1. Flow through Soils (ch7)

2. Energies Kinetic E (velocity) Strain E (fluid pressure)
Potential E (elevation)
Head: convert each form of energy into the equivalent potential energy and express it as the corresponding height.
units of LENGTH

3. Heads hv = velocity head (KE) hp = pressure head (SE)
he = elevation head (PE)
h = total head = hv + hp + he
(Bernoulli)
units of LENGTH

4. Heads in a tank of water…B

5. Head loss l head loss = Dh = h1 – h2
Fluid flows from point of high total head to point of low total head h2 1 2 l
head loss = Dh = h1 – h2

6. Hydraulic gradient
Rate at which the total head changes along a length

7. Heads in soils
Since velocity is slow through soils, we neglect the velocity head. Thus,

8. Soil piezometer The “pore water pressure” at A is Pressure head at A.hp
Pressure head at A. A
The “pore water pressure” at A is

9. Pore water pressures
uhydrostatic = uh = due to hydrostatic condition only
uexcess = ue = due to additional processes

10. Hydrostatic pore water pressure
Depth, z zw
zw1
zw2

11. One dimensional flow SOIL Flow is in one direction
Flow vectors: parallel
of equal magnitude
SOIL
Flow is in one direction

12. Flowrate through soil SOIL Flowrate = Q [m3/sec]
What is the flowrate through a soil?
Concrete dam
Flowrate =
Q [m3/sec]
SOIL

13. Darcy’s Law Assumptions: flow is laminar
soil properties do not D with time
Cross-sectional area to flow
Hydraulic conductivity
“permeability” [cm/s]
Hydraulic gradient

14. Finding k Dh A L
Measure Q
Figure 7.11 (text)

15. k fluid soil Measure of a soil-fluid system’s resistance to flow
depends on
soil
fluid
Void size
Fabric (structure)
Void continuity
Specific surface (drag)
Viscosity
Mass density

16. k
Units are in cm/sec
but
k = velocity

17. k SOIL TYPICAL VALUES [cm/s] gravel 101 – 102 sands 10-3 – 100 silts
10-8 – 10-3
clays
10-10 – 10-6
Probably soil’s most varying parameter (largest numerical range)

18. Lab testing sand clay “seam” k1 = 10-2 k2 = 10-6
Soil specimens
sand
clay “seam”
k1 = 10-2
k2 = 10-6
k – precision is on the order of +/- 50% or more!
Report values to one decimal place.

19. Lab testing (constant head test)Dh A L
Measure Q
Figure 7.11 (text)

20. In-situ testing
Slug test
Pumping test

21. Hazen’s Correlation k a pore size ~ (pore diameter)2
(pore diameter) ~ D10
For loose clean sands with 0.1mm < D10 < 3mm and Cu < 5
USE THESE UNITS!
k = [cm/sec]
C = Hazen’s coefficient = 0.8 – 1.2 (typical = 1)
D10 = [mm]

22. Example Compute seepage loss (Q) through the sand seam el. = 167.3m
clay
el. = 165m
sand
seam
256 m
3.2 m
Given: ksand = 4x10-2 cm/sec
reservoir length (into board) = 1000 m
Compute seepage loss (Q) through the sand seam

23. Solution Q = kiA k = 4x10-2 cm/sec
i = Dh/L = (167.3m – 165m) / 256m = 0.009
A = (3.2 m) (1000 m) = 3200 m2
Q = kiA = m3/sec = 41.5 m3/hr