civ3248 flow net workshop1 civ3248 groundwater,seepage and environmental engineering workshop (4)...
TRANSCRIPT
![Page 1: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/1.jpg)
CIV3248 Flow Net Workshop 1
CIV3248Groundwater,seepage and environmental engineering
•Workshop (4)
•Flownet sketching
•Keith H McKenry
![Page 2: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/2.jpg)
CIV3248 Flow Net Workshop 2
Intention:
•Mathematical insight.
•Practise sketching skills.
•Flow net compared with SEEPW output.
•Interpretation of flow nets
![Page 3: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/3.jpg)
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 & .
![Page 4: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/4.jpg)
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.
![Page 5: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/5.jpg)
CIV3248 Flow Net Workshop 5
Streamlines
Seepage
velocity
stream function value
dQ =
Stream tube
dQ
Unconfined flow: is a boundary streamline
![Page 6: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/6.jpg)
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.
![Page 7: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/7.jpg)
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).
![Page 8: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/8.jpg)
CIV3248 Flow Net Workshop 8
Equipotential / Total head lines
equipotential value = - H*k m3/s/m
![Page 9: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/9.jpg)
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.
![Page 10: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/10.jpg)
CIV3248 Flow Net Workshop 10
Flownet definition…2
Streamlines
Equipotential lines
(constant Total Head)
dq = 3
dq = 3
![Page 11: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/11.jpg)
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.
![Page 12: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/12.jpg)
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.
![Page 13: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/13.jpg)
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”.
![Page 14: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/14.jpg)
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.
![Page 15: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/15.jpg)
CIV3248 Flow Net Workshop 15
Confined Flow example
“Impermeable”
“Pervious”
Boundary streamlines
Boundary total head lines Total head difference
![Page 16: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/16.jpg)
CIV3248 Flow Net Workshop 16
Cross-section to scale: 10 mm = 1 m. W1
A
C D EF
B
Datum RL 60m
![Page 17: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/17.jpg)
CIV3248 Flow Net Workshop 17
Cross-section to scale: 10 mm = 1 m. W2
A
C D EF
B
Datum RL 60m
![Page 18: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/18.jpg)
CIV3248 Flow Net Workshop 18
Cross-section to scale: 10 mm = 1 m. W3
A
C D EF
B
Datum RL 60m
![Page 19: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/19.jpg)
CIV3248 Flow Net Workshop 19
Cross-section to scale: 10 mm = 1 m. W4
A
C D EF
B
Datum RL 60m
![Page 20: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/20.jpg)
CIV3248 Flow Net Workshop 20
Flownet Interpretataion
• Discharge (m3/sec/m)
• Pore pressure
• Hydraulic gradient.
![Page 21: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/21.jpg)
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.
![Page 22: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/22.jpg)
CIV3248 Flow Net Workshop 22
HL = 4 m
N = 3
N = 8
Q = k.HL.(N /N) = 7 x 10-5 . 4 .(3/8)
= 10.5 x 10-5 m3/s/m
K = 7 x 10-5 m/s
![Page 23: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/23.jpg)
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)
![Page 24: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/24.jpg)
CIV3248 Flow Net Workshop 24
RL95m
RL91m
RL72m
H=95m
H=94.5m
H=94mH=93.5m
H=93m H=92.5m
H=92m
H=91.5m
H=91m
Total head datum = RL 0m
RL80m
RL94m
RL83m
RL92.5m
A
B
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
DRL75m
![Page 25: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/25.jpg)
CIV3248 Flow Net Workshop 25
RL93m
RL91m
RL72m
H=93m
H=92.75m
H=92.5m
H=92.25mH=92m H=91.75m
H=91.5m
H=91.25m
H=91m
Total head datum = RL 0m
RL80m
RL92.5m
RL83m
RL91.75m
A
B
u = (H - z) * w
uA =(92.5 – 80)*9.8 = 123 kPauB =(91.75 – 83)*9.8 = 86 kPa
![Page 26: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/26.jpg)
CIV3248 Flow Net Workshop 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
![Page 27: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/27.jpg)
CIV3248 Flow Net Workshop 27
RL95m
RL91m
RL72m
H=95m
H=94.5m
H=94m
H=93.5mH=93m H=92.5m
H=92m
H=91.5m
H=91m
Total head datum = RL 0m
C
dL = 4.5m
dH = 0.5m(-)iC = dH /dL = 0.5 / 4.5 = 0.11
![Page 28: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/28.jpg)
CIV3248 Flow Net Workshop 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
![Page 29: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/29.jpg)
CIV3248 Flow Net Workshop 29
A
5.81
20e-0
03
Feet
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 1500
10
20
30
40
50
60
70
Seepw solution
![Page 30: CIV3248 Flow Net Workshop1 CIV3248 Groundwater,seepage and environmental engineering Workshop (4) Flownet sketching Keith H McKenry](https://reader035.vdocument.in/reader035/viewer/2022062308/56649c765503460f94929f8b/html5/thumbnails/30.jpg)
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.