The　Poisson-Nernst-Planck-Bikermann　(PNPB)　model,　in　which　the　ions　and　water　molecules　are　treated　as　different　species　with　non-uniform　sizes　and　valences　with　interstitial　voids,　can　describe　the　steric　and　correlation　effects　in　ionic　solution　neglected　by　the　Poisson-Nernst-Planck　and　Poisson-Boltzmann　theories　with　point　charge　assumption.　In　the　PNPB　model,　the　electric　potential　is　governed　by　the　fourth-order　Poisson-Bikermann　(4PBik)　equation　instead　of　the　Poisson　equation　so　that　it　can　describe　the　correlation　effect.　Moreover,　the　steric　potential　is　included　in　the　ionic　and　water　fluxes　as　well　as　the　equilibrium　Fermi-like　distributions　which　characterizes　the　steric　effect　quantitatively.　In　this　work,　we　analyze　the　self-adjointness　and　the　kernel　of　the　fourth-order　operator　of　the　4PBik　equation.　Also,　we　show　the　positivity　of　the　void　volume　function　and　the　convexity　of　the　free　energy.　Following　these　properties,　the　well-posedness　of　the　PNPB　model　in　equilibrium　is　given.　Furthermore,　because　the　PNPB　model　has　an　energy　dissipated　structure,　we　adopt　a　finite　volume　scheme　which　preserves　the　energy　dissipated　property　at　the　semi-discrete　level.　Various　numerical　investigations　are　given　to　show　the　parameter　dependence　of　the　steric　effect　to　the　steady　state.