Soil of consolidation with partially penetrated vertical drains under complicated loadings considering three-dimensional seepage in soil beneath vertical drain

The general solution in the Laplace transform field for the consolidation of soil with partially penetrated vertical drains under complicated time-dependent loadings is derived. In order to consider the three-dimensional seepage in the soil beneath vertical drain, an imaginary drain in the soil just below the tip of actual one is assumed. And then by the Laplace transform the average degree of consolidation, excess pore water pressure and settlement of the vertical drain under arbitrary loading could be calculated. According to numerical examples, the influences of parameters of partially penetrated vertical drains are investigated; and by using the solutions, the approximate methods so far available for the computation of average consolidation degree of soft soil with partially penetrated vertical drains are compared and discussed in detail.