Transcript Introduction to Soils - College of Engineering Home Page

Flow through Soils
(ch7)
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
Heads
hv = velocity head (KE)
hp = pressure head (SE)
he = elevation head (PE)
h = total head = hv + hp + he
(Bernoulli)
units of LENGTH
Heads in a tank of water…
A
B
Head loss
Fluid flows from
point of high total
head to point of
low total head
h1
2
h2
1
l
head loss = Dh = h1 – h2
Hydraulic gradient
Rate at which the total head changes along a length
dh
i
dl
Heads in soils
Since velocity is slow through soils, we neglect the
velocity head. Thus,
h  he  hp
Soil piezometer
hp
A
Pressure head at A.
The “pore water pressure” at A is
u   w  hp
Pore water pressures
uhydrostatic = uh = due to hydrostatic condition only
uexcess = ue = due to additional processes
u  ue  uh
Hydrostatic pore water pressure
uh   w  hp
zw1
zw
zw2
Depth, z
u h   w  z w1
uh   w  zw 2
One dimensional flow
Flow vectors: parallel
of equal magnitude
SOIL
Flow is in one direction
Flowrate through soil
What is the flowrate through a soil?
Concrete dam
Flowrate =
SOIL
Q [m3/sec]
Darcy’s Law
Assumptions:
flow is laminar
soil properties do not D with time
Q  kiA
Hydraulic conductivity
“permeability” [cm/s]
Hydraulic
gradient
Cross-sectional
area
to flow
Finding k
Dh
A
dh Dh
i

dl
L
L
Measure Q
Figure 7.11 (text)
Q
k
iA
k
Measure of a soil-fluid system’s resistance to flow
depends on
soil
Void size
Fabric (structure)
Void continuity
Specific surface (drag)
fluid
Viscosity
Mass density
k
Units are in cm/sec
but
k = velocity
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)
Lab testing
Soil
specimens
1
sand
clay “seam”
2
sand
k1 = 10-2
k2 = 10-6
k – precision is on the order of +/- 50% or more!
Report values to one decimal place.
Lab testing (constant head test)
Dh
A
Dh
i
L
L
Measure Q
Figure 7.11 (text)
Q
k
iA
In-situ testing
Slug test
Pumping test
Hazen’s Correlation
k a pore size ~ (pore diameter)2
(pore diameter) ~ D10
USE THESE UNITS!
For loose clean sands with 0.1mm < D10 < 3mm and Cu < 5
k  C  D10
2
k = [cm/sec]
C = Hazen’s coefficient = 0.8 – 1.2 (typical = 1)
D10 = [mm]
Example
el. = 167.3m
clay
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
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 = 0.0115 m3/sec = 41.5 m3/hr