Soil Mechanics

1. 1
Homework and quizzes scores will be averaged to account as 10% of total grade
Late homework will not be considered for credit.
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Problem1
For a moist soil, given that:
Volume of moist soil = 0.75 m3
,Weight of moist soil = 12.9 kN
Weight of dry soil = 11.25 kN and Specific gravity = 2.7
Calculate
1) Water content
2) Unit weight of sample
3) ) Dry unit weight, void ratio, porosity, degree of saturation and air content
Solution :
The weight of water is
Water content is given by
.
.
0.1467 14.67%
12.9
0.75
17.2 /
! 11.25
0.75
15 /
"!
1 # $
→ $
"!
& 1
Therefore
$
9.81 ( 2.7
15
& 1 0.766
)
$
1 # $
0.766
1 # 0.766
0.4337 43.37%
+
( "!
$
0.1467 ( 2.7
0.766
0.5171 51.71%
, )-1 & +. 0.4337-1 & 0.5171. 0.2094 20.94%
& !
Homework No.1 Properties of soil Due to 22 / 10 /2016
Student Name: Student No.
INTERNATIONA UNIVERSITY
FOR SCIENCE & TECHNOLOGY
!"#$%‫ا‬#'()%)*+,%‫وا‬ ‫%/!/)م‬ 0#1%‫ا‬ '%‫ا%2و‬
3'4%‫وا‬ '526%‫ا‬ 72*8%‫ا‬ 9:;
12.9 & 11.25 1.65

2. 2
Problem2
The unit weight of a soil sample is 18.2 kN/m3
at water content of 30.55 %. The
degree of saturation is increased from 30% to 80% when the water content is
increased by16%.
Required:
1) The degree of saturation of the soil sample
2) The specific gravity and void ratio
3) The air content of the soil sample.
Solution :
+
( "!
$
→ 0.3
( "!
$
… … … … … … . . -1.
+
( "!
$
→ 0.8
- # 0.16. ( "!
$
… … … … … … . . -2.
From equations (1) and (2), can be write
0.3
0.8
- # 0.16.
→ 0.096 9.6% →
"!
$
3.125
+
( "!
$
0.3055 ( 3.125 0.9547 95.47%
1 #
18.2
1 # 0.3055
13.94 /
"!
1 # $
3.125 $
1 # $
→ 13.94
3.125 $
1 # $
→ $ 0.834
"! 3.125 $ 3.125 ( 0.834 2.61
,
$
1 # $
-1 & +.
0.834
1.834
-1 & 0.9547. 0.0206 2.06%

3. 3
Problem 3
Dry soil with GS = 2.71 is mixed with 16% by weight of water and compacted to
produce a cylindrical sample of 38 mm diameter and 76 mm long with 6% air
content. Calculate the mass of the mixed soil that will be required and the void ratio
of the sample.
Solution :
The volume of the sample is
01
4
ℎ
0 -0.038.
4
0.076 8.62 ∗ 104
+
0.16 ( 2.71
$
0.4336
$
,
$
1 # $
-1 & +. → 0.06
$
1 # $
51 &
0.4336
$
6 → $ 0.525
!
7
1 # $
8.62 ∗ 104
1 # 0.525
5.639 ∗ 104
! "! ∗ ∗ ! 26.58 ∗ 5.639 ∗ 104
1.498 ≈ 1.5
∗ ! 0.16 ∗ 1.5 0.24
7 1.5 # 0.24 1.74
7 177.4 9
Problem 4
The water content of a 100% saturated soil is 34%, and the specific gravity is 2.65.
Determine the void ratio, dry unit weight, and porosity.
Solution :
+
( "!
$
→ $ ( "! 0.34 ∗ 2.65 0.901
"!
1 # $
2.65 ∗ 9.81
1 # 0.901
13.67 /
)
$
1 # $
0.901
1 # 0.901
0.474 47.4%

4. 4
Problem 5
A soil sample has a degree of saturation of 30.4 % and void ratio of 0.85.
How much water must be added per cubic meter of soil to increase the degree of
saturation to 70 %.
Solution :
The total volume is equal to one cubic meter
The volume of solids
!
7
1 # $
1
1 # 0.85
0.54
The volume of voids:
: 1 & 0.54 0.46
+
:
→ 0.304
:
→ 0.304 ∗ 0.46 0.1398
0.7 ∗ 0.46 0.322
∆ 0.322 & 0.1398 0.1822
∆ 0.1822 ∗ 9.81 1.787
Problem 6
For a given soil sample, the unit weight and air content are 17.89 kN/m3
and 17.04%,
respectively. If the degree of saturation is 58.26%, determine :
1) the void ratio, specific gravity and the water content
2) the dry unit weight , and saturated unit weight.
Solution :
,
$
1 # $
-1 & +. → 0.1704
$
1 # $
-1 & 0.5826. → $ 0.689
"!
1 # $
-1 # . → 17.89
9.81 "!
1 # 0.689
51 #
0.5826 ∗ 0.689
"!
6 → "! 2.678
0.5826 ∗ 0.689
2.678
0.1499 ≈ 0.15 15%
1 #
17.89
1 # 0.15
15.56 / ,)1
!<7
-"! # $.
1 # $
9.81-2.678 # 0.689.
1 # 0.689
19.56 /