Study on Failure Surface Morphology of Supporting Structures Under Extreme Climate–Mechanical Coupling Effects Based on Reinforcement Theory

The high-filling engineering of airports is common in mountainous cities, and as critical infrastructure for urban development, airports are prone to slope instability under extreme climate and mechanical coupling effects. Therefore, it is essential to investigate the geometric form of failure surfaces under limit stability conditions for airport slopes. The rational determination of the form of the rupture surface of a soil nailing support structure is a key factor in the structural safety of a project. In this study, we analyzed the rupture surface form and reinforcement mechanism of four common soil nailing support structures in engineering. First, we established theoretical model I and verified the consistency of the upper-limit theorem of plastic mechanics and energy conservation in this model. Next, a theoretical analytical model of the rupture surface form was established taking into consideration the existence of tension depth in a certain depth range at the top. The mathematical expressions of the rupture surface form with respect to h/H and L/H were derived by combining plasticity mechanics and energy conservation. Finally, the rupture surface forms of the structure were analyzed for different slope angles of soil nail-supported structures and different friction angles within the soil. The findings were compared with the rupture surface forms in the existing codes and literature. The results showed that L/H decreased continuously with the slope angle β of the soil nailing support structure and decreased gradually with an increasing friction angle φ within the soil. Furthermore, h/H decreased with the slope angle of the soil nailing support structure, but it showed a trend with the increase in soil internal friction angle and the slope angle of the soil nailing support structure. The analysis revealed that only in some specific cases were β and φ closely aligned with the values acquired using standard methods in specifications and the literature. The theoretical analysis provided important reference values for the design and improvement of soil nailing length in soil nailing support structures under certain conditions, thereby ensuring their enhanced stability and strength.