明挖隧道基坑张弦梁主动位移控制理论模型及应用

A Theoretical Model of Active Displacement Control Using Beam String Structure in Excavation for Open-cut Tunnel and Its Application

  • 摘要: 为实现张弦梁结构土体水平位移的主动精确控制,综合考虑围檩厚度、撑杆宽度与布置间距以及基坑开挖深度等因素对主动位移控制的影响,引入Heaviside函数表征撑杆集中荷载响应,以规避模型建立过程中分段多、边界复杂等难题;进而采用拉普拉斯变换求解高阶微分控制方程,建立张弦梁与Timoshenko梁的耦合力学模型,得到适用于不同土体参数和张弦梁结构特征的主动位移控制解析解模型,并建立剪力-弯矩-位移方程的统一显性表达式。工程案例验证表明,实测数据与模型计算值误差为8.74%。参数分析结果显示,改变撑杆宽度可使最大水平位移下降47.5%;对于16 m大跨度张弦梁,撑杆间距取4~6 m时位移控制效果最优。

     

    Abstract: To achieve precise control of horizontal soil displacement in beam string structures, the influences of factors such as waling thickness, strut width and spacing, and excavation depth on active displacement control are comprehensively considered. The Heaviside function is introduced to characterize the concentrated load response of the struts, thereby circumventing the difficulties of excessive segmentation and complex boundary conditions in model development. Subsequently, the Laplace transform is employed to solve the higher-order governing differential equations, and a coupled mechanical model integrating the beam string structure and Timoshenko beam theory is established. An analytical solution model for active displacement control, applicable to various soil parameters and beam string structural configurations, is derived, and unified explicit expressions for the shear-force, bending-moment, and displacement equations are formulated. Validation against an engineering case shows that the discrepancy between the measured data and the model predictions is 8.74%. Parametric analysis reveals that altering the strut width reduces the maximum horizontal displacement by 47.5%, and for a 16 m-span beam string structure, a strut spacing of 4~6 m yields optimal displacement control performance.

     

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