Chapter 3. Saturated Water Flow - LAWR
Chapter 3. Saturated Water Flow - LAWR
Chapter 3. Saturated Water Flow - LAWR
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SSC107 – Fall 2000 <strong>Chapter</strong> 3 Page 3-14<br />
Falling head method to measure the saturated hydraulic conductivity of uniform soil:<br />
This method is used if it is expected that K s is low<br />
water<br />
b(t)<br />
2<br />
Position 2: z 2 =L ; h 2 = b(t) ; H 2 = L+b(t)<br />
L<br />
1<br />
Position 1: z 1 =0 ; h 1 = 0 ; H 2 = 0<br />
• The soil is saturated and has an unknown saturated hydraulic conductivity value, K s<br />
• The head of water on top of the soil column decreases with time (t), and is equal to b(t)<br />
• For uniform size column, the flux coming out of the column is:<br />
J<br />
w<br />
db<br />
K b ( t ) +<br />
= = −<br />
L<br />
s<br />
dt L<br />
Or:<br />
db( t)<br />
K<br />
sdt<br />
= − , where b=b 0 at t=0 and b=b 1 at t=t 1<br />
b( t) + L L<br />
• Integrate and solve for K s at time t 1 : K<br />
s<br />
=<br />
L ⎡b<br />
ln⎢<br />
t ⎣ b<br />
o<br />
1 1<br />
+<br />
+<br />
L⎤<br />
⎥<br />
L ⎦<br />
✪ Special assignment: Derive the expression for K s , if the area of the water-filled<br />
tube (a) is much smaller than the area of the soil column (A)
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