Su tablasının permenant olmayan alçalması

Abstract

Bu çalışmada, alttaki geçirimsiz zeminden d kadar yukarıda bulunan ve tabanı su tablasına kadar uzanan bir dren hendeğinin su ile doldurulması sonucu oluşan ve değişik araştırmacılar tarafından teorik veya deneysel olarak incelenen permenant olmayan yeraltı suyu hareketi incelenmiştir. Birinci bölümde yeraltı suyu akımı ile ilgili genel bilgiler Darcy Kanunu esas alınarak verilmektedir. İkinci bölümde yeraltı su yüzeyinin zamanla değişen hareketi ile ilgili genel denklemler konu edilmektedir. Ayrıca, bu bölümde değişik zamanlarda değişik araştırmacıların probleme yaklaşımları ve elde ettikleri ifadeler yer almaktadır. Üçüncü bölümde Richards denkleminin ilgili başlangıç ve sınır, şartlan altında Sonlu Farklar formunda yazılarak elde edilen nümerik çözümü incelenmiştir. Nümerik sonuçlar grafik şeklinde ifade edilmiştir. Özel olarak dw/b = 0.8 için bu çalışmada elde edilen sonuçlar Watson ve Koussis tarafından elde edilen değerlerle karşılaştırılmıştır.

In this work, by the result of a drain ditch filling with water that is as d value up from impermeable base and its floor level is equal to water table, the underground water movement has been investigated. In this investigation, by the purpose of discussion of underground water movement, the Richard's equation developed for two direction of water movement was used. This diferantial equation was written as from of finite difference and soluted its numerical value. The work is expected to throw light on the contemporary problem of the multi-aspect improvement of grounds which are not usable for agricultural purposes. The drainage of minor lakes, shallow waters and moors having no economic values, the prevention of agricultural lands and inhabitad areas form floods, the removal of excess water that hinders the groth of agricultural plants and of water existing in the hollows of ground, the lowering ground water level of a desired degree for any purpose, the elimination of the water used for washing lands impregnated with salt are among the most important problems of present times especially in countries such as Turkey where agriculture is important. An introduction is made in the first chapter of this study in the following sequence:. The experimental principle ofthe Darcy's Law, the validity range of the Darcy's Law, Definiton of the Permeability Coefficient and its Formulation, Generalization of the Darcy's Law and derivation of the. Basic Equations, Study of the Velocity Potential of ground Water, Study of the Elasticity and Compressibility, derivation of the Velocity Potentiol of ground Water, Study of the Elasticity and Compressibility, derivation of the Differential Equations of the steady flow, derivation of the Differential Equations of the Non- Steady Flow, and the Limit Conditions are discussed. In the second chapter the studies regarding the unsteady movements of groundwater are viewed and it is seen that these studies are generally concerned with the design of drainage systems. Dumm (1954), stated that Glower had discovered an expression by using the Fourier series, for the ground water level height between the drains as follows: 2 2. 4. £ 1 -a m2K t/L2. mx n = - hr, z, - e sın -= - TC m=l,3,5, m L For the horizontal distance between the drains, Luthin (1959) found the formula: cK(t2-t!) X_j - ~- - - - - - hi n(ln^) n2 Kochina (1962) has investigated the unsteady movements of groundwater in the cases where reacharge and evaporation take place and determined the form of the water table for various evaporation rates. Stallman (1962) has analitically studied the unsteady ground water between two parallel drain ditches and determined the drawdown d(x,t) as a functions of time and space in the case where the water levels in the ditches are suddenly lowered by do. The relationship derived by Stallman is; d(x,t) = do(l-7= I e / ce/Y4ÜT ^ -u VI Kirkcham (1964) has determined the variation of water table between parallel drains where the flow is transformed to unsteady state by the termination of the reacharge. He has found the following relationship between the time and drawdown by tating the end of reacharge as the time origine: (h0-h) + L'F(x,o) In (-^) t = K n Bear ( 1 972) has found the drawdown d (x,t) as a function of space and time in the case where the water table is orriginally horizontal and flow is created by a sudden drop of dQ in the canal water level; nx2 A/2 d(x,t) = d0erfc(^-) Saydam (1975) has studied the non-steady movement of the ground water in a limited and unlimited two-dimensional water conduit, and suggested a way of solution by means of the finite differences method to determine the ground water level. Skaggs (1975) has applied the one-dimensional version of the Forcheimer's Equation to the ground water flow running down into two drain ditches that are parallel to each other, and determined the geometry of the water surface by using the finite differences method. Koussis (1979) has studied the ground water flow formed in case of a sudden and certain lowering of the water level in a water resevoir which is joined to a water -conduit. Koussis has taken the Forcheimer's equation as the mathematical model characterizing this event. By defining dimensionless entities, he has eliminated any dimensions of this equation and at first transformed the partial derivative, constant-coefficient differential equation of second degree thus formed into an VII ordinary differential equation by a proper transformation of variables, and then solved the equation by numerical methods. Higgins (1980) has studied the non-steady movement of the ground water flow formed in case if the water level in a drain ditch or a reservoir is lowered for a certain amount suddenly, and drawn the variation curves of the ground water level for various constant sections with time. By defining dimensionless entitities. Higgins has, after eliminating the dimensions of the corresponding differential equation and the boundary conditions, and solved the differential equation under the corresponding initial and boundary conditions. Watson and Koussis (1980) have restudied the problem treated by Koussis previnously, and by using the lines methods, solved the problem numerically. During the solution of the problem Forchiemers's equation was used as the one characterizing the flow zone. Savcı (1983) has studied theoretically the unsteady ground water movement caused by a sudden drop, dQ, and found the equation, 2e ? no + 7T n° =0 for the un-steady movement of the ground water surface. In third chapter, in the problems of underground water surface, for two direction movement of water under the concerned starting and baorder conditions of equation that was developed by Richard has been discussing in respect of finite difference method. In the area that was applied finite difference. 1 ). ax = az = 0.05 value is investigated for square-shoped net. 2). As the starting, the water table was assumed that is upas d value from impermeable base and equal to floor height (d=d1) VI 3). Time interval (ax) is constant and was taken as value of 0.005. x value was calculated with 0.005 value add. x = x+ Ax 4). For the up boarder provision, the error share should be stated according to willing rate. In the discussing problem the error share has been choosen as ± 0.001. In the result of solution, for the different rate of dw/b, chan ging curves between water table and range has been found for constant times. In this work, as special situation, the found results for dw/b = 0.8 have been compared with Watson and Koussis's values. In this comparison, the curves has been observed different from each other. The causes of difference-stated above as different corves- are starting and boarder conditions and using method for the problems.