An analytical method is developed for the interaction between two dissimilar piles subjected to vertical loadings in a finite soil layer with a rigid base. A fictitious soil column is assumed for the corresponding shaft and the moduli of the soil–pile rod are expressed as a Heaviside step function of the modulus. The vertical soil displacements and the shaft resistances are calculated as the combined contributions by the two dissimilar piles in terms of the respective local coordinate systems. The displacements and stresses in two different local coordinates are transferred from one to the other using Graf's addition theorem. The boundary value problem for the soil layer is solved using the method of separation of variables with a series of undetermined constants. The unknown constants can be determined by considering the compatibility along the interfaces of the two soil–pile rods and the surrounding soil. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the interaction between the two piles. Numerical results show that, for the dissimilar piles in the stiff soil, the effects of the difference of the pile lengths on the interaction factor are negligible. Also, the interaction factor of the dissimilar piles in the soft soil depends heavily on the difference in lengths.

中文翻译：

---

有限土层中两个异种桩之间相互作用的解析模型

针对具有刚性基础的有限土层中承受竖向荷载的两个异种桩之间的相互作用，提出了一种解析方法。假定对应轴的虚拟土柱，土桩杆的模量表示为模量的Heaviside阶跃函数。竖向土壤位移和竖井阻力计算为两个不同桩在各自局部坐标系下的总贡献。使用格拉夫加法定理将两个不同局部坐标中的位移和应力从一个传递到另一个。使用具有一系列未确定常数的变量分离方法解决了土壤层的边值问题。可以通过考虑沿两个土桩杆和周围土壤的界面的相容性来确定未知常数。进行了参数研究，以研究土-桩系统的特性对两桩之间相互作用的影响。数值结果表明，对于刚性土中的异种桩，桩长的不同对相互作用因子的影响可以忽略不计。而且，软土中异种桩的相互作用因子在很大程度上取决于长度的差异。桩长的差异对相互作用因子的影响可以忽略不计。而且，软土中异种桩的相互作用因子在很大程度上取决于长度的差异。桩长的差异对相互作用因子的影响可以忽略不计。而且，软土中异种桩的相互作用因子在很大程度上取决于长度的差异。