Subsurface drainage and its reversable facilities in subirrigation.

Teusdea, Alin Cristian ; David, Ioan ; Mancia, Aurora 等

1. INTRODUCTION

Subsurface drainage structures may be also employed in the case of subirrigations. The double use reduces the costs of these structures. For this purpose, the underground drainage structure must be firstly designed and then verified as a subirrigation system.

2. METHODS AND SAMPLES

Two-layered soil subsurface drainage structure is designed using Ernst relationship (Sutton, 1971; Beers, 1976; Martinez Beltran 1978; Wehry et al., 1982; Kroes & Van Dam, 2003) completed by David I. for a real drain with filter (Wehry et al., 1982, David, 1983).

The basic scheme of this structure is depicted in figure 1a where: z--is the drainage norm, h--is the hydraulic head, [K.sub.1], [K.sub.2]--are the hydraulic conductivities of the two soil layers, [D.sub.0]--is the distance between the drain separation layer ( the distance corresponds to the radial flow), [D.sub.1] = [D.sub.0] + 0,5 x h--is the water level above the drain (the distance corresponds to the horizontal flow in [K.sub.1] layer), [D.sub.2]--is the thickness of the layer below the drain, characterized by the hydraulic conductivity [K.sub.2], [D.sub.v] = h - the vertical distance of the vertical flow, [d.sub.0] - is the diameter of the drain tube and L--is the drain distance.

Ernst relationship for the calculation of the distance between ideal drains is (Sutton, 1971; Beers, 1976; Martinez Beltran 1978; Wehry et al., 1982; Kroes & Van Dam, 2003)

[FIGURE 1 OMITTED]

h = [h.sub.v] + [h.sub.o] + [h.sub.r] = q x L/K x ([[zeta].sub.o] + [[zeta].sub.v] + [[zeta].sub.r]) = q x L/K x [[zeta].sub.0], (1)

where [h.sub.0], [h.sub.v], [h.sub.r], are the hydraulic head losses due to the horizontal, vertical and radial flow, respectively, and [[zeta].sub.0] the total loss coefficient with an ideal drain. The resistance coefficients, [[zeta].sub.o], [[zeta].sub.v], [[zeta].sub.r], corresponding to three flow types are calculated according to the relationships below (Sutton, 1971; Beers, 1976; Martinez Beltran 1978; Wehry et al., 1982; Kroes & Van Dam, 2003)

[[zeta].sub.o] = L/8 x ([D.sub.0] + 0,5 x h); [[zeta].sub.v] = [d.sub.0] + h/L; [[zeta].sub.r] = 1/[pi] x 1n 2/[pi] x [D.sub.0]/[d.sub.0]. (2)

If the drains are real--with discontinuous slits--and overcastted with a filter, then David I. (David, 1983) proposes the addition to the Ernst relationship with a term for the load loss at the filter drain entrance, [[delta][h.sub.if],

h = [h.sub.0] + [delta][h.sub.if] = q x L/K x ([[zeta].sub.0] + [[zeta].sub.if]). (3)

The resistance coefficient at the filter drain entrance is given by the relationship (David, 1983)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where: n--is the number of slits situated on the circumference of the drain, b--is the width of the slit, l--is the length of the slit, B--is the distance between slits and [d.sub.f]--is the filter diameter. The coefficients [alpha] and [beta] are calculated in different ways: in the case of longitudinal slit (l > b) and in the case of transversal slit (l < b) (David, 1983).

The coefficient [chi] = [K.sub.f]/[K.sub.0] represents the proportion between the hydraulic conductivity coefficient of the filter, [K.sub.f], and of the soil around the drain, [K.sub.0] respectively.

The distance between the drains, L, results from the second order equation in L, which is given by the relationship (3) (only the positive term is retained). After the calculation of this distance, the design of the drainage structure is practically finished. The next step consists in a verification if the structure is fit for a subirrigation system (figure 1b), meaning that it may be used reversibly.

The goal of the subirrigation verification is to determine the level difference [h.sub.sub] = [H.sub.0] - [H.sub.m]. The difference represents the total load loss which secures the water reserve at the root level. The basic scheme of this structure is depicted in figure 1b. The notations are as it follows: p--the width of phreatic water, [H.sub.0]--the width of the saturated soil zone at the drain, [H.sub.m]--the width of the saturated soil zone midway between the drains, [D.sub.0]--the distance between drains and the impermeable layer, [L.sub.dr] = L--the drain distance, H--the height of the impermeable layer and K--the hydraulic conductivity of the soil. The total hydraulic head loss is composed of two components

[h.sub.sub] = [h.sub.o] + [h.sub.r] (6)

where: [h.sub.o]--is the hydraulic head loss due to the horizontal movement and [h.sub.r]--is the hydraulic head loss due to radial movement around the drain. These losses are defined by the relationships below (David, 1983)

[h.sub.o] = [epsilon]L/8K[T.sub.e], [T.sub.e] = [H.sub.0] + [H.sub.m]/2, [H.sub.0] = H - Z - [h.sub.if] - [h.sub.ld], (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[h.sub.if] = [epsilon][L.sub.dr]/2K x [[zeta].sub.if], (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

with [alpha] = [H.sub.0]/[H.sub.m].

From these relationships, [h.sub.if] is the hydraulic head at real drain with filter entrance, [h.sub.ld] is the hydraulic head loss along the drain of [X.sub.dr] = H/i with i slope, g = 9.81(m/[s.sup.2]) is the gravitational acceleration and [lambda] = 0.04 is the roughness coefficient.

The validation criterion of the drainage structure for the reversible usage (meaning, subirrigation) is described by the following relationship

([H.sub.c] + z) < H, [H.sub.c] = [H.sub.m] + [h.sub.sub] + [h.sub.if] + [h.sub.ld] (11)

where [H.sub.c] represents the water height in the collecting channel.

3. RESULTS AND DISCUSSIONS

Computer simulations were done involving the equation (1-5) for subsurface drainage, and (6-11) for subirrigation validation. Two examples were taken into consideration: the first with hydraulic head h = 1.1 m and the second with h = 0.6 m, with two values for H = 3.00 m and H = 4.75 m. The initial parameters were q = 0.01 mm/day, z = 0.6 m, [D.sub.0] = 0.5 m, [D.sub.1] = 0.8 m, [D.sub.2] = 2.0 m, [d.sub.0] = 0.065 m, [d.sub.f] = 0.073 m, l = 0.001 m, b = 0.005 m, B = 0.012 m, p = 1.6 and i = 0.02. The first situation considers an ideal drain, which means that there is no [[zeta].sub.if] coefficient involved. The second situation considers the real drain with filter which means that there is a real non-zero value of the [[zeta].sub.if] coefficient involved.

The drain distance, L, decreases with 4.16 % in the first example, from the ideal drain situation to the real drain with filter situation. In the second example, the drain distance, L, decreases with 13.74% in the first example, from the ideal drain situation to the real drain with filter situation. This means that the real drain with filter needs a smaller drain distance.

Subirrigation validation fails in the first three cases of the first example because the ([H.sub.c] + z) values are greater than the H values. The forth case generates a subsurface drainage structure that can be used in subirrigation, as the validation criterion ([H.sub.c] + z)< H is satisfied.

In the second example, all the four cases generate subsurface drainage structures that can be used in subirrigation, as the validation criterion ([H.sub.c] + z) < H is satisfied. Regardless of the H values, the ([H.sub.c] + z) values are smaller in the situation of real drain with filter than in the ideal drain situation. These results show that those subsurface drainage structures are more stable to subirrigation usages.

4. CONCLUSIONS

This paper studies the effect of using a real drain with filter in subsurface drainage design and its subirrigation validation. In the subsurface drainage design, the Ernst equations completed by David I. are used with a term for the load loss at the filter drain entrance. The subirrigation design is also accomplished with David I.'s equations. Computer simulation results point out that the subirrigation validation criterion is agreed upon only by the subsurface drainage system with real drain with the selected input parameters.

In the future research, we plan to verify if, according to this paper's analysis, the already designed subsurface drainage systems in the Western part of Romania are suitable for subirrigation.

5. REFERENCES

Beers, W.F.J. (1976). Computing Drain Spacings--A generalized method with special reference to sensitivity analysis and geo-hydrological investigations, pp. 14-19, IRLI Bulletin 15, Wageningen, The Netherlands.

David I. (1983). Uber ein berechnungsverfahren der verlusthohe beim eintrittswiderstand des wassers in die drainrohre / Calculation method of the head loss by the ground water entrance in drainage, pp. 3-20, Revue Roumaine des Sciences Techniques--Serie de Mecanique applique, Tome 28, Nr, 1, Bucharest.

Kroes J.G. & Van Dam, J.C. (2003). Reference Manual SWAP version 3.0.3, pp. 52-58, Alterra Report 773, Alterra, Green world Research, Wageningen.

Martinez Beltran, J. (1978), Drainage and Reclamation of Salt-Affected Soil--Bardenas Area Spain, pp. 276-278, ILRI, Publication 24, Wageningen.

Sutton J. (1971). Section 16 Drainage of agricultural land, USDA--Soil conservation Service, National Engeneering Handbook, pp. 4-1--4-122, Washington DC.

Wehry A.; David I. & Man E., (1982), Probleme actuale in tehnica drenajului / The present state of drainage technique, pp. 67-85, Editura Facla, Timisoara.