Location of closed tile drains

The drains must be placed so that the water table, midway between the drains, stays below the root zone plus the capillary rise. The depth of the drain then follows from Donnan's formula.

Data

• Root zone depth = 1.5 m, capillary rise = 0.3 m
• $K$ = 1.5 × 10⁻⁴ m/s; drain spacing $S$ = 200 m; depth of impervious layer = 10 m below ground
• Drainage capacity = 0.11 m³/s/km² = 0.11/10⁶ = $1.10\times10^{-7}$ m/s

Step 1: Highest permissible water table

Depth of the water table below ground at the mid-point = 1.5 + 0.3 = 1.8 m. Its height above the impervious layer:

$$b = 10 - 1.8 = 8.2\ \text{m}$$

Step 2: Height of the drain above the impervious layer

$$S^2=\frac{4K(b^2-a^2)}{q} \quad\Rightarrow\quad a^2 = b^2-\frac{qS^2}{4K}$$ $$\begin{aligned} a^2 &= 8.2^2-\frac{1.10\times10^{-7}\times200^2}{4\times1.5\times10^{-4}} \\ &= 67.24-7.333 = 59.907 \\ a &= 7.740\ \text{m} \end{aligned}$$

Step 3: Depth of drain below ground

$$\text{Depth} = 10 - 7.740 = 2.26\ \text{m}$$

Answer: lay the drains about 2.26 m (say 2.3 m) below the ground surface, i.e. 7.74 m above the impervious layer. The water table at the mid-point then stays 1.8 m below the surface, just below the root zone and capillary fringe.