Analytical Modeling of Flow-Induced Pore Pressure and Initial Bedform Deformation in Poroelastic Beds Using Biot’s Theory

This paper develops an analytical framework to quantify how flow-induced pore-pressure fields drive initial bedform deformation in soft, saturated porous beds. Starting from Biot’s poroelastic framework, the governing equations are simplified under assumptions of low soil stiffness, low permeability, and distinct time-scale separation between fast surface flow and slower bed responses. Closed-form analytical solutions are derived for both harmonic and localized rectangular bedforms, revealing asymmetric pore-pressure distributions characterized by negative upstream and positive downstream gradients. These gradients induce upward seepage at the pit shoulders, which is expected to promote erosion, while enhancing deposition within the pit interior. The proposed model provides a computationally efficient and physically interpretable framework for evaluating pore-pressure-driven bedform responses. Its applicability extends to practical scenarios such as bridge pier scour, pipeline burial, and coastal structure stability assessments.