To enhance the comprehension of the relevant laws governing the geoelectric field of levee leakage models under artificial current source excitation, and to improve the realism of numerical simulations, this study establishes coupled equations for the multi-physical fields involved, including the water current field, ion diffusion field, and stabilized electric field of the levee leakage model. Additionally, coupled conversion equations for the multi-physical attributes of porosity, moisture content, mineralization, and resistivity are formulated. The three-dimensional simulation of the geoelectric field in the levee leakage model is achieved utilizing a finite-infinite element multi-physical field numerical simulation platform. By leveraging this platform, the coupling of geoelectric field leakage is accurately simulated. Through dimensional numerical simulations of a typical dam leakage model, it is demonstrated that the electric field resulting from dam leakage comprises three components: the filtered electric field, the diffusion adsorption electric field, and the stabilized electric field, all of which are realistically reproduced. In the stabilized electric field, the dominant current density induced by the collector effect reaches amplitudes of several thousand millivolts, while the filtered and adsorbed electric fields play an enhancing role with amplitudes ranging from a few tens of microvolts to a few tens of millivolts. These findings provide a theoretical basis for the rapid monitoring of dam leakage channels.