Abstract: Based on indoor experiments， aggregate balance theory and fluid dynamics theory， mathematical models of vertical sand silo area and height were established. The core of sectional area calculation model is the effective sedimentation velocity which is equal to the ratio of the descent height of the liquid level and the sedimentation time. The height calculation model consists of compression layer， sedimentation layer， overflow layer， reserving sand space and stable sand height. Because the calculation of the compression layer height is the key part in the model， an equation on compression layer height and mortar concentration was put forward. Then this method was applied to a vertical sand silo. It was got that the diameter of the vertical sand silo is 10m， and the height of vertical sand silo is 26.5m. The field operation trial showed that the bottom flow volume fraction of sand silo can reach 44% (the mass fraction is 69%) and the volume fraction of over-flow water can be controlled under 3%， which means the concentration effect is very well.

Key words: filling, vertical sand silo, sectional area, effective sedimentation velocity, compression layer, silo height