变速荷载作用下加筋低路堤动力响应分析

为研究变速荷载作用下加筋低路堤的动力响应，将荷载假设成变速均布线荷载，并考虑由于荷载变速产生的水平向应力，将加筋低路堤视为层状各向同性弹性层，采用Goodman模型表示层间接触条件。利用Garlerkin法推导出Fourier变换域内加筋低路堤动力响应的控制方程，提出一种模态叠加法，Duhamel积分和Fourier逆变换相结合的方法推导出任意时刻动力响应的数值解。采用两个算例验证方法的正确性，分析层间接触条件、荷载加速度、路堤高度和筋材刚度对加筋低路堤动力响应的影响。结果表明：层间接触状态对路面结构层底部的位移影响显著，尤其对纵向位移影响很大，且变速状态下这种影响更加明显，工程中应尽量使加筋土上下表面处于完全连续状态；随着初速度和加速度的增加，路面结构层动挠度显著增加，地基土表面动应力峰值明显增加，动应力路径显著增大且沿顺时针偏转；加速度对于正应力和剪应力在加筋低路堤中的衰减有一定的影响；增加加筋材料刚度会导致应力在加筋低路堤中的衰减，剪应力比最大可减小47.9%,正应力比最大可减小29%。

Dynamic response of low height reinforced embankment under moving load with variable velocity

The dynamic response of low height reinforced embankment under load with variable velocity was investigated. The load was assumed to be a uniform load, and the horizontal stress caused by the variable velocity of the load was taken into consideration. The low height reinforced embankment was considered as a layered isotropic elastic layer, and the Goodman model was employed to represent the interlayer contact conditions. The governing equations of the dynamic response of low height reinforced embankment in the Fourier transform domain were derived using the Garlerkin method. The generalized numerical solutions were obtained using a combination method of modal superposition method, Duhamel integral, and Fourier inverse transform. Two examples were used to verify the correctness of the method. The influences of the interlayer state, acceleration, embankment height, and reinforcement modulus on the dynamic response of the low height reinforced embankment were investigated. Results show that the interlayer contact state had a significant effect on the deflection at the bottom of the pavement structure, especially on the longitudinal deflection, and the effect was greater when the load moved with variable velocity. Thus, the upper and lower surfaces should be in full contact in practical engineering. With the increase in the initial velocity and acceleration, the dynamic deflection and stress increased significantly, and the dynamic stress path on the foundation became larger and rotated clockwise. Acceleration had an effect on reducing the stress in low reinforced embankment. Increasing the stiffness of the reinforced material could effectively reduce shear stress ratio by 47.9% and normal stress by 29%.