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根据能量法中的格林公式以及桩微段和桩侧土微段的力平衡推导了多层地基中单桩的位移控制方程,该控制方程能综合考虑桩侧土的剪切和压缩过程。根据桩土系统的轴力和位移在各层地基边界处的连续条件以及传递矩阵法获得了多层地基中单桩在轴向荷载下的总刚度矩阵。由于位移函数非显式,因此运用迭代步骤进行求解,进而可以完全确定单桩的位移和力函数。结合算例1对本文方法进行了验证,结合算例2给出了桩侧和桩端土相互强化的一个弹性理论解释。最后结合一个工程实例对本文方法进行了验证。
Based on the Green formula in energy method and the force balance between pile micro-section and soil micro-section, the displacement control equation of single pile in multi-layer foundation is deduced. The governing equation can consider the shear and compression process of pile side soil. According to the continuous conditions of axial force and displacement of pile-soil system at the boundary of each layer of foundation and the transfer matrix method, the total stiffness matrix of single pile in multi-layered foundation under axial load is obtained. Since the displacement function is non-explicit, the iterative steps are used to solve the problem and the displacement and force function of the single pile can be completely determined. The method in this paper is validated by the example 1, and an elastic theoretical explanation of the mutual reinforcement between the pile and the pile tip is given in combination with the example 2. Finally, a project example is used to verify the method in this paper.