A coupled one-dimensional model for piping erosion under constant pressure drop

Internal erosion is a critical failure mechanism in earth structures. This paper presents a coupled one-dimensional hydraulic-transport-erosion model for pressurised piping under imposed inlet and outlet pressures. The reduced-order framework enables rapid parametric screening, boundary-condition assessment and verification-oriented analysis. It combines a Darcy-Weisbach closure, a concentration-dependent mixture resistance, and a threshold erosion law. Advective transport is solved with a conservative finite-volume MUSCL scheme; the erosion source is integrated analytically. Discharge is obtained at each step by a bracketing-bisection procedure satisfying the pressure boundary conditions. Results show that, without external outlet resistance, the constant‑pressure configuration is prone to runaway enlargement, clarifying the role of outlet resistance in sustaining erosion regimes. Numerical verification demonstrates that meaningful convergence requires the time step to be governed by the Courant condition, monitored via a simple diagnostic. The model provides an efficient reduced-order tool for analysing piping evolution and instability.