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.

This study investigates the rheological properties of saturated soft clay surrounding a tunnel using the generalized Voigt viscoelastic model. The model incorporates linear semi-permeability boundary conditions to describe the behavior of the clay. Furthermore, two-dimensional rheological consolidation control equations are derived based on the Terzaghi-Rendulic theory, considering the excess pore water pressure as a variable. To solve the equations, conformal transformation and separation of variables methods are employed, resulting in two independent equations representing the excess pore pressure in terms of time and space variables. The Laplace transformation and partial fractional summation method are then utilized to obtain the solution for excess pore pressure dissipation in the time domain. The reliability of the solution is verified by comparing it with the existing four-element Burgers and five-element model, both of which are derived from the generalized Voigt model. Furthermore, the influence of liner permeability, Kelvin body number, independent Newtonian dashpot viscosity coefficient, and tunnel depth on the dissipation and distribution of excess pore pressure is analyzed based on the established solutions. The findings indicate that a higher relative permeability of the liner and soil leads to an earlier onset of excess pore pressure dissipation and a faster dissipation rate. Increasing the number of Kelvin bodies results in slower dissipation rate. Moreover, larger independent viscous coefficients lead to smaller viscous deformation and faster dissipation rates. Additionally, greater tunnel depth prolongs soil percolation path, slowing down the dissipation of excess pore pressure. When the relative permeability coefficient is 0.01, the excess pore pressure gradually decreases with distance from the outer wall of the tunnel. However, when the relative permeability coefficient is 1, the excess pore pressure initially increases and then decreases with distance. As the relative permeability coefficient increases, the influence of the number of Kelvin bodies on the dissipation of super pore pressure diminishes, the variation in super pore pressure dissipation caused by different independent Newtonian dashpot viscosity coefficients gradually decreases, and the role of tunnel liners as new permeable boundaries within the soil layer is becoming increasingly prominent.

Based on Biot porous medium theory, considering the coupled reaction of soil skeleton rheology and pore pressure dissipation, the present work investigates the dynamic consolidation characteristics of saturated clay ground under cyclic loading. First, the rheological behavior of the soil skeleton was described by the fractional order Kelvin model. The dynamic consolidation governing equations for the saturated clay were established theoretically in a three-dimensional axisymmetric coordinate system. Second, the transform domain analytical solution of the dynamic consolidation of saturated clay was obtained using the Hankel-Laplace coupled transform method, and the solution in the time-space domain was further obtained through numerical inversion. Finally, the rheological consolidation behavior of saturated clay under cyclic loading and the influences of parameters were analyzed. The results show that the rheology of the soil skeleton had an inhibitory effect on pore water permeability; compared with elastic skeleton soil, the rheological clay had a slower settlement rate in the primary consolidation stage, a faster rate in the secondary consolidation stage, and greater long-term settlement. In addition, under cyclic loading, the pore pressure response in saturated clay lags behind the effective stress, and a larger viscous order is associated with faster development of cumulative settlement.