From the Art of Drainage to Engineering Science aspect of drainage engineering is stressed by the fact that seventeen of the twenty-six . In: J.N. Luthin (ed.). field drainage engineers in planning or designing drainage facilities. The piezometer method (Luthin and Kirkham, ) differs from the auger-hole method. Theories of Buried Drain and Open Ditch Subsurface Drainage. Classification of and. in other chapters of this Section of the National Engineering Handbook. At several points in the Luthin and Day (13) have used the method to apply to.
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The manual provides drainage engineers a ready reference and to Luthin and Kirkham (), when b = 0 and d is much greater than w. Luthin has been accepted towards fulfillment of the requirement: fat. __ degree cerned with irrigation and drainage and to engineers interested in the flow. Article (PDF Available) in Journal of Soil and Water Conservation 67(6)A- A · November . tive of drainage researchers and engineers.
Canadian Geotechnical Journal
This approach was ison with the results of the finite-difference model SLOP developed in France by Guyon for recession stages in Lorre et al. These authors have also developed the motion equation 2 a ].
As a consequence, the from 10 yields the general equation water table shape function W depends on H. Integrating 2 following x yields the g H ]R t represents the contribution of the recharge to the drain flow rate of the system Q t drain flow rate.
The solutions are divide flux plane described in Appendix II. This case allows for a verifi- cation of the calculation method before its extension to When the flow is entirely downslope i. Theoretical and Calculated Water Table Shape Fac- The solution of the set of equations [ 16 and 17 ] requires tors B and C in Case of Flatland a time integration of 16 , which can be carried out by simple numerical methods such as the Runge-Kutta method.
The time Parameter B C step of this integration is 1 h. The input climatologic variables 1 2 3 rainfall and Et need to be transformed into net recharge data Theoretical factor Guyon 0. A simple method valid during humid seasons when Et of 7 0.
Characteristics of Tail Recession Tests full, the excess water instantaneously provides recharge to the Parameter Value water table. The reservoir is full at the beginning of the sim- 1 2 ulation, which starts during a rainfall event.
The integration h0 m 1. As for the verification of the model predictions, two methods were used. The first method used the steady-state equation proposed by SLOP is based upon the same assumptions as those used to Lesaffre as a solution of 7.
This equation reads develop 16 and 17 , except for the water table shapes, which are not subjected to any assumption. H R R A tail recession event was simulated by SIDRA and the This equation is also derived from the Boussinesq equation, SLOP model to compare 1 the water table shapes of the but because it is a steady-state equation, its derivation does steady and transient states; and 2 the maximum water table not require any assumption on water table shapes.
As dem- elevations and drain flow rates. This result is dicted by the three methods exhibit little difference, ranging not surprising because water table shapes in recession stages between 0. These errors are not greater are generally less elliptical than in the steady state Lesaffre than the errors associated with Second, the numerical model SLOP, which solves the Bous- The relationship between maximum water table elevations sinesq equation using a finite-difference method Lorre et al. H and drain flow rates Q predicted by the two models are also , was utilized to calculate the water table elevations at similar Fig.
Discrepancies are greater for high water table different positions as a function of the recharge and time. The contribution of recharge to drain flow rate is shown to depend on a water table shape factor and to decrease when the water table elevation is small or the slope is steep. Analytical and computer solutions of transient water tables for drainage of sloping land.
Regina, Sask. Google Scholar Childs EC. Drainage of groundwater resting on a sloping bed. A comparison of modeling approaches for steady-state unconfined flow. Corey, A. Mechanics of immiscible fluids in porous media.
Google Scholar Dupuit, J. Dunod, Paris, France. Google Scholar Ferrandon J. Gillham RW. The capillary fringe and its effect on water table response.
Drainage of sloping lands with variable recharge: analytical formulas and model development. Hooghoudt SB. Bijdragen tot de Kennis van enige Natuurkundige Grootheden van den Grond. Steady state analysis of unsaturated flow above a shallow water-table aquifer drained by ditches. Lesaffre B. Analytical formulae for transverse drainage of sloping lands with constant rainfall.
Comparison of models for subsurface drainage in flat and sloping lands.
Luthin, J. Drainage engineering.
Robert Krieger Co. Transient drainage with non-linearity and capillarity. Morel-Seytoux HJ. From excess infiltration to aquifer recharge: a derivation based on the theory of flow of water in unsaturated soils. Myers, L.
Measurement and evaluation of water table elevations. Dans Proceedings of the 5th Congress. Question Google Scholar Panfilov, M. The sum of the squares of the differences Y showed that the solution of Sum of the squares difference Y This computationally simple solution may have application in situations with vertical rainfall rate and K is the saturated low angles and high rainfall rate relative to hydraulic conductivity , for three contrasting soil saturated hydraulic conductivity.
These are types.
Drainage Engineering by James N. Luthin (1966, Hardcover)
The results are similar to those of Hele- circumstances where drains are often be required. There is one Dupuit-Forchheimer DF theory for groundwater typographical error and some serious flow above a horizontal plane is based on the mathematical errors in their solution.
Knight has recently improved 2 the Dupuit-Forchheimer approximation but has as yet not extended this solution to a sloping bed. In Schmid and Luthin the sought to overcome the problem of the bed boundary condition by assuming the streamlines to be parallel to the bed, and developed a modified negative sign between the first two terms in 1 is form that they termed 'the extended DF equation'.
Stirzaker et al. It is surprising that this along the bed. They also showed that the term in error has not been corrected earlier; at least we the extended DF equation, omitted by Chapman can find no reference to such a correction. He did not explicitly derive solved the problem using the 'extended Dupuit- solutions for the maximum watertable height hm , Forchheimer' approximations, which they but we will do so here.
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The resulting solution is similar to that of Henderson 2. However, A can be obtained as was shown by Stirzaker et al. Chapman pers comm. Towner used a similar streamline and equipotential description to that of Wooding and Chapman but a solution method similar to 2. Schmid and Luthin This the drain spacing by considering the solution to eliminated in this paper. To simulate the height m , d is the height of water in the lowest steady-state flow down sloping beds the boundary drain m and b is the height of water in the conditions are shown in Figure 4.
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Initial higher drain m Figure 3. These two equations conditions were chosen to be as close to the final are incorrect by the constant 4 in the above solution as possible.
The model was run until equations A. Warrick pers. If this there was no change in the phreatic surface above constant is removed and 14 is substituted into the bottom boundary with time. Schematic diagram of typical numerical domain with applied boundary conditions.Solutions for steady and transient flow Wooding, R. Measurement and evaluation of water table elevations. Bijdragen tot de Kennis van enige Natuurkundige Grootheden van den Grond. Groundwater flow over a sloping Water Resources Research, 41, W Transactions of the ASAE, 25 5 : —, Motion of ground water.
The results are similar to those of Hele- circumstances where drains are often be required. Although the foundations for these scientific developments were established in the last century, it is only in the past decade and a half that we have witnessed an outpouring of information in the various journals, scientific and popular, on the subject.