A permeable pipe pile is proposed to accelerate the dissipation of excess pore-water pressure through drainage holes around the pile circumference into the pile’s cavity. This investigation generalizes the permeable pile–soil interface as an impeded boundary, based on which a mathematical model for soil consolidation around the permeable pile is derived. Subsequently, the influence of opening pattern, drainage hole-to-pipe pile radius ratio, and opening ratio on the consolidation efficiency is numerically investigated. A total of 240 numerical cases with different drainage hole-to-pipe pile radius ratios, opening ratios, and hydraulic conductivity ratios are calculated to determine the permeable pile–soil interface parameter using back-analysis, and an approximate expression for interface parameter is obtained. Comparing against experimentally measured excess pore-water pressure dissipation, the proposed technique with impeded drainage boundary can provide good evaluations for drainage characteristics at the permeable pile–soil interface and consolidation behavior of the surrounding soil. It is found that the spatial distribution pattern of drainage holes has negligible influence on the consolidation efficiency. Increasing the opening ratio (with constant opening size) or reducing the drainage hole-to-pipe pile radius ratio (with constant opening ratio) can both accelerate the consolidation efficiency.