Optimization of Deep Foundation Pit Support Scheme Based on Game Theory Combined Weighting and Cloud Model

The selection of foundation pit support schemes and parameters for subway stations critically impacts construction safety. This study develops a deep foundation pit support evaluation system, integrating subjective weights (Analytic Hierarchy Process) and objective weights (entropy method). A game theory-based combined weighting method and joint cloud model are constructed for optimal support scheme selection. Structural redundancy theory is employed to assess safety stability. Results demonstrate that game theory-enhanced combined weighting improves multi-attribute decision-making accuracy and model stability. The proposed model identifies the optimal diaphragm wall-internal support scheme, aligning with actual engineering designs, validating method reliability. During excavation, deep horizontal wall displacement and surface settlement outside the pit exhibit parabolic and "groove-shaped" patterns, respectively. Steel support axial force initially increases then decreases. Failure of the fourth-layer steel support significantly amplifies pit displacement and settlement, with redundancy dropping below other layers, indicating the lowest-layer support as a critical "weak component" requiring prioritized design and construction attention. These findings enhance safety evaluation precision and inform risk mitigation strategies for deep foundation pit engineering.