HOMEWORK SOLUTION

 

HW #8

 

GEOTECHNICAL ENGINEERING I

 

(Question no. 7.4, 7.7, 7.8, 7.12, ..Al-Khafaji textbook)

 

 


7.4              (a) See figure 1. and figure 2.

 

Pressure (kPa)

Void Ratio

20

0.853

40

0.848

80

0.838

160

0.82

320

0.778

640

0.689

1280

0.59

320

0.619

80

0.654

20

0.69

0

0.79

 

Figure 1.


                                                Figure 2.

 

 

(b) From figure 2.

Compression Index =

                                = 0.332

Recompression Index =

                                    = 0.057

 

(c) From figure 2. (according to Cassagrande)

      The past pressure (max) = 250 kPa

 


7.7              (a) See figure 3

            d0 = 3.5 mm

            d100 = 4.36 mm

 

Time (min)

Dial Reading (mm)

0

3.394

0.1

3.493

0.25

3.529

0.5

3.573

1

3.638

2

3.731

4

3.872

8

4.048

15

4.192

30

4.312

70

4.415

140

4.47

260

4.506

455

4.54

1440

4.609

 

Figure 3.

 

(b)               T50 = 0.197

ds   = 3.44 mm (from graph)

H    = Thickness/2=19.05/2mm

       =  9.525mm (permitted drainage top and bottom)

t50 = corresponds with ()

      = 4.5 min

 

 

so,        Cv =

 

(c)                Cv = 3.97 mm2/min = 3.97x 10-6 m2/min

av =

gw = 9800 N/m3

e = (e1+e2)/2 = (0.845+0.712)/2 = 0.7785

 

So,  k   =

            =

            = 175.10-6 N/min = 2.9 . 10-4 cm/s

           

(d)        Compression Index =

                                            

7.8              Sample thickness = 25.4 mm

t consolidation 50% = 10 min

Drained at top and bottom , Hlab = 25.4/2=12.7 mm

Clay stratum = 7 m thick (covered by layer of sand and underlain by impervious bedrock)

                                          So, Hfield = 7 m

 

In the lab

 

T50 = 0.197

T50 =

Cv =

 

 

In the field

t50 field =

 

 

7.12          Clay layer thickness = 3.5 m (drain at top and bottom)

So, Hfield = 3.5/2 = 1.75 m

            Load = 100 kPa

           

            T30 = 0.08

 

Assume            Cv = 2.5 m2/year = 0.007 m2/day

 

 

t30 =

           

            Note: The result depends on Cv assumed.