AbstractIn this investigation, an approximate analytical solution to the axisymmetric consolidation problem of unsaturated soils improved with vertical drain is presented under the equal-strain condition. The smear effect of soil, the well resistance of vertical drain, and the application of time-dependent loading are considered in the solution. Matrix analysis is used to solve the solution under constant loading for comparison against the available solution. The influence of soil parameters, smear parameters, and well resistance parameters on the consolidation behavior is investigated under ramp loading. Moreover, two types of loading which are noncyclic forms (i.e., instantaneous, multistage ramp, and exponential loading) and cyclic forms (i.e., triangular, sinusoidal, and cosine cyclic loading) are incorporated in the analyses. It is found that a higher hydraulic conductivity ratio in the undisturbed zone and a larger radius of the influence zone can speed up the consolidation process. The consolidation process is slowed down by increasing the radius of the disturbed zone and reducing its hydraulic conductivity, and the influence of hydraulic conductivity is more significant. The effect of radius and hydraulic conductivity of vertical drain on the consolidation behavior is similar. The consolidation behavior generally follows the pattern of the applied loading apparently.

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