<p>Piping driven by internal erosion is a major failure mode in levee engineering and exhibits strongly discontinuous mechanical behavior. To address the discontinuity in soil particles during erosion simulation, this study adopts a novel nonlocal transport theory to investigate soil swelling behavior and the transport mechanisms of detached particles. Specifically, three types of partial differential equations—Darcy’s law for fluid seepage and two diffusion equations for the swelling and transport of detached soil particles—are recast into a nonlocal framework using peridynamic differential operators. The solid volume fraction serves as the essential state variable to characterize the erosion process, while a discrimination parameter method is implemented to identify the specific phase of soil particles. In addition, a hybrid implicit–explicit algorithm is employed to enhance the computational efficiency in peridynamics. A soil column erosion case validates the reliability of the proposed model. The results reveal that abrupt variations in pore water pressure and the associated redistribution of the seepage field play a dominant role in driving channel formation, while the evolution of the solid volume fraction provides an effective descriptor of channel growth. Finally, the proposed model computes the evolution process of piping failure to elucidate the underlying mechanisms governing its development.</p>