Erosion mechanism of subsea tunnel considering non-linear seepage and linearly varying permeability coefficient with time

Abstract

The erosion mechanism of the subsea tunnel is complicated due to the unique submarine environment. Most research assumes the fluid follows Darcy's law and neglects the increasing permeability coefficient of the grouting zone with continuous chloride ion erosion. However, the grouting and lining zones exhibit relatively high density, causing the deviation of flow seepage from Darcy's law to non-Darcy's law. This paper aims to accurately study the erosion mechanism under non-Darcy seepage condition using Hansbo's non-linear seepage model. The entire erosion process is divided into three stages: (a) initial erosion, (b) developed erosion, and (c) rapid erosion. The focus is on investigating the erosion mechanism during the developed erosion stage, in which the grouting zone follows the linear segment of Hansbo's non-linear seepage law and the lining zone follows the curved segment under relatively high-water levels. The analytical solutions for the erosion depth and ion concentration are obtained, considering the linearly varying permeability coefficient of the grouting zone over time. Our proposed method is validated through the numerical simulation and established solution. In addition, parametric analyses are conducted including the service time and change of the permeability coefficient. It reveals that the pore pressure and erosion depth at different locations of the grouting zone increase approximately linearly as the water head acting on the ground surface increases. The erosion depth and ion concentration increase with the service time, with the most significant impact observed at the tunnel invert. A greater impact on the concentration is found closer to the surface of the grouting zone. The erosion depth is deeper considering the linearly varying permeability coefficient rather than a constant. However, the influence on ion concentration is minimal.