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PAT203 SOIL MECHANICS

PAT203 SOIL MECHANICS. PERMEABILITY & SEEPAGE PREPARED BY: LIYANA BINTI AHMAD SOFRI. Permeability. water. Dense soil - difficult to flow - low permeability. Loose soil - easy to flow - high permeability. Permeability And Drainage Characteristics Of Soils. Total Head at B.

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PAT203 SOIL MECHANICS

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  1. PAT203 SOIL MECHANICS PERMEABILITY & SEEPAGE PREPARED BY: LIYANA BINTI AHMAD SOFRI

  2. Permeability water Dense soil - difficult to flow - low permeability Loose soil - easy to flow - high permeability

  3. Permeability And Drainage Characteristics Of Soils

  4. Total Head at B Total Head at A The loss of head between A and B The head loss may be expressed as :

  5. where, v: discharge velocity, which is the quantity of water flowing in unit time through a unit gross cross-sectional area of soil (cm/s). k: coefficient of permeability or hydraulic conductivity (cm/s). q: flow rate (cm3/s). Q: volume of collected water (cm3). A: cross-sectional area (cm3). i: hydraulic gradient.

  6. A = Av + As

  7. Example 1 • Water flows through the sand filter as shown in fig. • The cross-sectional area & length of the soil mass are 0.250m2 & 2.00m, respectively. • The hydraulic head difference is 0.160 m • The coefficient of permeability is 6.90x10-4 m/s • Question: Determine the flow rate of water through the soil

  8. Typical values of Hydraulic Conductivity of Saturated Soils

  9. The total volume of water collected may be expressed as: Q: volume of water collected A: area of cross section of the soil sample t: duration of collection of water

  10. where: h1 = initial head difference at time = 0 h2 = final head difference at time T a = x-sectional area of standpipe A = x-sectional area of soil specimen L = length of soil specimen

  11. Example 2 • For a falling-head permeability test, the following values are given. • length of specimen = 200 mm • area of soil specimen = 1000 mm2 • area of standpipe = 40 mm2 • head difference at time 0 seconds = 500 mm • head difference at time 180 seconds = 300 mm. Calculate the hydraulic conductivity of the soil.

  12. Laplace equation of Continuity Flow in: Flow out: Flow in = Flow out (Continuity equation) By simplification, we get

  13. Laplace equation of Continuity From Darcy’s Law: Replace in the continuity equation If soil is isotropic (i.e. kx = kz = k) Laplace equation This equation governs the steady flow condition for a given point in the soil mass

  14. One-dimensional flow Discharge = Q = v. A = k . i . A= k (h/L). A

  15. Water In One-dimensional flow Head Loss or Head Difference or Energy Loss h =hA - hB i = Hydraulic Gradient hA Pressure Head (q) Water out Total Head Pressure Head hB A Soil Total Head B Elevation Head L = Drainage Path ZA Elevation Head ZB Datum

  16. Two-dimensional flow

  17. Two-dimensional flow

  18. Flow nets • Flow netsare the combination of flow lines and equipotential lines. • To complete the graphic construction of a flow net, one must draw the flow and equipotential lines in such away that: 1. The equipotential lines intersect the flow lines at right angles. 2. The flow elements formed are approximate squares. Flow channel Flow line Equipotential line

  19. Flow Net Drawing Technique • Draw to a convenient scale the geometry of the problem. • Establish constant head and no flow boundary conditions and draw flow and equipotential lines near boundaries. • Constant head boundaries (water levels) represent initial or final equipotentials • Impermeable (no-flow) boundaries are flow lines • Sketch flow lines by smooth curves (3 to 5 flow lines). • Flow lines should not intersect each other or impervious boundary • Draw equipotential lines by smooth curves adhering to right angle intersections and square grids conditions (aspect ratio =1). • Continue sketching and re-adjusting until you get squares almost everywhere. Successive trials will result in a reasonably consistent flow net.

  20. Boundary Conditions

  21. H 0 H H-Dh H-5Dh H-2Dh H-4Dh H-3Dh

  22. h1 = h1 - h2 h2

  23. Seepage Flow channel” L

  24. Flow element • In a flow net, the strip between any two adjacent flow lines is called a flow channel. • The drop in the total head between any two adjacent equipotential lines is called the potential drop. Seepage Calculation from Flow Net • If the ratio of the sides of the flow element are the same along the flow channel, then: • 1. Rate of flow through the flow channel per unit width perpendicular to the flow direction is the same. • Dq1 = Dq2 = Dq3 = Dq • 2. The potential drop is the same and equal to: Where H: head difference between the upstream and downstream sides. Nd: number of potential drops.

  25. From Darcy’s Equation, the rate of flow is equal to: Seepage Calculation from Flow Net • If the number of flow channels in a flow net is equal to Nf, the total rate of flow through all the channels per unit length can be given by:

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