Studies of recent decades have shown thousands of kilometers of transportation networks that have presented damage or failure from different types of flows, causing important traffic disruptions. Debris flows running adjacent (or in parallel) to river channels often explain the structural damage to road embankments caused by slope erosion. The probability of expected structural damage caused by a natural hazard may be modeled using fragility curves, which have been developed for transportation infrastructures like bridges and roads exposed to debris flows and are used in risk assessment. There are even fragility curves available to estimate the fragility of road embankments exposed to perpendicular debris flows. However, currently no model is available to estimate the road damage probability of embankments exposed to adjacent debris flows despite their important effects on traffic. This paper aimed to develop fragility curves for road embankments exposed to adjacent debris flows, considering mechanisms of exposed slopes subject to erosion and subsequent embankment instability. Models were calibrated considering flow characteristics in straight and bend channels including three damage states in terms of road traffic capacity loss. Monte Carlo simulations were performed to model potential damage, obtaining fragility curves for two types of roads. Curves were fit to log-normal distributions with a 99.5% confidence level. The analysis demonstrated that the geometric characteristics of road embankments explain their fragility, wherein lower heights and platform widths result in more probable expected damage. The analytical model developed confirmed that the erosive process intensifies in bend zones of channels, resulting in higher damage probability.