锁脚锚管受力分析的双参数弹性地基梁模型

 针对Winkler地基梁模型的固有缺陷，将能够反映地基连续性的Pasternak双参数地基梁模型引入到锁脚锚管–钢拱架的联合承载分析中，考虑锁脚锚管与钢拱架之间的变形协调与荷载传递，采用结构力学和弹性地基梁理论推导锁脚锚管挠度、剪力、弯矩和地基反力的解析表达式。分别通过算例和工程实例考察不同地基基床系数和剪切刚度对锁脚锚管力学行为的影响规律，并与Winkler地基梁模型进行比较。结果表明：基床系数越小，2种模型计算所得锁脚锚管剪力、弯矩以及地基反力等的差异越明显；由双参数模型所得的地基反力数值较大，而且分布范围更小，主要集中在锁脚锚管端部附近区域；由双参数模型所得的隧道下沉量要小于Winkler模型的计算值。给出了适当减小锁脚锚管长度，并增大其直径的建议。研究成果可为软弱围岩隧道支护设计提供理论参考。

Double parameters elastic foundation beam model of feet-lock pipes

To avoid the weakness of the Winkler beam model on elastic foundation，a two-parameter foundation model of Pasternak reflecting the continuity of the foundation was applied in the analysis of the feet-lock pipe combined with steel arch. The formulae to calculate the deflection，shear force，bending moment and foundation reaction of feet-lock pipes were derived using the theory of structural analysis and beam on elastic foundation under the consideration of the compatibility of deformation and load transfer between the feet-lock pipe and steel arch. The influence of subgrade coefficient and shear stiffness of the foundation on the mechanical behaviors of feet-lock pipe was investigated through examples and comparison with the Winkler model. It was found that the smaller subgrade coefficient resulted in the larger difference of two models of feet-lock pipe regarding values shear force，bending moment and foundation reaction. The double parameter model produced a lager foundation reaction and smaller distribution range，and the foundation reaction mainly concentrated in the region near the near-end of the feet-lock pipe. The tunnel settlement was less than that calculated from the Winkler model. Finally，it was suggested that the designed length of the feet-lock pipe should be reduced and its diameter should be increased reasonably so as to obtain the desired supporting effect.