移动周期简谐荷载下的振动响应规律及各种参数的影响(图7~16)。 结论 1. 所提周期性隧道-地层耦合解析模型的计算效率高, 预测结果准确, 可用于地铁列车振动环境影响预测。2. 由于荷载移动效应及多普勒效应, 荷载参数影响振动响应主频及频率分布带宽, 但地层参数及隧道参数的影响较小。3. 增加隧道埋深是降低地表振动水平的有效措施。4. 地表一定距离处的振动水平高于隧道正上方, 即出现振动放大区; 环评时应当重点关注放大区内的振动水平, 避免不利影响。 In this study, we propose a novel coupled periodic tunnel–soil analytical model for predicting ground-borne vibrations caused by vibration sources in tunnels. The problem of a multilayered soil overlying a semi-infinite half-space was solved using the transfer matrix method. To account for the interactions between the soil layer and tunnel structure, the transformation characteristics between cylindrical waves and plane waves were considered and used to convert the corresponding wave potentials into forms in terms of the Cartesian or cylindrical coordinate system. The induced ground-borne vibration was obtained analytically by applying a spatially periodic harmonic moving load to the tunnel invert. The accuracy and efficiency of the proposed model were verified by comparing the results under a moving constant and harmonic load with those from previous studies. Subsequently, the response characteristics under a spatially periodic harmonic moving load were identified, and the effects of a wide range of factors on the responses were systematically investigated. The numerical results showed that moving and Doppler effects can be caused by a spatially periodic harmonic moving load. The critical frequency and frequency bandwidth of the response are affected by the load type, frequency, velocity, and wavenumber in one periodicity length. Increasing the tunnel depth is an efficient way to reduce ground-borne vibrations. The effect of vibration amplification on the free surface should be considered to avoid excessive vibration levels that disturb residents.