Nonlinear consolidation of vertical drains with coupled radial–vertical flow considering well resistance

The consolidation behavior of ground with vertical drains is known to be greatly affected by the finite permeability of the sand drains, also called the effect of well resistance. However, up to now, no analytical methods have been reported for evaluating this effect on the nonlinear consolidation behavior of vertical drains. In this paper, by considering the nonlinear compressibility and permeability of soil during consolidation, the effect of well resistance was incorporated into the derivation of the equations that govern the nonlinear consolidation of a vertical drain with coupled radial–vertical flow. In addition, the smear effect was considered by assuming three decay patterns for the radial permeability coefficients of the soil toward the sand drain in the smeared zone. After obtaining the governing equations, a simplified analytical solution is derived for a general time-variable surcharge loading. Based on the general solution obtained, detailed solutions are provided for three special types of loading schemes: constant loading, single-stage loading, and multi-stage loading. The validity of the solution is verified by reducing it to several special cases and comparing these to existing solutions. Finally, the effect of the well resistance, the ratios of the compression index to the radial and vertical permeability indices, various loading schemes, and various variation patterns of the radial permeability coefficient of the soil in the smeared soil zone are investigated using parametric analysis.