Analytical Solution for Nonlinear Consolidation Considering Time-Dependent Well Resistance and Lateral Deformation under Vacuum Preloading

The consolidation behavior of a foundation with vertical drains under vacuum preloading is affected by the lateral deformation and well resistance. In this study, a nonlinear consolidation model is developed based on the assumptions of equal volumetric strain and time-dependent well resistance. The model considers the relationships between various factors, such as well resistance, linear attenuation of vacuum pressure, lateral deformation, and simultaneous vertical-radial seepage. An analytical solution of the model is provided, and its universality is verified. Additionally, the effects of different consolidation factors on the average consolidation degree (U over bar ) are analyzed, and the error in calculating U over bar without considering a single factor is evaluated. The results indicate that well resistance significantly affects the consolidation rate of soil without vertical seepage, particularly at the later stage of consolidation when the constant parameter A, which represents time-dependent well resistance, exceeds 1.0 x 10(-7) (s(-1)). Not considering the lateral deformation can result in an overestimated soil consolidation rate. For thin layer soils with low liquid limits, the effects of the consolidation factors on U over bar are ranked as follows: c(c)/c(k) (ratio of compression index to permeation index) > k(v) (vertical permeability coefficient) > v (Poisson's ratio) > k(1) (attenuation residual coefficient of vacuum pressure) > qw (discharge capacity of prefabricated vertical drains).