上覆弹性板双层地基在移动荷载作用下的动力响应

DYNAMIC RESPONSE OF AN ELASTIC SLAB RESTING ON DOUBLE-LAYERED SUBGRADE SUBJECTED TO MOVING LOAD

用Fourier变换及逆变换对移动荷载作用下路基路面系统的动力响应问题进行研究。考虑路基路面相互作用,假设一条形移动荷载作用在路面板的表面,地基以地下水位面为分界面分为双层,水位面以上为单相弹性土层,以下为饱和土层。考虑地基土层厚度有限,利用Lame对位移场的分解理论,引入势函数,并运用Fourier变换分别对弹性土层和饱和土层进行分析。在Fourier变换域内,结合边界条件,联立路面板、弹性土层和饱和土层的运动方程,得到土体竖向位移、应力和饱和土层内孔隙水压力的表达式;同时利用离散Fourier逆变换得到数值计算结果。计算结果表明,荷载速度、频率,饱和土层的渗透系数对地表竖向位移的影响很大;弹性土层厚度对竖向位移的影响依赖于荷载速度;弹性土层厚度以及弹性土层和饱和土层的相对刚度比对孔隙水压力有非常明显的影响。

The dynamic response of a subgrade-slab system subjected to harmonic strip moving load is investigated using the Fourier transform and the inverse Fourier transform. The subgrade-slab interaction is considered, and the pavement is treated as orthotropic elastic slab resting on a double-layered subgrade. Taking the soil layer above the groundwater table as elastic single-phase layer and the soil layer below the groundwater table as saturated medium, the governing equations of subgrade-slab system are solved in the transformed field domains of moving space considering the finite depth of layers, and Lame decomposition theorem of displacement field and potential functions. Considering the mixed boundary condition at the upper surface, the fixed boundary condition at the lowest surface and that the stress and displacement at the interface of the layers are continuous： analytical solutions of vertical displacement, stress and pore water pressure in saturated layer are derived using the Fourier transform and the inverse Fourier transform. Numerical results are obtained by using the inverse fast Fourier transform（IFFT）. Calculation results show that the vertical displacement of soil medium is considerably affected by the moving load velocity, frequency and the permeability of saturated layer. The influence of depth of elastic single-phase layer on vertical displacement depends on moving load velocity.The depth of elastic soil layer has great effect on pore water pressure in saturated layer, and the influence of the rigidity ratio between elastic single-phase layer and saturated layer on pore water pressure is similar to that of the depth of elastic soil.