Geosynthetic-encased stone column (GESC) technology for strengthening soft clay offers significant advantages in terms of cost-effectiveness, environmental sustainability, and engineering applicability. It is widely applied in treating soft foundations for railways, bridges, and embankments. This study evaluates the cyclic response of the geosynthetic-encased steel slag column (GESSC) composite foundation employing three-dimensional nonlinear finite element analysis. A numerical study is conducted to assess the cyclic response of floating GESSC considering the influence of key design variables, including cyclic load amplitude, loading frequency, geosynthetic encasement stiffness, and length-to-diameter ratio. Results show that both cyclic load amplitude and frequency affect the cumulative settlement and excess pore pressure within the GESSC foundation. Within specified limits, increasing the encasement stiffness and column length can significantly improve the GESSC load-bearing characteristics. The parametric study suggests an optimal geosynthetic encasement stiffness for the field prototype columns within the range of 4480-5760 kN/m and a critical steel slag column length of 10 times the column diameter. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).