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Water Movement in Soil and Rocks

Water Movement in Soil and Rocks. Two Principles to Remember:. Water Movement in Soil and Rocks. Two Principles to Remember:. Water Movement in Soil and Rocks. 1. Darcy’s Law. Two Principles to Remember:. Water Movement in Soil and Rocks. 1. Darcy’s Law.

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Water Movement in Soil and Rocks

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  1. Water Movement in Soil and Rocks

  2. Two Principles to Remember: Water Movement in Soil and Rocks

  3. Two Principles to Remember: Water Movement in Soil and Rocks 1. Darcy’s Law

  4. Two Principles to Remember: Water Movement in Soil and Rocks 1. Darcy’s Law • Continuity Equation: • mass in = mass out + change in storage “my name’s Bubba!”

  5. Water Movement in Soil and Rocks I. Critical in Engineering and Environmental Geology A. Dams, Reservoirs, Levees, etc. “ Pore Pressure”

  6. Water Movement in Soil and Rocks I. Critical in Engineering and Environmental Geology A. Dams, Reservoirs, Levees, etc. B. Groundwater Contamination Leaking Underground Storage Tanks Landfills Surface Spills

  7. Water Movement in Soil and Rocks I. Critical in Engineering and Environmental Geology A. Dams, Reservoirs, Levees, etc. B. Groundwater Contamination C. Foundations - Strength and Stability

  8. I. Critical in Engineering and Environmental Geology A. Dams, Reservoirs, Levees, etc. B. Groundwater Contamination C. Foundations - Strength and Stability

  9. II. Water Flow in a Porous Medium A. Goal: Determine the permeability of the engineering material

  10. II. Water Flow in a Porous Medium A. Goal: Determine the permeability of the engineering material Porosity Permeability

  11. II. Water Flow in a Porous Medium A. Goal: Determine the permeability of the engineering material Porosity Permeability Porosity (def) % of total rock that is occupied by voids. Permeability (def) the ease at which water can move through rock or soil

  12. II. Water Flow in a Porous Medium B. The Bernoulli Equation A Demonstration:

  13. II. Water Flow in a Porous Medium B. The Bernoulli Equation A Demonstration: Bernoulli's Principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases.

  14. II. Water Flow in a Porous Medium B. The Bernoulli Equation 1. Components of Bernoulli Total Energy = velocity energy + potential energy + pressure energy

  15. II. Water Flow in a Porous Medium B. The Bernoulli Equation 1. Components of Bernoulli Total Energy = velocity energy + potential energy + pressure energy Total Head = velocity head + elevation head + pressure head

  16. II. Water Flow in a Porous Medium B. The Bernoulli Equation 1. Components of Bernoulli Total Energy = velocity energy + potential energy + pressure energy Total Head = velocity head + elevation head + pressure head h = v2/2g + z + P/ρg Where: h = total hydraulic head (units of length) v = velocity g = gravitational constant z = elevation above some datum P = pressure (where P = ρg*Δh) ρ = fluid density

  17. II. Water Flow in a Porous Medium B. The Bernoulli Equation 1. Components of Bernoulli Total Energy = velocity energy + potential energy + pressure energy Total Head = velocity head + elevation head + pressure head h = v2/2g + z + P/ρg Where: h = total hydraulic head (units of length) v = velocity g = gravitational constant z = elevation above some datum P = pressure (where P = ρg*Δh) ρ = fluid density A quick problem……

  18. At a place where g = 9.80 m/s2, the fluid pressure is 1500 N/m2, the distance above a reference elevation is 0.75 m, and the fluid density is 1.02 103 kg/m3. The fluid is moving at a velocity of 1* 10-6 m/s. Find the hydraulic head at this point. h= v2/2g + z + P/g

  19. At a place where g = 9.80 m/s2, the fluid pressure is 1500 N/m2, the distance above a reference elevation is 0.75 m, and the fluid density is 1.02 103 kg/m3 . The fluid is moving at a velocity of 1* 10-6 m/s. Find the hydraulic head at this point. h= v2/2g + z + P/g (1*10-6 m/s)2 + +0.75 m + 1500 {(kg-m)/s2}m2 2 * 9.80 m/s2 9.80 m/s2 * 1.02 103 kg/m3

  20. At a place where g = 9.80 m/s2, the fluid pressure is 1500 N/m2, the distance above a reference elevation is 0.75 m, and the fluid density is 1.02 103 kg/m3 . The fluid is moving at a velocity of 1* 10-6 m/s. Gravity is 9.8 m/s2. Find the hydraulic head at this point. h= v2/2g + z + P/g (1*10-6 m/s)2 + +0.75 m + 1500 {(kg-m)/s2}m2 2 * 9.80 m/s2 9.80 m/s2 * 1.02 103 kg/m3 5.10 * 10-14 m + 0.75 m + 0.15 m = 0.90 m = hydraulic head

  21. II. Water Flow in a Porous Medium B. The Bernoulli Equation 1. Components of Bernoulli Total Energy = velocity energy + potential energy + pressure energy Total Head = velocity head + elevation head + pressure head h = v2/2g + z + P/ρg Total Head = velocity head + elevation head + pressure head h = zero + z + Ψ Where: h = total hydraulic head z = elevation head Ψ = pressure head

  22. II. Water Flow in a Porous Medium C. Darcy‘s Law Henri Darcy (1856) Developed an empirical relationship of the discharge of water through porous mediums.

  23. II. Water Flow in a Porous Medium C. Darcy‘s Law 1. The experiment K

  24. II. Water Flow in a Porous Medium C. Darcy‘s Law 2. The results • unit discharge α permeability • unit discharge α head loss • unit discharge α hydraulic gradient

  25. Also…..

  26. II. Water Flow in a Porous Medium C. Darcy‘s Law 2. The equation v = Ki

  27. II. Water Flow in a Porous Medium C. Darcy‘s Law 2. The equation v = Ki where v = specific discharge (discharge per cross sectional area) (L/T) * also called the Darcy Velocity * function of the porous medium and fluid

  28. Darcy’s Law: v = Ki where v = specific discharge (discharge per unit area) (L/T) K = hydraulic conductivity (L/T); also referred to as coefficient of permeability i = hydraulic gradient, where i = dh/dl (unitless variable)

  29. Darcy’s Law: v = Ki where v = specific discharge (discharge per unit area) (L/T) K = hydraulic conductivity (L/T); also referred to as coefficient of permeability i = hydraulic gradient, where i = dh/dl (unitless variable)

  30. Darcy’s Law: v = Ki where v = specific discharge (discharge per unit area) (L/T) K = hydraulic conductivity (L/T); also referred to as coefficient of permeability i = hydraulic gradient, where i = dh/dl (unitless variable) v = K dh dl

  31. Darcy’s Law: v = Ki where v = specific discharge (discharge per unit area) (L/T) K = hydraulic conductivity (L/T); also referred to as coefficient of permeability i = hydraulic gradient, where i = dh/dl (unitless variable) v = K dh dl If Q = VA, then Q = A K dh dl

  32. Darcy’s Law: The exposed truth: these are only APPARENT velocities and discharges Q = A K dh dl v = K dh dl Q = VA Vs.

  33. Darcy’s Law: The exposed truth: these are only APPARENT velocities and discharges QL = A K dh ne dl vL = K dh ne dl Where ne effective porosity VL = ave linear velocity (seepage velocity) QL = ave linear discharge (seepage discharge) Both of these variables take into account that not all of the area is available for fluid flow (porosity is less than 100%)

  34. Find the specific discharge and average linear velocity of a pipe filled with sand with the following measurements. K = 1* 10-4 cm/s dh = 1.0 dl = 100 Area = 75 cm2 Effective Porosity = 0.22

  35. Find the specific discharge and average linear velocity of a pipe filled with sand with the following measurements. K = 1* 10-4 cm/s dh = 1.0 dl = 100 Area = 75 cm2 Effective Porosity = 0.22 VL =-Kdh V =-Kdh nedl dl V = 1 * 10-6 cm/sec VL = 4.55 * 10-6 cm/sec How much would it move in one year? 4.55 * 10-6cm * 3.15 * 107sec * 1 meter = 1.43 meters for VL sec year 100 cm 0.315 m for V

  36. II. Water Flow in a Porous Medium • C. Darcy‘s Law • 3. The Limits Equation assumes ‘Laminar Flow’; which is usually the case for flow through soils.

  37. C. Darcy‘s Law 4. Some Representative Values for Hydraulic Conductivity

  38. II. Water Flow in a Porous Medium D. Laboratory Determination of Permeability

  39. II. Water Flow in a Porous Medium D. Laboratory Determination of Permeability 1. Constant Head Permeameter Q = A K dh dl Q*dl= K A dh

  40. Given: • Soil 6 inches diameter, 8 inches thick. • Hydraulic head = 16 inches • Flow of water = 766 lbs for 4 hrs, 15 minutes • Unit weight of water = 62.4 lbs/ft3 • Find the hydraulic conductivity in units of ft per minute Example Problem: Q = A K dh dl Q*dl= K A dh

  41. Q*dl= K A dh Example Problem:

  42. Q*dl= K A dh Example Problem:

  43. II. Water Flow in a Porous Medium D. Laboratory Determination of Permeability 2. Falling Head Permeameter More common for fine grained soils

  44. II. Water Flow in a Porous Medium D. Laboratory Determination of Permeability 2. Falling Head Permeameter

  45. E. Field Methods for Determining Permeability In one locality: “Perk rates that are less than 15 minutes per inch or greater than 105 are unacceptable measurements. “

  46. E. Field Methods for Determining Permeability • 1. Double Ring Infiltrometer

  47. E. Field Methods for Determining Permeability • 2. Johnson Permeameter

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