1. Design of channel and bench terraces Channel terrace designs are for situations in which there is need to drain water from the field in a channel. They are designed to limit erosion by drainage, not to maximise water retention.

2. FAO (Cons. Guide 3, p 120) give the following equations: H = SK1/3 (m) where H is the horizontal interval; S is the slope (%); K is a constant varying form 250 to 270 depending on the soil infiltration rate. A similar equation in British units (ft) is also given: H = 0.61S1/2 + 0.22

3. Design lengths and grades for terrace channels (after Hudson, 1981a)

4. Determining spacing of channel terraces Many formulae have been developed for determining the difference in height between two successive terraces This height difference is known as the vertical interval (Vl). Theoretical approach For steady-state conditions, the runoff (Qw) at slope length (L) on a hillside can be expressed as: Qw = (R-i) L cos q [see diagram]

5. where R is the rainfall intensity, i is the infiltration rate and q is the slope angle. L is typically about 30 m and velocity is typically about 0.5 to 1 m s-1 so the correct time period for R (remember intensity – duration curves) is about 0.5 to 1 minute, essentially the instantaneous rate

6. Maximum instantaneous rates for Africa are about 225 mm h-1 The minimum infiltration rate (which causes the maximum runoff) will occur on a soil that is already wet. Rates will vary from 2 mm h-1 to 80 mm h-1 for soils ranging from clay to sandy loam R-i thus varies from about 145 mm h-1 to 223 mm h-1 The velocity of flow is given by Manning's equation:

7. The flow Q for unit width is given by: Q = vA where A is the cross-section area. For a unit width, A is simply the depth of water h. (Remember that for for flow over a surface that the hydraulic radius, r, is also equal to the depth, h)

8. Thus we can write: The value for r can be re-arranged as:

9. Therefore: Rearranging for given values of R and i, say those for the one- hour rainfall with a ten-year return period. and for a pre-selected value of v, say the maximum permissible velocity for the soil gives a slope distance L which can be used as the distance between terraces down the slope:

10. A value of n = 0.01 is recommended for bare soil. The vertical interval is obtained from: VI = L sinq For example, if the peak rainfall is 250 mm h-1 and on a sandy soil, the minimum infiltration rate is 75 mm h-1, then the excess (R-i) is 175 mm h-1 or 0.05 mm s-1 , selecting a value for v = 0.5 m s-l; then for a slope of 3°:- L = 0.55/2 x 0.013/2 0.00005 x 0.1094 x 0.9886 Thus: L = 33.28 m and so Vl = 1.74 m

11. This treatment gives values which are rather higher than those obtained from empirical (trial and error) equations. An Excel module to investigate this is available on the web site. Channel dimensions In practice, the size of the channel leading the water away is also a consideration - later lecture. Qmax could be estimated from Hudson's method or some other method which applies to field sized watersheds.

12. The minimum wetted cross sectional area, Amin, of the terrace channel would be: Qmax/Vmax where Vmax is the maximum permissable velocity for the soil type. The method for designing channel dimensions will be considered later. If a constant gradient is to be used, the gradient chosen would be 0.25% to 0.5% depending on the soil (lower value for more erodible soils).

13. Table 2. Empirical formulae for channel terraces

14. Table 3. Formulae for bench terraces