Analytical Solution for Consolidation of Band-Shaped Drain Based on an Equivalent Annular Drain

Abstract

In general, prefabricated vertical drains (PVDs) used in practice are usually manufactured in band shapes. To analyze its consolidation in cylindrical coordinate system, the band-shaped drain was usually converted into an equivalent circular drain surrounded by soil forming a cylindrical unit cell. However, when the band-shaped drain is converted into a circular drain, either its perimeter or its cross-sectional area or even both of them will change. This will lead to a problem that the water exchange between the soil and the drain is consequently changed, because the water quantity flowing into the band-shaped drain along the horizontal direction is controlled by its perimeter, whereas the water flowing out of it along the vertical direction is controlled by its cross-sectional area. Therefore, the effect of the actual shape of the band-shaped drain could not be modeled precisely based on the equivalent circular drain as usual. In this context, this paper attempts to solve this problem by converting the band-shaped drain into an equivalent annular drain with the same outer perimeter and cross-sectional area before and after conversion. Based on the new equivalent annular drain, the analytical solutions are further obtained for four loading schemes, including instantaneously loading, ramp loading, multistage instantaneously loading, and multistage ramp loading. Then the effect of the actual shape of the band-shaped drain is investigated by comparing the results predicted by the present method to the methods with an equivalent circular drain reported in the literature. The results show that the average degree of consolidation predicted by the present method closely matches the result based on equal cross-sectional area, which indicates that the cross-sectional area of the band-shaped drain, not its perimeter, is the key for estimation of the quantity of flow through the drain. Finally, the present method is validated by several laboratory and field tests about the soil improvement technique with a band-shaped PVD. The predicted settlements by the present method and other methods with circular drains are compared to the measured settlement. Good agreements could be observed between the results by the present method and the measured data.