Datum h A = total head W.T. )h = h A - h B W.T. Impervious Soil pervious Soil h B = total head Seepage Through Porous Media

A B Soil Water In )h =h A - h B Head Loss or Head Difference or Energy Loss hAhA hBhB i = Hydraulic Gradient (q) Water out L = Drainage Path Datum hAhA W.T. hBhB )h = h A - h B W.T. Impervious Soil ZAZA Datum ZBZB Elevation Head Pressure Head Elevation Head Total Head q = v. A = k i A = k A hh L

Bernouli’s Equation: Total Energy = Elevation Energy + Pressure Energy + Velocity Energy or Total Head = Elevation Head + Pressure Head + Velocity Head h total = Z + P + V 2 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  2 g

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

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

Water In )h =h A - h B Head Loss or Head Difference or Energy Loss ZAZA hBhB A B Datum Porous Stone Porous Stone Seepage Through Porous Media i = Hydraulic Gradient Soil Water out L = Drainage Path L hAhA ZBZB

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

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

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

3 ft 4 ft 6 ft 12 ft   =110 pcf W.T.  =  =  =  = - = Total Stress Pore Water Pressure Total Stress Pore Water Pressure No Seepage Buoyancy WsWs WsWs WsWs WsWs WsWs u  = u  = u  = u  = Effective Stress  =  =  =  = 1 1  = u  =  = Effective Stress

3 ft 4 ft 6 ft 12 ft   =110 pcf W.T = Total Stress Pore Water Pressure No Seepage Buoyancy WsWs WsWs WsWs WsWs WsWs Effective Stress

3 ft 4 ft 6 ft 12 ft   =110 pcf W.T = Total Stress Pore Water Pressure No Seepage Buoyancy WsWs WsWs WsWs WsWs WsWs 3 ft 2 Effective Stress

3 ft 4 ft 6 ft 12 ft W.T. 4 Total Stress Pore Water Pressure Upward Seepage Buoyancy + Seepage Force WsWs WsWs WsWs WsWs WsWs = Pore Water Pressure 5 ft   =110 pcf Total Stress 4 2 Effective Stress

3 ft 4 ft 6 ft 12 ft   =110 pcf W.T = Total Stress Pore Water Pressure Total StressPore Water Pressure 3 ft Downward Seepage Buoyancy - Seepage Force WsWs WsWs WsWs WsWs WsWs Seepage Force Effective Stress

3 ft 4 ft 6 ft 12 ft   =110 pcf W.T. 3 ft 4 ft 6 ft 12 ft

q = A k i = A k hh L Flow Lines Equipotential Lines

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

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

)h)h u = [14 - (3. )h)]. ( water 14 in F eff = *( soil + * ( water - ( - )h) * ( water )h)h )h)h )h)h )h)h )h)h )h)h )h)h 3 in 2 in Buoyancy + Seepage Force WsWs WsWs WsWs WsWs WsWs In Flow Out Flow

Direction of Flow Rate of Discharge = q in X dZ Y Seepage Through Porous Media Rate of Discharge = q out Rate of Discharge = q in dy dx (Rate of Discharge) in = (Rate of Discharge) out IN q x(in) = dz. dy k x (Mh/Mx) q x(in) = dx. dz k y (Mh/My) OUT q x (out) = dz. dy k x (Mh/Mx + M 2 h/Mx 2 dx ) q x (out) = dx. dz k y (Mh/My + M 2 h/My 2 dy ) Equating q in and q out IN Z Two sets of curves