Based on the basic characteristics of the sand-free air-boosted vacuum preloading

a radial seepage calculation unit model centered on the booster pipe

which is a non-ideal well

is established

taking into account the spatiotemporal nonlinear characteristics of the well resistance of drainage plates and the relationship between the booster load and its pipe length. The nonhomogeneous partial differential control equations are consequently derived. According to the Sturm-Liouville eigentheory

the analytical solution to the excessive pore water pressure is obtained using the eigenfunction expansion method. Further

analytical expressions for calculating the excessive pore water pressure and the average consolidation degree of the foundation are provided under three typical practical pressurization modes

including constant pressurization loading

constant pressurization loading in the later stage

and intermittent pressurization in the later stage

respectively. Some examples show that the excessive pore water pressure increases as the length of the pressurized pipe increases

and always shows a nonlinear distribution that gradually increases with depth. After the pressurization is initiated

the excessive pore water pressure increases instantaneously

with a more pronounced increase in the middle and lower parts of the foundation

and subsequently

its dissipation rate also increases. The total pressurization duration has a significant impact on the consolidation degree of the foundation. When the pressurization loads are 20 kPa and 40 kPa

the consolidation degrees increase by approximately 8% and 9%

respectively

for a total pressurization duration of 100 d compared to 50 d.