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Water flow in saturated soil

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**1. **Water flow in saturated soil D A Cameron
Introduction to Civil and Mining Engineering

**3. **Head of Water Pressure head = height to which water rises to in a standpipe above the point

**4. **Confined Aquifer A water bearing layer, overlain and underlain by far less permeable soils.

**5. **Steady flow in soils – Laminar flow Assumptions to theory:
Uniform soil, homogeneous and isotropic
Continuous soil media
Small seepage flow (non turbulent flow)
Darcy’s Law of 1850

**6. **Darcy’s Law q = kiA
where q = rate of flow (m3/s)
i = hydraulic gradient
A = area normal to flow direction (m2)
k = coefficient of permeability (m/s)

**7. **Hydraulic Gradient, i

**8. **Hydraulic Conductivity Coefficient of permeability or just permeability
SATURATED soil permeability!
Hazen’s formula, for clean and almost uniform sands:

**9. **TYPICAL PERMEABILITIES Clean gravels > 10-1 m/s
Clean sands, sand-gravel 10-4 to 10-2 m/s
Fine sands, silts 10-7 to 10-4 m/s
Intact clays, clay-silts 10-10 to 10-7 m/s

**10. **Measuring Permeability [A] Laboratory
Constant head test
Falling head test
Other
[B] Field
Pumping tests
Borehole infiltration tests

**11. **1. Constant head permeameter

**12. **Constant head test Suitable for clean sands and fine gravels
EXAMPLE:
If the sample area is 4500 mm2,
the vertical distance between the 2 standpipe points is 100 mm,
?h is 75 mm
Outflow is 1 litre every minute
What is the coefficient of permeability?

**13. **Solution 1000 cm3/min
OR q = 16.7 cm3/sec = 16.7x10-6 m3/sec
i = 75/100 = 0.75
k = q/(iA)
= (16.7x10-6)/(0.75x4500x10-6) m/sec
k = 5 x 10-3 m/sec
Typically a clean sand or gravel permeability

**15. **Falling head test Suited to low permeability materials
silts and clays
Soil sample length, L, and area, A
Flow in the tube = flow in the soil

**16. **3. Field testing – drawdown test

**17. **Drawdown test Needs
a well-defined water table
and confining boundary
Must be able to
pull down water table
and create flow
(phreatic line = uppermost flow line)

**18. **Solution Axi-symmetric problem
By integration of Darcy’s Law,

**19. **TUTORIAL PROBLEMS A canal and a river run parallel, an average of 60 m apart. The elevation of water in the canal is 200 m and the river 193 m. A stratum of sand intersects both the river and canal below the water levels.
The sand is 1.5 m thick and is sandwiched between strata of impervious clay.
Compute the seepage loss from the canal in m3/s per km length of the canal, given the permeability of the sand is 0.65 mm/s.

**21. **SOLUTION q = kiA
k = 0.65 mm/s = 0.65 x 10-3 m/s
?h = 7 m
q = 0.65 x 10-3 x 0.117 x 1.5 m2/m length
q = 0.114 x 10-3 m3/sec /m length
q = 0.114 m3/sec/km length

**23. **Flow Lines – shortest paths for water to exit

**24. **Equipotentials Are lines of equal total head
Can be derived from boundary conditions
and flow lines

**25. **The Flow Net

**26. **Flownet Basics Water flow follows paths of maximum hydraulic gradient, imax
flow lines and equipotentials must cross at 90°, since:
imax = [?(?h) / bmin]

**29. **Flow Net Calculations Nd equal potential drops along length of flow? Then the head loss from one line to another is:
?(?h) = ?h / Nd
From Darcy’s Law

**30. **Flow Net Calculations BUT a = b
AND total flow for Nf “flow channels”,
per unit width is :

**31. **Example: if k = 10-7 m/sec, what would be the flow per day over a 50 m length of wall?

**32. **Calculations Nf = 3 or 4
Nd = 9 or 10?
?h = 35 m?
k = 10-7 m/sec Answer: 6.72 m3

**35. **Finite Difference spreadsheet solution
Author: Mahes Rajakaruna
emailed to students today

**39. **Other numerical approaches – FESEEP

**40. **FESEEP Output (University of Sydney)

**41. **Critical hydraulic gradient The value of i for which the effective stress in the saturated system becomes ZERO!
Consequences:
no stress to hold granular soils together
?soil may flow ?
“boiling” or “piping” = EROSION!

**44. **Critical hydraulic gradient Fs = ?h?wA
= (h1 – h2) ?wA
Fw = (?sat - ?w)AL
= (??)AL
Equating the 2 forces
i = ??/ ?w as before

**45. **Likelihood of Erosion

**46. **Minimising the risk of erosion 1. Add more weight at exit points

**47. **Lengthen flow path?

**48. **Summary Heads in soil
Darcy’s Law
Coefficient of permeability
Measurement of permeability
Flownets
Flownet rules
Seepage from flownets
Piping, boiling or erosion
Critical hydraulic gradient