Acepciones de Autonomía

Erosion is found to increase with increase in slope and length of the slope; this is due to corresponding increase in the velocity and volume of surface runoff. Erosion rate per unit area can be expressed as

Erosion

Area ~ S L^{m n} ...(3.1)

where the values of m and n are found to be different by different investigators. Values of m and n obtained by various investigators as given by Morgan (1979) are listed in Table 3.7. It can be seen that m and n are functions of process of erosion, magnitude of slope, steepness, length and vegetal cover.

Vegetation

Vegetation or plant cover reduces erosion of soil, its effectiveness depending on the height and continuity of canopy, density of ground cover and the root density. For a given temperature, as the precipitation increases the sediment yield in tons/km² increases and reaches a maximum value. If the

Example given 65% Silt + V.F. sand 20% Sand (0.1 = 0.2 mm)

canopy is near the ground it dissipates the kinetic energy of rain. Canopy on the ground also increases roughness and reduces the velocity of surface flow. Roots play an important role in reducing erosion rate. Roots create easy passages for water to infiltrate thereby increasing the infiltration rate and reducing the surface runoff. Small roots also bind the soil mass thereby increasing its resistance to erosion. Generally forests are the most effective in reducing erosion because of their canopy; dense grass is equally effective.

Experimental evidence indicates that the erosion-cover relationship is non-linear. As vegetal cover increases from zero there is a rapid decreases in soil loss; however beyond 60 percent cover, further increase in vegetal cover reduces the soil loss marginally. Table 3.8 shows the erosion-cover relationship generalised after Elwell (1980) and Elwell and Stocking (1974). It can be seen from Table 3.8 that for adequate erosion protection at least 60–70 percent of the ground should be covered by vegetation.

Table 3.8 Relationship between percent vegetal cover and percent reduction in soil loss

Mean seasonal vegetal cover % 100 80 60 40 20 10 5

Soil loss as a % of bare plot soil loss 0.5 1.5 5 10 32 60 70

It may be mentioned that there is an interaction between rainfall and vegetation in controlling erosion rates. Langbein and Schumm (1958) have found that vegetation bulk in kg/m² varies as the annual precipitation raised to a power greater than unity. With increasing precipitation the vegetation changes from desert shrubs to grassland to forest. As a result, when vegetation intensity becomes adequate it inhibits erosion. Hence, on a regional scale initially erosion rate increases with increase in annual precipitation, reaches a maximum and then decreases with further increase in precipitation. Schumm (1977) expressed the effect of

Table 3.7 Values of m and n in Eq. 3.1(Robinson 1977)

Investigator m n Conditions/Comments

Zingg 1.40 0.60 From five experimental stations in U.S.A.

Hudson and Jackson 2.0 — From experimental stations in Zimbabwe

Hovarth and Erodi 1.60 to 0.70 — m decreased with increase in slope in laboratory studies

Quinn, Morgan and Smith 0.70 to 1.0 — m increased as grass cover decreased

Kirkby 1.0 to 2.0 — For soil creep and splash erosion

1.3 to 2.0 0.3 – 0.7 For erosion by overland flow

— 1.0 – 2.0 For erosion with rilling

Fig. 3.7 Variation of sediment yield with mean annual precipitation and

temperature (Schumm 1977)

mean annual temperature and annual precipitation on sediment yield as shown in Fig. 3.7. It can be seen that as the annual temperature increases the peak of the sediment yield occurs at higher value of annual precipitation. This is so because at higher

Mean annual precipitation cm Meanannualsed.yieldtons/km2 400

0 300 200 100

0 40 80 120 160

5°C 10°C 15°C 20°C

temperature there is greater evapo-transpiration; hence less amount of precipitation is available for causing runoff. As a result, peak rate of sediment yield shifts to the right. However, studies by Walling and Kleo for 1296 measuring stations all over the world, by Sharma and Chatterji for small reservoirs in Rajasthan (India), by Dunne in Kenya, by Griffiths in New Zealand, and by Duglas in Australia do not support the universality of Fig. 3.7. (Tiwari 1993).

3.5 MECHANICS OF SHEET EROSION

As the rainfall occurs the overland flow normally occurs at shallow depth for a short distance without forming any small depressions or furrows called rills. The pre-rill flow is many times called inter-rill flow and associated erosion is known as inter-rill erosion. In this area the depth of flow and the corresponding shear on the surface are very small. Here the dominating factor influencing the surface erosion is rainfall impact. On the other hand, once the flow enters the rills and is concentrated, the depth of flow is large. Therefore erosion in rill-flow is related to the runoff characteristics; this erosion is sometimes called rill-erosion.

It may be mentioned that rills are not a permanent feature. Rills formed from one storm are often obliterated before the next storm of sufficient intensity, which can cause rilling. Most rill systems are discontinuous i.e., they have no connection with the main stream. Rills are usually initiated at a critical distance down the slope where overland flow becomes canalised. It may also be emphasized that rill erosion accounts for majority of erosion from the hillside. Mutchler and Young (1975) found that on a 4.5 m slope plots in U.S.A., over eight percent of material was transported in rills. Relative importance of rill erosion depends on the rill spacing. Smaller the spacing between rills greater will be the rill erosion.

Four processes associated with inter-rill and rill erosion can be identified as:

Soil detachment by rainfall;

Soil transport by rainfall;

Soil detachment by runoff;

Soil transport by runoff.

Mutchler and Young (1975) have summarised the mechanism of soil detachment by raindrops.

Raindrop sizes usually range from 7.0 mm to fine mist size and in any rainfall there are raindrops of various sizes. A normal or Gaussian distribution based on the raindrop volumes is usually assumed.

Hence median raindrop diameter d is that diameter for which equal amounts of volume are contained in larger and smaller drops than d. Laws and Parsons (1943) have found a relationship between intensity of rainfall I in mm/hour and d in mm as

d = 1.24 I^0.182 ...(3.2)

The raindrops attain a terminal fall velocity, which depends on their size, air density and temperature. Terminal fall velocity can be obtained from C_D versus Reynolds number diagram for a sphere, given in all textbooks on Fluid Mechanics. The terminal fall velocity for 5 mm drop will be about 9.0 m/s and it will be 1.0 m/s for 0.25 mm drop. Presence of strong wind has two effects on terminal fall velocity. Firstly it can increase the velocity of drops striking the land surface and secondly it causes raindrops to strike the surface at an angle to the vertical. The ability of rain to cause soil erosion is attributed to its rate and the distribution of drop size, both of which affect the energy load of a rainstorm. The erosivity of a rainstorm is attributed to its kinetic energy or momentum; both these

parameters can be related to rainfall intensity or total amount of rainfall. Rose (1960), Williams (1969) and Kinnell (1973) have related the erosivity rate to momentum of rainfall. Williams and Kinnell have given the following equations for momentum M:

log M = 0.711 log I – 1.461

M = 0.0213 I – 1.62

UVW

Here M is in dynes cm^–2 s^–1 and I is in mm/hour.

The kinetic energy of the rainfall is a major factor initiating soil detachment. Kinetic energy of rainfall can be either measured or can be computed if one knows the rain drop size distribution and corresponding terminal fall velocities. Investigators have used the following three forms of equations to relate kinetic energy E of rainfall expended per unit quantity of rainfall to the rainfall intensity I.

E a b I

E c b a I E b I a

= +

= +

-=

-U V|

W|

-log ( )

( ¹) ...(3.4)

Where a, b, c are empirical constants. Wischmeir and Smith (1958) gave the following equation

E = 13.32 + 9.78 log I ...(3.5)

where E is in J/m² .mm and I is the rainfall intensity in mm/hour. Hudson (1965) has given the following equation

E = 29.8 – 127 5.

I ...(3.6)

There are a large number of equations developed for E which are based on data from different regions such as Nigeria, Zimbabwe and U.S.A. It may be mentioned that for a given choice of equation for E, the kinetic energy for a storm having non-uniform rainfall intensity is computed by

(i) dividing the storm into small time increments in which the rainfall intensity can be assumed to the uniform;

(ii) determining the rainfall intensity in mm/hour for each time increment;

(iii) computing E_i for each intensity I_i using the chosen relationship between E and I;

(iv) determining E = SEi.

When the raindrop hits the soil surface there is a splash of water and its shape is as shown in Fig. 3.8. The splash shape parameters, which define its geometry, are crater width W, splash height H, splash angle b, sheet angle a and sheet radius r. These quantities change with respect to time and their variation with time as recorded by a high-speed camera is also shown in Fig. 3.8. The erosive action of raindrop is effective very early after the impact and in the vicinity of the centre of impact. Evidence indicates that the raindrop impact is most erosive where a thin layer of water about one fifth the drop diameter is present. If the surface water depth is about three drop diameters, it protects the soil from raindrop impact. As the splash height reduces and the crater width increases a horizontal flow velocity away from the splash is caused. This velocity among other parameters also depends on the ratio of water depth to drop diameter and is maximum when this ratio is 0.33, this horizontal component of velocity greatly increases the potential of this surface flow to transport detached soil particles.

It must also be mentioned that as the raindrop hits a thin water layer surface, a large number of smaller water droplets are produced. Mutchler (1971) found that one drop of 5.67 mm diameter on 0.10 mm water depth on a smooth glass produced as many as 4000 droplets which would eventually hit the soil surface, generate turbulence and throw additional material in suspension.

Raindrop impact effects are present in rills also; but because of relatively larger water depth compared to the size of drops, the impact effect is not so pronounced.