Adaptive stable node-based smoothed upper bound finite element limit analysis considering discontinuous velocity fields for soil-structure interaction problems

• An adaptive stable node-based smoothed upper bound FEA method with discontinuous velocity fields is proposed. • A SOCP formulation using the MC criterion, integrated with adaptive mesh refinement is developed. • Numerical examples validate the method's superior accuracy and computational efficiency. • The effects of interface roughness on failure modes and stability are systematically analyzed. An adaptive stable node-based smoothed upper bound finite element limit analysis (adaptive SNS-UBFELA) method is proposed for soil-structure interaction problems, in which discontinuous velocity fields along the soil-structure interface are considered. A second-order cone programming formulation is developed based on the Mohr-Coulomb yield criterion and the associated flow rule, and an adaptive mesh refinement scheme is incorporated to improve accuracy and efficiency. The method is implemented in MATLAB with the MOSEK solver and validated through several numerical examples. Results show that the proposed approach predicts plastic regions and limit loads in good agreement with analytical solutions, slip-line field theory, and adaptive T6-UBFELA, while providing higher accuracy and numerical robustness than adaptive and adaptive NS-UBFELA. Although slightly less accurate than T6-UBFELA, SNS-UBFELA achieves superior computational efficiency. Numerical examples involving footings and anchors further demonstrate that soil-structure interface roughness significantly influences failure modes and stability, highlighting the necessity of incorporating discontinuous velocity fields in numerical analysis. Overall, adaptive SNS-UBFELA is an efficient and robust tool for soil-structure interaction analysis in geotechnical engineering.