Stability Analysis of Semi-Cut-and-Cover Excavations via Copula Models: Width Effect, Reliability, and Asymmetric Deformation

Abstract Foundation pit engineering exhibits significant spatial effects, with stability and deformation closely related to excavation width. This study uses the copula theory to establish sliding, overturning, and heaving stability models that account for the width effect. By analyzing reliability indices, failure probabilities, and stability coefficients, the influence mechanism of width variation on the three failure modes is revealed. Meanwhile, numerical simulations are employed to investigate the internal forces and deformation characteristics of support structures of semi-cut-and-cover foundation pits under the width effect. The results indicate that different copula functions significantly affect failure probabilities, with the Clayton copula showing the best fit. The excavation width is negatively correlated with the reliability index, and the heaving stability coefficient is the most sensitive to width changes. The retaining structures on both the covered excavation and open-cut sides exhibit asymmetric deformation. With increasing width, soil disturbance range and interside differential deformation gradually expand. When pit width increases from 10 to 40 m, differential settlement rises from 1.39 to 3.65 mm and differential horizontal displacement from 0.79 to 8.14 mm, representing a 930% increase. The horizontal displacement of column piles increases markedly and is far more affected by the width effect than that of diaphragm walls.