L05-steady_state_flow - 1 5 STEADY STATE FLOW 5.1...

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5. STEADY STATE FLOW 5.1 Introduction The flow of water in soils can be very significant, for example: 1. It is important to know the amount of water that will enter a pit during construction, or the amount of stored water that may be lost by percolation through or beneath a dam. 2. The behaviour of soil is governed by the effective stress, which is the difference between total stress and pore water pressure. When water flows the pore water pressures in the ground change. A knowledge of how the pore water pressure changes can be important in considering the stability of earth dams, retaining walls, etc. 5.2 Darcy’s law Because the pores in soils are so small the flow through most soils is laminar. This laminar flow is governed by Darcy's Law which will be discussed below. 5.2.1 Definition of Head P z(P) Datum Fig 1 Definition of Head at a Point Referring to Fig. (1) the head h at a point P is defined by the equation h P u P z P w w ( ) ( ) ( ) = + γ (1) In this equation γ w (9.8 kN/m 3 ) is the unit weight of water, and u w (P) is the pore water pressure . 1 IMPORTANT z is measured vertically UP from the DATUM
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Note 1. The quantity u(P) / γ w is usually called the pressure head. 2. The quantity z(P) is called the elevation head (its value depends upon the choice of a datum). 3. The velocity head (not shown in Equation 1) is generally neglected. The only circumstances where it may be significant is in flow through rock-fill, but in this circumstance, the flow will generally be turbulent and so Darcy's law is not valid. Example - Calculation of Head 2 m 5 m X P Static water table Impermeable stratum Fig 2 Calculation of head using different datum 1 m 1 m 1. Calculation of Head at P Datum at the top of the impermeable layer w w ) P ( u γ 4 = z (P) = 1 m m 5 1 4 = + = w w ) P ( h γ γ 2. Calculation of Head at X Datum at the top of the impermeable layer w w ) X ( u γ 1 = z (X) = 4 m m 5 4 = + = w w ) X ( h γ γ It appears that when there is a static water table the head is constant throughout the saturated zone.
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