基于两阶段法的堆载对公路桥梁桩基础影响分析

Two-stage analysis of responses of bridge pile foundations to adjacent surcharge

首先基于布西奈斯克解,将表面作用有集中荷载时半无限弹性体的应力变形解在荷载作用区域利用复合辛普森公式进行数值积分,得到了表面处于不同形式的分布荷载作用下土体自由场水平及竖直方向应力和变形的计算公式。结合有限差分法及Mindlin位移解分别推导出弹性地基中桩顶作用有集中荷载时单桩桩、土单元的位移,两者结合便得到主动桩的分析方法。通过将堆载作用下的土体自由场位移施加于桩上把上述自由场分析及主动桩分析结合起来,推导出堆载作用下被动单桩的竖向和水平向承载特性的分析方法。选取地表附近作用有矩形均布荷载的计算工况,通过与有限元计算结果的对比验证了所提出的分析方法的正确性;将所提出的方法计算结果与某处工程案例中实测数据结果进行对比,分析表明利用该方法分析堆载对邻近桩基的水平及竖向影响是合理可靠的。

Based on the Boussiesq solution, a method for computing the distribution of the stress and the deformation in homogeneous soil with several different kinds of loads including rectangular loads and strip loads acting exclusively on the surface of a half elastic space is given by means of integration of the Boussiesq equations of a concentrated force acting on the surface. The integration is realized by numerical integration, the composite Simpson's rule, with dividing the acting area of the distributed loads into numerous tiny rectangles. Meanwhile, the deformation of discrete pile elements, which derives from the finite difference analysis,is given with pile subjected to concentrated force or moment on the pile top. In the same way, deformation of discrete soil elements around the pile is given based on the Mindlin solution. With the combination of the deformations of pile and soil elements, the interactions between discrete pile-soil elements are calculated to solve the responses of 'active pile'. Then, combining the analysis of soil in free field and that of 'active pile' mentioned above, with the displacement of free field imposed on the pile, we thus get solutions of the stress, moment and deformation along the passive pile. Consequently, a method which can be used to calculate free-field movements and stress of soil, strain and stress of 'active pile', as well as the responses of passive piles subjected to different kinds of external loads acting at the surface of soil, is given based on the analysis above. The validity of the method proposed above is testified. A pile subjected to a rectangular uniform load at the surface of soil nearby is taken as an example.Comparisons are made between results from the method proposed in the paper and those from finite element method(FEM), which testifies the method is reasonable. Furthermore, a project case of piled bridge abutment is taken for verification. Results from the method given above are in good accordance with the original data from the in-situ test from the published paper. Therefore, the method could be used to calculate the response of bridge piles with embankment loads nearby.