张丙强, 李佳遥, 潘钦锋等.移动荷载作用下底部局部脱空地基梁力学响应研究[J].河南理工大学学报（自然科学版）,2024,43(4):162-168.

ZHANG B Q, LI J Y, PAN Q F, et al.Dynamic responses of a beam to moving loads on an elastic foundation overlying voids[J].Journal of Henan Polytechnic University(Natural Science) ,2024,43(4):162-168.

移动荷载作用下底部局部脱空地基梁力学响应研究

张丙强1, 李佳遥1, 潘钦锋1, 黄志斌2

1.福建工程学院 土木工程学院，福建 福州  350118;2.中铁二十四局集团福建铁路建设有限公司，福建 福州  350013

摘要: 目的 针对地基由于塑性变形、雨水冲蚀等引起混凝土路面底部产生的脱空效应， 方法将底部局部脱空混凝土路面简化为跨越空洞的弹性地基梁，采用Kelvin地基模型模拟路基对路面的作用，建立移动荷载作用下局部脱空地基梁动力响应控制方程，运用振型叠加法推导地基梁动力响应解析解。通过与既有理论方法计算结果对比，验证本文方法的正确性。然后采用推导出的理论解析解探讨荷载移动速度、地基弹性系数、地基梁抗弯刚度和脱空区宽度对地基梁动力响应的影响。 结果 分析表明：忽略地基梁底部局部脱空的影响，将导致地基梁动力响应理论计算值偏小。地基梁底部局部脱空对脱空区正上方梁的振动位移影响较大，而对脱空区外侧地基梁的振动位移影响较小。地基梁抗弯刚度越小，脱空区宽度对地基梁中点振动位移最大值的影响越显著。当地基梁底部脱空区宽度与梁计算长度的比值为2/9时，地基梁中点振动位移最大值约为不考虑地基梁底部脱空影响时的5倍。增大地基梁抗弯刚度和地基弹性系数可以减小跨越空洞区地基梁中点振动位移，但当地基梁底部脱空区宽度大于1/3梁的计算长度时，提高既有地基弹性系数的控制效果反而较差。 结论 混凝土路面底部脱空会加剧车辆荷载下的动力响应。

关键词:局部脱空梁;动力响应;模态叠加法;移动荷载;黏弹性地基

doi:10.16186/j.cnki.1673-9787.2023040061

基金项目:国家自然科学基金资助项目（51508097）；福建省自然科学基金资助项目（2020J01882）

收稿日期:2023/04/27

修回日期:2023/08/11

出版日期:2024/07/15

Dynamic responses of a beam to moving loads on an elastic foundation overlying voids

ZHANG Bingqiang1, LI Jiayao1, PAN Qinfeng1, HUANG Zhibin2

1.School of Civil Engineering，Fujian University of Technology，Fuzhou  350118，Fujian，China;2.China Railway 24th Bureau Group Fujian Railway Construction Co.， Ltd.，Fuzhou  350113，Fujian，China

Abstract: Objectives To explore the influence of local voids due to plastic deformation or rainwater erosion on the pavement dynamic responses to moving load，  Methods a concrete pavement with local voids was simplified as an elastic beam spanning a void， and the equation for the dynamic responses of the elastic beams on the Kelvin foundation with local voids under moving loads was established. The modal superposition method was used to solve the dynamic responses of a beam overlying voids under moving loads. Compared with the calculation results from the existing theoretical methods， the proposed analytical solutions for the dynamic response of foundation beams were verified. The influences of the parameters on the dynamic response of the beam were studied， including the moving speed of the load， the width of local voids underlying the beam， the elastic coefficient of the foundation， and the bending stiffness of the beam.  Results Neglecting the influence of local voids underneath the beam caused the theoretical results to be less than the true data. The local voids underneath the beam had a significant influence on the dynamic responses of the beam directly above the void， while the influence on the beam outside the void was minor. As the bending stiffness of the foundation beam decreases， the influence of the void width on the maximum displacement of vibration of the foundation beam at the midpoint became significant. When the void width was 2/9 of the length of the beam，the maximum vibrating displacement at the midpoint of the beam was about 5 times of that without considering the void underlying the beam. Increasing the bending stiffness of the beam and the elastic coefficient of the foundation could reduce the vibrating displacement at the midpoint of the beam. However， the effect of improving the foundation elastic coefficient was minor when the void width underlying the beam was 1/3 of the length of the beam.  Conclusions The local voids underneath the concrete pavement exacerbate the vibration of the pavement under vehicle load.

Key words:beams overlying voids;dynamic response analysis;modal superposition method;moving load;viscous foundation