Chapter 6
Gs ρ w
6.1 ρd =
G w
1+ s
S
ρw w ρd @ S (kg/m3)
Gs (kg/m3) (%) 70% 80% 90% 100%
5 2228 2273 2310 2340
10 1922 1991 2047 2095
2.65 1000
15 1690 1770 1838 1896
20 1508 1594 1668 1732
The plot is shown below.
2400
S = 70%
S = 80%
2200 S = 90%
S = 100%
Dry Density (kg/m3)
2000
1800
1600
1400
4 8 12 16 20 24
w (%)
6.2 Eq. (6.4):
γw 9.81 9.81
w (%) γzav (kN/m3)
γ zav = = = . 5 23.18
1 1 w + 0.3731
w+ w+ 10 20.73
Gs 2.68 15 18.75
20 17.11
The table can now be prepared. 25 15.74
31
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 6.3 γ
γd =
Weight of W w(%)
γ = 1+
Volume soil mass, W V w 100
(ft3) (lb) (lb/ft3) (%) (lb/ft3)
1
30 3.92 117.6 5.0 111.9
1
30 4.12 123.6 7.5 114.9
1
30 4.29 128.7 10.0 117.0
1
30 4.37 131.1 12.5 116.5
1
30 4.45 133.5 15.0 116.0
1
30 4.35 130.5 17.5 111.0
1
30 4.20 126.0 20.0 105.0
a. The plot of γd versus w is shown. γd(max) ≈ 117.5 lb/ft3 @ wopt = 10.8%
Gsγ w ( 2.68)( 62.4)
b. γ d = ; 117.5 = ; e ≈ 0.42
1+ e 1+ e
wGs (0.108)( 2.68)
S= = = 0.684 = 68.4%
e 0.423
32
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Gs ρ w
6.1 ρd =
G w
1+ s
S
ρw w ρd @ S (kg/m3)
Gs (kg/m3) (%) 70% 80% 90% 100%
5 2228 2273 2310 2340
10 1922 1991 2047 2095
2.65 1000
15 1690 1770 1838 1896
20 1508 1594 1668 1732
The plot is shown below.
2400
S = 70%
S = 80%
2200 S = 90%
S = 100%
Dry Density (kg/m3)
2000
1800
1600
1400
4 8 12 16 20 24
w (%)
6.2 Eq. (6.4):
γw 9.81 9.81
w (%) γzav (kN/m3)
γ zav = = = . 5 23.18
1 1 w + 0.3731
w+ w+ 10 20.73
Gs 2.68 15 18.75
20 17.11
The table can now be prepared. 25 15.74
31
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 6.3 γ
γd =
Weight of W w(%)
γ = 1+
Volume soil mass, W V w 100
(ft3) (lb) (lb/ft3) (%) (lb/ft3)
1
30 3.92 117.6 5.0 111.9
1
30 4.12 123.6 7.5 114.9
1
30 4.29 128.7 10.0 117.0
1
30 4.37 131.1 12.5 116.5
1
30 4.45 133.5 15.0 116.0
1
30 4.35 130.5 17.5 111.0
1
30 4.20 126.0 20.0 105.0
a. The plot of γd versus w is shown. γd(max) ≈ 117.5 lb/ft3 @ wopt = 10.8%
Gsγ w ( 2.68)( 62.4)
b. γ d = ; 117.5 = ; e ≈ 0.42
1+ e 1+ e
wGs (0.108)( 2.68)
S= = = 0.684 = 68.4%
e 0.423
32
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
