桩筏结构复合地基中筏板受力分析的理论计算模型与试验研究

由于缺乏刚性桩复合地基之上筏板受力的合理计算公式,目前中国高速铁路桩筏结构复合地基中筏板的设计计算仍采用简化算法,其计算结果的准确合理性尚不满足要求,为此拟对桩筏基础之上的筏板进行理论求解。选取桩筏结构中单桩作用的筏板区域作为求解单元,将该单元结构视为位于单桩和Winkler弹性地基共同支撑的四边滑支Reissner矩形中厚板,将Reissner矩形中厚板的基本方程导入Hamilton体系,利用辛几何中的分离变量及本征函数展开等方法,求出矩形中厚板弯曲问题的解析解,进而可求得复合地基上筏板的内力、挠度、桩顶反力和桩间土压力等设计值。最后将现场试验实测值与理论模型解析解的计算结果进行对比,结果采用文中理论模型计算得到的筏板弯矩、桩顶轴力及桩间土压应力等与现场实测结果吻合较好,表明在桩筏结构复合地基的筏板设计中,提出的理论模型是一种准确可靠的计算方法。

Theoretical and experimental studies on forces acting on raft of pile-raft composite foundation

At present, some simplified algorithms are still used in the design of pile-raft composite foundation of high-speed railway in China because of the lack of a reasonable formula. But their results can not meet the accuracy requirements. The theoretical solution to the raft is essentially studied. In order to get the analytical solution to the raft of the pile-raft foundation, the acting area of a single pile on the raft is selected as an element for solution. The element is regarded as a Reissner rectangular moderately thick plate with four edges shear free-clamped on the Winkler elastic foundation on piles. During calculation, the basic elasticity equation for Reissner rectangular moderately thick plates is transferred into the Hamiltonian system. By separation of variables in Symplectic geometry and characteristic function, the analytic solutions to the bending problems of the rectangular plates with medium and thick thickness can be obtained, and then the internal force, displacement, counter-force at pile top and pressure between the soils and the piles can be calculated. By comparing the measured values with the present analytical solutions, it is shown that the calculated moment of the raft, axial force and pressure between the soils and the piles agree with the measured values. The proposed method is proved to be reliable and can be adopted for the design of the pile-raft composite foundation.