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.