中文摘要：

针对软土区顶部加箍碎石桩复合地基,根据理论上较为严密的极限分析上限法,通过构建协调的速度场,综合考虑土重和加箍段桩侧摩阻力等因素的影响,基于能量平衡原理推导出了单桩极限承载力递推计算公式。在此基础上,利用随机优化搜索方法搜索出临界滑裂面,从而获得更为合理、严密的顶部加箍碎石桩极限承载力计算方法。最后,结合典型的工程实例进行了对比验证和参数分析,结果表明：计算结果与实测值、既有方法计算值相比相对误差在5.4%范围内,最优顶部加箍深度约为桩体半径的8倍,可为工程实践提供一定的参考。

英文摘要：

Based on the upper-bound limit analysis, which is theoretically rigorous, the bearing capacity of the composite foundation of upper geosynthetics-encased stone column （UGESC） in soft soil is analyzed through constructing the consistent velocity field and considering the effect of gravity and skin friction of the encased section of the stone column. An equation for calculating the ultimate bearing capacity of single UGESC is proposed based on the energy balance principle. Based on this, a stochastic optimal method is used to search for the critical sliding surface, and a more reasonable and rigorous solution for ultimate bearing capacity of UGESC is derived. A case study is performed, showing that the relative errors of the calculated results are less than 5.4% compared to the previous results in the literatures. The optimal value of upper encased depth is about eight times the pile radius. The procedure proposed in this paper can provide certain reference for engineering practice.