基于线性地基反力法和土体的弹塑性本构关系，对桩顶水平反力系数不为零时的水平受荷桩进行了研究，给出了桩顶土屈服临界荷载(水平力、弯矩)的耦合关系式。研究结果表明，当荷载大于临界荷载时，桩顶土发生塑性屈服，其塑性屈服深度随荷载的增加而增加，但其塑性区扩展速率随桩顶荷载的增加而逐渐减小。给出了弹性区与塑性区桩内力耦合的矩阵方程及其迭代求解格式；利用曲面拟合软件给出了塑性区换算深的计算公式。通过工程算例验证，证明该方法可靠快捷，便于手算，值得推广。%Based on the elastic-plastic constitutive relation and linear subgrade reaction method, the laterally loaded pile is studied considering the anti-force coefficient of top foundation, and the coupled relationship of critical load ( horizontal force, moment) is given when the top soil of the pile yields. The results show that the top soil begin to yield when the lateral load rea-ches to the critical load, and the plastic depth increases with the load, but the expansion rate of plastic zone gradually decreases with the load's increasing. The coupling matrix equations of the pile internal force in elastic zone and plastic zone are given, and also its iterative solution format is obtained. The formula of conversion depth of plastic zone is given by surface fitting software. Through a numerical example, the presented method is proved reliable and effective.
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