Semi-Analytical Study of Pile–Soil Interaction on a Permeable Pipe Pile Subjected to Rheological Consolidation of Clayey Soils

Permeable pipe pile, a novel pile foundation integrating drainage and bearing functions, improves the bearing capacity of the pile foundation by accelerating the consolidation of the soil around the pile. In this study, a mathematical model is established to simulate the consolidation of surrounding clayey soils and the pile–soil interaction, where the rheological properties of the soils are described with the fractional derivative-based Merchant model, and the impeded drainage boundary is used to simulate the pile–soil interfacial drainage boundary. Corresponding solutions for pile–soil relative displacement, skin friction, and axial force on the pile shaft are derived by means of semi-analytical methods, and they are validated by comparing with experimental results and numerical simulation results. Based on the proposed semi-analytical model, a series of parametric analyses are conducted to investigate the influences of fractional orders, viscosity coefficients, pile–soil interface parameters, and pile-head loads on the pile–soil interaction characteristics. It is observed that during the transition stage, the axial force increases linearly with depth in the plastic segment, and then increases nonlinearly in the elastic segment until it decreases after reaching the neutral plane. In the elastic segment, the axial force on the pile shaft for a given time increases with the increases in the fractional order or the pile–soil interface parameter, but decreases with the increase of viscosity coefficient.