For a laterally loaded pile with its head keyed into the cap, pile head actually rotates in spite of the restraint of the cap. Being aware of this fact, some parameters were put forward to represent the degree of rotational restraint at pile top, and many calculation methods of lateral pile responses were then developed. However, the presented solutions are only for piles under pure lateral loads. In fact, they are usually under the vertical loads simultaneously, caused by the weights of themselves and superstructures. Besides, the slight initial inclination of pile shaft is inevitable in engineering. Some researchers raised solutions of lateral responses of the slightly inclined single pile under combined vertical and lateral loads, but the partially fixed-head condition and the elastoplasticity of soil were not considered. In this study, elastoplastic semi-analytical solutions of lateral responses of the slightly inclined single pile under combined vertical and lateral loads were deduced, in which the rotational restraint coefficient was used to represent the degree of rotational restraint at pile top, and the three-parameter model of the coefficient of subgrade reaction was employed. The computer program was developed thereafter. The effectiveness and advantage of the obtained solutions were validated by the comparison among existing solutions, presented solutions and model test results. Sensitivity analysis was carried out for parameters such as the initial inclination angle of pile shaft, the rotational restraint coefficient, and the vertical load. Eventually, effects of each parameter on lateral pile responses were presented and discussed.

对于侧向加载的桩，其头部键在帽中，尽管帽受到约束，但桩头实际上仍在旋转。意识到这一事实，提出了一些参数来表示桩顶的旋转约束程度，然后开发了许多横向桩响应的计算方法。但是，提出的解决方案仅适用于纯侧向荷载下的桩。实际上，它们通常同时承受垂直荷载，这是由于它们自身和上部结构的重量引起的。此外，在工程中不可避免地会出现轻微的桩身初始倾斜。一些研究人员提出了在垂直和水平荷载共同作用下微倾角单桩的侧向响应的解决方案，但未考虑部分固定头部的条件和土壤的弹塑性。在这个研究中，推导了小倾角单桩在竖向和竖向共同荷载作用下的横向响应的弹塑性半解析解，其中旋转约束系数代表桩顶的旋转约束程度，并采用三参数模型进行了分析。采用路基反应系数。此后开发了计算机程序。通过对现有解决方案，提出的解决方案和模型测试结果进行比较，验证了所获得解决方案的有效性和优势。对桩身的初始倾斜角度，旋转约束系数和垂直载荷等参数进行了敏感性分析。最终，提出并讨论了每个参数对侧向桩响应的影响。