UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Name:______________ DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING Date:_______________

Fall 2013 1

CEE 380 Fall 2013 – HOMEWORK SOLUTIONS #4 Seepage (Due September 26, 2013)

PLEASE ADHERE TO THE HOMEWORK GUIDELINES POSTED ON COMPASS AND IN

THE SYLLABUS

SHOW ALL WORK FOR EACH PROBLEM ON ENGINEERING PAPER

SUBMIT YOUR SCANNED SOLUTION ON COMPASS2G

1. A soil sample is 250 mm long and 125 cm2 in cross-section. The water level at one end of the

block is 290 cm above a fixed reference point, and the water level at the other end is 115 cm

above the same reference point. The flow rate (Q) is 400 cm3 in 2 min.

a) hydraulic conductivity (permeability) of the specimen (cm/sec)

b) discharge velocity under the test conditions (cm/sec)

2. A falling head permeability test is run on a soil sample that is 10 cm long and 20 cm2 in cross-

section. The standpipe has a cross-sectional area of 20 cm2 and the head drops from 30 cm to

15cm in 4 min 30 sec. Find the coefficient of permeability (k) of the soil sample and determine

the probable soil type.

3. For cases I, II, and III:

Case I Case II Case III

a) Determine the pressure head (hp), elevation head (he), and total head (ht), at points A, B

(center of sample), and C for each case. “D” is the location of the datum to be

considered.

4m

4m

2m

Datum

Datum

4m

4m

1m

Datum

5m

4m

4m

A

B

C A, D

B

C

D

A B C

D

UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Name:______________ DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING Date:_______________

Fall 2013 2

b) Plot the variation of hp, he, and ht in the plots provided on the following pages (be

sure to plot your values such that they are easily distinguished from each other).

Submit these plots with the scanned copy of your homework. Case I:

Case II:

0 2 4 6 8 10

Ele

vati

on

(m

)

Head (m)

0

2

4

6

8

10

-2

4m

4m

2m

Datum Datum

Datum

4m

4m

1m

0

2

4

6

8

10

0 2 4 6 8 10

Ele

vati

on

(m

)

Head (m)

UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Name:______________ DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING Date:_______________

Fall 2013 3

Case III:

c) Determine discharge velocity and seepage velocity if the soil specimen has k = 0.06 cm/s,

and e = 0.6 for each case.

-2

0

2

4

6

8

10

0 2 4 6 8 10

He

ad (

m)

Horizontal Distance (m)

Datum

5m

4m

4m-2

0

2

4

6

8

10

0 2 4 6 8 10H

ead

(m

)

Horizontal Distance (m)

Datum

5m

4m

4m

UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Name:______________ DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING Date:_______________

Fall 2013 4

4. A permeability apparatus is designed to be a rectangular tube with height of 20 cm and side

length of 10 cm. The coefficients of permeability of Soil 1 and Soil 2 are 0.05cm/sec and

0.01cm/sec, respectively. Compute the discharge q (cm3/sec) for each case:

Case I: Only Soil 1 is filled.

Case I: Soil 1 and Soil 2 are filled parallel to each other.

Case III: Soil 1 is filled on top of Soil 2.

L=

20 c

m

10 cm

Soil 1

h

=2

5 c

m

L=

20 c

m

5 cm

Soil

1

h

=2

5 c

m

Soil

2

5 cm

L1=

10cm

Soil 1

h=

25 c

m

10 cm

Soil 2

L2=

10cm

Case I Case II Case III