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Flow through Soils (ch7)

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Flow through Soils(ch7)

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

hv = velocity head (KE)

hp = pressure head (SE)

he = elevation head (PE)

h = total head = hv + hp + he

(Bernoulli)

units of LENGTH

A

B

h1

2

h2

1

l

Fluid flows from point of high total head to point of low total head

head loss = Dh = h1 – h2

Rate at which the total head changes along a length

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

hp

Pressure head at A.

A

The “pore water pressure” at A is

uhydrostatic = uh = due to hydrostatic condition only

uexcess = ue = due to additional processes

zw1

zw

zw2

Depth, z

Flow vectors: parallel

of equal magnitude

SOIL

Flow is in one direction

What is the flowrate through a soil?

Concrete dam

Flowrate =

Q [m3/sec]

SOIL

Cross-sectional area to flow

Hydraulic conductivity

“permeability” [cm/s]

Hydraulic gradient

Assumptions:

flow is laminar

soil properties do not D with time

Dh

A

L

Measure Q

Figure 7.11 (text)

fluid

soil

Measure of a soil-fluid system’s resistance to flow

depends on

Void size

Fabric (structure)

Void continuity

Specific surface (drag)

Viscosity

Mass density

Units are in cm/sec

but

k = velocity

TYPICAL VALUES [cm/s]

SOIL

101 – 102

gravel

sands

10-3 – 100

10-8 – 10-3

silts

clays

10-10 – 10-6

Probably soil’s most varying parameter (largest numerical range)

Soil specimens

sand

clay “seam”

1

sand

2

k1 = 10-2

k2 = 10-6

k – precision is on the order of +/- 50% or more!

Report values to one decimal place.

Dh

A

L

Measure Q

Figure 7.11 (text)

Slug test

Pumping test

USE THESE UNITS!

k a pore size

~ (pore diameter)2

(pore diameter) ~ D10

For loose clean sands with 0.1mm < D10 < 3mm and Cu < 5

k = [cm/sec]

C = Hazen’s coefficient = 0.8 – 1.2 (typical = 1)

D10 = [mm]

el. = 167.3m

clay

el. = 165m

clay

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

Q = kiA = 0.0115 m3/sec = 41.5 m3/hr

Q = kiA

k = 4x10-2 cm/sec

i = Dh/L = (167.3m – 165m) / 256m = 0.009

A = (3.2 m) (1000 m) = 3200 m2