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CIV3248 Groundwater,seepage and environmental engineering

CIV3248 Groundwater,seepage and environmental engineering. Workshop (4) Flownet sketching Keith H McKenry. Intention:. Mathematical insight. Practise sketching skills. Flow net compared with SEEPW output. Interpretation of flow nets. Mathematics.

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CIV3248 Groundwater,seepage and environmental engineering

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  1. CIV3248Groundwater,seepage and environmental engineering • Workshop (4) • Flownet sketching • Keith H McKenry CIV3248 Flow Net Workshop

  2. Intention: Mathematical insight. Practise sketching skills. Flow net compared with SEEPW output. Interpretation of flow nets CIV3248 Flow Net Workshop

  3. Mathematics. • Steady state: conservation of mass, continuity equation, stream function (), streamlines. • Energy balance: Potential function (), total head lines, irrotational flow (flow around a curve by distortion rather than rotation). • Laplaces Equation for  & . CIV3248 Flow Net Workshop

  4. Streamlines • Seepage velocity vector is tangent to streamline. • Streamlines cannot cross. • Commence on inflow boundary, finish at outflow boundary. • Streamlines have constant stream function value. CIV3248 Flow Net Workshop

  5. Streamlines Unconfined flow: y1 is a boundary streamline • stream function value dQ = y2 - y1 y1 Stream tube dQ y2 y3 Seepage velocity CIV3248 Flow Net Workshop

  6. Streamlines and stream function (x,y), • Two streamlines define a streamtube. • Streamtube width is inversely proportional to local seepage velocity. • Difference in in stream function value equals the discharge between two streamlines defining the stream tube. CIV3248 Flow Net Workshop

  7. Total head lines • Total head = -  / k • Lines of constant value of potential function. • Zero hydraulic gradient zero flow • orthogonal to streamlines (cross at right angles). CIV3248 Flow Net Workshop

  8. Equipotential / Total head lines F = equipotential value = - H*k m3/s/m f1 f3 f2 CIV3248 Flow Net Workshop

  9. Flownet definition…1 • Selection of streamlines and total head lines. • Constant difference in stream function values between all streamlines. • Constant difference in potential function values between all total head lines. • Same difference value for both stream function and potential function. CIV3248 Flow Net Workshop

  10. Flownet definition…2 F = 24 Streamlines F = 27 F = 30 F = 33 dq = 3 dq = 3 Equipotential lines (constant Total Head) Y = 11 Y = 8 Y = 5 CIV3248 Flow Net Workshop

  11. Flownet features • Orthogonal net. • Inscribed circles. • Diagonals to curvilinear squares form another orthogonal net. • Ratio of number of streamtubes to number of potential drops is constant for a given flow boundary. CIV3248 Flow Net Workshop

  12. Flownet Examples • Based on explicit functions for total head and stream function. • Prior to the advent of cheap computers much mathematical effort was expended on techniques to allow explicit equations to fit a wide range of boundary geometries. CIV3248 Flow Net Workshop

  13. Basis • For a given boundary geometry, only ONE true flownet exists. • Find the true flow net by “trial and correct”. CIV3248 Flow Net Workshop

  14. Strategy • Identify the two streamlines and two total total head lines that define the problem. • For 4 or 5 STREAM TUBES draw the 3 or 4 internal streamlines. • Draw TOTAL HEAD lines to attempt to form curvilinear squares (a true flownet). • Adjust the trial lines to get better curvilinear squares. CIV3248 Flow Net Workshop

  15. Confined Flow example Boundary total head lines Total head difference “Pervious” Boundary streamlines “Impermeable” CIV3248 Flow Net Workshop

  16. Cross-section to scale: 10 mm = 1 m. W1 C D E  F    B  A Datum RL 60m CIV3248 Flow Net Workshop

  17. Cross-section to scale: 10 mm = 1 m. W2 C D E  F    B  A Datum RL 60m CIV3248 Flow Net Workshop

  18. Cross-section to scale: 10 mm = 1 m. W3 C D E  F    B  A Datum RL 60m CIV3248 Flow Net Workshop

  19. Cross-section to scale: 10 mm = 1 m. W4 C D E  F    B  A Datum RL 60m CIV3248 Flow Net Workshop

  20. Flownet Interpretataion • Discharge (m3/sec/m) • Pore pressure • Hydraulic gradient. CIV3248 Flow Net Workshop

  21. Discharge per unit width (Q m3/sec/m) Q = k.HL.(N /N) • k - coefficient of permeability. • HL - drop in Total Head across flow. • N - number of stream tubes. • N - number of potential drops. • Note N might not be an integer. CIV3248 Flow Net Workshop

  22. Q = k.HL.(N /N) = 7 x 10-5 . 4 .(3/8) = 10.5 x 10-5 m3/s/m Ny = 3 Nf = 8 HL = 4 m f0 f8 y0 f1 f7 y1 f6 K = 7 x 10-5 m/s y2 f2 f4 f3 f5 y3 CIV3248 Flow Net Workshop

  23. Pore Pressure “u” at a point • Identify total head value of all constant total head lines relative to datum. • Find total head at point by interpolation “H”. • Identify elevation head of point “z”. • u = (H - z) * w (w = unit weight of water) CIV3248 Flow Net Workshop

  24. u = (H - z) * w uA =(94 – 80)*9.8 = 137 kPa uBD =(94 – 75)*9.8 = 186 kPa uB =(92.5 – 83)*9.8 = 93 kPa RL95m RL94m RL92.5m RL91m H=91m H=95m H=91.5m H=94.5m B RL83m RL80m A H=92m RL75m D H=93m H=92.5m H=94m H=93.5m RL72m CIV3248 Flow Net Workshop Total head datum = RL 0m

  25. u = (H - z) * w uA =(92.5 – 80)*9.8 = 123 kPa uB =(91.75 – 83)*9.8 = 86 kPa RL93m RL91.75m RL91m RL92.5m H=91m H=93m H=91.25m H=92.75m B RL83m RL80m A H=91.5m H=92.5m H=92m H=91.75m H=92.25m RL72m CIV3248 Flow Net Workshop Total head datum = RL 0m

  26. Hydraulic gradient at a point - “i” • Interpolate streamline through the point. • Determine difference in total head between constant total head lines either side of point “dH”. • Measure real distance between these constant total head lines along the interpolated streamline “dL” • i = dH /dL CIV3248 Flow Net Workshop

  27. dH = 0.5m (-)iC = dH /dL = 0.5 / 4.5 = 0.11 RL95m RL91m H=91m H=95m H=91.5m H=94.5m dL = 4.5m C H=92m H=94m H=93m H=92.5m H=93.5m RL72m CIV3248 Flow Net Workshop Total head datum = RL 0m

  28. Upward seepage flow:Critical hydraulic gradient at exit - Icrit • Liquifaction of soil may occur if the exit hydraulic gradient exceeds a critical value such that effective stress equals zero. • Icrit = (Gs - 1)/(e +1) Gs - Specific gravity of soil particles e - Void Ratio • Icrit ~ 1.0 CIV3248 Flow Net Workshop

  29. Seepw solution CIV3248 Flow Net Workshop

  30. Conclusion: flow net sketching • Limited to isotropic soils, homogeneous flow • Quick, simple equipment, • Analysis of multiple geometry for design. • Check on computer packages. CIV3248 Flow Net Workshop

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