No Slide Title

DatumhA = total headW.T.)h = hA - hBW.T.Impervious SoilImpervious Soilpervious SoilhB= total headSeepage Through Porous MediaABSoilWater In)h =hA - hBHead Loss orHead Difference or Energy LosshAhBi = Hydraulic Gradient(q)WateroutL = Drainage PathDatumhAW.T.hB)h = hA - hBW.T.Impervious SoilImpervious SoilZADatumZBElevation HeadPressure HeadPressure HeadElevation HeadTotal HeadTotal Headq = v . A = k i A = k ADhLBernoulis Equation:

Total Energy = Elevation Energy + Pressure Energy + Velocity Energy

or

Total Head = Elevation Head + Pressure Head + Velocity Head

htotal = Z + P + V2

Darcys Law:

v % i v = discharge velocity & i = hydraulic gradientv = k i k = coefficient of permeability

v = k )h/L

Rate of Discharge = Q = v.A = k ()h/L).A

g2 gTo determine the rate of flow, two parameters are needed

* k = coefficient of permeability* i = hydraulic gradientk 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 loss2- flow net

Water In)h =hA - hBHead Loss orHead Difference or Energy LosshAhBABDatumPorousStonePorousStoneSeepage Through Porous Mediai = Hydraulic GradientSoilWateroutL = Drainage PathLWater In)h =hA - hBHead Loss orHead Difference or Energy LossZAhBABDatumPorousStonePorousStoneSeepage Through Porous Mediai = Hydraulic GradientSoilWateroutL = Drainage PathLhAZB14 ft3 ft12 ftIn FlowOut Flow2 ft4 ftDatum3 ft3 ft8 ftPiezometerABCDu = 6 x 62.4u = 14 x 62.4No SeepageBuoyancyWsWsWsWsWs17 ft3 ft12 ftIn FlowOut Flow2 ft4 ftDatum3 ft3 ft8 ftPiezometerABCDu = 6 x 62.4 + DuDuu = 17 x 62.4Upward SeepageBuoyancy + Seepage ForceWsWsWsWsWs10 ft3 ft12 ftIn FlowOut Flow2 ft4 ftDatum3 ft3 ft8 ftPiezometerABCDu = 6 x 62.4 - Duu = 17 x 62.4Downward SeepageBuoyancy - Seepage ForceWsWsWsWsWsSeepage Force3 ft4 ft6 ft12 ftg1 =110 pcfW.T.s1 =s2 =s3 =2345s4 =-=Total StressPore WaterPressureTotal StressPore Water Pressure2345No SeepageBuoyancyWsWsWsWsWsu1 =u2 =u3 =u4 =Effective Stresss1 =s2 = s3 =s4 =11s5 =u5 =s5 =Effective Stress3 ft4 ft6 ft12 ftg1 =110 pcfW.T.1234-=Total StressPore WaterPressureNo SeepageBuoyancyWsWsWsWsWsEffective Stress3 ft4 ft6 ft12 ftg1 =110 pcfW.T.1345-=Total StressPore WaterPressureNo SeepageBuoyancyWsWsWsWsWs3 ft2Effective Stress3 ft4 ft6 ft12 ftW.T.4Total StressPore Water PressureUpward SeepageBuoyancy + Seepage ForceWsWsWsWsWs=Pore WaterPressure5 ftg1 =110 pcf1354-Total Stress42Effective StressEffective Stress3 ft4 ft6 ft12 ftg1 =110 pcfW.T.1234-=1234Total StressPore WaterPressureTotal StressPore Water Pressure3 ftDownward SeepageBuoyancy - Seepage ForceWsWsWsWsWsSeepage ForceEffective StressEffective Stress3 ft4 ft6 ft12 ftg1 =110 pcfW.T.W.T.3 ft4 ft6 ft12 ft

q = A k i = A k DhLFlow LinesEquipotentialLinesFlow LinesEquipotential LinesFlow ElementFlow LinesPrinciples of the Flow NetFlow LinesFlow LinesPiezometer)h = head loss = one dropDatumTotal Head = Elevation head + Pressure headElevation HeadPressure Head12345Principles of the Flow NetEquipotential LinesTotal heads along this line are the sameFlow Element827653412)hu = [14 - (3. )h)].(water14 inFeff = *(soil + * (water - ( - )h) * (water)h)h)h)h)h)h)h3 in2 inBuoyancy + Seepage ForceWsWsWsWsWsIn FlowOut FlowDirection of FlowRate of Discharge = qinXdZYSeepage Through Porous MediaRate of Discharge = qoutRate of Discharge = qoutRate of Discharge = qinRate of Discharge = qinRate of Discharge = qindydx(Rate of Discharge)in = (Rate of Discharge)outINqx(in) = dz . dy kx (Mh/Mx)qx(in) = dx . dz ky (Mh/My)

OUTqx (out) = dz . dy kx (Mh/Mx + M2h/Mx2 dx )qx (out) = dx . dz ky (Mh/My + M2h/My2 dy )

Equating q in and q outIN

ZTwo sets of curves