以地基土冻胀变形理论为基础，从桩基冻胀力与桩侧土体冻胀位移的关系出发，引入经典黏弹性力学理论及Mindlin半空间作用集中力的弹性解，从理论上导出了桩基冻胀力三维黏弹性问题的积分方程表达式。运用单纯形法将室内实测蠕变数据反演得到三参量模型系数，并通过已有文献中现场实测数据拟合得到土体冻结深度、自由冻胀量，以及桩基冻拔位移随时间的函数，用于桩基冻胀力的理论计算。数值算例表明，按上述推导的桩基冻胀力三维黏弹性表达式计算的冻胀力沿深度分布规律与已有计算结果吻合较好。首次以理论的方法得到了桩基冻胀力的“时空分布”三维曲面，能较直观地反映冻胀力的分布规律。

Based on the frost heaving deformation theory of foundation soil, an integral equation for three-dimensional viscoelastic problem of pile frost heaving force computation is theoretically derived, with considering the relationship between frost heaving force of pile and displacement of pile lateral soil, and introducing the classical theory of viscoelastic mechanics and the Mindlin solution of concentrated force in an elastic half-space. Three-parameter model coefficients are inverted from the creep testing data measured by the simplex method. In addition, the freezing depth of soil body, the amount of free frost heave and the variation of frost heaving displacement of pile foundation vs. time are obtained by fitting the field monitoring data available in the literature, and they are utilized in theoretical calculation of the frost heaving forces of pile foundation. Numerical examples indicate that the distribution of the frost heaving force along the depth calculated with the proposed equation agrees very well with the measured values and previous results of calculations. The spatiotemporal three-dimensional presentation of the frost heaving force is obtained, which can intuitively show the frost heaving force distribution.