Probabilistic stability analysis of bolt-reinforced rock slopes considering corrosion based on sparse polynomial chaos expansions

Abstract

This study presents a probabilistic analysis of bolt-reinforced rock slopes subjected to corrosion. The analysis integrates sparse polynomial chaos expansions (SPCEs) with Monte Carlo simulations (MCS). A deterministic model for slope stability is developed using the kinematic approach of limit analysis, incorporating the generalized Hoek-Brown failure criterion and a corrosion model to capture the time-dependent degradation of anchor axial force. Parameters related to the rock mass and bolt system are modeled as random variables. The SPCE surrogate model is built from a small set of input–output samples, enabling efficient MCS-based probabilistic evaluation. Results show that increasing input uncertainty broadens and lowers the probability density function of the safety factor, though the mean value remains nearly unchanged. Failure probabilities increase significantly with uncertainty, especially at initially low failure levels. Correlated input variables lead to more concentrated distributions and reduced failure probabilities, while assuming independence yields more conservative estimates. The lognormal distribution produces sharper and narrower curves than the normal distribution, particularly in low-probability regions. Among various failure modes, corrosion-induced bond degradation between the bolt and grout has a greater impact on system reliability than tensile failure of bolts. Sensitivity analysis reveals that the uniaxial compressive strength of the rock mass (${\sigma }_{\mathrm{ci}}$), geological strength index ($\mathrm{GSI}$), and parameters of rock hardness ($m_i$) are the most influential parameters, especially after 100 years of service. These findings underscore the need for a probabilistic framework to accurately assess the long-term stability of bolt-reinforced slopes that are susceptible to corrosion.