Vulnerability model for cantilever retaining walls subject to scour

Retaining walls are widely used to stabilise slopes and support infrastructure such as bridge abutments, culverts, and roads over or adjacent to waterways. These structures can be susceptible to scour-induced erosion and undermining at their toe, which can lead to significant damage and collapse. This paper presents a comprehensive yet simplified analytical formulation to evaluate the reduction in retaining wall capacity caused by scour. First, a model is proposed to describe the scour process at retaining walls. Based on this model, the degradation of retaining wall capacity is formulated by considering various potential failure modes. The proposed formulation, validated against numerical simulations using PLAXIS, is non-dimensionalised to derive simple expressions for describing the effect of scour across different wall geometries, soil properties, and water depths. A simplified approach is then introduced to estimate the scour vulnerability of retaining walls, expressing the conditional probability of wall failure with increasing scour levels. The study provides a practical tool for engineers and infrastructure asset managers to support rapid risk prioritisation of retaining walls exposed to scour, highlighting the most critical parameters influencing the vulnerability of these structures.