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对承受高速移动荷载的饱和多孔地基动应力响应开展了解析理论研究。引入势函数,进行Helmholtz代换,通过傅里叶变换得到了承受矩形分布的竖向与水平向移动荷载的三维饱和地基动应力的基本函解,数值积分求解逆变换,进而得到移动荷载下饱和地基动应力响应的理论解。基于饱和多孔介质的动应力理论解,分析了移动荷载速度及频率的动应力响应,进一步分析了水平及竖向移动荷载耦合作用下饱和地基的动应力。理论分析表明,荷载速度及其频率诱发地基动应力水平的放大效应,动应力水平随荷载移动速度增大呈现指数型放大效应,移动速度接近剪切波速时动应力水平达到峰值,而荷载速度与频率引发的动应力放大效应随地基深度增大而增强。考虑水平动载的耦合效应,地基的动剪应力和水平向正应力水平显著增大,而竖向动正应力变化不大。
The dynamic stress response of saturated porous ground subjected to high-speed moving loads is studied theoretically. The potential function is introduced to carry out Helmholtz substitution. The fundamental solutions to the dynamic stress in the three-dimensional saturated soil subjected to the vertical and horizontal moving loads subjected to the rectangular distribution are obtained by Fourier transform. The numerical integration is solved for the inverse transformation so that the saturation under the moving load Theoretical Solution of Ground Dynamic Stress Response. Based on the theoretical solution of dynamic stress in saturated porous media, the dynamic stress response of moving load velocity and frequency is analyzed, and the dynamic stress of saturated soil under horizontal and vertical moving loads is analyzed. The theoretical analysis shows that the amplifying effect of dynamic stress level induced by load velocity and frequency, the dynamic stress level exhibits exponential amplification effect with the increase of load moving velocity, and the dynamic stress level reaches its peak when the moving velocity approaches shear wave velocity. However, The frequency-induced dynamic stress amplification effect increases with the depth of the ground. Considering the coupling effect of horizontal dynamic load, the dynamic shear stress and the horizontal normal stress of the foundation increase significantly, while the vertical dynamic stress does not change much.