1DFlow-permeability- - Permeability Soils are permeable due to the existence of interconnected voids through which water can flow from points of

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Permeability Soils are permeable due to the existence of interconnected voids through which wa- ter can flow from points of high energy to points of low energy. The study of the flow of water through permeable soil media is important in soil mechanics. It is necessary for estimating the quantity of underground seepage under various hydraulic con- ditions, for investigating problems involving the pumping of water for underground construction, and for making stability analyses of earth dams and earth-retaining structures that are subject to seepage forces. 6.1 Bernoullil's Equation From fluid mechanics, we know that, according to Bernoulli's equation, the total head at a point in water under motion can be given by the sum of the pressure, velocity, and elevation heads. or t t t Pressure Velocity Elevation head where h = total head u = pressure v = velocity g = acceleration due to gravity y,,, = unit weight of water Note that the elevation head, Z, is the vertical distance of a given point above or be- low a datum plane. The pressure head is the water pressure, u, at that point divided by the unit weight of water, 7,. If Bernoulli's equation is applied to the flow of water through a porous soil
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140 Chapter 6 Permeability 1 1 Datum Figure 6.1 Pressure, elevation, and total heads for flow of water through soil I medium, the term containing the velocity head can be neglected because the seepage velocity is small, and the total head at any point can be adequately represented by I Figure 6.1 shows the relationship among pressure, elevation, and total heads for the flow of water through soil. Open standpipes called piezometers are installed at points A and B. The levels to which water rises in the piezometer tubes situated at points A and B are known as the piezometric levels of points A and B, respectively. The pressure head at a point is the height of the vertical column of water in the pie- zometer installed at that point. The loss of head between two points, A and B, can be given by The head loss, Ah, can be expressed in a nondimensional form as where i = hydraulic gradient L = distance between points A and B-that is, the length of flow over which the loss of head occurred In general, the variation of the velocity v with the hydraulic gradient i is as shown in Figure 6.2. This figure is divided into three zones: 1. Laminar flow zone (Zone I) 2. Transition zone (Zone 11) 3. Turbulent flow zone (Zone 111)
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6.2 Darcy's Law 141 A Zone 111 Turbulent flow zone Zone I1 Transition zone 8 - Zone I ' Larninarflow zone + Hydraulic gradient, i Figure 6.2 Nature of variation of v with hydraulic gradient, i When the hydraulic gradient is gradually increased, the flow remains laminar in Zones I and 11, and the velocity, v, bears a linear relationship to the hydraulic gradi- ent. At a higher hydraulic gradient, the flow becomes turbulent (Zone 111). When the hydraulic gradient is decreased, laminar flow conditions exist only in Zone I. In most soils, the flow of water through the void spaces can be considered lam- inar; thus,
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This note was uploaded on 02/27/2011 for the course CE 383 taught by Professor Marika during the Spring '07 term at Purdue University-West Lafayette.

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1DFlow-permeability- - Permeability Soils are permeable due to the existence of interconnected voids through which water can flow from points of

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