A new analytical model for consolidation with multiple vertical drains
Various analytical theories of consolidation for soils with vertical drains have been proposed in the past. Most conventional theories are based on a cylindrical unit cell that contains only a single vertical drain. This paper described a new analytical model where a vertical drain located at the centre (the 'inner vertical drain') and is surrounded by two or three vertical drains (the 'outer vertical drains'), the number of which depends on whether the configuration is triangular or rectangular. Both types of drains are combined into a cylindrical unit cell, and the water is assumed to flow both inwards to the inner vertical drain and outwards to the outer vertical drains distributed around the circumference. The outer radial boundary of the unit cell is regarded as a permeable boundary, with a drainage capacity of two or three separate vertical drains for triangular and rectangular configurations, respectively. The smear effects and the drainage resistances for both the inner and outer vertical drains are considered in the analysis as well. In this way, the equations governing the consolidation process with multiple vertical drains are derived, and the corresponding analytical solutions are obtained for instantaneously loading, ramp loading and multi-stage of instantaneously loading and multi-stage of ramp loading. The present solutions are finally compared with several conventional solutions for a single vertical drain in the literature. The results show that the present model predicts the same average degree of consolidation as conventional models do, which verifies the correctness of this new model. Finally, the settlement predicted by the present solution is compared with the measured settlement from a field test at the Port of Brisbane, Australia, which shows a good agreement between them.