矩形均布垂直荷载下三层地基竖向附加应力与位移解析方法

The existing theoretical methods cannot reasonably and practicably analyze vertical additional stresses and displacements in a 3-layer ground, which is common in actual engineering. To solve this theoretical calculation problem, a semi-infinite layered elastic model for the 3-layer ground was established based on the elastic theory. According to the proposed transformation of intermedium variables, the state space theory and the Hankel integral transformation, the closed-form analytical solutions to the vertical additional stresses and displacements under a rectangular uniform load on the 3-layer ground, were deduced. Also, an effective numerical calculation tactic was provided to carry out the proposed method to avoid the possible numerical overflow. Meanwhile, an approach for the integral upper bound to obtain the high-accuracy numerical results of the settlements at the ground surface and the vertical stresses and displacements in the ground was put forward. Analytical results of some examples show that, the proposed solutions agree well with the numerical results via FLAC3D, and the error between the proposed model and the finitely deep foundation model based on China codes is about 8%. If the 1st layer thickness of the multi-layer ground with greatly different 3 layers is larger than the load width, the error of the additional stresses calculated according to the current codes will be very high. As for the ground sequentially including medium, soft and hard layers from the surface, the proposed solutions are obviously less than those obtained with the traditional method for homogeneous ground within the range where the ratio of the soil depth to the load width is not more than 0.75. If the soil depth is over the range, the traditional method will underestimate the additional stress in the ground. Moreover, the proposed method reveals that the thicknesses of the upper 2 layers have a great influence on the additional stresses in the upper and middle areas of the ground, and the stress dispersion efficiency along the depth evidently increase with the thickness of the 1st layer under the surface.