6.1 The importance of land preparations
6.2 Small-scale land levelling
6.3 Traditional engineering approach
6.4 Laser land levelling
Levelling, smoothing and shaping the field surface is as important to the surface system as the design of laterals, manifolds, risers and outlets is for sprinkler or trickle irrigation systems. It is a process for ensuring that the depths and discharge variations over the field are relatively uniform and, as a result, that water distributions in the root zone are also uniform. These field operations are required nearly every cropping season, particularly where substantial cultivation following harvest disrupts the field surface. The preparation of the field surface for conveyance and distribution of irrigation water is as important to efficient surface irrigation as any other single management practice the farmer employs.
There are perhaps two land levelling philosophies: (1) to provide a slope which fits a water supply; and (2) to level the field to its best condition with minimal earth movement and then vary the water supply for the field condition. The second philosophy is generally the most feasible. Because land levelling is expensive and large earth movements may leave significant areas of the field without fertile topsoil, this second philosophy is also generally the most economic approach.
Land levelling always improves the efficiency of water, labour and energy resources utilization. The levelling operation, however, can be the most intensively disruptive cultural practice applied to the field and several factors should be considered before implementing a land levelling project. Major topographical changes will nearly always reduce crop production in the cut areas until fertility can be replaced. Similarly, equipment traffic can so compact or pulverize the soil that water penetration is a major problem for some time. The farmer has many activities which contribute to his productivity and therefore require his skill and labour. The irrigation system should be designed with him (or her) in mind. A field levelled to high standards is generally more easily irrigated than one where undulations require special attention.
New equipment is continually being introduced which provides the capability for more precise land levelling operations. One of the most significant advances has been the adaptation of laser control in land levelling equipment. The equipment has made level basin irrigation particularly attractive since the final field grade can be very precise. Comparisons with less precise techniques have clearly shown that laser-levelled fields achieve better irrigation and production performance. Nevertheless, for most irrigated agriculture, laser-controlled precision is unfeasible because of the high cost of such equipment unless a large number of farmers form a cooperative or a government programme is started with subsidized land levelling as one component in an effort to improve farm production.
Most small-scale farming operations rely on animal power or small mechanized equipment which an individual can own and operate. As the irrigator waters his fields season after season he is able to observe the locations of high and low spots on the field. Then as he prepares the fields between plantings, he tries to move soil from the high spots to the low ones. Over a period of several years individual fields are smoothed enough to be watered fairly well. Figures 62 and 63 show two examples of these operations. In Figure 62, a farmer is preparing land for paddy and using the ponded water level on the field to direct him to the high and low spots. Since this is a normal land preparation practice, it does not represent an extra task for the irrigator. Figure 63 shows a similar operation using mechanized equipment for typical annual crops and again one sees that the field preparation also readies the seed bed for planting. Beyond these technologies one may observe various levels of mechanization and an array of implements. The one feature common to most small-scale land levelling is the trial and error nature of the practices and the long-term incorporation of land levelling with seed bed preparation. Another feature is that no technical or engineering inputs are needed.
Figure 62. A typical land smoothing operation using animal power
Figure 63. Levelling and smoothing a field as part of tractor-based farming operations
6.3.1 Initial considerations
6.3.2 Engineering phase
6.3.3 Adjusting for the cut/fill ratio
6.3.4 Some practical problems
6.3.5 An example problem
Initially, the field should be studied and an overall irrigation strategy identified. Once accomplished, the land levelling programme derived from traditional engineering practice can be initiated. The first step is to establish the plane of the field. This involves placing a reference grid on the field, surveying the existing topography of the field by establishing the elevations of the grid points, and calculating the new field topography by adjusting the grid elevations to correspond to the desirable plane. This is the engineering phase of the land levelling procedure. Once the surface design has been determined, a land levelling operation begins. This is typically a private contractor utilizing his equipment to move the earth into the new position on the field, and the adequacy of the land levelling is dependent on the skill of the equipment operator.
Surveying and mapping the field involves setting a uniform grid system on the field and establishing the field topography. This need not be a complicated procedure. One corner of the field can be chosen as a starting point and the first stake can be located one-half grid spacing from either boundary. Then a row of stakes can be measured and set using a transit or level and tape. The instrument is set up over the first stake and sighted along a line parallel to the boundary. Usually this is accomplished by going to the opposite edge and locating a stake one-half grid spacing from the edge. Then, using the instrument for alignment, the first row of stakes is measured into place. With the instrument located over the same stake and aligned along the first row, the next step is to turn the alignment 90° by either measuring a right triangle or by using the instrument angle indicators if available. The new alignment is used to locate another stake row along the other field axis. Each of the remaining stakes can be placed visually by sighting against the two stakes at the field edges. The grid spacing can be set at convenient lengths so long as it is square and consistent (this is not technically required but it simplifies the calculations). In the US, the typical grid spacing is 100 feet by 100 feet (30.5 m by 30.5 m). However this would be too large in many countries with small fields. It is suggested that the surveyor use a multiple of 10 m as a spacing and select one that divides the field into at least 5 percent subareas.
The field stakes provide the basis of the field survey. The level or transit can be located in a central area and rod readings taken from each stake position. It is generally advisable to locate a benchmark near the field from which to reference the readings as elevations. In addition, readings taken from the location of water supply structures are also useful for designing the head ditches, watercourses and drainage channels. It is assumed that the basic principles of land surveying are known and practiced during this phase of the land levelling operation.
An initial decision as to the method of surface irrigation will dictate field slope. Basins are designed to be level in both field directions. Borders are similar in having zero cross-slope, but may have advance slopes of up to 2 or 3 percent, depending on crop and soil conditions. Furrow irrigation systems work well with advance slopes up to 1 to 3 percent and cross-slopes of 0.5 to 1.5 percent. If the average natural slopes are greater than these ranges, terraces or benches should be planned.
There are several ways to compute the new field slope including some that are inspection methods requiring some experienced judgment. A formal method, called the 'plane method,' will be used here.
The plane method is a simple least squares or linear regression fit of field elevations to a two-dimensional plane. Subsequent adjustments are made in the elevation of the plane centroid to compensate for variable cut/fill ratios. If the field has a basic X-Y orientation, the plane equation is written as:
E(X, Y) = AX + BY + C (117)
in which:
E = elevation of the X, Y coordinate;
A, B = regression coefficients; and
C = elevation of the origin or reference point for the calculations of field topography using Eq. 117.
The first step in evaluating the constants, A, B and C, is to determine the weighted average elevations of each grid point in the field. The purpose of the weighing is to adjust for any boundary stakes that represent larger or smaller areas than given by the standard grid dimension. The weighing factor is defined as the ratio of actual area represented by a grid point to the standard area. The grid point area is assumed to be the proportional area surrounding the stake or other identification of the grid point elevation. The weighing factor is:
(118)
where:
q ij = weighing factor of the grid point identified as the ith stake row and the jth stake column;Aij = area represented by the (i, j) grid point; and
As = area represented by the standard grid dimension.
The next step is to determine the average elevation of each row and column. For the ith row, Ei, is:
(119)
in which:
N' = number of stake columns; and
Eij = elevation of the (i, j) coordinate found from field measurements E(X, Y).
A similar expression can be written for finding the average elevation of the jth stake column, Ej:
(120)
where N" is the number of stake rows.
The next step is to locate the centroid of the field with respect to the grid system. For convenience, an origin can be located one grid spacing in each direction from the first stake position, i.e. the initial stake position on the field. The distance from the origin to the centroid in the X dimension is found by:
(121)
where:
X = x distance from origin to centroid;
Xj = x distance from origin to the jth stake column position; and
(122)
Similarly,
(123)
in which:
Y = y distance from the origin to centroid;
Yi = y distance from origin to the ith stake row position; and
(124)
The fourth step is to compute a least squares line through the average row elevations in both field directions. The slope of the best fit line through the average X-direction elevation (Ej) is A and is found by:
(125)
For the best fit slope in the Y-direction, the slope, B, is.
(126)
Finally, the average field elevation, EF, can be found by summing either Ei or Ej and dividing by the appropriate number of grid rows. This elevation corresponds to the elevation of the field centroid (X, Y). Thus, Eq. 117 can be solved for C as follows:
C = EF - A X - B X (127)
An adjusted elevation for each stake can be computed with Equation 110 and compared to the measured values. The differences are the necessary cuts or fills. Before these computations are undertaken, however, the slopes in both field directions must be checked to see if they are within satisfactory limits. For example, if the intended system is a border irrigation system, the cross-slope should be zero (A = 0) and the cuts and fills would need to be based on this condition. A second note concerns the fact that cuts and fills do not balance because of variations in soil density. This adjustment will be covered in a following section.
In most cases, the best fit plane and the subsequent adjusted elevation will result in different total volumes of cuts or fills. A simple and rapid calculation of these respective volumes can be made as follows.
(128)
and,
(129)
in which:
Vc = volume of cuts, m3;
Vf = volume of fills, m3;
A = grid area m or n, m3;
Cm = depth of cut at grid point m, in metres, and
Fn = depth of fill at grid point n, in metres.
The cut/fill ratio r is:
r = Vc / Vf (130)
and should be in the range of 1.1 to 1.5 depending on the soil type and its condition.
The necessity of having cut/fill ratios greater than one for land levelling operations stems from the fact that in disturbing the soil, the density is changed (the fill soil is more dense because its structure has been destroyed). Selecting a cut/fill ratio remains a matter of judgement. If the value arrived at by least squares is not in the range of 1.1 to 1.5, the elevation of the field centroid, C, is raised or lowered until the value of r is appropriate. This adjustment is determined by:
(131)
where r' is the cut/fill ratio required in the design.
Equations 130 and 131 assume that none of the 'cut' grid points become 'fill' points or vice-versa. Consequently, in some cases it will be necessary to iterate a few times to get the proper cut/fill ratio.
Equation 128 is usually less formal than required for contracting purposes. Some more complete estimators include the prismoidal formula, the 'average end area method,' and the 'four corners method.' The 'four corners method' is simplest to use and is suggested by the USDA (1970). The formula for all complete grid spacings is:
(132)
in which:
Ai = area of the grid square i, m2;
Nc = number of cuts at the four corners of the grid square; and
Cj and Fm = cut and fill depths in m, but they are taken as absolute values so they both have the same sign, positive.
At the field edges and corners, if complete grid spacings are not present, the cut volume must be computed separately. The procedure is to assume the elevations of the field boundaries are the same as the nearest stake and would thereby have the same cut or fill dimensions. Equation 132 is then utilized with appropriate Ai value corresponding to the actual edge area.
The engineering design derived from the procedures above results in a field design which should provide the irrigator with a system that will satisfy his irrigation practices and yield efficient and uniform waterings if managed properly. Between the design and the operable system is the land levelling operation itself. Generally, a contractor must be retained to move the earth, after which the field topography is checked and if necessary the contractor refines his job with additional work. The skill and efficiency of the equipment operator is critical to how well the field levelling is finally accomplished. A good operator may be able to provide a field grade within plus or minus 10 cm; a poor operator perhaps double this value. The first of the practical problems is the arrangements between the irrigator and the contractor. The work should be checked and fall within the 10 cm limits before it is accepted and reimbursed.
Land levelling is likely to be not only the most disruptive operation applied to the field but also the most costly. One method of reducing cut volumes, and therefore the cost, is to subdivide the field into terraces or benches. Usually, earthwork is minimized when the terrace runs parallel to the direction of highest field slope but to be sure, the cut volumes should be checked with the alternative field layouts.
Operators develop field movement patterns based on their own judgement and experience. A cut-haul-fill pattern of travel that maximizes the efficiency of the land levelling operation tends to be one in which the routes are of nearly equal length. Such a strategy prevents the over-use of travel lanes and minimizes the haul and return distances. Where manually controlled equipment is used, many operators establish a bench mark grid over the field by cutting and filling strips on both sides of a stake to the desired grade. Then the median areas can be levelled to grade to better precision. Good operators make cut and fill passes which are relatively uniform and their equipment is seen to operate at fairly uniform speeds, particularly during loading passes.
Earth may be used to raise the elevation of roadways, or prepare a raised pad for headland facilities. In the computation setting field cuts and fills, the volume of the earth needed for these miscellaneous requirements should be deducted in the cut/fill ratio calculation.
The topography of surface irrigated fields, even after levelling, is not a static feature of the land. Year to year variations in tillage operations disturb the surface layers as well as shift their lateral position. The loose soils may settle differently depending upon equipment travel or depths of irrigation water applied. Consequently, a major land levelling operation will correct the macro-topographical problems but annual levelling or planing is needed to maintain the field surface by correcting micro-topographical variations.
Booher (FAO, 1974) devotes a chapter in his manual on surface irrigation to land levelling. Included is an example problem around which useful suggestions are made regarding the methods and equipment for levelling the field into a workable surface irrigated field. The problem that is developed utilizes a different approach to that suggested herein so it will be partially repeated for purposes of both illustration and comparison.
The first six columns and the first eight rows of Booher's example field have been extracted and are shown in Figures 64 and 65. The locations of the field boundaries have been changed relative to the grid system to illustrate the importance of weighing grid point elevations based on the areas they represent. In the following example the standard grid spacing is 20 m by 20 m and begins one-half spacing from the upper left corner of the field (represented by the grid point [i, A] in Figure 65). The standard grid area is 400 m2, but one will note that grid points adjacent to the right field boundary represent 500 m2. One point, the lower right grid represents an area of 375 m2.
Figure 64. Example problem field layout
Figure 65. Initial field elevations in metres
The first step in the calculation of the revised field plane is to determine the grid point weighing factors using Eq. 118. Using the standard area per point as 400 m2, the weighing coefficients, q ij, are shown in Figure 66. The row and column weights are the sum of the grid point weights and are shown to the left and at the bottom of Figure 66.
Figure 66. Grid point weighing coefficients
Using the column and row weights, Eqs. 119 and 120 are used to calculate the average elevation of the respective rows and columns. These data are included along the left and bottom of Figure 65.
The field centroid is calculated with Eqs. 121 to 124 using the distances from the origin and the row and column weights. For the X coordinate of the centroid, this calculation is:
and for the Y coordinate:
Note that the origin is 10 m to the right and 10 m above the stake at grid position [i, A].
The next step is to run a linear regression through the average row and column elevations using Equations 125 and 126. These procedures are fairly standard on hand-held calculators and microcomputers so the calculations will not be shown here. The slope of the field from right to left is 0.000373 (A) and that from top to bottom is -0.002247 (B). It can also be mentioned that standard regression techniques will also yield an intercept value representing the elevation with which the best fit line through the average elevations will intercept the X and Y axis running through the origin. These intercepts can be ignored.
The final calculations involving the revised field plane involve the calculation of the C value in Eq. 117 as outlined in the paragraph preceding Eq. 127. The average elevation at the centroid of the field is determined by summing the average row or column elevations. This value is also shown in Figure 65 as 1.557 m. From Eq. 127, then:
C = 1.577 - 0.000373 * 72 - (-.002746 * 87.743) = 1.7911 m
The resulting equation of the field plane defined by the procedure so far is:
E(X, Y) = .000373 * X - .002746 * Y + 1.7911
If this relationship is used to recompute the elevations at each grid point, the cuts and fills are identified as the positive (fills) or negative (cuts) differences between the computed elevations and the original topography. Figure 67 shows these results as the upper number near the grid points.
Figure 67. First determination of cuts and fills for the example problem
In order for the earthwork to balance in the field after levelling, the volume of cuts should exceed the fills by 10 to 30 percent. For the 6th row shown below, Eqs. 128 and 129 are evaluated as follows:
|
|
| |
+.11 |
+.03 |
-.01 |
-.01 |
-.02 |
0 |
| |
|
vi |
| |
* |
* |
* |
* |
* |
* |
| |
Volume of Cuts for Row vi = (-.01) * 400 + (-.01) * 400 + (-.02) * 400 = -16 m3
or since the sign is irrelevant, the cut volume along row 6 is 16 m3, and for the fills:
Volume of Fills for Row vi = 400 * (.11 + .03 + .000) = 56 m3
Determining the cuts and fills of each row and then summing yields a total cut volume of 627 m3 and a total fill volume of 1007 m3. Dividing the cut volume by the fill volume gives a cut/fill ratio of about 0.62, which of course is not satisfactory.
Assuming the cut/fill ratio should be about 1.3, Equation 131 can be used to recompute the elevation of the field centroid, C. The change in centroid elevation is determined by summing the area of each cut station times the depth of cut. There are 17 cut points in which the grid area is 400 m2, 2 involving the 500 m2 left boundary points, and 4 cuts along the 300 m grid points along the lower field boundary. Thus the area summation in the denominator of Equation 124 is 9000 m2. The remainder of Equation 124 is then:
This calculation assumes that none of the previous fill locations become cut locations. To test this assumption, 0.033 m is subtracted from each cut and fill depth in Figure 67 and the results are shown in Figure 68. It is noted that 2 fill locations have become cut points.
Figure 68. Second determination of cuts and fills for the problem
Recomputing the volume of cuts from Eq. 128 and the fills from Eq. 129 yields the following cut/fill ratio (Eq. 130):
This value is slightly more than the 1.3 assumed in adjusting the C value in Eq. 117 and reflects the problem of grid points changing from cuts to fills (or vice versa in other cases). If the error had been greater, another iteration would be suggested. Not in this case, however, and the final field plane is as shown in Figure 68 with the subscript cuts and fills.
If the field is intended for borders and basins, the procedure is the same except that the A and/or B slopes in Eq. 117 would be zero. Similarly, if the field is to be terraced, the procedure is applied separately to the grid points in each terrace area.
The last engineering step is the formal computation of the volume of cuts for contractual purposes. This is illustrated for the evaluation of Eq. 132 for the area between rows v and vi. The final cut/fill depths for rows vii and viii are shown below.
|
v |
| |
* |
* |
* |
* |
* |
* |
| |
|
|
| |
+.28 |
+.18 |
+.05 |
+.01 |
0 |
+.05 |
| |
|
|
| |
|
|
|
|
|
|
| |
|
|
| |
|
|
|
|
|
|
| |
|
vi |
| |
* |
* |
* |
* |
* |
* |
| |
|
|
| |
+.08 |
-.01 |
-.04 |
-.04 |
-.05 |
-.04 |
| |
It is assumed that the depth of fill at the left boundary is .28 m at row v and .08 m at row vi. Similarly, the fill and cut at the right boundary are .05 m at row v and -.04 at row vi respectively. Equation 132 is evaluated as follows:
|
Grid Points |
Computations |
Total |
||
|
| |
* |
|
|
|
|
+.28 |
+.28 |
|
|
|
|
|
|
= |
0 m3 |
|
|
| |
* |
|
|
|
|
+.08 |
+.08 |
|
|
|
|
|
|
|
|
|
|
* |
* |
|
|
|
|
+.28 |
+.18 |
|
|
|
|
|
|
= |
.02 m3 |
|
|
* |
* |
|
|
|
|
+.08 |
-.01 |
|
|
|
|
|
|
|
|
|
|
* |
* |
|
|
|
|
+.018 |
+.05 |
|
|
|
|
|
|
= |
.89 m3 |
|
|
* |
* |
|
|
|
|
-.01 |
-.04 |
|
|
|
|
|
|
|
|
|
|
* |
* |
|
|
|
|
+.05 |
+.01 |
|
|
|
|
|
|
= |
4.57 m3 |
|
|
* |
* |
|
|
|
|
-.04 |
-.04 |
|
|
|
|
|
|
|
|
|
|
* |
* |
|
|
|
|
+.01 |
+.0 |
|
|
|
|
|
|
= |
8.10 m3 |
|
|
* |
* |
|
|
|
|
-.04 |
-.05 |
|
|
|
|
|
|
|
|
|
|
* |
* |
|
|
|
|
0 |
+.05 |
|
|
|
|
|
|
= |
5.79 m3 |
|
|
* |
* |
|
|
|
|
-.05 |
-.04 |
|
|
|
|
|
|
|
|
|
|
* |
| |
|
|
|
|
+.05 |
+.05 |
|
|
|
|
|
|
= |
4.44 m3 |
|
|
* |
| |
|
|
|
|
-.04 |
-.04 |
|
|
|
|
|
|
Total |
|
23.81 m3 |
Repeating these calculations for each grid area yields a total cut volume of 946.02 m3 which is very close to the 959 m3 estimated with Eq. 128.
It is perhaps worthwhile mentioning at this point that microcomputer programmes have been written to perform land levelling computations as illustrated above. Some of these are commercially available, some can be acquired by tracking down the programmer.
The advent of the laser-controlled land levelling equipment has marked one of the most significant advances in surface irrigation technology. One such system is shown in Figure 69. It has four essential elements: (1) the laser emitter; (2) the laser sensor; (3) the electronic and hydraulic control system; and (4) the tractor and grading implement.
Figure 69. Two views of land levelling equipment using laser control systems
The laser emission device, like that pictured in Figure 70, involves a battery operated laser beam generator which rotates at relatively high speed on an axis normal to the field plane. This rotating beam thereby effectively creates a plane of laser light above the field which can be used as the levelling reference rather than the elevation survey at discrete grid points in conventional land levelling techniques. Various beam generators are equipped with self-adjustment mechanisms that allow the plane of the beam to be aligned in any longitudinal or latitudinal slope desired. This reference plane of laser light is an extremely advantageous factor in the levelling operation because it is not affected by the earth movement, does not require a field survey to establish the high and low spots, and does not require the operator to judge the magnitude of cuts and fills. The distance between the laser beam and the earth surface is defined such that deviations from this distance become the cuts and fills. With laser systems, there is little or no need for the exhaustive engineering calculations of the conventional approach. The cost of levelling is usually contracted on the basis of money per equipment hour. The laser emitter is generally located on a tripod or other tower-like structure on or near the field and at an elevation such that the laser beam rotates above any obstructions on the field as well as the levelling equipment itself. The beam is targeted and received by a light sensor mounted on a mast attached to the land grading implement. The sensor is actually a series of detectors situated vertically so that as the grading implement moves up or down, the light is detected above or below the centre detector. This information is transmitted to the control system which actuates the hydraulic system to raise or lower the implement until the light again strikes the centre detector. It is in this manner that the sensor on the mast is continually aligned with the plane on the laser beam and thereby references the moving equipment with the beam. It is important to note that the sensitivity of the laser sensor system is at least 10 to 50 times more precise than the visual judgement and manual hydraulic control of an operator on the tractor. Consequently, the land levelling operation is correspondingly more accurate. The skill of the operator is substantially less critical to the levelling which allows farmers and other personnel access to the land grading equipment.
Figure 70. Close up view of laser beam emmitter
The electronic and hydraulic control systems generally have two operating modes. In the first, or observation mode, the mast itself moves up or down according to the undulations in the field as the operator drives the equipment over the field in a grid-like fashion. The monitor in the tractor yields elevation data from which the operator can determine average field elevations and slopes. In other words, the system operates as a self-contained surveying system. In this mode, the blade of the grading implement is fixed in place and only the sensor mast moves. In the second mode, or planing mode, the mast position is fixed relative to the implement blade which is then raised or lowered in response to the land topography. The beam plane is located the appropriate distance above the field centroid and at the desired slopes. By adjusting the height of the mast sensor relative to this plane and the centroid, the cutting and filling is accomplished simply by driving the tractor over the field. However, in many cases, the depth of cuts will exceed the depth which can be cut with the power of the tractor and the operator must override the automatic controls in order to keep the equipment operating.
The fourth element of the levelling system is the tractor - grading implement combination. This equipment is generally standard agricultural tractors and land graders in which the hydraulic and control systems have been modified to operate under the supervision of the electronic controller supplied with the laser emitter and sensor devices. The tractor needs to be carefully selected so that it is not under-powered and its hydraulic system is strong enough to work with the laser-imposed frequency of movements and adjustments. The grading implement can be as simple as a land plane which scrapes the earth and moves only as much as can be pushed in front of the blade or a complex piece of equipment which loads and carries earth. The former is used primarily for small levelling jobs, smoothing and repeat grading. The latter is usually better for initial levelling where cuts are larger and in the preparation of level basins where the cuts are also larger than in bordered or furrowed fields.
As a final note on levelling in general and laser levelling is particular, it is probable that the importance of accurate field grading has been under estimated. The precision improves irrigation uniformity and efficiency and as a result the productivity of water and land. On large fields, the improved productivity has been shown to pay economic dividends that easily exceed the cost of the levelling. However, the equipment is expensive and quite beyond all but the largest of farmers. In the developing countries, laser-guided equipment is being demonstrated and tested. There remains the solution as to how such equipment can be made useful for the small farmer.
