Distribution patterns of final negative pressure in vacuum preloading

The distribution patterns of the final negative pressure are investigated in vacuum preloading under impeded bottom boundary in order to demonstrate the degenerated properties of vacuum degree and to determine the final vertical effective stress. Firstly, the equivalent relation of consolidation equations between vacuum preloading and surcharge preloading is established according to the boundary homogenizing theory. The distribution patterns of the final negative pressure with depth are obtained. Secondly, according to the steady seepage equation of post-consolidation, the distribution properties of the final negative pressure are studied for single-layer ground, multi-layer ground and sand-drained ground. The study shows that the final negative pressure decreases along depth under impeded boundary condition. For the single-layer ground or sand-drained ground with a constant water flux of vertical drain, the final negative pressure decreases single-linearly along depth. For the multi-layers ground or sand-drained ground with piecewise constant water flux of vertical drain, the final negative pressure decreases piecewise-linearly along depth. For the ground with continuous permeability coefficient or sand-drained ground with continuous water flux of vertical drain, the final negative pressure decreases nonlinearly along depth. The rate of final negative pressure increases with the permeability coefficient of boundary. The final negative pressure decreases slowly in high permeable layer. The larger the ratio of permeability coefficient between the upper layer and the bottom layer is, the larger the final negative pressure at bottom boundary is, and vice versa. The case study shows that the ground model with impeded boundary can reasonably simulate the properties that the final negative pressure and the final vertical effective stress decrease with depth in vacuum preloading.