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Seepage Through Porous Media. W.T. Impervious Soil. ) h = h A - h B. pervious Soil. W.T. h A = total head. Impervious Soil. h B = total head. Datum. W.T. Impervious Soil. ) h = h A - h B. D h. W.T. q = v . A = k i A = k A. Water In. h A. L. Impervious Soil. h B. Datum.

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  1. Seepage Through Porous Media W.T. Impervious Soil )h = hA - hB pervious Soil W.T. hA = total head Impervious Soil hB= total head Datum

  2. W.T. Impervious Soil )h = hA - hB Dh W.T. q = v . A = k i A = k A Water In hA L Impervious Soil hB Datum 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

  3. Bernouli’s Equation: Total Energy = Elevation Energy + Pressure Energy + Velocity Energy or Total Head = Elevation Head + Pressure Head + Velocity Head htotal = Z + P + V2 Darcy’s Law: v % i v = discharge velocity & i = hydraulic gradient v = k i k = coefficient of permeability v = k )h/L Rate of Discharge = Q = v.A = k ()h/L).A g 2 g

  4. To determine the rate of flow, two parameters are needed * k = coefficient of permeability * i = hydraulic gradient k can be determined using 1- Laboratory Testing [constant head test & falling head test] 2- Field Testing [pumping from wells] 3- Empirical Equations i can be determined 1- from the head loss 2- flow net

  5. Seepage Through Porous Media Water In L = Drainage Path Head Loss or Head Difference or Energy Loss i = Hydraulic Gradient )h =hA - hB hA Water out hB Datum Soil B A Porous Stone Porous Stone L

  6. Seepage Through Porous Media Water In L = Drainage Path Head Loss or Head Difference or Energy Loss i = Hydraulic Gradient )h =hA - hB hA Water out hB B Soil A Porous Stone ZA Porous Stone ZB L Datum

  7. Ws Ws Ws Ws Ws Buoyancy No Seepage Piezometer In Flow 3 ft D Out Flow 2 ft C u = 6 x 62.4 4 ft 14 ft B 12 ft u = 14 x 62.4 8 ft A 3 ft 3 ft Datum

  8. Upward Seepage Ws Ws Ws Ws Ws Buoyancy + Seepage Force In Flow Piezometer 3 ft Du D Out Flow 2 ft C u = 6 x 62.4 + Du 4 ft 17 ft B 12 ft u = 17 x 62.4 8 ft A 3 ft 3 ft Datum

  9. Seepage Force Ws Ws Ws Ws Ws Buoyancy - Seepage Force Downward Seepage Piezometer 3 ft In Flow D 2 ft C Out Flow u = 6 x 62.4 - Du 4 ft B 12 ft u = 17 x 62.4 10 ft 8 ft A 3 ft 3 ft Datum

  10. Ws Ws Ws Ws Ws Buoyancy No Seepage 1 1 g1 =110 pcf W.T. 3 ft 2 2 4 ft 3 3 - 6 ft = 4 4 12 ft 5 5 Total Stress Effective Stress Pore Water Pressure Effective Stress Pore Water Pressure Total Stress s1 = u1 = s1 = s2 = u2 = s2 = s3 = u3 = s3 = s4 = u4 = s4 = s5 = u5 = s5 =

  11. Ws Ws Ws Ws Ws Buoyancy No Seepage W.T. 1 g1 =110 pcf 3 ft 4 ft 2 - 6 ft = 3 12 ft 4 Effective Stress Total Stress Pore Water Pressure

  12. Ws Ws Ws Ws Ws Buoyancy No Seepage W.T. 1 3 ft 2 g1 =110 pcf 3 ft 4 ft 3 - 6 ft = 4 12 ft 5 Effective Stress Total Stress Pore Water Pressure

  13. Ws Ws Ws Ws Ws Buoyancy + Seepage Force Upward Seepage 1 5 ft g1 =110 pcf W.T. 3 ft 2 4 ft 3 - = 6 ft 4 12 ft 54 4 Pore Water Pressure Total Stress Effective Stress Pore Water Pressure Effective Stress Total Stress

  14. Seepage Force Ws Ws Ws Ws Ws Buoyancy - Seepage Force Downward Seepage g1 =110 pcf W.T. 3 ft 1 1 3 ft 4 ft 2 2 - = 6 ft 3 3 12 ft 4 4 Pore Water Pressure Total Stress Effective Stress Effective Stress Total Stress Pore Water Pressure

  15. g1 =110 pcf W.T. 3 ft W.T. 3 ft 4 ft 4 ft 6 ft 6 ft 12 ft 12 ft

  16. Dh q = A k i = A k L Equipotential Lines Flow Lines

  17. Principles of the Flow Net Equipotential Lines Flow Lines Flow Lines Flow Element

  18. Principles of the Flow Net )h = head loss = one drop Pressure Head Piezometer Total Head = Elevation head + Pressure head 1 2 3 Flow Lines Flow Lines 4 5 Flow Element Elevation Head Equipotential Lines Total heads along this line are the same Datum

  19. Ws Ws Ws Ws Ws Buoyancy + Seepage Force In Flow )h )h )h 3 in )h )h )h )h )h Out Flow 2 in 8 Feff = *(soil + * (water - ( - )h) * (water 7 14 in 6 u = [14 - (3. )h)].(water 5 4 3 2 2 1

  20. Seepage Through Porous Media IN qx(in) = dz . dy kx (Mh/Mx) qx(in) = dx . dz ky (Mh/My) OUT qx (out) = dz . dy kx (Mh/Mx + M2h/Mx2 dx ) qx (out) = dx . dz ky (Mh/My + M2h/My2 dy ) Equating q in and q out Direction of Flow Two sets of curves Rate of Discharge = qout Rate of Discharge = qin Z dy X dZ Y Rate of Discharge = qin Rate of Discharge = qout dx Rate of Discharge = qin (Rate of Discharge)in = (Rate of Discharge)out Rate of Discharge = qin IN

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