Potential theory for dual‐depth subsurface drainage of ponded land

Dual‐depth subsurface drainage is considered to be more effective in removing excess water from soil than single‐depth drainage, but this problem has not been analyzed in detail. Therefore, assuming that uniform, water‐saturated soil covered by ponded water and overlying an impervious barrier is drained by equally spaced, alternating deep circular drain tubes, existing potential flow theory for a single‐depth drainage system was extended. Sample calculations with the newly derived equations show that a dual‐depth subsurface drainage system can be highly effective to remove excess water from soil. For example, a relative drain discharge of 160% is calculated when new drain tubes, added at the 0.60 m depth, are placed midway between the original drain tubes, which are 25 m apart and at the 1.20 m depth. In this calculation we have assumed that the impervious layer is at the 3.0 m depth, the radius of the tubes is 0.05 m, the soil hydraulic conductivity is 1 m/d, and the thickness of the ponded water is 0.0 m. For the same conditions, but with the additional tubes at the 1.20 m depth (same depth as original tubes), the relative drain discharge becomes nearly 200%, and with the additional tubes at the 2.40 depth (1.20 m below original tubes) it is more than 250%. When the impervious layer is at a greater depth and when the original drain spacing is more than 25.0 m, the relative drain discharge becomes even larger. The effectiveness of the dual‐depth tube system becomes particularly large, if the second tube system is placed below the level of the first one.