Soil Mechanics
(1)
Fff
Soil Mechanics
(1)
Fff
Chapter (1)
Physical properties
(1)
2011
Soil Mechanics for Second Year
Civil Engineering
Course Content:
Δϴ΋Ύϳΰϴϔϟ΍ ι΍ϮΨϟ΍
Chapter (1): Physical Properties.
Chapter (2): Grain Size Distributions.
ΕΎΒϴΒΤϠϟ ϰϤΠΤϟ΍ ϊϳίϮΘϟ΍
ΔΑήΘϟ΍ ϡ΍Ϯϗ
Chapter (3): Soil Consistency.
ΔΑήΘϟ΍ ϒϴϨμΗ
Chapter (4): Soil Classification.
ΔΑήΘϟ΍ ϚϣΩ
Chapter (5): Soil Compaction.
Chapter (6): Hydraulic Properties of the Soil.
ΔΑήΘϠϟ ΔϴϜϴϟϭέΪϴϬϟ΍ ι΍ϮΨϟ΍
Chapter (7): Stress Due to Applied Load.
ΔϴΟέΎΨϟ΍ ϝΎϤΣϷ΍ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϹ΍
Chapter (8): Consolidation.
Soil Mechanics (1)
ΪϠμΘϟ΍
Chapter (1)
Physical properties
(2)
2011
Chapter (1)
Physical Properties
ΔΑήΘϠϟ Δϴ΋Ύϳΰϴϔϟ΍ ι΍ϮΨϟ΍
-: Ϧϣ ΎϬϟ ϲόϴΒτϟ΍ ϊοϮϟ΍ ϲϓ ΔΑήΘϟ΍ ϥϮϜΘΗ
- Particles
ΕΎΒϴΒΣ
˯Ύϣ
- water
˯΍Ϯϫ
- Air
Solid
Va
Wa = 0
Vw
Ww
Vv
Void
Vt
Water
Air
Ws
Vs
Natural state
Prism
Vt = ΔΑήΘϠϟ ϰϠϜϟ΍ ϢΠΤϟ΍
Ws = ΐϠμϟ΍ ˯ΰΠϟ΍ ϥίϭ
Vv = ΕΎϏ΍ήϔϟ΍ ϢΠΣ
Ww = ˯ΎϤϟ΍ ϥίϭ
Vs = ΐϠμϟ΍ ˯ΰΠϟ΍ ϢΠΣ
Wa = zero = ˯΍ϮϬϟ΍ ϥίϭ
Vw = ˯ΎϤϟ΍ ϢΠΣ
Wt = ϰϠϜϟ΍ ϥίϮϟ΍
Va = ˯΍ϮϬϟ΍ ϢΠΣ
Soil Mechanics (1)
Wt
Chapter (1)
Physical properties
(3)
2011
Physical Properties
ΕΎϏ΍ήϔϟ΍ ΔΒδϧ
1) Void ratio: (e)
e
Vv
Vv
Vs
Vs
ΔΑήΘϠϟ ΐϠμϟ΍ ˯ΰΠϟ΍ ϢΠΣ ϰϟ· ΕΎϏ΍ήϔϟ΍ ϢΠΣ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
e 0.5 0.8 o Sand
e 0.7 1.1 o Clay
ΔϴϣΎδϤϟ΍
2) Porosity: (n)
n
Vv
Vv
Vt
Vt
ΔΑήΘϠϟ ϰϠϜϟ΍ ϢΠΤϟ΍ ϰϟ· ΕΎϏ΍ήϔϟ΍ ϢΠΣ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
n
0.0 1.0
ϊΒθΘϟ΍ ΔΟέΩ
3) Degree of saturation: (Sr)
Sr
Vw
Vv
Vv
Vw
ΔΑήΘϟ΍ ϲϓ ΓΩϮΟϮϤϟ΍ ΕΎϏ΍ήϔϟ΍ ϢΠΣ ϰϟ· ˯ΎϤϟ΍ ϢΠΣ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
Soil Mechanics (1)
Chapter (1)
(4)
2011
Sr = 0.0
Sr = 100
Dry ΔϓΎΟ
Saturated
4) Water content : ( Wc )
Wc
Physical properties
Sr = 0- 100
ΔόΒθϣ
ΔϠϠΒϣ
Wet
ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍
Ww
Ws
Ww
Ws
ΔΑήΘϠϟ ΐϠμϟ΍ ˯ΰΠϟ΍ ϥίϭ ϰϟ· ˯ΎϤϟ΍ ϥίϭ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
ΔϓΎΜϜϟ΍
5) Unit weight (density): (J)
W
ϥίϮϟ΍
J
ϢΠΤϟ΍
V
ϢΠΤϟ΍ ϰϟ· ϥίϮϟ΍ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
Jb
Jd
Js
Jsat.
Jsub.
˯ΎϤϟ΍ ΔϓΎΜϛ ϥ΃ φΣϻ
Jw = 1 t/m3 = 1 g/cm3 = 10 kN/m3
3
3
=
62.4
Ib/ft
= 1000
kg/m
Soil Mechanics (1)
P
Chapter (1)
Physical properties
(5)
2011
a) Bulk density: (Jb)
J
b
ΔϴϠϜϟ΍ ΔϓΎΜϜϟ΍
Wt
Vt
ΔΑήΘϠϟ ϰϠϜϟ΍ ϢΠΤϟ΍ ϰϟ· ϰϠϜϟ΍ ϥίϮϟ΍ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
˯ΎϤγϷ΍ Ϧϣ ήϴΜϜϟ΍ ΎϬϟ ϭ
Bulk = natural = total = wet = moist
b) Dry density: (Jd)
J
ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍
Ws
Vt
d
ΔΑήΘϠϟ ϰϠϜϟ΍ ϢΠΤϟ΍ ϰϟ· ΐϠμϟ΍ ˯ΰΠϟ΍ ϥίϭ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
c) Density of solid part: (Js)
J
s
ΐϠμϟ΍ ˯ΰΠϟ΍ ΔϓΎΜϛ
Ws
Vs
ΔΑήΘϠϟ ΐϠμϟ΍ ˯ΰΠϟ΍ ϢΠΣ ϰϟ· ΐϠμϟ΍ ˯ΰΠϟ΍ ϥίϭ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
Soil Mechanics (1)
Chapter (1)
Physical properties
(6)
2011
ΔόΒθϤϟ΍ ΔϓΎΜϜϟ΍
d) Saturated density: (Jsat.)
J
Wt
Vt
sat
ΔΑήΘϟ΍ ϊΒθΗ ΔϟΎΣ ϲϓ ϰϠϜϟ΍ ϢΠΤϟ΍ ϰϟ· ϰϠϜϟ΍ ϥίϮϟ΍ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
ΓέϮϤϐϤϟ΍ ΔϓΎΜϜϟ΍
e) Submerged density: (Jsub.)
J sub. J sat. J w
( Ϯ˰ϔ˰τϟ΍ ΔΠϴΘϧ ) ˯ΎϤϟ΍ ΔϓΎΜϛ ΎϬϨϣ Ρϭήτϣ ΔόΒθϤϟ΍ ΔϓΎΜϜϟ΍ ϲϫ
6) Specific gravity: (Gs)
Gs
ϲϋϮϨϟ΍ ϥίϮϟ΍
Js
Jw
˯ΎϤϟ΍ ΔϓΎΜϛ ϰϟ· ΐϠμϟ΍ ˯ΰΠϟ΍ ΔϓΎΜϛ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
( 2.6 - 2.8 ϦϴΑ ΎϬΘϤϴϗ Ρϭ΍ήΘΗϭ
Soil Mechanics (1)
Chapter (1)
Physical properties
(7)
2011
7) Relative density: (Dr)
Dr
emax eo
emax emim
ΔϴΒδϨϟ΍ ΔϓΎΜϜϟ΍
Vmax Vo
Vmax Vmim
ςϘϓ sand ΔϴϠϣήϟ΍ ΔΑήΘϟ΍ ϒϴϨμΘϟ ϡΪΨΘδΗ
emim. = dense state (ΎϬπόΑ Ϧϣ ΍ΪΟ ΔΒϳήϗ ΕΎΒϴΒΤϟ΍ ϥϮϜΗ) ΔϔϴΜϜϟ΍ ΔϟΎΤϟ΍
= compacted state
emax. = loose state (ΎϬπόΑ Ϧϣ ΍ΪΟ ΓΪϴόΑ ΕΎΒϴΒΤϟ΍ ϥϮϜΗ) ΔϜϜϔϤϟ΍ ΔϟΎΤϟ΍
eo = natural state (ΔόϴΒτϟ΍ ϲϓ ϲϫ ΎϤϛ ΕΎΒϴΒΤϟ΍ ϥϮϜΗ) ΔϴόϴΒτϟ΍ ΔϟΎΤϟ΍
= in-situ state
= field state
Vmax = loose state
ΔϜϜϔϤϟ΍ ΔϟΎΤϟ΍ ϰϓ ϢΠΤϟ΍
Vmim = dense state
ΔϔϴΜϜϟ΍ ΔϟΎΤϟ΍ ϰϓ ϢΠΤϟ΍
Vo = natural state
ΔϴόϴΒτϟ΍ ΔϟΎΤϟ΍ ϰϓ ϢΠΤϟ΍
Soil
Very loose
Loose
Medium
Dense
Very dense
Dr (%)
0 - 15
15 - 35
35 - 65
65 - 85
85 - 100
Soil Mechanics (1)
Chapter (1)
Physical properties
(8)
2011
φΣϻ
1
J
Dr
J
mim
1
J
1
mim
o
1
J
max
n
(1) Ÿ e
1 n
e
( 2) Ÿ n
1 e
(3) Ÿ sr * e Gs * Wc
( 4) Ÿ J d
(5) Ÿ J b
φϔΣ
φϔΣ
ΎϬΗΎΒΛ· ΏϮϠτϣ Ϧϴϧ΍ϮϘϟ΍ ξόΑ ϙΎϨϫ
Jb
1 Wc
Gs sr * e
(
) *J w
1 e
Soil Mechanics (1)
Chapter (1)
Physical properties
(9)
2011
ϢΠΤϟ΍ ϭ ϥίϮϟ΍ ϦϴΑ Δϗϼόϟ΍
φϔΣ
Vw
w
Ww
Vs
s
Ws
Ws Gs * J w *Vs
Ww J w *Vw
ΕΎ˰ΗΎ˰Β˰ΛϹ΍
Prove that
Jb
§ Gs sr * e ·
¨
¸ *J w
© 1 e ¹
OR
Find the relation between
Jb, Gs, Sr, e, Jw
Soil Mechanics (1)
φϔΣ
ήϴϐΘϳ ϻ ΖΑΎΛ ΐϠμϟ΍ ˯ΰΠϟ΍
ήϴϐΘϳ ϻ ΖΑΎΛ ΐϠμϟ΍ ˯ΰΠϟ΍
a
Chapter (1)
Physical properties
(10)
2011
ΕΎΒΛϹ΍ Ε΍ϮτΧ
( ϢϬϓάΣ ) ϢϬΑ ΃ΪΒϧ ϻ ( J or Gs ) Ϫϴϓ ϥϮϧΎϘϟ΍ ϥΎϛ ΍Ϋ· -˺
ϢϬϴϓ ΪΣ΍ϭ ϱ΄Α ΃ΪΒϧ ( Sr, e ) ϰϘΒΗ -˻
e
Vv
Vs
1= ϡΎϘϤϟ΍ νήϔϧ
Assume
(Vs = 1)
VV = e
Prism ϲϓ νϮόϧ -˼
e
Sr*e
1
Sr*e*Jw
Gs*Jw
Vw Vw
Sr
Vv e
Vw Sr * e
Soil Mechanics (1)
Chapter (1)
Physical properties
(11)
2011
( Jb ) ϪΑ ΃ΪΒϧ ϻ ϱάϟ΍ ϲϓ νϮόϧ -˽
Wt
Vt
Sr * e * J w Gs * J w
1 e
( Sr * e Gs ) * J w
1 e
Jb
Jb
Jb
Prove that
Jb
Jd
1 Wc
OR
Find the relation between
Jb, Jd, Wc
ΕΎΒΛϹ΍ Ε΍ϮτΧ
( ϢϬϓάΣ ) ϢϬΑ ΃ΪΒϧ ϻ ( J or Gs ) Ϫϴϓ ϥϮϧΎϘϟ΍ ϥΎϛ ΍Ϋ· -˺
ΎϬΑ ΃ΪΒϧ (Wc ) ϰϘΒΗ -˻
Wc
Ww
Ws
Soil Mechanics (1)
Chapter (1)
Physical properties
(12)
2011
1= ϡΎϘϤϟ΍ νήϔϧ
Assume (Ws = 1)
Wc = Ww
Prism ϲϓ νϮόϧ -˼
Wc
Jw
1
Gs
Wc
1
(Jd , Jb ) ϪΑ ΃ΪΒϧ ϻ ϱάϟ΍ ϲϓ νϮόϧ -˽
Jb
Jd
J
J
J
d
b
1 Wc
Vt
Wt
Vt
1
Vt
(2)
1
1 Wc
J
d
(1)
b
1 Wc
Soil Mechanics (1)
Chapter (1)
Physical properties
(13)
2011
Prove that
Sr * e Gs *Wc
OR
Find the relation between
Sr, e, Gs, Wc
ΕΎΒΛϹ΍ Ε΍ϮτΧ
( ϢϬϓάΣ ) ϢϬΑ ΃ΪΒϧ ϻ ( J or Gs ) Ϫϴϓ ϥϮϧΎϘϟ΍ ϥΎϛ ΍Ϋ· -˺
ΎϬΑ ΃ΪΒϧ (Wc, Sr, e ) ϰϘΒΗ -˻
Vv
Vs
e
1= ϡΎϘϤϟ΍ νήϔϧ
Assume (Vs = 1)
e = Vv
Prism ϲϓ νϮόϧ -˼
e
1
Sr e
Sr e Jw
Gs Jw
Soil Mechanics (1)
Chapter (1)
Physical properties
(14)
2011
(Wc, Gs) ϪΑ ΃ΪΒϧ ϻ ϱάϟ΍ ϲϓ νϮόϧ -˽
Ϫϴϓ ξϳϮόΘϟ΍ ϢΘϳ ϻ ΖΑΎΛ
Gs
Ww
Sr * e * J w
Ws
Gs * J w
Sr * e
Gs
Wc
Wc
Prove that
e
n
1 e
OR
Find the relation between
e, n
ΕΎΒΛϹ΍ Ε΍ϮτΧ
( ϢϬϓάΣ ) ϢϬΑ ΃ΪΒϧ ϻ ( J or Gs ) Ϫϴϓ ϥϮϧΎϘϟ΍ ϥΎϛ ΍Ϋ· -˺
ϢϬϨϣ ϱ΄Α ΃ΪΒϧ (n, e ) ϰϘΒΗ -˻
e
Vv
Vs
Assume (Vs = 1)
e = Vv
Soil Mechanics (1)
Chapter (1)
Physical properties
(15)
2011
Prism ϲϓ νϮόϧ -˼
e
1
(n) ϪΑ ΃ΪΒϧ ϻ ϱάϟ΍ ϲϓ νϮόϧ -˽
vv
vt
n
e
1 e
Prove that
n
e
1 n
OR
Find the relation between
e, n
ΕΎΒΛϹ΍ Ε΍ϮτΧ
( ϢϬϓάΣ ) ϢϬΑ ΃ΪΒϧ ϻ ( J or Gs ) Ϫϴϓ ϥϮϧΎϘϟ΍ ϥΎϛ ΍Ϋ· -˺
Soil Mechanics (1)
Chapter (1)
Physical properties
(16)
2011
ϢϬϨϣ ϱ΄Α ΃ΪΒϧ (n, e ) ϰϘΒΗ -˻
n
Vv
Vt
Assume (Vt = 1)
n = Vv
Prism ϲϓ νϮόϧ -˼
n
1
1-n
(e) ϪΑ ΃ΪΒϧ ϻ ϱάϟ΍ ϲϓ νϮόϧ -˽
vv
vs
e
n
1 n
Try: Prove that
Jb
Gs * J w (1 Wc)
(1 e)
Soil Mechanics (1)
Chapter (1)
Physical properties
(17)
2011
Prove that
(J s J d )J w
(J s * J d )
Wc( sat.)
OR
Find the relation between
Wc, JsJdJw
ΕΎΒΛϹ΍ Ε΍ϮτΧ
ϢϬϨϣ ϱ΄Α ΃ΪΒϧ ( JsJdJw) ΔϟϻΪΑ ϪϠϛ ϥϮϧΎϘϟ΍ -˺
Js
Ws
Vs
Assume (Vs = 1)
Js = Ws
ϊΒθΘϟ΍ ΔϟΎΣ ϰϓ ϦϜϟ ϭ Prism ϲϓ νϮόϧ -˻
Js
Jd
Js
1
Jd
w
1
S
·
§Js
¨¨
1 ¸¸J w
¹
©Jd
Js
Soil Mechanics (1)
Chapter (1)
Physical properties
(18)
2011
Jd
Ws
Vt
Vt
Js
Jd
Js
Vt
(Wc) ϲϓ νϮόϧ -˼
§Js
·
¨¨
1 ¸¸ J w
©Jd
¹
Ww
Ws
Wc
Js
Js Jd Jw
Jd *J s
Wc
Prove that
Sr
Wc
Wc ( sat .)
OR
Find the relation between
Sr, WcWc(sat)
ΕΎΒΛϹ΍ Ε΍ϮτΧ
( Wc ) ˰Α ΃ΪΒϧ -˺
Soil Mechanics (1)
Chapter (1)
Physical properties
(19)
2011
Ww
Ws
Wc
Assume (Ws = 1)
˱Wc = Ww
Ww
Ws
Wc( sat )
˱Wc = Ww (sat.)
(ϊΒθϣ ήΧϷ΍ϭ ˯΍Ϯϫ ϲϓ ΪΣ΍ϭ ) ϦϴΗήϣ Prism Ϣγήϧ -˻
a
Wc
Jw
VV =
w
Wc
S
Wc( sat )
Jw
(Wc / J w )
(Wc( sat ) / J w )
Sr
Vw
Vv
Sr
Wc
Wc ( sat )
Soil Mechanics (1)
w
Wc(sat)
S
Chapter (1)
Physical properties
(20)
2011
( ήΟΎΤϤϟ΍ Δϟ΄δϣ ϲϓ ) φΣϻ
(1)
(2)
Pit ήΠΤϣ
Embankment
ϲΑ΍ήΗ Ϊγ
e1
e2
V1
V2
Jd2
J d1
1 e1
1 e2
V1
V2
Ϟ΋ΎδϤϟ΍ ω΍Ϯϧ΃
Ϧϴόϣ ϢΠΣ ϭ΃ ϥίϭ ΔϤϴϗ ΎϬΑ ΔϟΎδϣ
Ϧϴόϣ ϢΠΣ ϭ΃ ϥίϭ ΔϤϴϗ ΎϬϴϓ ΪΟϮϳ ϻ ΔϟΎδϣ
prism ˰ϟ΍ Ϣγέ ϢΘϳ ΔϟΎδϣ ϯ΍ Δϳ΍ΪΑ ϲϓ
prism ˰ϟ΍ Ϣγέ ϢΘϳ ΔϟΎδϣ ϯ΍ Δϳ΍ΪΑ ϲϓ
a
a
w
w
S
S
Assume
ΕΎϴτόϤϟ΍ ϡ΍ΪΨΘγΎΑ prism ˰ϟ΍ ˯΍ΰΟ΃ ϸϤϧ
Vs = 1
ϡ΍ΪΨΘγ΍ ϊϣ
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (1)
Physical properties
1
2011
Ϧϴϧ΍ϮϘϟ΍ κΨϠϣ
1) Ÿ e
3) Ÿ Sr
Vv
Vs
Vw
Vv
Vv
Vt
2) Ÿ n
4 ) Ÿ Wc
5) Ÿ J b
Wt
Vt
6) Ÿ J
7) Ÿ J s
Ws
Vs
8 ) Ÿ J sat
9) Ÿ J sub. J sat. J w
11 ) Ÿ Dr
d
10 ) Ÿ Gs
e max e o
e max e mim
Ww
Ws
Ws
Vt
Wt
Vt
Js
Jw
ΎϬΗΎΒΛ· ΏϮϠτϣ Ϧϴϧ΍ϮϘϟ΍ ξόΑ ϙΎϨϫ
e
n
13) Ÿ n
12) Ÿ e
1 e
1 n
Jb
14) Ÿ sr * e Gs * Wc
15) Ÿ J d
1 Wc
Gs sr * e
) *J w
16) Ÿ J b (
1 e
Soil Mechanics (1)
Chapter (1)
Physical properties
2
2011
ϢΠΤϟ΍ ϭ ϥίϮϟ΍ ϦϴΑ Δϗϼόϟ΍
Ws
Gs * J w * Vs
Ww
J w * Vw
( ήΟΎΤϤϟ΍ Δϟ΄δϣ ϲϓ ) φΣϻ
(1)
(2)
Pit ήΠΤϣ
Embankment
ϲΑ΍ήΗ Ϊγ
e1
e2
V1
V2
V1
V2
1 e1
1 e2
Soil Mechanics (1)
Jd2
J d1
Chapter (1)
Physical properties
3
2011
Example (1)
The bulk density of soil sample is 1.97 gm/cm3 and
its water content 20 % taking the specific gravity
2.65, find the void ratio and degree of saturation.
Solution
Given
Jw
Jb = 1.97 gm/cm3
1 .0
Wc = 20 %
Gs = 2.65
a
1.61
0.53
w
0.53
1
S
2.65
Assume Vs = 1
Ws = Gs * 1 * Jw = 2.65
Soil Mechanics (1)
Chapter (1)
4
2011
Physical properties
Ww
Wc
Ws
Ww
0.2
Ÿ Ww 0.53
2.65
Ww J w * Vw Vw
1.0
Wt
Jb
Vt
2.65 0.53
1.97
Ÿ Vt 1.61
Vt
Vv 1.61 1
e
0.61
Vs
1
Vw
0.53
Sr
0.86 86%
Vv 1.61 1
Example (2)
The bulk and dry densities of soil sample are 1.77
and 1.5 t/m3 respectively, if the degree of saturation
is 60 % what is the specific gravity and porosity.
Then calculate the quantity of water added for full
saturation without change of volume.
Soil Mechanics (1)
Chapter (1)
Physical properties
5
2011
Solution
Given
Jb = 1.77 t/m3
Jd = 1.5 t/m3
Sr = 60 %
a
0.66Gs
0.18Gs
w
0.18Gs
1
S
Gs
Assume Vs = 1
Ws
Gs * J w
Ws
Jd
Vt
GS
1 .5
Ÿ Vt
Vt
Gs
0 .66 Gs
Soil Mechanics (1)
Chapter (1)
Physical properties
6
2011
Wt
Vt
Jb
1 . 77
Wt
Ÿ Wt
0 . 66 Gs
1 . 18 Gs
Vw
Sr
Vv
0 . 18 Gs
0 .6
Ÿ Gs
0 . 66 Gs 1
2 . 72
a
1.82
n
Vv
Vt
Full saturated
1.82 1
1.82
0.49
w
0.49
1
S
2.72
0.82
w
0.82
1
S
2.72
0.45
45%
1.82
Weight of water = 0.82 - 0.49 = 0.33 ton
Per unit volume of solid part
Soil Mechanics (1)
Chapter (1)
Physical properties
7
2011
Example (3)
An earth embankment is to be compacted to a dry
density of 1.84 t/m3, the bulk density and water
content of a borrow pit are 1.77 t/m3 and 8 %
respectively, calculate the volume of excavation of
borrow pit which corresponds to 1 m3 of
embankment.
Solution
Given
Embankment
Jd = 1.84 t/m
ήΠΤϣ
Borrow pit
Jb = 1.77 t/m3
3
Wc = 8 %
V2 = 1 m3
Jd
Jd
V1
V2
J d2
J d1
V1
1
1 . 84
Ÿ V 1 ( pit )
1 . 64
Jb
V1 = ???
1 Wc
1.77
1 0.08
1 . 12 m 3
Soil Mechanics (1)
1.64
Chapter (1)
Physical properties
8
2011
Example (4)
The weight of a partially soil sample is 600 gm and
its volume is 365 cm3 after oven drying the weight
of the sample reduced to 543 gm. Taking the
specific gravity 2.67, find the water content, void
ratio and degree of saturation. If the sample is
saturated with water without change of volume,
find the saturated density.
Solution
Given
Wt = 600 gm
Vt = 365 cm3
W dry = Ws = 543
Gs = 2.67
a
365
57
w
57
600
203.4
S
543
Soil Mechanics (1)
Chapter (1)
Physical properties
9
2011
Ws
Gs * J w *Vs
543 2.67 *1*Vs Ÿ Vs 203.4
Ww J w *Vw Vw 57
Ww 57
0.105 10.5%
Ws 543
Vv 365 203.4
e
0.795
Vs
203.4
Vw
57
Sr
0.353 35.3%
Vv 365 203.4
Wc
ήϴϐΘϳ ϻ ΖΑΎΛ ΐϠμϟ΍ ˯ΰΠϟ΍
161.6
Full saturated
w
161.6
704.6
365
203.4
J sat .
Wt
Vt
704 . 6
365
S
1 . 93 t / m 3
Soil Mechanics (1)
543
Chapter (1)
Physical properties
10
2011
Example (5) (mid term 2010)
A saturated 100 cm3 clay sample has a natural water
content of 15 % . If the specific gravity of the soil solids
is 2.7, what will be the volume of the sample when the
water content is 25 %.
Solution
Given:
Case (1)
Case (2)
Vt = 100 cm3
Vt = ???
Wc = 15 %
Wc = 25 %
Gs = 2.7
Jw = 1 g/cm3
Case (1)
Vs + Vw = 100
(1)
Ww
0.15
Ws
Ww 0.15 * Ws
WC
w
Vw
Vs
S
2.7Vs
100
Vw 0.15 * 2.7 * Vs
Vw 0.405 * Vs
(2)
From (1), (2)
Vw
Vw = 28.83
,
Ww = 28.83 ,
Vs = 71.17
Ws = 192.16
Soil Mechanics (1)
Chapter (1)
Physical properties
11
2011
Case (2)
WC
Ww
Ws
0.25
Vw
w
Vw
71.17
S
192.16
ˮˮˮ
Ww 0.25 * Ws
Ww 0.25 *192.16
Ww 48.04
Vw 48.04
Vt
71.17 48.04 119.21
Soil Mechanics (1)
Chapter (1)
2011
12
Soil Mechanics (1)
Physical properties
Soil Mechanics
(1)
Fff
Zagazig University
Faculty of Engineering
Structural Eng. Department
˺
Soil Mechanics (1)
Sheet (1)
Physical Properties
1) A sample of soil obtained from a test pit is one cubic centimeter in
volume and weight 140 gm, after oven drying the sample weight
125 gm. calculate the water content, moist unit weight, dry unit
weight.
2) A 150 cubic centimeter sample of wet soil scales 250 gm when
saturated and 162 gm when oven dried. Calculate the dry unit
weight, water content, void ratio, specific gravity.
3) Laboratory test on sample of saturated soil show that the void ratio
is 0.45 and the specific gravity is 2.65. Determine the wet unit
weight of the soil and its water content
4) The moisture content of an undisturbed sample of clay existing in a
volcanic region is 265 % at 100 % of saturation. The specific
gravity is 2.7. Find the saturated and submerged densities.
5) For a soil in natural state, given e = 0.70, Wc = 22 % and Gs =
2.69
a) Determine the moist unit weight, dry unit weight and degree
of saturation.
b) If the soil is made completely saturated by adding water, what
would its moisture content be at that time? Also find the
saturated unit weight.
6) Determine the wet density, dry density, void ratio, water content
and degree of saturation for a sample of moist soil which has a
mass of 18.18 Kg and occupies a total volume of 0.009 m3. When
dried in an oven, the dry mass is 16.13 Kg. the specific gravity is
2.70.
Zagazig University
Faculty of Engineering
Structural Eng. Department
˻
Soil Mechanics (1)
7) An undisturbed cylindrical soil sample, with diameter 8.0 cm, and
height of 25.0 cm is taken from the borehole. The moist sample has
a mass of 2371.0 gm and after drying in an oven has a dry mass of
1948.0 gm. The specific gravity of the solid particles is 2.72.
Determine water content, bulk, dry, saturated and submerged unit
weight of soil, void ratio, porosity and degree of saturation.
8) A cylinder contains 500 cm3 of loose dry sand which weight 750
gm and under load of 20 t/m2, the original volume decreased by 3
% and then by vibration the volume decreased by 10 %, assume the
solid density of sand grains is 2.65 t/m3. compute the void ratio,
porosity, dry density corresponding to each of the following cases:
a) Loose sand (original state)
b) Under static load
c) Loaded and vibrated
9) A clayey soil has natural moisture content of 15.18 %. The specific
gravity of soil is 2.72. Its saturation percentage is 70.81 %. The soil
is allowed to absorb water. After some time the saturation increase
to 90.8 %. Find out the water content of the soil in the latter case.
10) A saturated 100 cm3 clay sample has a natural water content of 15
% . If the specific gravity of the soil solids is 2.7, what will be the
volume of the sample when the water content is 25 %.
11) A sample of moist quartz sand was obtained by carefully pressing a
sharpened cylinder with a volume of 150 cm3 into the bottom of an
excavation. The sample was trimmed flush with the end of the
cylinder and the total weight was found to be 325 gm. In the
laboratory the dry weight of the sand alone was found to be 240 gm
and the weight of the empty cylinder 75 gm. Laboratory testes on
the dry sand indicated emax = 0.80 and emim = 0.48. (Assuming Gs =
2.66). Calculate: Wc, e, Sr. Jd, and Dr
Chapter (1)
Physical properties
(1)
2011
Solution
1) A sample of soil obtained from a test pit is one cubic
foot in volume and weight 140 gm, after oven drying
the sample weight 125 gm. calculate the water
content, moist unit weight, dry unit weight.
Given:
Vt = 1 ft3
,
Wt = 140 gm
Wdry = Ws = 125 gm
Req.
Wc , Jd , Jb
a
1 ft3
w
15
140
S
125
Soil Mechanics (1)
Chapter (1)
2011
Wc
Jb
Jd
Physical properties
(2)
Ww
15
0 . 12 12 %
Ws
125
Wt
140
140 gm / ft 3
Wt
1
Ws
125
125 gm / ft 3
Vt
1
2) A 150 cubic centimeter sample of wet soil scales 250
gm when saturated and 162 gm when oven dried.
Calculate the dry unit weight, water content, void
ratio, specific gravity.
Given:
Vt = 150 cm3
,
Wt = 250 gm
Wdry = Ws = 162 gm
,
Req.
Jd , Wc , e , Gs
Soil Mechanics (1)
saturation
Chapter (1)
Physical properties
(3)
2011
88
w
88
150
250
62
S
162
Ws 162
1 . 08 gm / cm 3
Jd
150
Vt
88
Ww
0 . 54 54 %
Wc
162
Ws
Vv 88
1 . 42
e
62
Vs
J s 162 / 62
2 . 61
Gs
Jw
1
Soil Mechanics (1)
Chapter (1)
Physical properties
(4)
2011
3) Laboratory test on sample of saturated soil show that
the void ratio is 0.45 and the specific gravity is 2.65.
Determine the wet unit weight of the soil and its water
content
Given:
e = 0.45
,
Gs = 2.65
,
saturation
Req.
Jb , Wc
0.45
w
0.45
1.45
3.1
1
S
2.65
Assume Vs = 1.0
Soil Mechanics (1)
Chapter (1)
(5)
2011
Physical properties
Vv Vv
0 . 45 Ÿ Vv Vw
Vs
1
Wt
3 .1
2 . 14 gm / cm 3
Jb
Vt
1 . 45
Ww
0 . 45
Wc
0 . 17 17 %
Ws
2 . 65
e
0 . 45
4) The moisture content of an undisturbed sample of
clay existing in a volcanic region is 265 % at 100 %
of saturation. The specific gravity is 2.7. Find the
saturated and submerged densities.
Given:
Wc = 265 % , Gs = 2.7 , saturation
Req.
Jsat. , Jsub.
Assume Vs = 1.0
Soil Mechanics (1)
Chapter (1)
Physical properties
(6)
2011
7.15
w
7.15
8.15
9.85
1
Wc
J sat .
J sub .
S
2.7
Ww Ww
2 .65
Ÿ Ww 7 .15
Ws
2 .7
Wt 9 .85
1.21t / m 3
Vt 8 .15
J sat . J w 1.21 1 0.21t / m 3
5) For a soil in natural state, given e = 0.70, Wc = 22 %
and Gs =2.69. a) Determine the moist unit weight, dry
unit weight and degree of saturation. b) If the soil is
made completely saturated by adding water, what
would its moisture content be at that time? Also find
the saturated unit weight.
Soil Mechanics (1)
Chapter (1)
Physical properties
(7)
2011
Given:
e = 0.7 , wc = 22 %, Gs = 2.69
Req.
a)Jb JdSr
b) WcJsatsaturated state
a
0.7
w
0.59
0.59
8.15
9.85
S
1
Wc
e
0.22
Ww
Ws
Vv
Ÿ 0 .7
Vs
2.69
Ww
Ÿ Ww
2.69
Vv
Ÿ Vv
1 .0
Soil Mechanics (1)
0 .7
0 .59
Chapter (1)
2011
Jb
Jd
Physical properties
(8)
Wt
Vt
Ws
Vt
2.69 0 .59
1 .93
1 .7
2.69
1 .59
1 .7
Vw
Vv
0 .59
0 .7
Sr
0 .85
Saturated state
0.7
w
0.7
1.7
1
Wc
J sat .
Ww
Ws
Wt
Vt
S
2.69
0 .7
0 . 26
2 . 69
2 . 69 0 . 7
1 . 99 t / m 3
1 .7
Soil Mechanics (1)
Chapter (1)
Physical properties
(9)
2011
6) Determine the wet density, dry density, void ratio,
water content and degree of saturation for a sample of
moist soil which has a mass of 18.18 Kg and occupies
a total volume of 0.009 m3. When dried in an oven,
the dry mass is 16.13 Kg. the specific gravity is 2.70.
Sol.
w
5.9*10-3
0.009
2.05*10-3
3.1*10-3
a
Jb
Wt
Vt
18 .18
0 .009
2.05
18.18
S
16.13
2020 kg / m 3
Ϧϴϧ΍ϮϘϟ΍ ϰϓ ϖϴΒτΘϟ΍ ϢΘϳ ΍άϜϫ ϭ
Soil Mechanics (1)
Chapter (1)
Physical properties
(10)
2011
7) An undisturbed cylindrical soil sample, with diameter
8.0 cm, and height of 25.0 cm is taken from the
borehole. The moist sample has a mass of 2371.0 gm
and after drying in an oven has a dry mass of 1948.0
gm. The specific gravity of the solid particles is 2.72.
Determine water content, bulk, dry, saturated and
submerged unit weight of soil, void ratio, porosity and
degree of saturation.
Sol.
V
4
S
4
8 cm
(d ) 2 * h
(8 ) 2 * 25
8 cm
V
S
1256 cm 3
a
540
423
w
423
1256
2371
716
S
1948
Soil Mechanics (1)
Chapter (1)
Physical properties
(11)
2011
ϊΒθΘϟ΍ ΔϟΎΣ ϰϓ
540
w
540
1256
716
S
1948
Ϧϴϧ΍ϮϘϟ΍ ϰϓ ϖϴΒτΘϟ΍ ϦϜϤϳ
Ϟ΋ΎδϤϟ΍ ϲϗΎΑ
H.W.
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (2)
Grain Size Distribution
1
2011
Chapter (2)
Grain Size Distribution
ΕΎΒϴΒΤϠϟ ϰϤΠΤϟ΍ ϊϳίϮΘϟ΍
ϰϠϋ Ϟμϔϟ΍ ΔϘϳήσ ΪϤΘόΗ ϭ ϢΠΤϟ΍ ΐδΣ ΔΑήΘϟ΍ ΕΎϧϮϜϣ Ϟμϓ Ϯϫ
ΔΑήΘϟ΍ ωϮϧ
Coarse soil ΔϨθΧ ΔΑήΗ
Fine soil ΔϤϋΎϧ ΔΑήΗ
Sand , gravel
Silt , clay
Ϧϣ ήΒϛ΍ ΕΎΒϴΒΤϟ΍ ϢΠΣ
Ϧϣ ήϐλ΍ ΕΎΒϴΒΤϟ΍ ϢΠΣ
0.074 mm
0.074 mm
ΔϨθΨϟ΍ ΔΑήΘϟ΍ Ϟμϔϟ
ΔϤϋΎϨϟ΍ ΔΑήΘϟ΍ Ϟμϔϟ
Sieve analysis
=
Dry analysis
=
Mechanical analysis
Hydrometer analysis
=
Wet analysis
=
Sedimentation analysis
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
2
2011
1) Sieve analysis
ϞΧΎϨϤϟΎΑ ϞϴϠΤΘϟ΍
-:ίΎϬΠϟ΍
ϞΨϨϤϟ΍ ΔΤΘϓ ϞϘϳ
W1
W2
W3
W4
W5
W6
ί΍ΰϫ
-:ΔΑήΠΘϟ΍ Ε΍ϮτΧ
ΔϳϮΌϣ ΔΟέΩ ˺˺˹ ΪϨϋ ΔϋΎγ ˻˽ ΓΪϤϟ ϥήϔϟ΍ ϲϓ ΔΑήΘϟ΍ ϒϴϔΠΗ ϢΘϳ -˺
ΎϬϧίϭ ΔϔϔΠϤϟ΍ ΔΑήΘϟ΍ Ϧϣ ΔϨϴϋ άΧ΍ ϢΘϳ -˻
ςϟΰϟ΍ ΔϟΎΣ ϲϓ ϢΠϛ (˺˹-˾)
Ϟϣήϟ΍ ΔϟΎΣ ϲϓ ϢΠϛ (˺-˹̄˾)
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
3
2011
ϞΧΎϨϤϟ΍ ϰϠϋ΃ ΔϨϴόϟ΍ ϊοϭ -˼
ΔϘϴϗΩ ˺˾ ΓΪϤϟ ί΍ΰϬϟ΍ ϞϴϐθΗ -˽
ϞΨϨϣ Ϟϛ ϰϠϋ (ϊΟ΍ήϟ΍)ίϮΠΤϤϟ΍ ϥίϮϟ΍ ΪϳΪΤΗ ϢΘϳ -˾
ΕΎΑΎδΤϟ΍ ξόΑ ϞϤϋ ϭ ϝϭΪΟ ϦϳϮϜΘΑ ϡϮϘϧ -˿
( grading curve) ϲΒϴΒΤϟ΍ ΝέΪΘϟ΍ ϰϨΤϨϣ Ϣγέ ϢΘϳ -̀
A
Sieve size
(mm)
Wt. retained
ίϮΠΤϤϟ΍ ϥίϮϟ΍
50.8
38.1
19.05
9.52
4.76
2.38
2.0
1.19
0.595
0.42
0.297
0.21
0.14
0.074
0.063
W1
W2
W3
W4
W5
W6
W7
B = total
Commutative
Wt. retained
ϲϤϛ΍ήΘϟ΍
B
C
Wt. passing
% passing
έΎϤϟ΍ ϥίϮϟ΍
w1
w1+w2
W1+w2+w3
weight –A
C = (B / Total weight)*100
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
4
2011
(grading curve ) ϲΒϴΒΤϟ΍ ΝέΪΘϟ΍ ϰϨΤϨϣ Ϣγέ
:ϲϠϳ ΎϤϛ semi-log scale αΎϴϘϣ ϰϠϋ ϲΒϴΒΤϟ΍ ΝέΪΘϟ΍ ϰϨΤϨϣ Ϣγέ ϢΘϳ
( % passing ) ϲγ΃έ ήΧ΃ ϭ ( sieve size ) ϲϘϓ΃ έϮΤϣ Ϣγέ ϢΘϳ -˺
Ϣγ ˺ Ϟϛ ΔϳϭΎδΘϣ ΕΎϓΎδϣ ϰϟ· ϲγ΃ήϟ΍ έϮΤϤϟ΍ ϢϴδϘΗ -˻
% Passing
S = Ϣγ ˾-˼ Ϟϛ ΔϳϭΎδΘϣ ΕΎϓΎδϣ ϰϟ· ϲϘϓϷ΍ έϮΤϤϟ΍ ϢϴδϘΗ -˼
100
90
80
70
60
50
40
30
20
10
0
S = 3-5 cm
100
10
1
0.1
Seive Size
0.01
0.001
ΔϴγΎϴϗ ϞΧΎϨϣ ϦϛΎϣ΃
:ϲϠϳ ΎϤϛ ϲϘϓϷ΍ έϮΤϤϟ΍ ϰϠϋ ϞΧΎϨϤϟ΍ ϦϛΎϣ΃ ΪϳΪΤΗ -˽
ϞΨϨϤϟ΍ ΎϬϴϓ ϊϗ΍Ϯϟ΍ ΓήΘϔϟ΍ ΪϳΪΤΗ ήϴϐμϟ΍ ϞΨϨϤϟ΍ Ϧϣ x ΪόΑ ϰϠϋ ϞΨϨϤϟ΍ ϥΎϜϣ νήϔϧ -
X
S >log( D ) log( small ) @
ϪόϴϗϮΗ ΏϮϠτϤϟ΍ ϞΨϨϤϟ΍
Soil Mechanics (1)
-
Ϧϣ ήϴϐμϟ΍ ϞΨϨϤϟ΍
Chapter (2)
2011
Ex: sieve (26.7)
X
1 ήϴϐμϟ΍
10
3 . 0 >log( 4 . 75 ) log( 1) @
X
2 . 03 cm
0.01 ήϴϐμϟ΍
0.1
Sieve (0.074)
X
100
10 ήϴϐμϟ΍
3 . 0 >log( 26 . 7 ) log( 10 ) @ 1 . 3 cm
Sieve (4.75)
% Passing
Grain Size Distribution
5
3 . 0 >log( 0 . 074 ) log( 0 . 01 ) @
100
90
80
70
60
50
40
30
20
10
0
2 . 61 cm
XD10
D60
100
10
D30
1
0.1
Seive Size
D10
Soil Mechanics (1)
0.01
0.001
Chapter (2)
Grain Size Distribution
6
2011
ϰϠϋ ϝϮμΤϟ΍ ϦϜϤϳ ϰϨΤϨϤϟ΍ Ϧϣ
D 10 Ÿ
ΕΎΒϴΒΤϟ΍ Ϧϣ % ˺˹ ϩΪϨϋ ήϤϳ ϱάϟ΍ ήτϘϟ΍
D 30 Ÿ
ΕΎΒϴΒΤϟ΍ Ϧϣ % ˼˹ ϩΪϨϋ ήϤϳ ϱάϟ΍ ήτϘϟ΍
D 60 Ÿ
ΕΎΒϴΒΤϟ΍ Ϧϣ % ˿˹ ϩΪϨϋ ήϤϳ ϱάϟ΍ ήτϘϟ΍
D10
ΔϤϴϗ ϰϠϋ ϞμΤϧ ϒϴϛ
3 .0>log( D10 ) log( 0 .01) @
X D10
ήϴϐμϟ΍ ΔϬΟ Ϧϣ Ϣγήϟ΍ Ϧϣ ΓήτδϤϟΎΑ αΎϘΗ
D30
ΔϤϴϗ ϰϠϋ ϞμΤϧ ϒϴϛ
3 .0>log( D30 ) log( 0 .1) @
X D30
ήϴϐμϟ΍ ΔϬΟ Ϧϣ Ϣγήϟ΍ Ϧϣ ΓήτδϤϟΎΑ αΎϘΗ
D60
X D60
ΔϤϴϗ ϰϠϋ ϞμΤϧ ϒϴϛ
3 .0>log( D60 ) log(1) @
ήϴϐμϟ΍ ΔϬΟ Ϧϣ Ϣγήϟ΍ Ϧϣ ΓήτδϤϟΎΑ αΎϘΗ
ϲΒϴΒΤϟ΍ ΝέΪΘϟ΍ ϰϨΤϨϣ ϡ΍ΪΨΘγ΍
Uses of grading curve:
1) Uniform coefficient (Cu)
Cu
D 60
Ÿ
D10
ϡΎψΘϧϻ΍ ϞϣΎόϣ
ΔΑήΘϟ΍ ϒϴϨμΗ ϲϓ ϡΪΨΘδϳ
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
7
2011
(B.S.) ϱΰϴϠΠϧϹ΍ ϡΎψϨϟ΍
(ASTM) ϲϜϳήϣϷ΍ ϡΎψϨϟ΍
Uniform Non-uniform Well
5
Poor
15
Cc
Poor
3) Effective diameter (D10)
(sand)
4
(gravel)
ΔΑήΘϟ΍ ϒϴϨμΗ ϲϓ ϡΪΨΘδϳ
Well
1
6
˯ΎϨΤϧϻ΍ ϞϣΎόϣ
2) Curvature coefficient (Cc)
( D 30 ) 2
Ÿ
D 60 * D10
Well
Poor
3
˯ΎϨΤϧϻ΍ ϞϣΎόϣ
ΪϳΪΤΗ ϲϓ ϡΪΨΘδϳϭ ΕΎΒϴΒΤϟ΍ Ϧϣ % ˺˹ ϩΪϨϋ ήϤϳ ϱάϟ΍ ήτϘϟ΍
Hazen's formula ϝϼΧ Ϧϣ ϚϟΫϭ ( K ) ΔϳΫΎϔϨϟ΍ ϞϣΎόϣ
K
C * ( D10 ) 2
C = Constant (1-10)
C=1
ΔΑήΘϟ΍ ωϮϧ ϰϠϋ ΪϤΘόϳ
for sand
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
8
% passing
2011
2
4
1
3
Size
ΎΒϳήϘΗ ΪΣ΍ϭ αΎϘϣ ΎϬΑ ΔϨϴόϟ΍
1) Uniform:
2) Non-uniform:
Ϟϛ ΎϬΑ βϴϟϭ ΓΩΪόΘϣ ΕΎγΎϘϣ ΎϬΑ ΔϨϴόϟ΍
ΔϳϭΎδΘϣ ήϴϏ ΐδϨΑ ΕΎγΎϘϤϟ΍ Ϟϛ ΎϬΑ ϭ΃ ΕΎγΎϘϤϟ΍
3) Well graded:
(΍ΪΟ Γήϴϐλ ΎϬΗΎϏ΍ήϓ) ΕΎγΎϘϤϟ΍ Ϟϛ ΎϬΑ ΔϨϴόϟ΍
4) Gap graded:
ΔμϗΎϧ ΕΎγΎϘϤϟ΍ ξόΑ ΎϬΑ ΔϨϴόϟ΍
Note:
Poorly graded
Uniform
Non-Uniform
Gap graded
Soil Mechanics (1)
Chapter (2)
9
2011
1) Wet analysis (Hydrometer)
Grain Size Distribution
ήΘϣϭέΪϴϬϟ΍
-:ίΎϬΠϟ΍
Reading
Z
Bulb
Hydrometer
˼
Ϣγ˺˹˹˹ έΎΒΨϣ
-:ΔΑήΠΘϟ΍ Ε΍ϮτΧ
˯Ύϣ ϪΑ ˼ Ϣγ ˺˹˹˹ έΎΒΨϣ έΎπΣ· ϢΘϳ -˺
ϢΟ ˾˹ ΎϬϧίϭ ˻˹˹ Ϣϗέ ϞΨϨϤϟ΍ Ϧϣ ΓέΎϤϟ΍ ΔΑήΘϟ΍ Ϧϣ ΔϨϴϋ άΧ΍ ϢΘϳ -˻
ΙΪΤϳ ϥ΃ ϰϟ· ήϤΘδϤϟ΍ Νήϟ΍ ϊϣ έΎΒΨϤϟ΍ ϞΧ΍Ω ΔϨϴόϟ΍ ϊοϭ ϢΘϳ -˼
έΎΒΨϤϟ΍ ϞΧ΍Ω ΕΎΒϴΒΤϠϟ ϊϳίϮΗ
ΔϴϨϣί ΓήΘϓ Ϟϛ Ε΍˯΍ήϗ άΧ΍ ϭ έΎΒΨϤϟ΍ ϲϓ ήΘϣϭέΪϴϬϟ΍ ϊοϭ ϢΘϳ -˽
( 0.5,1,2,4,8,……..30 mim. , 1,2,4,8,…..24 hr )
ϲΒϴΒΤϟ΍ ΝέΪΘϟ΍ ϰϨΤϨϣ Ϣγέϭ ΕΎΑΎδΤϟ΍ ξόΑ ϞϤόΑ ϡϮϘϧ -˾
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
10
2011
Stock's law
Ϟ΋Ύδϟ΍ ϞΧ΍Ω Δϳή΋΍Ϊϟ΍ ΔΒϴΒΤϟ΍ ρϮϘγ Δϋήγ
ΔΒϴΒΤϟ΍ ήτϗ ϊΑήϣ ϊϣ ϱΩήσ ΐγΎϨΘΗ
V v D2
D
C * D2
Js Jw
C
18 P
V
V
ΚϴΣ
ΕΎΒϴΒΤϟ΍ Δϋήγ = V -˺
ΕΎΒϴΒΤϟ΍ ήτϗ = D -˻
ΔΒϠμϟ΍ ΕΎΒϴΒΤϟ΍ ΔϓΎΜϛ = Js -˼
Ϟ΋Ύδϟ΍ ΔΟϭΰϟ = P -˽
P ( poise )
981
V
Z
t
gm . sec . / cm 2
Js Jw
* D2 Ÿ D
18 P
ΔΒϴΒΤϟ΍ ρϮϘγ ΔϓΎδϣ = Z
ΔΒϴΒΤϟ΍ ρϮϘγ Ϧϣί = t
Soil Mechanics (1)
Chapter (2)
11
2011
Grain Size Distribution
( N ) έΎϤϟ΍ ΔΒδϧ ϰϠϋ ϞμΤϧ ϒϴϛ
At time zero
Wt
Vt
Ws
Vt
Ws
Vt
Ws
Vt
Ws
Vt
Ws
Vt
Ws
Vt
Ji
Ji
Ji
Ji
Ji
Ji
Ji
J initial
J ( time )
N
ΔΑήΠΘϟ΍ Δϳ΍ΪΑ ϲϓ
Ws Ww
Vt
Vw
Ww
Vt
Vs
J w * Vw
Vt
J w * (Vt Vs )
Vt
Vs
)
J w (1 Vt
Ws
)
J w (1 Vt * Gs * J w
Ws
Jw Vt * Gs
1
Ws
Jw (1 )Ÿ N
Vt
Gs
Ws
1
Jw N *
* (1 )
Vt
Gs
Wt . ˜ of ˜ particles D
Ws
Soil Mechanics (1)
w
Ww
S
Ws
Ws = Gs Jw Vs
Ww =Jw Vw
100 %
Chapter (2)
Grain Size Distribution
12
2011
ϥ΃ ΚϴΣ
Ws = ΔϨϴόϟ΍ ϥίϭ
% passing
Vt = (˼Ϣγ˺˹˹˹) έΎΒΨϤϟ΍ ϢΠΣ
Sieve analysis
Hydrometer analysis
Size
No. 200 = 0.074 mm
What the meaning of Cu = 1.0
Cu
D60
ŸŸ D60
D10
D10
ϲΒϴΒΤϟ΍ ΝέΪΘϟ΍ ϰϨΤϨϣ ϥ΃ ϚϟΫ ϰϨόϳ
ΔΑήΘϟ΍ ϥϮϜΗ ϲϟΎΘϟΎΑϭ ΎϣΎϤΗ ϲγ΃έ ϥϮϜϳ
very uniform soil
Soil Mechanics (1)
ϲΒϴΒΤϟ΍ ΝέΪΘϟ΍ ϰϨΤϨϣ
Soil Mechanics
(1)
Fff
Zagazig University
Structural Eng. Department
˺
Faculty of Engineering
Soil Mechanics (1)
Sheet No. (2)
Grain Size Distribution
1- a) discuss the difference between the following:
i)
Dry analysis and wet analysis.
ii) Well Graded and poorly graded.
b) Draw the grain size distribution curve for two soils A and B where
the total weight of the sample is 500 gm for each soil. Calculate, i)
uniformity coefficient of each soil and comment on the results,
ii) effective diameter of each sample.
Sieve opening, mm 4.78 2.41 1.20 0.6 0.3 0.15 0.075 pan
Wt. retained (A), gm ---- 72
91 75 182 15
55
10
Wt. retained (B), gm ---- ---4
8 201 52
227
8
2- A sieve analysis performed on two soils produced the following data.
Particle
size, mm
% finer
(A)
% finer
(B)
18.8 9.4 4.75 2.0 0.42 0.25 0.15 0.075 0.05 0.005 0.002
92
84
70
65
52
44
30
24
20
11
8
---
---
---
100
98
95
90
82
72
41
21
Mix the two soils in such proportions that resulting mixture which will
contain 26 % of 0.005 mm clay. Draw the grading curve for the mixture
and classify it.
3- Proof the general equation used to determine the drain size
distribution for fine soil particles by means of Hydrometer.
4- A soil sample consisting of particles of size 0.50 mm to 0.08 mm is
put on the surface of still water of a tank 5 m deep. Determine the time
Zagazig University
Faculty of Engineering
Structural Eng. Department
˻
Soil Mechanics (1)
required for the settlement of the coarsest and the finest particles of the
sample to the bottom of the tank. Take Gs = 2.68 andP = 0.01 poise.
5- During a sedimentation test for grain size analysis, the corrected
hydrometer reading in a 1000 ml uniform soil suspension at the
commencement of sedimentation is 1.028. after 30 minutes, the
corrected hydrometer reading is 1.012 and the corresponding effective
depth is 10.5 cm, determine:
i)
The total mass of solid dispersed in 1000 ml of suspension.
ii) The particle size corresponding to the 30 minutes reading.
iii) The percentage finer than this size, take Gs = 2.67
and P = 0.01 poise.
6- Particles of 5 different sizes are mixed in the proportions shown
below and enough water is added to make 1000 ml of the suspension.
The temperature of the suspension is 20o C.
Particle size (mm) 0.05 0.02 0.01 0.005 0.001
Weight (gm)
7
20 18
4
5
If it is insured that the suspension is mixed so as have a uniform
distribution of particles. All particles have a specific gravity of 2.7,
assume Jw = 1 gm/cm3, t = 20o C, P 0.01 poise.
i) What is the largest particles size present at a depth of 6 cm after
minutes of start sedimentation?
ii)What is the specific gravity of the suspension at a depth of 6 cm
after 5 minutes of start of sedimentation.
iii)How long should be the sedimentation be allowed so that all the
particles have settled below 6 cm.
Chapter (2)
Grain Size Distribution
(1)
2011
Sheet No. (2)
Grain Size Distribution
1) a) discuss the difference between the following:
i) Dry analysis and wet analysis.
Dry analysis wet analysis
Soil
Course soil
Fine soil
Size
> 0.075 mm <0.075 mm
Tools
sieves
Hydrometer
Example Sand, gravel Silt, clay
ii)
Well graded and poorly graded.
Well graded
Poorly graded
ΐδϨΑ ΕΎγΎϘϤϟ΍ Ϟϛ ΎϬΑ ΔϨϴόϟ΍
ΔϳϭΎδΘϣ
1) Uniform
ΎΒϳήϘΗ ΪΣ΍ϭ αΎϘϣ ΎϬΑ ΔϨϴόϟ΍
2) Non-uniform
Ϟϛ ΎϬΑ βϴϟϭ ΓΩΪόΘϣ ΕΎγΎϘϣ ΎϬΑ ΔϨϴόϟ΍
ΕΎγΎϘϤϟ΍
3) Gap graded
ΔμϗΎϧ ΕΎγΎϘϤϟ΍ ξόΑ ΎϬΑ ΔϨϴόϟ΍
Well
Cc
1
3
Poor
Poor
1
Soil Mechanics (1)
3
Cc
Chapter (2)
(2)
2011
Grain Size Distribution
b) Draw the grain size distribution curve for two soils
A and B where the total weight of the sample is 500
gm for each soil. Calculate, i) uniformity coefficient of
each soil and comment on the results, ii) effective
diameter of each sample.
Sieve opening, mm 4.78 2.41 1.20 0.6 0.3 0.15 0.075 pan
Wt. retained (A),gm ---- 72 91 75 182 15
55 10
Wt. retained (B),gm ---- ---- 4
8 201 52 227 8
Sol.
For Soil (A)
sieve
open
4.78
2.41
1.2
0.6
0.3
0.15
0.075
pan
Wt. retained
of (A)
------72
91
75
182
15
55
10
commulative
Wt. Ret.
-----72
163
238
420
435
490
500
Soil Mechanics (1)
Passing
%
Wt. passing
-----100
428
85.6
337
67.4
262
52.4
80
16
65
13
10
2
0
0
Chapter (2)
Grain Size Distribution
(3)
2011
For Soil (B)
Wt. retained of Commulative Passing
%
(B)
sieve open
Wt. Ret.
Wt. passing
4.78
----------------100
2.41
--------------100
1.2
4
4
496
99.2
0.6
8
12
488
97.6
0.3
201
213
287
57.4
0.15
52
265
235
47
0.075
227
492
8
1.6
pan
8
500
0
0
100
90
Soil A
80
Soil B
% Passing
70
60
50
40
30
20
10
0
10
1
0.1
sieve open
Soil Mechanics (1)
0.01
Chapter (2)
Grain Size Distribution
(4)
2011
For Soil (A)
D60 = 0.85
D10 = 0.15
Cu
D60
D10
0.85
0.15
5.67
(B.S.) ϱΰϴϠΠϧϹ΍ ϡΎψϨϟ΍
(ASTM) ϲϜϳήϣϷ΍ ϡΎψϨϟ΍
Uniform Non-uniform Well
5 5.67
Poor
5.67 6
15
Soil is Non-uniform
Well
(sand)
Soil is Poor
For Soil (B)
D60 = 0.31
D10 = 0.085
Cu
D60
D10
0.31
3.65
0.085
Soil is uniform
OR
Soil is Poor
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
(5)
2011
2)A sieve analysis performed on two soils produced the
following data.
Particle
26.7 18.8 9.4 4.75 2.0 0.42 0.25 0.15 0.075 0.05 0.005 0.002
size, mm
% finer
100 92 84 70 65 52
44
30
24
20
11
8
(A)
% finer
----- --- --- 100 98
95
90
82
72
41
21
(B)
Mix the two soils in such proportions that resulting mixture
which will contain 26 % of 0.005 mm clay. Draw the
grading curve for the mixture and classify it.
A˶
+
B˶
=
X
+
1-X
=
0.11
0.41
Mix˶
1
0.26
X * 0.11 + (1-X) * 0.41 = 1* 0.26
X = 0.5 ,
(1-X) = 0.5
ϥϮϜϳ ϦϜϟ ϭ mix ˰ϟ΍ ϝϭΪΟ ϦϳϮϜΗ ϢΘϳ
Mix. = 0.5 * A + 0.5 * B
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
(6)
2011
size, mm 26.7 18.8 9.4 4.75
2.0
0.42 0.25 0.15 0.075 0.05 0.005 0.002
% (A)
100
92
84
70
65
52
44
30
24
20
11
8
% (B)
---
---
---
---
100
98
95
90
82
72
41
21
Mix.
100
96
92
85
82.5
75
69.5
60
53
46
26
14.5
100
90
B
70
% Passing
A
Mix.
80
60
50
40
30
20
10
0
100
10
1
0.1
0.01
0.001
sieve open
3)Proof the general equation used to determine the drain size
distribution for fine soil particles by means of Hydrometer.
Ρήθϟ΍ Γήϛάϣ ϲϓ ΕΎΒΛϹ΍
Soil Mechanics (1)
Chapter (2)
Grain Size Distribution
(7)
2011
4) A soil sample consisting of particles of size 0.50 mm
to 0.08 mm is put on the surface of still water of a tank
5 m deep. Determine the time required for the settlement
of the coarsest and the finest particles of the sample to
the bottom of the tank. Take Gs = 2.68 andP = 0.01 poise.
Sol.
:φΣϻ
ϲϫ Ϧϴϧ΍Ϯϗ ΙϼΜΑ ΎϬϠΣ ϢΘϳ Ϟ΋ΎδϤϟ΍ Ϧϣ ωϮϨϟ΍ ΍άϫ
C * D2
J s J w
ŸŸ C
18P
Z
ŸŸ V
t
1) Ÿ V
2) Ÿ J i (t
3) Ÿ J t
0)
1 ·
Ws §
J w ¨1 ¸
Vt © Gs ¹
1 ·
N *Ws §
Jw ¨1 ¸
Vt © Gs ¹
ΐϴγήΘϟ΍ Δϳ΍ΪΑ commencement of sedimentation ϝΎϗ ΍Ϋ΍
t = 0.0
JL
Soil Mechanics (1)
Chapter (2)
2011
(8)
Soil Mechanics (1)
Grain Size Distribution
Chapter (2)
2011
(9)
Grain Size Distribution
5)During a sedimentation test for grain size analysis, the
corrected hydrometer reading in a 1000 ml uniform
soil suspension at the commencement of sedimentation
is 1.028. after 30 minutes, the corrected hydrometer
reading is 1.012 and the corresponding effective depth
is 10.5 cm, determine:
i) The total mass of solid dispersed in 1000 ml of
suspension.
ii)The particle size corresponding to the 30 minutes
reading.
iii) The percentage finer than this size,
take Gs = 2.67 and P = 0.01 poise.
Soil Mechanics (1)
Chapter (2)
2011
(10)
Soil Mechanics (1)
Grain Size Distribution
Chapter (2)
2011
(11)
Grain Size Distribution
6) Particles of 5 different sizes are mixed in the
proportions shown below and enough water is added to
make 1000 ml of the suspension. The temperature of the
suspension is 20o C.
Particle size (mm) 0.05 0.02 0.01 0.005 0.001
Weight (gm)
7
20 18
4
5
If it is insured that the suspension is mixed so as have a
uniform distribution of particles. All particles have a
specific gravity of 2.7, assume Jw = 1 gm/cm3, t = 20o C,
P ҏ0.01 poise.
i) What is the largest particles size present at a depth of 6
cm after 5 minutes of start sedimentation?
ii) What is the specific gravity of the suspension at a
depth of 6 cm after 5 minutes of start of sedimentation.
iii) How long should be the sedimentation be allowed so
that all the particles have settled below 6 cm.
Soil Mechanics (1)
Chapter (2)
2011
(12)
Soil Mechanics (1)
Grain Size Distribution
Chapter (2)
2011
(13)
Soil Mechanics (1)
Grain Size Distribution
Chapter (2)
2011
(14)
Soil Mechanics (1)
Grain Size Distribution
Soil Mechanics
(1)
Fff
Chapter (3)
Consistency of fine soil
1
2011
Chapter (3)
Consistency of fine soil
ΔϤϋΎϨϟ΍ ΔΑήΘϟ΍ ϡ΍Ϯϗ
ϞϜθΘϟ΍ ϰϠϋ (ΔϴϴϤτϟ΍ ϭ ΔϴϨϴτϟ΍) ΔϤϋΎϨϟ΍ ΔΑήΘϟ΍ ΓέΪϗ Ϧϋ ΓέΎΒϋ Ϯϫ
(ςϟΰϟ΍ϭ Ϟϣήϟ΍) ΔϨθΨϟ΍ ΔΑήΘϠϟ ϡΪΨΘδΗ ϻϭ
ϡ΍ϮϘϟ΍ ΩϭΪΣ
Atterberg limits (consistency limits):
ϩΎϴϤϟ΍ ϒϴϔΠΗ
a
a
w
w
w
S
S
S
S
w
S
ϩΎϴϣ ΔϓΎο·
Volume
Solid
State
Semisolid
state
S.L.
Plastic
state
P.L.
Liquid
state
L.L.
Soil Mechanics (1)
Wc
Chapter (3)
Consistency of fine soil
2
2011
1) Liquid limit: (L.L.)
ΔϟϮϴδϟ΍ ΪΣ
ϰϟ· ΔϠ΋Ύδϟ΍ ΔϟΎΤϟ΍ Ϧϣ ΔΑήΘϟ΍ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ΍ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
Ϟ΋΍Ϯδϟ΍ ϙϮϠγ ΔΑήΘϟ΍ ϚϠδΗ ϩΪϨϋ ϱάϟ΍ϭ βϜόϟ΍ ϭ΃ ΔϧΪϠϟ΍ ΔϟΎΤϟ΍
(Γήϴϐλ κϗ ΔϣϭΎϘϣ ΎϬϟ) ΔΟΰϠϟ΍
Casagrande's method:
Ϊϧ΍ήΟ΍ίΎϛ ΔϘϳήσ
Ϊϧ΍ήΟ΍ίΎϛ ίΎϬΟ
Ϊϧ΍ήΟ΍ίΎϛ ίΎϬΟ
Grooving tools ϖθϟ΍ Γ΍Ω΃
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
3
2011
:ΔϘϳήτϟ΍ Ε΍ϮτΧ
˽˹ Ϣϗέ ϞΨϨϤϟ΍ Ϧϣ ΓέΎϣ ΔϤϋΎϧ ΔΑήΗ Ϧϣ ΔϨϴϋ έΎπΣ· ϢΘϳ (˺
βϧΎΠΘϣ ςϴϠΧ ϦϳϮϜΘϟ ΪϴΠϟ΍ ΐϴϠϘΘϟ΍ ϊϣ ΔΑήΘϠϟ ˯ΎϤϟ΍ Ϧϣ ΔϴϤϛ ΔϓΎο· (˻
ΔϘΗϮΒϟ΍ ϲϓ Ϫόοϭϭ ςϴϠΨϟ΍ Ϧϣ ˯ΰΟ άΧ΍ (˼
ϲϟϮσ ϖη ϞϤϋ ϢΘϳ ϖθϟ΍ Γ΍Ω΃ ϡ΍ΪΨΘγΎΑ (˽
ϖθϟ΍ Ϧϣ Ϣϣ ˺˼ ϖϠϐϟ Δϣίϼϟ΍ ΕΎΑήπϟ΍ ΩΪϋ ΪϳΪΤΗ ϭ ίΎϬΠϟ΍ ϞϴϐθΗ (˾
ϯήΧ΃ ϩΎϴϣ ΔϴϤϛ ϡ΍ΪΨΘγ΍ ϊϣ ΔϘΑΎδϟ΍ Ε΍ϮτΨϟ΍ βϔϧ έ΍ήϜΗ ϢΘϳ (˿
Wc
N
ΕΎΑήπϟ΍ ΩΪϋ ϭ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ ϦϴΑ Δϗϼόϟ΍ Ϣγέ (̀
liquid limit ϰϠϋ ϝϮμΤϠϟ
Wc
L.L.
Flow line
Log. (N)
N = 25
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
4
2011
Liquid limit: (L.L.)
ΔϟϮϴδϟ΍ ΪΣ
ϰѧϟ· ΔϠ΋Ύѧδϟ΍ ΔѧϟΎΤϟ΍ Ϧѧϣ ΔѧΑήΘϟ΍ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ΍ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
Ϟ΋΍Ϯѧѧδϟ΍ ϙϮϠѧѧγ ΔѧѧΑήΘϟ΍ ϚϠѧѧδΗ ϩΪѧѧϨϋ ϱάѧѧϟ΍ϭ βѧѧϜόϟ΍ ϭ΃ ΔѧѧϧΪϠϟ΍ ΔѧѧϟΎΤϟ΍
ϖѧѧη ϖѧѧϠϏ ϦѧѧϜϤϳ ϩΪѧѧϨϋ ϱάѧѧϟ΍ ϭ (Γήϴϐѧѧλ κѧѧϗ ΔѧѧϣϭΎϘϣ ΎѧѧϬϟ ) ΔѧѧΟΰϠϟ΍
Ϊϧ΍ήΟ΍ίΎϛ ΔϘϳήσ ϝϼΧ Ϧϣ ϚϟΫϭ ΔΑήο ˻˾ ϡ΍ΪΨΘγΎΑ Ϣϣ ˺˼ ϪϟϮσ
2) Plastic limit: (P.L.)
ΔϧϭΪϠϟ΍ ΪΣ
ϰϟ· ΔϧΪϠϟ΍ ΔϟΎΤϟ΍ Ϧϣ ΔΑήΘϟ΍ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ΍ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
ΔΒϠμϟ΍ ΔΒη ΔϟΎΤϟ΍
:ΔϘϳήτϟ΍ Ε΍ϮτΧ
˽˹ Ϣϗέ ϞΨϨϤϟ΍ Ϧϣ ΓέΎϣ ΔϤϋΎϧ ΔΑήΗ Ϧϣ ΔϨϴϋ έΎπΣ· ϢΘϳ (˺
βϧΎΠΘϣ ςϴϠΧ ϦϳϮϜΘϟ ΪϴΠϟ΍ ΐϴϠϘΘϟ΍ ϊϣ ΔΑήΘϠϟ ˯ΎϤϟ΍ Ϧϣ ΔϴϤϛ ΔϓΎο· (˻
Soil Mechanics (1)
Chapter (3)
5
2011
Consistency of fine soil
ϕΰϤΘϳ ϥ΃ ϥϭΪΑ ςϴΧ ϦϳϮϜΗ ΔϟϭΎΤϣϭ ςϴϠΨϟ΍ Ϧϣ ˯ΰΟ άΧ΍ (˼
ϕΰϤΘϟ΍ Δϳ΍ΪΑ ΪϨϋ ςϴΨϟ΍ ήτϗ ΪϳΪΤΗ (˽
ϯήΧ΃ ϩΎϴϣ ΔϴϤϛ ϡ΍ΪΨΘγ΍ ϊϣ ΔϘΑΎδϟ΍ Ε΍ϮτΨϟ΍ βϔϧ έ΍ήϜΗ ϢΘϳ (˾
Wc
d
ςϴΨϟ΍ ήτϗ ϭ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ ϦϴΑ Δϗϼόϟ΍ Ϣγέ (˿
Wc
Plastic limit ϰϠϋ ϝϮμΤϠϟ
P.L.
d
d = 3 mm
Plastic limit: (P.L.)
ΔϧϭΪϠϟ΍ ΪΣ
ΔѧϟΎΤϟ΍ ϰѧϟ· ΔѧϧΪϠϟ΍ ΔѧϟΎΤϟ΍ Ϧѧϣ ΔѧΑήΘϟ΍ ϝϮѧΤΘΗ ϩΪѧϨϋ ϱάѧϟ΍ ϲ΋ΎѧϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
ϕΰϤΗ ΙϭΪΣ ϥϭΩ Ϣϣ ˼ ϩήτϗ ςϴΧ ϦϳϮϜΗ ϦϜϤϳ ϩΪϨϋ ϱάϟ΍ϭ ΔΒϠμϟ΍ ΔΒη
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
6
2011
εΎϤϜϧϻ΍ ΪΣ
3) Shrinkage limit: (S.L.)
ϰѧϟ· ΔΒϠѧμϟ΍ ΔΒѧη ΔѧϟΎΤϟ΍ Ϧѧϣ ΔѧΑήΘϟ΍ ϝϮѧΤΘΗ ϩΪѧϨϋ ϱάѧϟ΍ ϲ΋ΎѧϤϟ΍ ϯϮѧΘΤϤϟ΍ Ϯϫ
ϱϭΎѧѧδϣ εΎѧѧϤϜϧϻ΍ ΔѧѧϟΎΣ ϲѧѧϓ ˯ΎѧѧϤϟ΍ ϢѧѧΠΣ ϥϮѧѧϜϳ ϩΪѧѧϨϋ ϱάѧѧϟ΍ϭ ΔΒϠѧѧμϟ΍ ΔѧѧϟΎΤϟ΍
.ΔϓΎΠϟ΍ ΔϟΎΤϟ΍ ϲϓ ˯΍ϮϬϟ΍ ϢΠΤϟ
a
w
S
S
dry
S.L.
Va( dry ) Vw( S .L.)
Classify of the soil:
(L.L. & P.L. & S.L.)ϡ΍ΪΨΘγΎΑ ΔΑήΘϟ΍ ϒϴϨμΗ
1) Plasticity index ( IP )
ΔϧϭΪϠϟ΍ ήηΆϣ
ΔϧϭΪϠΑ ϪϟϼΧ ΔΑήΘϟ΍ ϑήμΘΗ ϱάϟ΍ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
Ip
L.L. P.L.
Ip
plasticity
soil
0
Non-plastic
Sand
<7
7-17
>17
Low plastic
Med. Plastic
High plastic
Silt
Silty - clay
clay
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
7
2011
2) Consistency index ( Ic )
ϡ΍ϮϘϟ΍ ήηΆϣ
(Relative plasticity)
ϲόϴΒτϟ΍ ΔΑϮσήϟ΍ ϯϮΘΤϣ ϭ ΔϟϮϴδϟ΍ ΪΣ ϦϴΑ ϕήϔϟ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
ΔϧϭΪϠϟ΍ ήηΆϣ ϰϟ·
Ic
L.L. Wc
Ip
L.L. Wc
L. L P . L.
Ic
Soil type
0
Very soft
0-0.25
Soft
0.26-0.5
Med. Stiff
0.51-0.75
Stiff
0.76-1.0
Very stiff
>1.0
Extremely stiff
3) Liquidity index ( IL )
ΔϟϮϴδϟ΍ ήηΆϣ
ϰϟ· ΔϧϭΪϠϟ΍ ΪΣ ϭ ϲόϴΒτϟ΍ ΔΑϮσήϟ΍ ϯϮΘΤϣ ϦϴΑ ϕήϔϟ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
ΔϧϭΪϠϟ΍ ήηΆϣ
IL
IL
Wc P.L.
Ip
1 Ic
Wc P.L.
L. L P . L.
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
8
2011
4) Flow index ( If )
ϥΎϳήδϟ΍ ήηΆϣ
( flow line ) ϥΎϳήδϟ΍ ςΧ Ϟϴϣ Ϧϋ ΓέΎΒϋ Ϯϫ
Wc
L.L.
Flow line
Log. (N)
N = 25
Wc1 Wc 2
log( N 2 ) log( N1 )
If
5) Toughness index ( It )
ΔϧΎΘϤϟ΍ ήηΆϣ
ϥΎϳήδϟ΍ ήηΆϣ ϰϟ· ΔϧϭΪϠϟ΍ ήηΆϣ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
It
Ip
If
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
9
2011
6) Activity of clay ( Ac )
Ϧϴτϟ΍ ρΎθϧ
ΔϴϨϴτϟ΍ ΔΑήΘϠϟ ϰϤΠΤϟ΍ ήϴϐΘϟ΍ ϯΪϣ ΪϳΪΤΘϟ ήηΆϣ Ϯϫ
ϢΠΤϟ΍ ϰϓ ΓΩΎϳί
Collapse soil
ϢΠΤϟ΍ ϰϓ κϘϧ
Ip
% fines 0 . 002 mm
mm 0.002 Ϧϣ ϞϗϷ΍ ϢϋΎϨϟ΍ ΔΒδϧ
% passing
Ac
Swelling soil
% fines
Size
0.002
Ac
< 0.75
0.75-1.4
>1.4
activity
In-active
Med. active
active
Soil Mechanics (1)
Chapter (3)
10
2011
Consistency of fine soil
7) Unconfined compression strength ( qu )
(ςϘϓ ϦϴτϠϟ ) ρΎΤϣ ήϴϐϟ΍ ςϐπϟ΍ ΔϣϭΎϘϣ
(L/D = 2) Ϧϴτϟ΍ Ϧϣ ΔϨϴϋ έΎπΣ· ϢΘϳ
P
'L
P
A
' L
L
V
V
H
qu
H
qu
Clay type
0 - 0.25
Very soft clay
0.25 - 0.5
Soft clay
0.5 - 1
Med. clay
1-2
Stiff clay
2-4
Very stiff clay
>4
Hard clay
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
11
2011
8) Sensitivity of clay ( ˳St )
Ϧϴτϟ΍ ΔϴγΎδΣ
Ϧϣ undisturbed ϪϫϮθϣ ήϴϏ ΔϨϴόϟ ρΎΤϣ ήϴϐϟ΍ ςϐπϟ΍ ΩΎϬΟ· ϦϴΑ ΔΒδϨϟ΍ ϲϫ
ϞϴϜθΗ ΓΩΎϋ· ΎϬϟ ΙΪΣ Ϧϴτϟ΍ Ϧϣ ΔϨϴόϟ ρΎΤϣ ήϴϐϟ΍ ςϐπϟ΍ ΩΎϬΟ· ϰϟ· Ϧϴτϟ΍
remolded
qu (undisturbe d )
qu ( remolded )
St
St
sensitivity
<1
Insensitive
1–2
Low sensitive
2–4
Med. sensitive
4–8
sensitive
8 – 16
Very sensitive
> 16
Extra sensitive
Quick clay ϰϤδϳ (St > 16) Ϫϟ ϱάϟ΍ Ϧϴτϟ΍
9) Degree of shrinkage ( ˳D.O.S. )
εΎϤϜϧϻ΍ ΔΟέΩ
ΔΑήΘϠϟ ϲϠλϷ΍ ϢΠΤϟ΍ ϰϟ· ϢΠΤϟ΍ ϲϓ ήϴϐΘϟ΍ έ΍ΪϘϣ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
D.O.S
Vo Vdry
Vo
'V
Vo
ϲϠλϷ΍ ϢΠΤϟ΍ =
Vo
ϑΎΠϟ΍ ϢΠΤϟ΍ = Vdry
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Zagazig University
Structural Eng. Department
Faculty of Engineering
˺
Soil Mechanics (1)
Sheet No. (3)
Soil Consistency
1- A) Define: liquid limit, plastic limit, shrinkage limit, plasticity index.
B) the liquid an plastic limits of a soil are 87 % and 35 %
respectively, natural water content is 43%. Find the liquidity index
and draw the relation between the water content and liquidity index
for this soil for water content ranging between the plastic and the
liquid limits.
2- The following index properties were determined for two soils A & B
Property
Soil (A)
Soil (B)
L.L
0.62
0.34
P.L
0.26
0.19
Wc
38 %
25 %
Gs
2.72
2.67
Sr
1.0
1.0
From the above table, determine which of these soils:
1) contains more clay particles
2) Has a greater wet density
3) Has a greater dry density
4) Has a greater void ratio
3- The liquid limit, water content and the plastic limit of clay soil were
determined in the laboratory as follows. Find consistency index &
liquidity index for each soil:
Zagazig University
Structural Eng. Department
˻
Faculty of Engineering
Soil Mechanics (1)
Soil
L.L %
Wc %
P.L %
A
15
12
10
B
78
34
28
C
55
40
35
D
41
35
31
4- For the given data determine the liquid limit of a given sample of silt:
Moist wt. of sample
7.49
6.41
8.606
7.72
Dry wt. of sample
6.15
5.235
7.006
6.27
Number of blows
40
34
24
20
Determine also the flow and toughness indexes of this soil.
5- Sample of clay soil has a liquid limit of 62 % and its plasticity index
is 32 %
a) what is the degree of stiffness of this soil if the natural water
content is 34 %
b) calculate the shrinkage limit if the void ratio of the sample at its
shrinkage limit is 70 % , Gs = 2.70
6- Sample of clay weight 34.8 gm at its liquid limit. After drying the
clay, its weight is 19.4 gm and its volume is 10 cm3. if the Gs = 2.7 of
clay determine its L.L and S.L.
Chapter (3)
Soil Consistency
(1)
2011
Sheet No. (3)
Soil Consistency
1- A) Define: liquid limit, plastic limit, shrinkage limit,
plasticity index.
Liquid limit: (L.L.)
ΔϟϮϴδϟ΍ ΪΣ
ΔϧΪϠϟ΍ ΔϟΎΤϟ΍ ϰϟ· ΔϠ΋Ύδϟ΍ ΔϟΎΤϟ΍ Ϧϣ ΔΑήΘϟ΍ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ΍ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
κѧϗ ΔѧϣϭΎϘϣ ΎѧϬϟ ) ΔѧΟΰϠϟ΍ Ϟ΋΍Ϯѧδϟ΍ ϙϮϠѧγ ΔΑήΘϟ΍ ϚϠδΗ ϩΪϨϋ ϱάϟ΍ϭ βϜόϟ΍ ϭ΃
ϚѧϟΫϭ ΔΑήѧο ˻˾ ϡ΍ΪΨΘѧγΎΑ Ϣϣ ˺˼ ϪϟϮσ ϖη ϖϠϏ ϦϜϤϳ ϩΪϨϋ ϱάϟ΍ ϭ (Γήϴϐλ
Ϊϧ΍ήΟ΍ίΎϛ ΔϘϳήσ ϝϼΧ Ϧϣ
Plastic limit: (P.L.)
ΔϧϭΪϠϟ΍ ΪΣ
ΔΒѧη ΔѧϟΎΤϟ΍ ϰѧϟ· ΔѧϧΪϠϟ΍ ΔѧϟΎΤϟ΍ Ϧѧϣ ΔѧΑήΘϟ΍ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ΍ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
ϕΰϤΗ ΙϭΪΣ ϥϭΩ Ϣϣ ˼ ϩήτϗ ςϴΧ ϦϳϮϜΗ ϦϜϤϳ ϩΪϨϋ ϱάϟ΍ϭ ΔΒϠμϟ΍
Shrinkage limit: (S.L.)
εΎϤϜϧϻ΍ ΪΣ
ΔѧϟΎΤϟ΍ ϰѧϟ· ΔΒϠѧμϟ΍ ΔΒη ΔϟΎΤϟ΍ Ϧϣ ΔΑήΘϟ΍ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ΍ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ Ϯϫ
˯΍ϮѧϬϟ΍ ϢѧΠΤϟ ϱϭΎѧδϣ εΎѧϤϜϧϻ΍ ΔѧϟΎΣ ϲѧϓ ˯ΎϤϟ΍ ϢΠΣ ϥϮϜϳ ϩΪϨϋ ϱάϟ΍ϭ ΔΒϠμϟ΍
.ΔϓΎΠϟ΍ ΔϟΎΤϟ΍ ϲϓ
a
w
S
S
dry
S.L.
Va( dry ) Vw( S .L.)
Soil Mechanics (1)
Chapter (3)
Soil Consistency
(2)
2011
Plasticity index ( IP )
ΔϧϭΪϠϟ΍ ήηΆϣ
ϲѧѧϓ ϡΪΨΘѧѧδϳ ϱάѧѧϟ΍ ϭ ΔѧѧϧϭΪϠΑ ϪѧѧϟϼΧ ΔѧѧΑήΘϟ΍ ϑήѧѧμΘΗ ϱάѧѧϟ΍ ϲ΋ΎѧѧϤϟ΍ ϯϮѧѧΘΤϤϟ΍ Ϯѧѧϫ
ΔΑήΘϟ΍ ϒϴϨμΗ
L.L. P.L.
Ip
B) the liquid an plastic limits of a soil are 87 % and 35 %
respectively, natural water content is 43%. Find the
liquidity index and draw the relation between the water
content and liquidity index for this soil for water
content ranging between the plastic and the liquid
limits.
given
L.L = 87 %
P.L = 35 %
Wc = 43 %
Req.
1) IL
2) Draw relation (Wc, IL)
IL
Wc P.L.
Ip
Wc = 35
43 35
87 35
Soil Mechanics (1)
87
0 .15
Chapter (3)
Soil Consistency
(3)
2011
IL
1.0
0.15
Wc˱
43
87
2- The following index properties were determined for two
soils A & B
Property
Soil (A)
Soil (B)
L.L
0.62
0.34
P.L
0.26
0.19
Wc
38 %
25 %
Gs
2.72
2.67
Sr
1.0
1.0
From the above table, determine which of these soils:
1)Which soil contains more clay particles
2) Has a greater wet density
3) Has a greater dry density
4) Has a greater void ratio
Soil Mechanics (1)
Chapter (3)
Soil Consistency
(4)
2011
1) Which soil contains more clay particles
ήΜϛ΃ clay ϰϠϋ ϱϮΘΤΗ ήΒϛ΍ IP ΎϬϟ ϲΘϟ΍ ΔΑήΘϟ΍
For soil (A)
Ip
Ip
L.L. P .L.
0 .62 0 .26
0 .36
0 .34 0 .19
0 .15
For soil (B)
Ip
Soil (A) has more clay
1.03
w
1.03
0.67
w
0.67
1
S
2.72
1
S
2.67
Soil (A)
Soil (B)
ήΒϛ΍ Ϧϣ ΩΪΤϧ ϭ ΔΑήΗ ϞϜϟ JbJde ΏΎδΣ ϢΘϳ
Soil Mechanics (1)
Chapter (3)
Soil Consistency
(5)
2011
3- The liquid limit, water content and the plastic limit of
clay soil were determined in the laboratory as follows.
Find consistency index & liquidity index for each soil:
Soil
L.L %
Wc %
P.L %
A
15
12
10
B
78
34
28
C
55
40
35
D
41
35
31
For soil (A)
Ic
IL
L.L Wc . 15 12
15 10
Ip
1 Ic 0 .4
0 .6
For soil (B)
Ic
IL
L.L Wc . 78 34
Ip
78 28
1 Ic 0 .12
0 .88
For soil (C)
Ic
IL
L.L Wc . 55 40
Ip
55 35
1 Ic 0 .25
0 .75
Soil Mechanics (1)
Chapter (3)
Soil Consistency
(6)
2011
4- For the given data determine the liquid limit of a given
sample of silt:
Moist wt. of sample
7.49
6.41
8.606
7.72
Dry wt. of sample
6.15
5.235
7.006
6.27
Number of blows
40
34
24
20
Determine also the flow and toughness indexes of this
soil.
Sol.
Wc
Ww
Ws
Wt( moist ) Wt( dry )
Wt( dry )
Wc, %
21.8
22.5
22.8
23.2
Number of blows
40
34
24
20
24.0
23.5
To scale
23.0
22.5
22.0
21.5
21.0
100
25
Soil Mechanics (1)
10
Chapter (3)
Soil Consistency
(7)
2011
L.L = 22.8 %
Wc1 Wc 2
If
Log ( N 1 ) Log ( N 2 )
If
0.228 0.218
Log ( 40 ) Log ( 24 )
IT
Ip
If
0.045
5- Sample of clay soil has a liquid limit of 62 % and its
plasticity index is 32 %
a) what is the degree of stiffness of this soil if the
natural water content is 34 %
b) calculate the shrinkage limit if the void ratio of the
sample at its shrinkage limit is 70 % , Gs = 2.70
a)
Ic
LL Wc
LL Pl
62 34
32
0.875
b) e = 70 %
Gs = 2.7
Soil Mechanics (1)
Chapter (3)
Soil Consistency
(8)
2011
Vv
e
Vs
assume
Vs
1
Vv
0.7
w
0.7
1
S
2.7
0 .7
Ww
Ws
SL
0 .7
2 .7
SL
φϔΣ
0 . 26
e
Gs
φΣϻ
φϔΣ
6- Sample of clay weight 34.8 gm at its liquid limit. After
drying the clay, its weight is 19.4 gm and its volume is 10
cm3. if the Gs = 2.7 of clay determine its L.L and S.L.
Given
L.L
Wt = 34.8 gm
S.L
Ws = 19.4 gm
Vt = 10 cm3
Req.
L.L, P.L
Soil Mechanics (1)
Gs = 2.7
Chapter (3)
Soil Consistency
(9)
2011
S.L
L.L
15.4
7.18
S
Ww
SL
Ws
15 .4
S .L
19 .4
19.4
79 .4
2.8
w
2.8
7.18
S
19.4
10
w
34.8
15.4
Ww
SL
Ws
2 .8
S .L
19 .4
Soil Mechanics (1)
14 .5
Soil Mechanics
(1)
Fff
Chapter (4)
Soil Classification
(1)
2011
Chapter (4)
Soil Classification
ΔΑήΘϟ΍ ϒϴϨμΗ
βѧѧϔϧ ΎѧѧϬϟ ϲѧѧΘϟ΍ ΔѧѧϋϮϤΠϤϟ΍ ϊѧѧϣ ΔѧѧΑήΗ Ϟѧѧϛ ϊѧѧοϭ Ϯѧѧϫ ΔѧѧΑήΘϟ΍ ϒϴϨѧѧμΗ
ϦϴѧϤΘϬϤϟ΍ ϦϴΑ ϰϟϭϷ΍ ΐσΎΨΘϟ΍ Δϐϟ ϲϬϓ ϲγΪϨϬϟ΍ ϙϮϠδϟ΍ ϭ ι΍ϮΨϟ΍
.ΔΑήΘϟ΍ ΎϜϴϧΎϜϴϣ ϢϠόΑ
:ϲϫ ϒϴϨμΘϠϟ ϕήσ ΓΪϋ ΪΟϮϳϭ
1- Particle size classification (M.I.T. classification)
2- Textural classification
3- Unified soil classification system (U.S.C.S)
4- American Association of Highway and Transportation
Officials (AASHTO)
1) Particle size classification (M.I.T. classification)
ΎϬϧϮϛ ΚϴΣ Ϧϣ ΔΑήΘϟ΍ ωϮϧ ΪϳΪΤΘϟ ΕΎΒϴΒΤϟ΍ ϢΠΣ ϰϠϋ ϒϴϨμΘϟ΍ ΍άϫ ΪϤΘόϳ
-:ϲϠϳ
ΎϤϛ ΝέΪΘϣ αΎϴϘϣ ϝϼΧ Ϧϣ ϚϟΫϭ Ϧϴσ -ϲϤσ – Ϟϣέ – ςϟί
Soil Mechanics (1)
Chapter (4)
Soil Classification
(2)
2011
ΐδϧ ΪϳΪΤΗ ϦϜϤϳ ϱήΧ΃ϭ ΔΑήΗ ϦϴΑ Ϟμϔϳ ϱάϟ΍ Ϣϗήϟ΍ ΔϓήόϤΑ
% of gravel
ςϟΰϟ΍ ΔΒδϧ
% of sand
Ϟϣήϟ΍ ΔΒδϧ
% of silt
ϲϤτϟ΍ ΔΒδϧ
% of clay
Ϧϴτϟ΍ ΔΒδϧ
100
P3
P2
P1
0.0
2 mm
0.06 mm
0.002 mm
% of gravel = 100 - P3
% of sand = P3 - P2
% of silt = P2 – P1
% of clay = P1
Soil Mechanics (1)
Chapter (4)
(3)
2011
Soil Classification
2) Textural classification:ΐδϧ ϦϴΑ ςΑήϳ ΚϠΜϣ ϞϜη ϰϠϋ ϊοϭ ϪϧϷ ΚϠΜϤϟ΍ ϒϴϨμΘΑ ϡΎψϨϟ΍ ΍άϫ ϰϤδϳ
.ϲϠϳ ΎϤϛ ΔΑήΘϟ΍ ΕΎϧϮϜϣ Ϧϣ ϥϮϜϣ Ϟϛ ΩϮΟϭ ΔΒδϧ ϰϠϋ ΍ΪϤΘόϣ ΔΑήΘϟ΍ ΕΎϧϮϜϣ
Ex:
% of sand = 20 %
% of clay = 60 %
The soil is Clay
% of silt = 20 %
Ex:
% of gravel = 7 %
% of sand = 25 %
% of clay = 25 %
ςϟΰϟ΍ ΔΒδϧ ΩΎόΒΘγ΍ ΪόΑ ΔϟΪόϣ ΐδϧ ΏΎδΣ Ϧϣ ΪΑϻ
% of silt = 43 %
Soil Mechanics (1)
Chapter (4)
2011
% sand
% silt
% clay
Soil Classification
(4)
25
* 100 26 . 9 %
93
43
* 100 46 . 2 %
93
25
26 . 9 %
93
The soil is
Sand-silt-clay
ϲϟΎΘϟ΍ ϝϭΪΠϟ΍ ϡΪΨΘδϧ ΔΑήΘϟ΍ Ϣγ΍ ϲϓ ςϟΰϟ΍ ήϴΛ΄Η ϞΧΪϧ ϰΘΣ ϭ
The soil is
Sand-silt-clay
% (˺˾-˾) ςϟΰϟ΍ ξόΑ ΎϬΑ
3) Unified soil classification system (U.S.C.S)
Γήϴϐλ ϝΎϤΣϷ ΔοήόϤϟ΍ ΔΑήΘϟ΍ ϒϴϨμΘϟ ϡΪΨΘδϳ ΔѧΑήΘϟ΍ ωϮѧϨϟ ΓΰѧϴϤϤϟ΍ ίϮѧϣήϟ΍ ξόΑ ϰϠϋ ΍ΪϤΘόϣ ϒϴϨμΘϟ΍ ϢΘϳ :ϲϠϳ ΎϤϛ ϲϫ ϭ
-G
-S
Gravel
Sand
-O
- Pt
Organic soil
Peat
Soil Mechanics (1)
Chapter (4)
2011
-M
-C
-H
-L
-I
Soil Classification
(5)
Silt
-W
Well graded
Clay
-P
Poor graded
High plasticity
Low plasticity
Medium plasticity
:ϲϠϳ ΎϤϴϓ ϩέΎμΘΧ΍ ϦϜϤϳ ϝϭΪΟ ϝϼΧ Ϧϣ ϒϴϨμΘϟ΍ ϢΘϳ % passing # 200 = 0.074 mm
% passing # 200 > 50 %
% passing # 200 < 50 %
Fine soil (clay or silt)
Coarse soil (gravel or sand)
Plasticity chart (A-line)
% passing # 4.0 = 4.75 mm
Cassagrand chart
% passing # 4.0 > 50 %
Sand
Soil Mechanics (1)
% passing # 4.0 < 50 %
Gravel
Chapter (4)
(6)
2011
Soil Classification
ϕήΤϟΎΑ ϭ΃ ΔΤ΋΍ήϟΎΑ ϭ΃ ήμΒϟΎΑ ΎϬμΤϓ ϢΘϳ ϪϧΎϓ ( peat ) ϢΤϔϠϟ ΔΒδϨϟΎΑ
Plasticity chart (A-line)
(Cassagrand chart)
Clay
IP
Silt
35 %
50 %
Soil Mechanics (1)
L.L
Chapter (4)
Soil Classification
(7)
2011
4- (AASHTO) ϮΘη΃
AASHTO
Coarse Soil
A-1
A-3
A-2
Fine Soil
A-4 A-5 A-6 A-7
A-1-a A-1-b
A-7-5 A-7-6
A-2-4 A-2-5 A-2-6 A-2-7
A-1-a
ΔѧπϔΨϨϣ ΔϤϋΎϨϟ΍ Ω΍ϮϤϟ΍ Ϧϣ ΔτϴδΑ ΔΒδϧ ϲϠϋ ϱϮΘΤΗ ΝέΪΘϟ΍ ΓΪϴΟ ςϟί Ϧϋ ΓέΎΒϋ
ΔϧϭΪϠϟ΍
A-1- b
ΓΪϴΟ ΔΑήΗ ήΒΘόΗ ϦθΧ Ϟϣέ Ϧϋ ΓέΎΒϋ
A- 3
ϲϫϭ clay ϭ΃ silt ϲϠϋ ϱϮΘΤϳ ϻ ΕΎΒϴΒΤϟ΍ ΏέΎϘΘϣ ϢϋΎϧ Ϟϣέ Ϧϋ ΓέΎΒϋ
ΔϧϭΪϠϟ΍ ΔϤϳΪϋ ΔΑήΗ
Soil Mechanics (1)
Chapter (4)
2011
Soil Classification
(8)
A- 2
ΔΒѧδϧ ΎѧϬϟ ϲѧΘϟ΍ϭ ΔѧϤϋΎϧ Ω΍Ϯѧϣ ϱϮѧΘΤΗ ΔϨѧθΧ Ω΍Ϯѧϣ Ϧѧϣ ω΍Ϯϧ΃ ΓΪϋ Ϧϋ ΓέΎΒϋ
ϪϧϭΪϟ
A- 4
˻˹˹ Ϣϗέ ϞΨϨϣ Ϧϣ ήΜϛ΃ ϭ΃ % ̀˾ ϪϨϣ ήϤϳ silt Ϧϋ ΓέΎΒϋ
A- 5
ΔΌϴγ Ω΍Ϯϣ ϭ ΔϴσΎτϣ Ω΍Ϯϣ ϲϠϋ ϱϮΘΤϳ silt Ϧϋ ΓέΎΒϋ
A-6
˻˹˹ Ϣѧϗέ ϞѧΨϨϣ Ϧѧϣ ήѧΜϛ΃ ϭ΃ % ̀˾ ϪѧϨϣ ήѧϤϳ plastic clay Ϧѧϋ ΓέΎѧΒϋ
ϩΎϴϤϟ΍ κΘϤΗ ΎϣΪϨϋ ΎϬΗϮϗ ΪϘϔΗϭ ΓήϴΒϛ ϪϴϤΠΣ Ε΍ήϴϴϐΗ ΎϬϟ ΙΪΤϳϭ
A-7
ΔѧϴσΎτϣ Δѧϧήϣ ι΍ϮѧΧ ΎѧϬϟϭ ϲϟΎѧϋ liquid limit ΎѧϬϟ clay Ϧѧϋ ΓέΎѧΒϋ
ΓήϴΒϛ ϪϴϤΠΣ Ε΍ήϴϴϐΗϭ
Soil Mechanics (1)
Chapter (4)
Soil Classification
(9)
2011
ϒϴϨμΘϟ΍ ϢΘϳ ϒϴϛ
# 40
A-2
A-3
A-4
A-5
A-6
A-7
50%
A-1-b
30%
A-1-a
10 15
25
35
# 200
A-2 ϦϴΑ ϖϳήϔΘϟ΍
IP
A-2-6
A-2-7
A-2-4
A
A-2-5
10
40
L.L
Soil Mechanics (1)
Chapter (4)
Soil Classification
(10)
2011
A-4, A-5, A-6, A-7 ϦϴΑ ϖϳήϔΘϟ΍
IP
A-7-6
A-6
A-7-5
10
A-4
A-5
40
L.L
PI < L.L – 30
A-7-5
PI > L.L – 30
A-7-6
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (4)
Soil Classification
(1)
2011
Ex: for the following table
Soil # 200 # 4.0
Cu
Cc
LL
Pl
A
30
70
7
2.5
40
25
B
70
100
--
--
60
30
Classify the following soil according to U.S.C.S
Soil (A)
- % passing # 200 = 30 % < 50 %
Course soil
- % passing # 4 = 70 % > 50 %
Sand soil
- Cc = 2.5
- Cu = 7
- Ip = L.L – P.L = 40 – 25 = 15
The soil is ( Sw-Sc )
Soil Mechanics (1)
Chapter (4)
Soil Classification
(2)
2011
Soil (B)
- % passing # 200 = 70 % > 50 %
Fine soil
A-line ϡ΍ΪΨΘγ΍ ϢΘϳ
- Ip = L.L – P.L = 60 – 30 = 30
IP
35 % 50 %
The soil is (CH)
Ex: (mid term 2007)
Soil # 4.0 # 200 D10 mm D30 mm D60 mm LL Pl
A
98
16
0.045
0.13
0.32
48 20
B
44
3
0.16
1.2
4.85
--- ---
C
90
8
0.1
0.32
0.9
36 26
D
100
63
---
---
---
26 26
Soil Mechanics (1)
Chapter (4)
(3)
2011
Soil Classification
Classify the following soil according to U.S.C.S
Solution
Soil (A)
- % passing # 200 = 16 % < 50 %
Course soil
- % passing # 4 = 98 % > 50 %
Sand soil
Cu
D60
D10
0.32
7.11
0.045
(D30 ) 2
Cc
D60 * D10
(0.13) 2
1.17
0.32* 0.045
- Ip = L.L – P.L = 48 – 20 = 28
The soil is ( Sw-Sc )
Try of
Soil (B), Soil (C), Soil (D)
Soil Mechanics (1)
Chapter (4)
Soil Classification
(4)
2011
Ex:
Soil
# 40
# 200
LL
Pl
A
35
17
-----
-----
B
60
20
60
10
C
90
8
-----
------
D
------
63
49
26
Classify the following soil according to AASHTO
Soil (A)
- % passing # 200 = 17 %
- % passing # 40 = 35 %
Then the soil is (A-1-b)
Soil Mechanics (1)
Chapter (4)
(5)
2011
Soil (B)
- % passing # 200 = 20 %
- % passing # 40 = 60 %
Then the soil is (A-2)
PI = 60 – 10 = 50
L.L = 60
Then the soil is (A-2-7)
Soil Mechanics (1)
Soil Classification
Chapter (4)
(6)
2011
Soil Classification
Soil (D)
- % passing # 200 = 63 %
Then the soil is (A-4) or (A-5) or (A-6) or (A-7)
PI = 49 - 26 = 23
L.L = 49
Then the soil is (A-7)
L.L – 30 = 49 – 30 = 19
P.I > L.L – 30
Then the soil is (A-7-6)
Soil Mechanics (1)
Chapter (4)
Soil Classification
(7)
2011
Mid term 2008
Sieve analysis was carried out on a soil sample. The percentage
finer than 0.425 mm was used to determine L.L and P.L of the
fines. The results are: L.L = 43 %, P.L = 23 %
Dim.(mm) 4.76 2.0 1.4 0.6 0.425 0.25 0.15 0.075
% finer
75
60 45 30
25
20
15
10
Classify this soil according to unified system
Soil Mechanics (1)
Chapter (4)
2011
(8)
Soil Mechanics (1)
Soil Classification
Soil Mechanics
(1)
Fff
Chapter (5)
Soil Compaction
(1)
2011
Chapter (5)
Soil Compaction
Δ˰˰Αή˰Θϟ΍ Ϛ˰˰ϣΩ
ϲΟέΎΧ ϞϤΣ
Jd
Ws
n
Vt p
ϖϳήσ Ϧϋ ΔΑήΘϠϟ ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ΓΩΎϳί ΎϬϨϣ νήϐϟ΍ ΔϴϠϤϋ Ϧϋ ΓέΎΒϋ Ϯϫ
ϲΟέΎΧ ϞϤΣ ήϴΛ΄Η ΖΤΗ ϚϟΫ ϭ ΕΎΒϴΒΤϟ΍ ϦϴΑ ΕΎϏ΍ήϔϟ΍ κϘϧ
Compaction in Lab.
ϞϤόϤϟ΍ ϲϓ ϚϣΪϟ΍
1) Standard proctor test (S.P.T.)
ϲγΎϴϘϟ΍ έϮΘϛϭήΑ έΎΒΘΧ΍
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(2)
2011
-:ΔΑήΠΘϟ΍ Ε΍ϮτΧ
.˻˹ Ϣϗέ ϞΨϨϤϟ΍ Ϧϣ ϩέΎϣ ΔϓΎΟ ΔΑήΗ έΎπΣ· ϢΘϳ -˺
.βϧΎΠΘϣ ςϴϠΧ ϦϳϮϜΗ ϭ ΔϓΎΠϟ΍ ΔΑήΘϠϟ ˯ΎϤϟ΍ Ϧϣ ΔϴϤϛ ΔϓΎο· ϢΘϳ -˻
4–6%
coarse soil
8 – 10 %
fine soil
ΔϘΒσ Ϟϛ ϚϣΩ ϊϣ ΕΎϘΒσ ΙϼΛ ϰϠϋ ΐϟΎϘϟ΍ ϲϓ ςϴϠΨϟ΍ ϊοϭ ϢΘϳ -˼
ωΎϔΗέ΍ Ϧϣ ςϘδΗϭ ϢΠϛ ˻̄˾ ΎϬϧίϭ Δϗήτϣ ϡ΍ΪΨΘγΎΑ ΔΑήο ˻˾
Ϣγ ˼˹̄˾
W1
ύέΎϓ ΐϟΎϘϟ΍ ϥίϭ ΪϳΪΤΗ -˽
W2
ΔΑήΘϟ΍ + ΐϟΎϘϟ΍ ϥίϭ ΪϳΪΤΗ -˾
ΔΑήΘϠϟ ΔϴϠϜϟ΍ ΔϓΎΜϜϟ΍ ΏΎδΣ -˿
W2 W1
Vt Ÿ 1000
Jb
ΔΑϮσήϟ΍ ϯϮΘΤϣ ΪϳΪΤΗ ϭ ΐϟΎϘϟ΍ ϞΧ΍Ω Ϧϣ ΔΑήΘϟ΍ Ϧϣ ˯ΰΟ άΧ΍ -̀
W3
ϥήϔϟ΍ ϰϓ ΎϬόοϭ ϞΒϗ ΔϨϴόϟ΍ ϥίϭ
W4
ϥήϔϟ΍ Ϧϣ ΎϬΟ΍ήΧ· ΪόΑ ΔϨϴόϟ΍ ϥίϭ
Wc
W3 W4
W4
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(3)
2011
ΔΑήΘϠϟ ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ΏΎδΣ -́
Jd
Jb
(1 Wc )
ϯήΧ΃ ϩΎϴϣ ΔΒδϧ ϡ΍ΪΨΘγ΍ ϊϣ ΔϘΑΎδϟ΍ Ε΍ϮτΨϟ΍ βϔϧ έ΍ήϜΗ -̂
Jd
Wc
Wc, Jd ϦϴΑ Δϗϼόϟ΍ Ϣγέ ϢΘϳ
-˺˹
Jd
Jd max.
Wc
O.M.C.
O.M.C. = Optimum moisture content
Jd max. = maximum dry density
Soil Mechanics (1)
ϞΜϣϵ΍ ΔΑϮσήϟ΍ ϯϮΘΤϣ
ΔϓΎΟ ΔϓΎΜϛ ϲμϗ΍
Chapter (5)
Soil Compaction
(4)
2011
2) Modified proctor test (M.P.T.)
ϝΪόϤϟ΍ έϮΘϛϭήΑ έΎΒΘΧ΍
ϑϼΘΧ΍ ϊϣ standard ˰ϟ΍ βϔϧ Ϯϫ
S.P.T.
M.P.T.
Wt. of hammer
2.5 kg
4.5 kg
Drop height
30.5 cm
45 cm
Layers
3 - layers
5 - layers
No. of blows
25 blows
25 blows
Uses
ΔϔϴϔΨϟ΍ ϝΎϤΣϷ΍
ΔϳΩΎόϟ΍ ϕήτϟ΍ ϭ
ΔϠϴϘΜϟ΍ ϝΎϤΣϷ΍
Ε΍έΎτϤϟ΍ ϕήσ ϭ
Factors affecting compaction:
1- Water content
ϚϣΪϟ΍ ϲϓ ήΛ΄Η ϲΘϟ΍ Ϟϣ΍Ϯόϟ΍
ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍
2- Compaction effort
ϚϣΪϟ΍ ΪϬΟ
3- Soil type
ΔΑήΘϟ΍ ωϮϧ
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(5)
2011
ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍
1- Water content
Jd
Jd max.
Dry side
Wet side
Stage ( I )
Stage ( II )
Wc
O.M.C.
Stage ( I )
Stage ( II )
ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ Ω΍ΩΰΗ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ ΓΩΎϳΰΑ
ΔΑϮσήϟ΍ ϯϮΘΤϣ Ϧϋ ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ ΓΩΎϳΰΑ
ΪϋΎδΗ ˯ΎϤϟ΍ ϥϻ ΔϤϴϗ ϲμϗ΃ ϲϟ· ϞμΗ ϰΘΣ
ϢΠΣ Ϟϐθϳ ˯ΎϤϟ΍ ϥϻ ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ϞϘΗ ϞΜϣϵ΍
ΪϋΎδΗ ΎϤϣ ΎϬπόΑ ϕϮϓ ΕΎΒϴΒΤϟ΍ ϕϻΰϧ΍ ϲϠϋ
ΓΩΎϳί ϰϠϋ ΪϋΎδΗ ΎϤϣ ΕΎϏ΍ήϔϟ΍ Ϧϣ ήϴΒϛ
ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ΓΩΎϳί ϲϟΎΘϟΎΑϭ ϢΠΤϟ΍ κϘϧ ϰϠϋ
ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ϞϘΗ ϲϟΎΘϟΎΑϭ ϢΠΤϟ΍
2- Compaction effort: (E)
ϚϣΪϟ΍ ΪϬΟ
Jd
M.P.T.
S.P.T.
Wc
Soil Mechanics (1)
Chapter (5)
(6)
2011
Soil Compaction
E nŸ J d max n O.M .C p
ϞΜϣϷ΍ ΔΑϮσήϟ΍ ϱϮΘΤϣ ϞϘϳ ϭ ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ΪϳΰΗ ϚϣΪϟ΍ ΔϗΎσ ΓΩΎϳΰΑ
E
W *H * N *n
V
W=
ΔϗήτϤϟ΍ ϥίϭ
H = ρϮϘδϟ΍ ωΎϔΗέ΍
N=
ΕΎϘΒτϟ΍ ΩΪϋ
n = ΕΎΑήπϟ΍ ΩΪϋ
E SPT
2 . 5 * 30 . 5 * 3 * 25
1000
5 .7
E MPT
4 . 5 * 45 * 5 * 25
1000
25 . 3
E MPT
E SPT
25 . 3
5 .7
4 .4
Soil Mechanics (1)
Chapter (5)
2011
3- Soil type
Soil Compaction
(7)
ΔΑήΘϟ΍ ωϮϧ
Gravel
Sand
Silt
Clay
Size nŸ J d max n O .M .C p
ΔΑϮσήϟ΍ ϱϮΘΤϣ ϞϘϳ ϭ ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ΪϳΰΗ ΕΎΒϴΒΤϟ΍ ϢΠΣ ΓΩΎϳΰΑ
ϞΜϣϵ΍
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (5)
Soil Compaction
(1)
2011
Compaction in field
ϊϗϮϤϟ΍ ϲϓ ϚϣΪϟ΍
ϝΎѧϤϋ΄Α ΔѧτΒΗήϤϟ΍ ϊϳέΎѧθϤϟ΍ ϲѧϓ Δϴѧδϴ΋ήϟ΍ ΕΎѧΒϠτΘϤϟ΍ ΪѧΣ΍ ΔѧΑήΘϟ΍ ϚѧϣΩ ϞΜϤϳ
.Ε΂ѧѧθϨϤϟ΍ ΕΎѧѧγΎγ΃ ϭ ΔѧѧϴΑ΍ήΘϟ΍ ΩϭΪѧѧδϟ΍ ϭ ϕήѧѧτϟ΍ ΎѧѧϬϤϫ΃ Ϧѧѧϣ ϲѧѧΘϟ΍ϭ ΔѧѧΑήΘϟ΍
ήϴΛ΄ѧѧΗ ΖѧѧΤΗ ΔѧѧΑήΘϠϟ ΔѧѧϓΎΠϟ΍ ΔѧѧϓΎΜϜϟ΍ ΓΩΎѧѧϳί ΔѧѧϴϠϤϋ ΎѧѧϬϧ΄Α ϚϣΪѧѧϟ΍ ΔѧѧϴϠϤϋ ϑήѧѧόΗϭ
...ϑΪϬΑ ϚϟΫϭ ϝΎϤΣϷ΍
.ΔΑήΘϟ΍ ϞϤΤΗ ΓέΪϗ ΓΩΎϳί .ΔΑήΘϟ΍ ρϮΒϫ ϞϴϠϘΗ ϲϟΎΘϟΎΑ ϭ ΕΎϏ΍ήϔϟ΍ ΔΒδϧ ϞϴϠϘΗ .ΔϴηΎϤϜϧϻ΍ ϭ ΔϴηΎϔΘϧϹ΍ ΔΑήΘϠϟ ΔϴϤΠΤϟ΍ Ε΍ήϴϐΘϟ΍ ϞϴϠϘΗ .ϩΎϴϤϠϟ ΔΑήΘϟ΍ ΔϳΫΎϔϧ ϞϴϠϘΗ .ΔΑήΘϠϟ ϥΎϣϵ΍ ϞϣΎόϣ ΓΩΎϳί ΔΑήΘϟ΍ ωϮϧ ϰϠϋ ΪϤΘόΗ ΔϔϠΘΨϣ Ε΍Ϊόϣ ϡ΍ΪΨΘγΎΑ ϊϗϮϤϟ΍ ϲϓ ΔΑήΘϟ΍ ϚϣΩ ϢΘϳ
:ϲϟΎΘϟ΍ Ε΍ΪόϤϟ΍ Γάϫ Ϧϣϭ
1- Smooth wheel rollers:
Δϴτϟΰϟ΍ ϭ ΔϴϠϣήϟ΍ ΔΑήΘϟ΍ ϚϣΪϟ ϡΪΨΘδϳ
Soil Mechanics (1)
Chapter (5)
(2)
2011
Soil Compaction
2- Pneumatic-type rollers:
ΔϜγΎϤΘϣ ήϴϐϟ΍ϭ ΔϜγΎϤΘϤϟ΍ ΔΑήΘϠϟ ϡΪΨΘδϳ
3- Sheep-foot rollers
Ϧϴτϟ΍ϭ ϲϤτϟ΍ ϞΜϣ ΔϜγΎϤΘϤϟ΍ ϭ ΔΟΰϠϟ΍ ΔΑήΘϠϟ ϡΪΨΘδϳ
Soil Mechanics (1)
Chapter (5)
2011
(3)
Soil Compaction
4- Compaction by rammers
ϡ ˼-˻ ϰϟ· ϞμΗ ϕΎϤϋϷ ΔΑήΘϟ΍ ϚϣΪϟ ϡΪΨΘδϳ
5- Dynamic compaction
Δϴτϟΰϟ΍ ϭ ΔϴϠϣήϟ΍ ΔΑήΘϟ΍ ϭ ϡΩήϟ΍ ΔΑήΗ
Soil Mechanics (1)
Chapter (5)
(4)
2011
Soil Compaction
6- Vibrating plates
(ΔϴϠϣήϟ΍ ΔΑήΘϠϟ) Γήϴϐμϟ΍ ΕΎΣΎδϤϠϟ ϡΪΨΘδϳ
7- Vibrofloating
ϭ ΔϜϜϔϤϟ΍ ΔϴϠϣήϟ΍ ΔΑήΘϟ΍ ϚϣΪϟ ϡΪΨΘδϳ
ΓήϴΒϛ ϕΎϤϋϷ Δϴτϟΰϟ΍
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(5)
2011
Relative Compaction (R.c)
ϲΒδϨϟ΍ ϚϣΪϟ΍
ϻ ϡ΃ ϝϮΒϘϣ ϊϗϮϤϟ΍ ϲϓ ϚϣΪϟ΍ ϲϠϋ ϢϜΤϠϟ ϡΪΨΘδϳ
J d ˜ field
J d max
Rc
ϥ΍ ϲϠϋ ΕΎϔλ΍ϮϤϟ΍ κϨΗϭ
Rc > 95 %
Refused
Accepted
Refused
Jd max
Jd max
Range of Wc
Wc1
O.M.C Wc2
Range of Wc = (O.M.C – Wc1)
(O.M.C + Wc2)
ϰϠϋ ΕΎϔλ΍ϮϤϟ΍ κϨΗ ϭ
Range of Wc = (O.M.C ± 2%)
ϚϣΪϟ΍ ΓΩΎϋ·ϭ ϩΎϴϣ ΔϓΎο· ϢΘϳ Wc1 ϞΒϗ ϊϘϳ ϭ νϮϓήϣ ϚϣΪϟ΍ ϥΎϛ Ϯϟ ϚϣΪϟ΍ ΓΩΎϋ·ϭ ϒΠΘϟ ΔΑήΘϟ΍ ϙήΗ ϢΘϳ Wc2 ΪόΑ ϊϘϳ ϭ νϮϓήϣ ϚϣΪϟ΍ ϥΎϛ Ϯϟ -
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(6)
2011
Sand cone test:
ϲϠϣήϟ΍ ρϭήΨϤϟ΍ έΎΒΘΧ΍
(Sand replacement test)
(Compacted control test)
-: ΔΑήΠΘϟ΍ Ε΍ϮτΧ
W1 ήϔΤϟ΍ ΞΗΎϧ ϊϴϤΠΗ ϊϣ ϊϗϮϤϟ΍ ϲϓ ΓήϔΣ ϞϤϋ ϢΘϳ -˺
Wc ϲ΋ΎϤϟ΍ ϯϮΘΤϤϟ΍ ΪϳΪΤΗ ϭ ϥήϔϟ΍ ϲϓ ΔΑήΘϟ΍ ϒϴϔΠΗ ϢΘϳ -˻
ϡ΍ΪΨΘγΎΑ ϞϣήϟΎΑ ΓήϔΤϟ΍ ˯Ϟϣ ϢΘϳ ΔϓΎΜϜϟ΍ ϡϮϠόϣ Ϟϣέ ϡ΍ΪΨΘγΎΑ -˼
ΔϓΎΜϜϟ΍ ρϭήΨϣ
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(7)
2011
ϢΠΣ ΏΎδΣ ϢΘϳ ΓήϔΤϟ΍ ϲϓ ΩϮΟϮϤϟ΍ Ϟϣήϟ΍ ϥίϭ ΔϴϣϮϠόϤΑ -˽
W sand
V hole
ΓήϔΤϟ΍
J sand
ΔΑήΘϠϟ ΔϴϠϜϟ΍ ΔϓΎΜϜϟ΍ ΪϳΪΤΗ -˾
W1
V hole
Jb
ΔΑήΘϠϟ ΔϓΎΠϟ΍ ΔϓΎΜϜϟ΍ ΪϳΪΤΗ -˿
J d field
Rc
Jb
(1 Wc )
J d ˜ field
J d max
Air void ratio (na)
˯΍ϮϬϟ΍ ΔΒδϧ
Va
na
Va
Vt
Vt
ΔΑήΘϠϟ ϰϠϜϟ΍ ϢΠΤϟ΍ ϰϟ· ˯΍ϮϬϟ΍ ϢΠΣ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(8)
2011
Relation (na, n, Sr)
Vv
n(1-Sr)
n
n
n*Sr
Vt
1
Vw Vw
1-n
Sr
Vv
n
Vw n * Sr
Va
na
n (1 Sr )
Vt
Relation (na, Gs, Wc, Jd, Jw)
Vt
Vs Vw Va
Va
Vt ϰϠϋ ΔϤδϘϟΎΑ
Vs Vw Va
Vt
Vt
Vt
Vs Vw
(1 na )
Vt
Vt
Vt
Vw
1
(1 na)
(1 na)
Ws
Ww Ws
*
Gs*J w *Vt J w *Vt Ws
Jd
Gs*J w
J d *Wc
Jw
Vs
Note
Jd
Ww
Ws
Jd
(1 na ) * Gs * J w
(1 Gs * Wc )
Wc
Soil Mechanics (1)
Ws
Vt
J w * Vw
Gs * J w * Vs
Ww
Ws
Chapter (5)
Soil Compaction
(9)
2011
Zero air voids: (ZAV)
na = 0
Saturation line
Jd
Gs * J w
(1 Gs * Wc )
-: ˰Α ΰϴϤΘϳϭ ςϘϓ ϱήψϧ ϰϨΤϨϣ ϮϬϓ ϞϤόϤϟ΍ ϰϓ ΪΟϮϳ ϻ ϰϨΤϨϤϟ΍ ΍άϫ
.ϚϣΪϟ΍ ϰϨΤϨϣ βϤϳ ϻ -˺
.˯ΎϤϟ΍ ϰϓ ΐ΋΍Ϋ ˯΍Ϯϫ ΩϮΟϮϟ ϚϟΫ ϭ ΔόϴΒτϟ΍ ϰϓ ΪΟϮϳ ϻ -˻
ϚϣΪϟ΍ ϰϨΤϨϣ ΔΤλ ϰϠϋ ϢϜΤϠϟ ϡΪΨΘδϳ -˼
5%
10 %
For 5 % of air voids
Jd (5 %) = 0.95 *Jd (zav)
For 10 % of air voids
Jd (10 %) = 0.9 *Jd (zav)
Soil Mechanics (1)
ZAV
Soil Mechanics
(1)
Fff
Chapter (5)
Soil Compaction
2011
Sol.
Wc, %
10.1 11.8 14.2 16.3 17.6 18.9
Jd, t/m3
1.65 1.71 1.79
Jd, t/m3(na = 0)
1.8
1.76 1.72
2.1
2.04 1.94 1.86 1.82 1.78
Jd, t/m3(na = 5%) 2.0
1.93 1.84 1.77 1.73 1.69
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
10
11
12
13
14
15
16
17
Soil Mechanics (1)
18
19
20
Chapter (5)
Soil Compaction
2011
Sol.
Given:Jd t/m3 g/cm3
Wc = 12.5 %
10 cm
Gs = 2.66
Req.
1) Sr
2) na
3) Ww, Wdry
5.0
V
S
4
( 5 ) 2 * 10
a
196.3
42.95
w
42.95
386.55
129.2
S
343.6
Soil Mechanics (1)
196 . 3
Chapter (5)
Soil Compaction
2011
Ws
Vt
Ww
Wc
Ws
Vw
Sr
Vv
Va
na
Vt
Jd
Ws
ŸŸ Ws 343 .6
196 .3
Ww
0.125
ŸŸ Ww 42.95
343 .6
42.95
0.616
69.7
24.15
0.123
196 .3
1.75
Ww 42.95
Ws Wdry 343 .6
Rc = 95 %
Req.
Range of water content
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
1.9
1.85
1.8
1.75
1.7
1.65
1.6
5
10
Wc1
15
Wc2
20
Range of water content = ( 11.5 – 17.4 )
Soil Mechanics (1)
25
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Final (2008)
In a highway construction 95 % compaction is required for the
soil at a moisture content = optimum – 2 % to + 2 %. The soil
has the following compaction curve:Wc %
14
16
18
20
22
24
Jd (gm/cm3) 1.89 2.139 2.17 2.21 2.119 2.069
If a sample 900 cm3 volume is taken from the compacted layer.
Its weight is 1.8 kg and lost 0.3 kg after drying. Gs = 2.7.
i)
Is that sample meet the specification? why?
ii)
What is the degree of saturation of this sample?
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Final (2007)
1.95
dry unit weight, g/cc
The adjacent figure shows the results
from a laboratory standard Proctor test.
Find the maximum dry density and the
optimum moisture content. If the
contractor is asked to attain a relative
compaction of 95 % what is the
minimum dry density that is allowed and
the corresponding range of moisture
content
1.9
1.85
1.8
1.75
4
Soil Mechanics (1)
9
14
water content, %
19
Chapter (5)
Soil Compaction
2011
Mid term (2008)
As a part of compaction control druing the construction of an
embankement, a series of density tests were conducted by using
sand replacement method (sand cone)and the following data
were reported for one of the tests:Weight of the soil excavated from hole = 1080 gm
Weight of the soil excavated from hole after dry = 930 gm
Weight of the sand filling the hole and cone = 1790 gm
Volume of the cone = 750 cm3
Bulk denisty of sand used in the test = 1.42 gm/cm3
The compaction test was carried out on the same soil in the
laboratory (volume of the mould = 950 cm3). The following
results were obtained:
Observation No.
1
2
3
4
5
6
Weight of wet soil, gm 1700 1890 2030 1990 1960 1920
Water content, %
7.7 11.5 14.6 17.5 19.5 21.2
The specific gravity of soil grains = 2.7
i) Calculate the dry denisty, void ratio, degree of saturation and
air content of the soil in both site and laboratory
ii) Determine the relative compaction. Comment on the results.
iii) If the soil gets fully saturated calculate the changes in its water
content and bulk density (assume, total volume remains same)
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Chapter (5)
Soil Compaction
2011
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Mid-Term Exam
2011
Mid-Term Exam
˺
Soil Mechanics (1)
2011
Soil Mechanics
(1)
Fff
Chapter (6)
Hydraulic properties
1
2011
of soil
Chapter (6)
Hydraulic properties of soil
ΔΑήΘϠϟ ΔϴϜϴϟϭέΪϴϬϟ΍ ι΍ϮΨϟ΍
ΎϬϟϼΧ Ϧϣ ˯ΎϤϟ΍ έϭήϣ ˯ΎϨΛ΍ ΔΑήΘϟ΍ ϙϮϠγ Δγ΍έΩ Ϯϫ
ϰϫ ˯΍ΰΟ΍ ΙϼΛ Δγ΍έΩ ϢΘϳ ϭ
Geo-static stress
Permeability
Flow net
νέϵ΍ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϵ΍
ΔϳΫΎϔϨϟ΍
ϥΎϳήδϟ΍ ΔϜΒη
νέϵ΍ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϵ΍
1) Geo-static stress
a) Effective stress: ( V )
ϝΎόϔϟ΍ ΩΎϬΟϻ΍
ΔΑήΘϟ΍ ΕΎΒϴΒΣ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϻ΍ Ϯϫ
¦
V
˯ΎϤϟ΍ ΖΤΗ
Jsub.
Jsub. = Jsat.Jw
J *h
˯ΎϤϟ΍ ϕϮϓ
J
ϩΎτόϤϟ΍
JbJdJsat.
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2
2011
of soil
-:ϝΎόϔϟ΍ ΩΎϬΟϹ΍ ΔϴϤϫ΃
ΔϴϤΠΤϟ΍ Ε΍ήϴϐΘϟ΍ Ϧϋ ΔϟϮΌδϤϟ΍ -˺
( W ) κϘϟ΍ ΔϣϭΎϘϣ Ϧϋ ΔϟϮΌδϤϟ΍ -˻
b) Pore water pressure: (neutral stress)
˯ΎϤϟ΍ ςϐο
˯ΎϤϟ΍ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϹ΍ Ϯϫ
¦J
U
w
* hw
Jw ˯ΎϤϟ΍ ΔϓΎΜϛ
hw = ˯ΎϤϟ΍ ΢τγ ϦϴΑ ϭ ΎϫΪϨϋ ΏΎδΤϟ΍ ΏϮϠτϤϟ΍ ΔτϘϨϟ΍ ϦϴΑ Δϴγ΃ήϟ΍ ΔϓΎδϤϟ΍
c) Total stress: (V )
ϰϠϜϟ΍ ΩΎϬΟϻ΍
˯ΎϤϟ΍ ϥίϭϭ ΔΑήΘϟ΍ ΕΎΒϴΒΣ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϻ΍ Ϯϫ
V
˯ΎϤϟ΍ ΖΤΗ
Jsat.
V
¦J *h
˯ΎϤϟ΍ ϕϮϓ
J
ϩΎτόϤϟ΍
JbJdJsat.
V U
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
3
2011
of soil
Ϟ΋ΎδϤϟ΍ ϞΤϟ ΎϬψϔΣ ΏϮϠτϣ ϝϭϵ΍ Ϟμϔϟ΍ Ϧϣ Ϧϴϧ΍ϮϘϟ΍ ξόΑ
Ÿ sr * e Gs *Wc
Ÿ Jb
§ Gs sr * e ·
¨
¸ *J w
© 1 e ¹
Ex:Find the stress at point
A, B
Jb
h1
B
Jsat.
h2
A
At point (A):-
V
¦J * h
J b * h1 J sat. * h2
U J w * hw J w * h2
V J b * h1 J sub. * h2
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
4
2011
of soil
At point (B):-
V
¦J *h
J b * h1
U
J w * hw
Zero
V
J b * h1
Δϳήόθϟ΍ ΔϴλΎΨϟΎΑ ˯ΎϤϟ΍ ωΎϔΗέ΍ ΔϟΎΣ ϰϓ
1
h1
Jb
2
3
hc
Jsat.
4
Jsat.
h2
5
At point (1):-
V
U
zero
zero
V
zero
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
5
2011
of soil
At point (2):-
V
J b * h1
U
zero
V
J b * h1
At point (3):-
V
J b * h1
U J w * hc
V
V U
J b * h1 J w * hc
At point (4):-
V
J b * h1 J sat . * h c
U
zero
V
J b * h1 J sat . * h c
At point (5):-
V
J b * h1 J sat. * hc J sat. * h2
U J w * h2
V
J b * h1 J sat. * hc J sub. * h2
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
6
2011
Surcharge
of soil
ωίϮϤϟ΍ ϞϤΤϟ΍ ήϴΛ΄Η
h1
Jb
h2
Jsat.
A
At point (A):-
V
q J b * h1 J sat . * h2
U
J w * h2
V
q J b * h1 J sub. * h2
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
7
2011
of soil
νέϻ΍ ΢τγ ϰϠϋ΍ ˯ΎϤϟ΍ ΖϧΎϛ ΍Ϋ΍
h1
Jw
h2
Jsat.
A
At point (A):-
V
U
J sat . * h2 J w * h1
J w * ( h1 h2 )
V
J sub . * h2
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
8
2011
of soil
ϥΎϳήδϟ΍ ήϴΛ΄Η
Effect of flow
a) Down-ward flow
(ϰσ΍Ϯϟ΍ Ϧϋ ϰϟΎόϟ΍ ˯ΎϤϟ΍ ΏϮδϨϣ ϕήϓ ) H
ϞϔγϷ ϥΎϳήδϟ΍
h1
Soil
Jsat
h2
A
A
At point (A-A):-
V J sat. * h2 J w * h1
ήϴϐΘϳ ϻ ΖΑΎΛ
U J w * (h1 h2 ) J w * H
Jw + έ΍ΪϘϤΑ ϞϘϳ
ΔϤϳΪϘϟ΍ ΔϤϴϘϟ΍
V J sub. * h2 J w * H
Jw + έ΍ΪϘϤΑ Ϊϳΰϳ
ΔϤϳΪϘϟ΍ ΔϤϴϘϟ΍
ϝΎόϔϟ΍ ΩΎϬΟϻ΍ Ω΍Ωΰϳ Ϟϔγϻ ˯ΎϤϟ΍ ΔϛήΣ ϥ΍ φΣϼϧ
Jw + έ΍ΪϘϤΑ
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
9
2011
of soil
ϰϠϋϷ ϥΎϳήδϟ΍
b) Up-ward flow
H
h1
Soil
Jsat
h2
A
A
At point (A-A):-
V J sat. * h2 J w * h1
ήϴϐΘϳ ϻ ΖΑΎΛ
U J w * (h1 h2 ) J w * H
Jw + έ΍ΪϘϤΑ Ϊϳΰϳ
ΔϤϳΪϘϟ΍ ΔϤϴϘϟ΍
V J sub. * h2 J w * H
Jw + έ΍ΪϘϤΑ ϞϘϳ
ΔϤϳΪϘϟ΍ ΔϤϴϘϟ΍
ϝΎόϔϟ΍ ΩΎϬΟϻ΍ ϞϠϘϳ ϰϠϋϻ ˯ΎϤϟ΍ ΔϛήΣ ϥ΍ φΣϼϧ
Jw + έ΍ΪϘϤΑ
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
10
2011
Hydraulic gradient (
i
H
)
of soil
ϰϜϴϟϭέΪϴϬϟ΍ ϞϴϤϟ΍
T
h1
h2
L
i
i
tan T
H
L
.......... .......... ....
ϰσ΍Ϯϟ΍ Ϧϋ ϰϟΎόϟ΍ ˯ΎϤϟ΍ ΏϮδϨϣ ϕήϓ
ΔΑήΘϟ΍ ϞΧ΍Ω ˯ΎϤϟ΍ έΎδϣ ϝϮσ
ϥϮϜϳ ϥΎϳήδϟ΍ Ϛηϭ ϰϠϋ ΔΑήΘϟ΍ ϥϮϜΗ ΎϣΪϨϋ ϭ
V J sub. * h2 J w * H
J sub. * h2 J w * H
H J sub.
icr
h2 J w
zero
Soil Mechanics (1)
Chapter (6)
11
2011
i cr
icr
J sub.
Jw
Hydraulic properties
of soil
Critical Hydraulic gradient
Gs 1
1 e
ΔΑήΘϟ΍ ι΍ϮΧ Ϧϣ ΔϴλΎΧ
Piping = boiling = heaving = quick sand
ϥ΍έϮϔϟ΍ ΓήϫΎχ
ϭ (shear stress ) κѧϘϟ΍ Ε΍ΩΎϬΟ΍ Ϟϛ ΔΑήΘϟ΍ ΎϬϴϓ ΪϘϔΗ ΓήϫΎχ ϲϫ
˯ΎѧѧϨΛ΍ ϚѧѧϟΫϭ ( V
) ΔѧѧϛήΤϟ΍ Ϛѧѧηϭ ϰѧѧϠϋ ΔѧѧΑήΘϟ΍ ϥϮѧѧϜΗ ΎѧѧϬϴϓ ϰѧѧΘϟ΍
ΔѧΑήΘϟ΍ ϰѧϓ ΎѧΒϟΎϏ ΙΪΤΗ ΓήϫΎχ ϲϬϓ .ϰϠϋ΃ ϰϟ· Ϟϔγ΍ Ϧϣ ˯ΎϤϟ΍ έϭήϣ
.ΔϴϨϴτϟ΍ ΔΑήΘϟ΍ ϰϓ ΓέΩΎϧϭ ΔϴϠϣήϟ΍
Scour ήΤϧ
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
12
2011
of soil
:ΏΎδΣ ϢΘϳ ϥ΍έϮϔϟ΍ ΓήϫΎχ ΙϭΪΣ ϰϠϋ ϢϜΤϠϟ
i
H
L
icr
J sub.
Jw
Gs 1
1 e
i icr Ÿ No ˜ piping
ϥ΍έϮϓ ΙΪΤϳ ϻ
icr Ÿ critical
ϥ΍έϮϔϟ΍ Ϛηϭ ϰϠϋ
i ! icr Ÿ piping
ϥ΍έϮϓ ΙΪΤϳ
i
How to prevent (overcome) piping
ϥ΍έϮϔϟ΍ ϊϨϣ
ΔΑήΘϟ΍ ϞΧ΍Ω ˯ΎϤϟ΍ έΎδϣ ϝϮσ ΓΩΎϳί -˺
Sheet pile wall
ΔϴϧΪόϣ ή΋ΎΘγ
Soil Mechanics (1)
Chapter (6)
13
2011
Hydraulic properties
of soil
΄θϨϤϟ΍ ϒϠΧ ϥ΍ίϭ΍ ϊοϭ -˻
Weights
filters ΕΎΤηήϣ ϡ΍ΪΨΘγ΍ -˼
Filters
Design of filter:
-: ˰Α ΢ηήϤϟ΍ ΔΑήΗ ΰϴϤΘΗ
ΝέΪΘϟ΍ ΓΪϴΟ ΔΑήΗ -˺
% ˾ Ϧϋ Ϊϳΰϳ ϻ ˻˹˹ Ϣϗέ ϞΨϨϤϟ΍ ϰϠϋ έΎϤϟ΍ -˻
4 D85 ( soil ) ! D15 ( filter ) ! 4 D15 ( soil ) -˼
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
14
2011
of soil
85 %
Soil
Filter
B
15 %
A
4D85 D85 4D15 D15
(D15)
15% έΎϣ ΔΒδϧ ΪϨϋ ήτϘϟ΍ ΪϳΪΤΗ -˺
(A) ΔτϘϧ ϰϠϋ ϝϮμΤϠϟ ϲγ΃έ ϊϠτϧ ΎϬϨϣ ϭ (4D15) ϥΎϜϣ ΪϳΪΤΗ -˻
(D85)
85% έΎϣ ΔΒδϧ ΪϨϋ ήτϘϟ΍ ΪϳΪΤΗ -˼
(B) ΔτϘϧ ϰϠϋ ϝϮμΤϠϟ ϲγ΃έ ϊϠτϧ ΎϬϨϣ ϭ (4D85) ϥΎϜϣ ΪϳΪΤΗ -˽
filter ΔϘτϨϣ ϥϮϜΗ ϲΘϟ΍ ϭ ΔΑήΘϟ΍ ϰϨΤϨϤϟ ϥΎϳί΍Ϯϣ ϥΎϴϨΤϨϣ Ϣγήϧ A, B Ϧϣ -˾
filter ˰ϟ΍ ΔϘτϨϣ ϲϓ ϊϘϳ ΔΑήΗ ϰϨΤϨϣ ϱ΃
filter ϥϮϜΗ ϥ΃ ΔΑήΘϟ΍ ϩάϫ ΢ϠμΗ ΍Ϋ·
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (6)
Hydraulic properties
1
2011
of soil
Chapter (6)
Hydraulic properties of soil
ΔΑήΘϠϟ ΔϴϜϴϟϭέΪϴϬϟ΍ ι΍ϮΨϟ΍
ΎϬϟϼΧ Ϧϣ ˯ΎϤϟ΍ έϭήϣ ˯ΎϨΛ΍ ΔΑήΘϟ΍ ϙϮϠγ Δγ΍έΩ Ϯϫ
ϰϫ ˯΍ΰΟ΍ ΙϼΛ Δγ΍έΩ ϢΘϳ ϭ
Geo-static stress
Permeability
Flow net
νέϵ΍ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϵ΍
ΔϳΫΎϔϨϟ΍
ϥΎϳήδϟ΍ ΔϜΒη
ΔΑήΘϟ΍ ΔϳΫΎϔϧ
2) Permeability of soil
ΎϬϟϼΧ Ϧϣ ˯ΎϤϟ΍ έϭήϤΑ ΡΎϤδϟ΍ ϰϠϋ ΔΑήΘϟ΍ ΓέΪϗ ϰϫ
K ΔϳΫΎϔϨϟ΍ ϞϣΎόϤΑ ΎϬϨϋ ήΒόϳ ϭ
K = Coefficient of permeability
Darcy Law
ϰγέ΍Ω ϥϮϧΎϗ
i
h1
h2
V
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2
2011
of soil
V vi
ϊϣ ϱΩήσ ΐγΎϨΘΗ ΔΑήΘϟ΍ ϰϓ ˯ΎϤϟ΍ ϥΎϳήγ Δϋήγ
ϲϜϴϟϭέΪϴϬϟ΍ ϞϴϤϟ΍
V
V
const . * i
K *i
-: ΚϴΣ
ΔΑήΘϟ΍ ϞΧ΍Ω ˯ΎϤϟ΍ ϥΎϳήγ Δϋήγ = V
ΔϳΫΎϔϨϟ΍ ϞϣΎόϣ = K
ϰϜϴϟϭέΪϴϬϟ΍ ϞϴϤϟ΍ = i
i
H
L
..........
..........
....ϕήϓ
ϰσ΍Ϯϟ΍
Ϧϋ ϰϟΎόϟ΍
˯ΎϤϟ΍ ΏϮδϨϣ
ΔΑήΘϟ΍ ϞΧ΍Ω ˯ΎϤϟ΍ έΎδϣ ϝϮσ
H
A
L
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
3
2011
Q A *V
V
Q
t
of soil
K *i * A
ϑήμΘϟ΍ ϝΪόϣ = Q
ϥΎϳήδϟ΍ ϩΎΠΗ΍ ϰϠϋ ΔϳΩϮϤόϟ΍ ΔΣΎδϤϟ΍ = A
Ϧϣΰϟ΍ = t
Ϧϴόϣ Ϧϣί ϝϼΧ ϩΎϴϤϟ΍ ΔϴϤϛ = V
Discharge velocity
ϑήμΘϟ΍ Δϋήγ
ΔΑϮδΤϤϟ΍ Δϋήδϟ΍ ϰϫ ϭ ϪϠϛ ΔΑήΘϟ΍ ωΎτϗ ϝϼΧ ϩΎϴϤϟ΍ Δϋήγ ϰϫ
Ϧϣ ϰγέ΍Ω ϥϮϧΎϗ
V K *i
Q A *V
K *i * A
ΕΎΒϴΒΤϟ΍ ΔΣΎδϣ ΎϬϴϓ ΎϤΑ ΎϬϠϛ ΔΣΎδϤϟ΍ ϰϫ = A
Seepage velocity
ϥΎϳήδϟ΍ Δϋήγ
ςϘϓ ΔΑήΘϟ΍ ΕΎϏ΍ήϓ ϝϼΧ ϩΎϴϤϟ΍ Δϋήγ ϰϫ
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
4
2011
of soil
Q
AV * V S
A *V
VS
A *V
AV
V
n
VS
K *i
n
K
P
*i
KP = coefficient of percolation
Av = area of voids
΢ϴηήΘϟ΍ ϞϣΎόϣ
ΕΎϏ΍ήϔϟ΍ ΔΣΎδϣ
ΔϳΫΎϔϨϟ΍ ϞϣΎόϣ ΏΎδΣ
ΔϳΫΎϔϨϟ΍ ϞϣΎόϣ ΏΎδΤϟ ϕήσ ΙϼΛ ϙΎϨϫ
1- Lab. tests
2- Field test
3- Empirical equations
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
5
2011
of soil
1- Lab. tests:
a) Constant Head Test
ΖΑΎΜϟ΍ ςϐπϟ΍ ΔϘϳήσ
coarse soil (Sand, Gravel)
ΔϨθΨϟ΍ ΔΑήΘϠϟ ϡΪΨΘδϳ
Soil
( t ) ϩέ΍ΪϘϣ Ϧϴόϣ Ϧϣί ϰϓ ˯ΎϤϟ΍ Ϧϣ ΔϴϤϛ ϊϴϤΠΗ ϢΘϳ
Q
K
h
K * *A
L
V *L
h*t* A
V
t
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
6
2011
of soil
ήϴϐΘϤϟ΍ ςϐπϟ΍ ΔϘϳήσ
b) Falling Head Test
ΔϤϋΎϨϟ΍ ΔΑήΘϠϟ ϡΪΨΘδϳ
fine soil (silt, clay)
a
h1
h2
Soil
A
K
L
a * L § h1 ·
Ln ¨¨ ¸¸
t*A
© h2 ¹
Δϴγ΃ήϟ΍ ΔΑϮΒϧϻ΍ ϊτϘϣ ΔΣΎδϣ = a
(ΔϨϴόϟ΍ ωΎϔΗέ΍) ϥΎϳήδϟ΍έΎδϣ ϝϮσ = L
(ΔϳΎϬϨϟ΍ ϭ Δϳ΍ΪΒϟ΍ Ϧϣί ϕήϓ) ΔΑήΠΘϟ΍ Ϧϣί = t
(ήϴΒϜϟ΍) ΔΑήΠΘϟ΍ Δϳ΍ΪΑ ϲϓ ˯ΎϤϟ΍ ωΎϔΗέ΍ = h1
(ήϴϐμϟ΍) ΔΑήΠΘϟ΍ ΔϳΎϬϧ ϲϓ ˯ΎϤϟ΍ ωΎϔΗ έ΍ = h2
Soil Mechanics (1)
-:ΚϴΣ
Chapter (6)
Hydraulic properties
7
2011
2- Field tests: (in-situ test)
a) Unconfined Test
K
(pumping test)
(ήΤϟ΍ ϥΎϳήδϟ΍) ϡϮϜΤϣ ήϴϐϟ΍ ϥΎϳήδϟ΍
§ r2
Q
Ln ¨¨
2
2
S ( h2 h1 ) © r1
b) Confined test
K
of soil
·
¸¸
¹
(ήΤϟ΍ ήϴϐϟ΍ ϥΎϳήδϟ΍) ϡϮϜΤϣ ϥΎϳήδϟ΍
§ r2
Q
Ln ¨¨
2SD ( h2 h1 ) © r1
Soil Mechanics (1)
·
¸¸
¹
Chapter (6)
2011
8
Hydraulic properties
of soil
ΪΣ΍ϭ ΔψΣϼϣ ήΌΑ ΩϮΟϭ ΔϟΎΣ ϰϓ
ΪΣ΍ϭ ΔψΣϼϣ ήΌΑ ΩϮΟϭ ΔϟΎΣ ϰϓ
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
9
2011
of soil
3- Empirical equations:
a) Hazen formula
K
C * ( D10 ) 2
C = Constant (1-10)
C=1
ΔΑήΘϟ΍ ωϮϧ ϰϠϋ ΪϤΘόϳ
for sand
Permeability of stratified soil
ΕΎϘΒτϟ΍ ΓΩΪόΘϣ ΔΑήΘϟ΍ ΔϳΫΎϔϧ
ϰϘϓϵ΍ ϥΎϳήδϟ΍
a) Horizontal flow
i cons tant
h
q
1m
q1
K1
H1
q2
K2
H2
q3
K3
H3
L
q q1 q2 q3
Keq. * i * H K1* i * H1 K 2 * i * H 2 K 3* i * H 3
Keq. * H K1* H1 K 2 * H 2 K3* H 3
Keq. K X
¦ K1* H1 K 2 * H 2 ....... ¦ K * H
¦ H1 H 2 .........
¦H
Soil Mechanics (1)
H
Chapter (6)
Hydraulic properties
10
2011
b) Vertical flow
of soil
ϲγ΃ήϟ΍ ϥΎϳήδϟ΍
V, q = constant
K1
H1
K2
H2
K3
H3
h h1 h2 h3
V *H
h
Ÿh
H
K
V * H V * H1 V * H2 V * H3
K
K1
K2
K3
V
H
K
K*
H1 H2 H3
K1 K2 K3
Keq. K y
¦ H1 H 2 ......... ¦ H
H
§ H1 H 2
·
.........
¸ ¦
¦¨© K1 K 2
K
¹
Soil Mechanics (1)
H
Soil Mechanics
(1)
Fff
Chapter (6)
Hydraulic properties
1
2011
of soil
Chapter (6)
Hydraulic properties of soil
ΔΑήΘϠϟ ΔϴϜϴϟϭέΪϴϬϟ΍ ι΍ϮΨϟ΍
ΎϬϟϼΧ Ϧϣ ˯ΎϤϟ΍ έϭήϣ ˯ΎϨΛ΍ ΔΑήΘϟ΍ ϙϮϠγ Δγ΍έΩ Ϯϫ
ϰϫ ˯΍ΰΟ΍ ΙϼΛ Δγ΍έΩ ϢΘϳ ϭ
Geo-static stress
Permeability
Flow net
νέϵ΍ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϵ΍
ΔϳΫΎϔϨϟ΍
ϥΎϳήδϟ΍ ΔϜΒη
ϥΎϳήδϟ΍ ΔϜΒη
3) Flow net
Flow channel
Flow lines
Equipotent lines
Field
Drop head
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2
2011
of soil
ϞΧ΍Ω ˯ΎϤϟ΍ ϥΎϳήγ Ϧϋ ήϴΒόΘϠϟ ΔϟΩΎόϣ Laplace ϢϟΎόϟ΍ ϊοϭ
w 2h
w 2 h ΔΑήΘϟ΍
2
wx
wz 2
0 .0
Laplace ΔϟΩΎόϤϟ ϰγΪϨϫ ϞϴΜϤΗ Ϧϋ ΓέΎΒϋ ϰϫ : ϥΎϳήδϟ΍ ΔϜΒη
ΔΑήΘϟ΍ ϞΧ΍Ω ˯ΎϤϟ΍ ϥΎϳήγ Ϧϋ ήΒόΗ ϰΘϟ΍ϭ
Flow lines: ϥΎϳήδϟ΍ ρϮτΧ
ΔΑήΘϟ΍ ϞΧ΍Ω ˯ΎϤϟ΍ έΎδϣ Ϧϋ ήΒόΗ ρϮτΧ ϰϫ
Flow channel: ϥΎϳήδϟ΍ ΓΎϨϗ
ϦϴϴϟΎΘΘϣ ϥΎϳήγ ϲτΧ ϦϴΑ ΓέϮμΤϤϟ΍ ΔϘτϨϤϟ΍ ϰϫ
Equipotent lines:(ςϐπϟ΍) ΪϬΠϟ΍ ϯϭΎδΗ ρϮτΧ
ςϐπϟ΍ ϰϓ ΔϳϭΎδΘϤϟ΍ ςϘϨϟ΍ ϦϴΑ ϞμΗ ρϮτΧ ϰϫ
Drop head:ΪϬΠϟ΍ ϰϓ ΪϘϔϟ΍
ϦϴϴϟΎΘΘϣ ΪϬΟ ϯϭΎδΗ ϲτΧ ϦϴΑ ΓέϮμΤϤϟ΍ ΔϘτϨϤϟ΍ ϰϫ
Field:
ϝΎΠϤϟ΍
ϯϭΎδΗ ϲτΧ ϭ ϦϴϴϟΎΘΘϣ ϥΎϳήγ ϲτΧ ϦϴΑ ΓέϮμΤϤϟ΍ ΔϘτϨϤϟ΍ ϰϫ
ΎΒϳήϘΗ ϊΑήϣ ϥϮϜϳ ϥ΍ Ϧϣ ΪΑϻϭ ϦϴϴϟΎΘΘϣ ΪϬΟ
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
3
2011
of soil
:ϥΎϳήδϟ΍ ΔϜΒη Ϣγέ Ε΍ϮτΧ
ΐγΎϨϣ Ϣγέ αΎϴϘϤΑ Δϟ΄δϤϟ΍ Ϣγέ -˺
.ϥΎϳήδϟ΍ ρϮτΧ Ϣγέ -˻
΄θϨϤϠϟ ϖλϼϣ ϥϮϜϳ ϥΎϳήγ ςΧ ϝϭ΃ ΓάϔϨϣ ήϴϐϟ΍ ΔϘΒτϠϟ ϖλϼϣ ϥϮϤϳ ϥΎϳήγ ςΧ ήΧ΃ ρϮτΧ 5 Ϧϋ ϞϘϳ ϻ ϥΎϳήδϟ΍ ρϮτΧ ΩΪϋ ΔϳϭΎδΘϣ ϥΎϳήδϟ΍ ρϮτΧ ϦϴΑ ΔϓΎδϤϟ΍ Smooth ˯ΎδϠϣ ρϮτΧ ϥΎϳήδϟ΍ ρϮτΧ ϥϮϜΗ ϥ΃ -
.ΪϬΠϟ΍ ϯϭΎδΗ ρϮτΧ Ϣγέ -˼
(ϲϟΎόϟ΍ ˯ΎϤϟ΍) U.S. ϰϓ νέϼϟ ϖλϼϣ ϥϮϜϳ ΪϬΟ ϯϭΎδΗ ςΧ ϝϭ΃ (ϲσ΍Ϯϟ΍ ˯ΎϤϟ΍) D.S. ϰϓ νέϼϟ ϖλϼϣ ϥϮϜϳ ΪϬΟ ϯϭΎδΗ ςΧ ήΧ΃ -
Field ϦϳϮϜΘϟ ϥΎϳήδϟ΍ ρϮτΧ ϰϠϋ ΔϳΩϮϤϋ ΪϬΠϟ΍ ϱϭΎδΗ ρϮτΧ Smooth ˯ΎδϠϣ ρϮτΧ ΪϬΠϟ΍ ϯϭΎδΗ ρϮτΧ ϥϮϜΗ ϥ΃ -
H
Example (1)
A
Soil Mechanics (1)
B
Chapter (6)
2011
Hydraulic properties
4
of soil
Nf = No. of flow channel = 4.0
Nd = No. of drop head = 15
Example (2)
H
Nf = No. of flow channel = 4.0
Nd = No. of drop head = 13
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
5
2011
of soil
ϥΎϳήδϟ΍ ΔϜΒη ΕΎϣ΍ΪΨΘγ΍
Uses of flow net
ϑήμΘϟ΍ ΏΎδΣ
1) Seepage discharge ( q )
q
Nf
K *H *
Nd
Ϣγήϟ΍ Ϧϣ
.ϰσ΍Ϯϟ΍ Ϧϋ ϰϟΎόϟ΍ ˯ΎϤϟ΍ ΏϮδϨϣ ϕήϓ = H
.ΔϳΫΎϔϨϟ΍ ϞϣΎόϣ = K
φΣϻ
-:ΔΑήΘϟ΍ ωϮϧ ϰτόϣ ϥΎϛ Ϯϟ
.ΕΎϫΎΠΗϻ΍ ϊϴϤΟ ϰϓ ι΍ϮΨϟ΍ βϔϧ ΎϬϟ ΔΑήΗ ϰϫ = Isotropic soil
Kx = Kz
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
6
2011
of soil
ΔϘΑΎδϟ΍ Ε΍ϮτΨϟ΍ βϔϧ ϰϫ Δϟ΄δϤϟ΍ ϞΣ
.ΕΎϫΎΠΗϻ΍ ϊϴϤΟ ϰϓ ΎϬλ΍ϮΧ ϒϠΘΨΗ ΔΑήΗ ϰϫ = In-isotropic soil
Kx z Kz
-:ϰϠϳ ΎϤϛ ΎϤϫ Ϧϴ΋ΰΟ ϰϓ ϒϠΘΨϳ Δϟ΄δϤϟ΍ ϞΣ
In-isotropic soil
q
K
Nf
K *H *
Nd
Ϣγήϟ΍ ϞΒϗ ϦϜϟ ϭ Δϟ΄δϤϟ΍ Ϣγέ ϢΘϳ
ϰϓ ΔϴϘϓϵ΍ ΩΎόΑϵ΍ Ώήο ϢΘϳ
Kx * Kz
Soil Mechanics (1)
Kz
Kx
Chapter (6)
Hydraulic properties
7
2011
No. of pumps
N
of soil
(q) Ϧϣ κϠΨΘϠϟ Δϣίϼϟ΍ ΕΎΨπϤϟ΍ ΩΪϋ
q
1
pump ˜ capacity
2) Seepage pressure ( Ps )
ϥΎϳήδϟ΍ ςϐο
n ·
§
Ps J w * H * ¨1 ¸
© Nd ¹
ΔΑϮϠτϤϟ΍ ΔτϘϨϟ΍ ϰΘΣ drop head ϰϓ ΪϘϔϟ΍ Ε΍ήϣ ΩΪϋ = n
Soil Mechanics (1)
Chapter (6)
8
2011
For
Example (1)
Ps A
Ps B
Hydraulic properties
of soil
5 ·
§
J w * H * ¨1 ¸
15 ¹
©
12 . 5 ·
§
J w * H * ¨1 ¸
15 ¹
©
3) Uplift ϰϠϋϵ ϊϓΪϟ΍ ΓϮϗ
ΓΪϋΎϘϟ΍ ΔϳΎϬϧ ϭ Δϳ΍ΪΑ ΪϨϋ seepage pressure ΏΎδΣ ϢΘϳ
Example (1)
2 ·
§
Ps A J w * H * ¨ 1 ¸
© 15 ¹
§ 12 ·
Ps B J w * H * ¨ 1 ¸
© (1)15 ¹
Soil Mechanics
Chapter (6)
Hydraulic properties
9
2011
of soil
W = ΄θϨϤϟ΍ ϥίϭ
W =J volume =J A 1
F .O .S
W
t 1 . 0 Ÿ safe
F
For Example (2)
ΔϳΎϬϧ ϭ Δϳ΍ΪΑ ΪϨϋ seepage pressure ΏΎδΣ ϢΘϳ
ΔϓΎδϣ ϰϠϋ D.S. ϰϓ ϊϘϳ ΔΑήΘϟ΍ Ϧϣ ˯ΰΟ
ΔϴϧΪόϤϟ΍ ΓέΎΘδϟ΍ Ϧϣ D/2
Soil Mechanics (1)
Chapter (6)
2011
10
Soil Mechanics (1)
Hydraulic properties
of soil
Chapter (6)
Hydraulic properties
11
2011
of soil
8 .5 ·
§
H
*
*
1
¨
¸
A
w
13 ¹
©
10 . 5 ·
§
J w * H * ¨1 Ps B
¸
13 ¹
©
D
J sub . * D *
W
*1
2
§ Ps A Ps B · D
F
¨
¸*
2
©
¹ 2
W
t 1 Ÿ safe
F .O . S
F
Ps
J
ϥ΍έϮϔϟ΍
4) Piping
icr
J sub.
Jw
i
'h
L min .
'h
Gs 1
1 e
H
Ÿ
Nd
ΪϬΠϟ΍ ϲϓ ΪϘϔϟ΍ έ΍ΪϘϣ
Soil Mechanics (1)
Chapter (6)
2011
Hydraulic properties
12
of soil
ΪϬΟ ϱϭΎδΗ ϰτΧ ήΧ΃ ϦϴΑ Δϴγ΃ήϟ΍ ΔϓΎδϤϟ΍ ϰϫ = Lmin
.Ϣγήϟ΍ Ϧϣ αΎϘΗ ϭ
Example (1)
Example (2)
i ! icr Ÿ piping
i icr Ÿ No ˜ piping
FOS
icr
! 1 .0
i
Soil Mechanics (1)
Chapter (6)
2011
13
Examples
Soil Mechanics (1)
Hydraulic properties
of soil
Chapter (6)
2011
14
Soil Mechanics (1)
Hydraulic properties
of soil
Chapter (6)
2011
15
Soil Mechanics (1)
Hydraulic properties
of soil
Chapter (6)
2011
16
Soil Mechanics (1)
Hydraulic properties
of soil
Chapter (6)
2011
17
Soil Mechanics (1)
Hydraulic properties
of soil
Chapter (6)
2011
18
Soil Mechanics (1)
Hydraulic properties
of soil
Soil Mechanics
(1)
Fff
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (6)
Hydraulic properties
2011
of soil
Examples
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
It is required to excavate a trench in the soil formation shown
in figure as below.
i) Find the depth to which the excavation can be safely
carried without causing instability due to uplift of
groundwater.
ii) Find the lowered groundwater depth, if the excavation
is to be extended to 7m
2m
8 m Clay
Jsat t/m3
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2011
of soil
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (7)
1
2011
Stresses in soil
Chapter (7)
Stresses due to loads
ϝΎϤΣϵ΍ ΔΠϴΘϧ ΩΎϬΟϻ΍
Types of loads:-
ϝΎϤΣϷ΍ ω΍Ϯϧ΍
1- Point load = Concentrated load
ΰϛήϤϟ΍ ϞϤΤϟ΍
P
2- Line load
ϰτΨϟ΍ ϞϤΤϟ΍
ήϴγ΍Ϯϣ ςΧ ϭ΍ έϮγ Ϧϣ ΞΗΎϧ 3- Strip load
Δϴτϳήη ΔΣΎδϣ ϰϠϋ ϞϤΤϟ΍
Soil Mechanics (1)
Chapter (7)
Stresses in soil
2
2011
ΔΣΎδϣ ϰϠϋ ϞϤΤϟ΍
4- Rectangle area
q
1- Point load = Concentrated load
ΰϛήϤϟ΍ ϞϤΤϟ΍
P
Z
A
Vz
r
P
I* 2
Z
I = influence factor
I
3
2S
§
1
¨¨
2
r
z
1
(
/
)
©
·
¸¸
¹
2.5
Soil Mechanics (1)
Chapter (7)
Stresses in soil
3
2011
ϰϨΤϨϣ Ϧϣ ϪϴϠϋ ϝϮμΤϟ΍ ϦϜϤϳ ϭ΍
I
2- Line load
Vz
ϰτΨϟ΍ ϞϤΤϟ΍
q
I*
Z
q
I = influence factor
I
·
2§
1
¨¨
¸
2 ¸
S © 1 ( x / z) ¹
2
Z
A
Soil Mechanics (1)
x
Chapter (7)
4
2011
Stresses in soil
ϰϨΤϨϣ Ϧϣ ϪϴϠϋ ϝϮμΤϟ΍ ϦϜϤϳ ϭ΍
I
m = x/z
n = y/z
ϞϤΤϟ΍ ϝϮσ = y
:φΣϻ
ΎϫΪϨϋ ΏΎδΤϟ΍ ΏϮϠτϤϟ΍ ΔτϘϨϟ΍ Ϧϣ ΔϴϘϓϷ΍ ΔϓΎδϤϟ΍ = X, r
ϞϤΤϟ΍ ήϴΛ΄Η ϥΎϜϣ ϭ
ΎϫΪϨϋ ΏΎδΤϟ΍ ΏϮϠτϤϟ΍ ΔτϘϨϟ΍ Ϧϣ Δϴγ΃ήϟ΍ ΔϓΎδϤϟ΍ = Z
ϞϤΤϟ΍ ήϴΛ΄Η ϥΎϜϣ ϭ
Soil Mechanics (1)
Chapter (7)
Stresses in soil
5
2011
Example:
For the shown system of loads determine the
stresses at point (A)
P3, P4
20 t/m
P1, P2
4.0
3.0
Elev.
5.0
A
P4 = 50
P2 = 70
3.0
Plan
P1 = 80
P3 = 60
Solution
ϝΎϤΣϵ΍ Ϧϣ ϦϴϋϮϧ Ϧϣ ϥϮϜΘΗ Δϟ΄δϤϟ΍ ϥ΍ φΣϻ
΍ΪΣ ϰϠϋ ωϮϧ Ϟϛ ΏΎδΣ ϢΘϳ
ϚϟΫ ΪόΑ ΩΎϬΟϻ΍ ϊϤΟ ϢΘϳ ϭ
Soil Mechanics (1)
Chapter (7)
Stresses in soil
6
2011
1- Point load:
load
r
Z
(r/Z)2
80
70
60
50
0
3
4
5
5
5
8
8
0 0.478
0.36
0.25
0.39
I
P/Z2
Vz
6
2- Line load:
X = 4.0 m
Z = 5.0 m
·
2§
1
¨¨
¸
I
2¸
S © 1 (x / z) ¹
Vz
q
I*
Z
2
·
2§
1
¨¨
¸
2¸
S © 1 (4 / 5) ¹
20
0.236 *
5
Total stress = Vz + 6
Soil Mechanics (1)
2
0.236
0.95
Chapter (7)
2011
7
Stresses in soil
ΰϛήϤϟ΍ ϞϤΤϟ΍ Ϟϔγ΃ ΩΎϬΟϷ΍ ϊϳίϮΗ ϝΎϜη΃
Soil Mechanics (1)
Chapter (7)
Stresses in soil
8
2011
ϪϠϴτΘδϤϟ΍ ΔΣΎδϤϟ΍
3- Rectangle area
ϕήσ ΙϼΜΑ ΩΎϬΟϻ΍ ϊϳίϮΗ ϢΘϳ
a) Approximate method
Δϳή΋΍Ϊϟ΍ϭ ΔόΑήϤϟ΍ϭ ΔϠϴτΘδϤϟ΍ ΔΣΎδϤϠϟ ϡΪΨΘδΗ
q
Z
'V
Z/2
L
Z/2
ϲγ΃έ ˻ : ϰϘϓ΍ ˺ ϞϴϤΑ ΩΎϬΟϻ΍ ϊϳίϮΗ ϢΘϳ
q * B * L 'V * (B z)(L z)
ϕϮϓ ϲϟ΍ ΔΣΎδϤϟ΍
'V
q*B*L
(B z)(L z)
ΖΤΗ ϲϟ΍ ΔΣΎδϤϟ΍
Soil Mechanics (1)
Chapter (7)
9
2011
q*
'V
Stresses in soil
S
4
( D)2
'V *
S
4
( D z)2
( D) 2
q
( D z)2
b) Loaded rectangular area
ϪϠϤΤϤϟ΍ ΔΣΎδϤϟ΍ ϥΎϛέ΍ Ϧϣ Ϧϛέ Ϟϔγ΍ ΩΎϬΟϻ΍ ΏΎδΤϟ ϡΪΨΘδΗ
ϞϤΤϟΎΑ
VA q*I
Chart Ϧϣ ϪΑΎδΣ ϢΘϳ
Soil Mechanics (1)
Chapter (7)
Stresses in soil
10
2011
˰Α ϰϨΤϨϤϟ΍ ϞΧΪϧ
n
m
B
Z
L
Z
ϞϤΤϟ΍ ϥΎϜϣ ϭ ΔτϘϨϟ΍ Ϧϣ Δϴγ΃ήϟ΍ ΔϓΎδϤϟ΍ = Z
ϞϤΤϠϟ ήϴϐμϟ΍ ϝϮτϟ΍ = B
ϞϤΤϠϟ ήϴΒϜϟ΍ ϝϮτϟ΍ = L
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
11
:φΣϻ
ΔΣΎδϤϟ΍ ϞΧ΍Ω ϊϘΗ ΔτϘϨϟ΍ ΖϧΎϛ ΍Ϋ΍
ϰϓ (A) ϥϮϜΗ Ϫϴϓ ˯ΰΟ Ϟϛ ˯΍ΰΟ΍ ϰϟ΍ ϞϴτΘδϤϟ΍ ϢϴδϘΗ ϢΘϳ
ϪϧΎϛέ΃ Ϧϣ Ϧϛέ
A
V A q*(I1 I2 I3 I4 )
ΔΣΎδϤϟ΍ ΝέΎΧ ϊϘΗ ΔτϘϨϟ΍ ΖϧΎϛ ΍Ϋ΍
V A q * I( A286) I( A176) I( A253) I( A143)
Soil Mechanics (1)
Chapter (7)
Stresses in soil
12
2011
c) Newmark chart
ϙέΎϣϮϴϧ
chart ϡ΍ΪΨΘγΎΑ ϞϜη ϱϵ ϡΪΨΘδΗ
Newmark chart
ϙϮϠΑ
Soil Mechanics (1)
Chapter (7)
Stresses in soil
13
2011
ϞΤϟ΍ Ε΍ϮτΧ
chart ˰ϟ΍ ϰϠϋ ΩϮΟϮϤϟ΍ ΓήτδϤϟΎΑ AB ςΨϟ΍ ϝϮσ αΎϴϗ -˺
ΚϴΣ Ϣγήϟ΍ αΎϴϘϣ ΪϳΪΤΗ -˻
AB ( cm )
Z (m )
ϩΎτόϤϟ΍ ϪϤγήϟ΍ Ϧϣ αΎϘϳ
Ϣγήϟ΍ αΎϴϘϤΑ ΎϬΘΠϴΘϧ ΩΎϬΟϵ΍ ΏΎδΣ ΏϮϠτϤϟ΍ ΔΣΎδϤϟ΍ Ϣγέ -˼
ΏϮϠτϤϟ΍ ΔτϘϨϟ΍ ϥϮϜΗ ΚϴΤΑ chart ˰ϟ΍ ϰϠϋ ϪϤγήϟ΍ ϊοϭ ϢΘϳ -˽
ή΋΍ϭΪϟ΍ ΰϛήϣ ϰϓ ΎϫΪϨϋ ΩΎϬΟϵ΍ ΏΎδΣ
(N) ΔΣΎδϤϟ΍ ϞΧ΍Ω ΓΩϮΟϮϤϟ΍ ΕΎϛϮϠΒϟ΍ ΩΪϋ ΪϳΪΤΗ -˾
N = 38
Soil Mechanics (1)
Chapter (7)
Stresses in soil
14
2011
ΩΎϬΟϹ΍ ΏΎδΣ -˿
V
0.005 * N * q
ϩΎτόϤϟ΍ ΔΣΎδϤϟ΍ Ϟϔγ΃ ήΛΆϤϟ΍ ΩΎϬΟϹ΍
P
q
ΰϛήϣ ϞϤΣ ϲτόϣ ϥΎϛ ΍Ϋ·
P
L*B
ϦϴΘΣΎδϣ ΩϮΟϭ ΔϟΎΣ ϰϓ
q1
q2
N1
N2
V 0.005* (N1 * q1 N2 * q2 )
ϰϟϭϷ΍ ΔΣΎδϤϟ΍ ϞΧ΍Ω ΓΩϮΟϮϤϟ΍ ΕΎϛϮϠΒϟ΍ ΩΪϋ = N1
ΔϴϧΎΜϟ΍ ΔΣΎδϤϟ΍ ϞΧ΍Ω ΓΩϮΟϮϤϟ΍ ΕΎϛϮϠΒϟ΍ ΩΪϋ = N2
Soil Mechanics (1)
Chapter (7)
Stresses in soil
15
2011
Contact pressure
βϣϼΘϟ΍ ςϐο
ΔΑήΘϟ΍ϭ αΎγϷ΍ ϦϴΑ βϣϼΘϟ΍ ΢τγ ϰϠϋ ϲγ΃ήϟ΍ ΩΎϬΟϹ΍
ϰϠϋ ΪϤΘόϳ ϭ
ΔΑήΘϟ΍ ωϮϧ -˺
ΔΑήΘϟ΍ Δϧϭήϣ -˻
αΎγϷ΍ Γ˯ΎδΟ -˼
Isobars = Pressure bulbs
ςϐπϟ΍ ϯϭΎδΗ ρϮτΧ
ςϐπϟ΍ ϰϓ ΔϳϭΎδΘϤϟ΍ ςϘϨϟ΍ ϦϴΑ ϞμΗ ρϮτΧ Ϧϋ ΓέΎΒϋ ϰϫ
Soil Mechanics (1)
Chapter (7)
2011
16
Soil Mechanics (1)
Stresses in soil
Soil Mechanics
(1)
Fff
Chapter (7)
2011
Stresses in soil
˺
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˻
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˼
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˽
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˾
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˿
Final 2005
Find the stress at point (O)
Z ˰ϟ ϦϴΑϮδϨϣ ΩϮΟϭ φΣϼϧ
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
̀
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
́
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
̂
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺˹
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺˺
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺˻
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺˼
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺˽
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺˾
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺˿
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺̀
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺́
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˺̂
Soil Mechanics (1)
Chapter (7)
2011
Stresses in soil
˻˹
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (8)
Consolidation
(1)
2011
Chapter (8)
Consolidation
ΪϠμΘϟ΍
Compressibility
ΔϴσΎϐπϧϻ΍
a
a
w
w
S
S
ϝΎѧѧϤΣϷ΍ ΩϮѧѧΟ ϭ ΔѧѧΠϴΘϧ ϢѧѧΠΤϟ΍ ϲѧѧϓ κϘϨѧѧϟ΍ ϰѧѧϠϋ ΔѧѧΑήΘϟ΍ ΓέΪѧѧϗ ϲѧѧϫ
ΔΠϴΘϧ ϢΠΤϟ΍ ϲϓ κϘϨϟ΍ ϥϮϜϳ ϭ ΔϴΟέΎΨϟ΍
(έΩΎϧ ) ΐϠμϟ΍ ˯ΰΠϟ΍ ϢΠΣ ϲϓ κϘϧ -˺
(έΩΎϧ) ˯ΎϤϟ΍ ϢΠΣ ϲϓ κϘϧ -˻
ΔΑήΘϟ΍ Ϧϣ ˯ΎϤϟ΍ ΝϭήΧ -˼
ΔΑήΘϟ΍ Ϧϣ ˯΍ϮϬϟ΍ ΝϭήΧ -˽
Soil Mechanics (1)
Chapter (8)
Consolidation
(2)
2011
ΪϠμΘϟ΍
Consolidation
w
S
w
S
ΖѧΤΗ ρΎϐѧπϧϻ΍ ϰѧϠϋ ΔόΒѧθϤϟ΍ ΔѧϴϨϴτϟ΍ ΔѧΑήΘϟ΍ ΓέΪѧϗ Ϧϋ ΓέΎΒϋ Ϯϫ
ϝϼѧΧ ΔѧΑήΘϟ΍ Ϧѧϣ ˯ΎѧϤϟ΍ ΝϭήѧΧ ΔΠϴΘϧ ϚϟΫ ϭ ΔϴΟέΎΨϟ΍ ϝΎϤΣϷ΍ ήϴΛ΄Η
.ΔϨϴόϣ ΔϴϨϣί ΓήΘϓ
Consolidation in Lab. ϞϤόϤϟ΍ ϲϓ ΪϠμΘϟ΍
Oedometer ϡ΍ΪΨΘγΎΑ ϞϤόϤϟ΍ ϲϓ ΪϠμΘϟ΍ ϞϤϋ ϢΘϳ
Soil Mechanics (1)
Chapter (8)
Consolidation
(3)
2011
V
Loading plate
Dial gauge
2 cm
Soil
7.5 cm
ring
Porous plate
Tank
ΔΑήΠΘϟ΍ Ε΍ϮτΧ
ϞϜθϟΎΑ ΎϤϛ ΎϫΩΎόΑ΃ ΔΑήΘϟ΍ Ϧϣ ΔϠϘϠϘϣ ήϴϏ ΔϨϴϋ ΰϴϬΠΗ ϢΘϳ -˺
˯ΎϤϟΎΑ ΎϣΎϤΗ ΓέϮϤϐϣ ϥϮϜΗ ρήθΑ ίΎϬΠϟ΍ ϲϓ ΔϨϴόϟ΍ ϊοϭ ϢΘϳ -˻
˻
Ϣγ/ϢΠϛ ˹̄˻˾ ϩέ΍ΪϘϣ ΩΎϬΟΈΑ ΔϨϴόϟ΍ ϞϴϤΤΗ ϢΘϳ -˼
ϲϟΎΘϟ΍ ϮΤϨϟ΍ ϰϠϋ ΔϋΎγ ˻˽ ϝϼΧ ϢΠΤϟ΍ ϲϓ ήϴϐΘϟ΍ αΎϴϗ ϢΘϳ -˽
(0.5, 1, 2, 4, 8, 15, 30 min., 1, 2, 4, 8, 16, 24 hr)
ϥϮϜϳ Γήϣ Ϟϛ ϲϓ ϭ ήΧ΃ ΩΎϬΟ· ϡ΍ΪΨΘγΎΑ ˽ ϭ ˼ ΓϮτΨϟ΍ έ΍ήϜΗ -˾
˻
Ϣγ/ϢΠϛ ˹̄˻˾ Ύϫέ΍ΪϘϣ ΓΩΎϳΰΑ
(0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, ………)
ΏΎδΤϟ ΕΎϴϨΤϨϣ ΓΪϋ Ϣγέ ϭ ΕΎΑΎδΣ ΓΪϋ ϞϤϋ ϢΘϳ -˿
Compression Characteristics
ρΎϐπϧϻ΍ ΕϼϣΎόϣ
Soil Mechanics (1)
Chapter (8)
Consolidation
(4)
2011
Compression Characteristics
(av, mv, E, Cc, Cs)
ρΎϐπϧϻ΍ ΕϼϣΎόϣ
ϞϤθΗ ϲΘϟ΍ϭ
1- Coefficient of Compressibility (av)
e
eo
av
1
'e
'e
'V
2
e1
Vo
V1
'V
V
ΩΎϬΟϹ΍ ϲϓ ήϴϐΘϟ΍ ϰϟ· ΕΎϏ΍ήϔϟ΍ ΔΒδϧ ϲϓ ήϴϐΘϟ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
eo = Δϴ΋΍ΪΘΑϻ΍ ΕΎϏ΍ήϔϟ΍ ΔΒδϧ
Vo = ςϘϓ ΔΑήΘϟ΍ ϥίϭ Ϧϣ ΞΗΎϨϟ΍ ϝΎόϔϟ΍ ΩΎϬΟϹ΍
Vo
¦J * h
Chapter (6)
'V ϲΟέΎΨϟ΍ ϞϤΤϟ΍ ΔΠϴΘϧ ΩΎϬΟϹ΍ ϲϓ ΓΩΎϳΰϟ΍
'V
Chapter (7)
Soil Mechanics (1)
Chapter (8)
Consolidation
(5)
2011
2- Coefficient of Volume Change (mv)
e
eo
1
'e
2
e1
Vo
'V
V
V1
mv
Hv
'V
mv
'e
1
*
' V 1 eo
mv
av
1 eo
Hv
'v
Vo
'H
Ho
ΩΎϬΟϹ΍ ϲϓ ήϴϐΘϟ΍ ϰϟ· ϰϤΠΤϟ΍ ϝΎόϔϧϻ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
Hv = volumetric strain ϰϤΠΤϟ΍ ϝΎόϔϧϻ΍
Soil Mechanics (1)
'e
1 eo
Chapter (8)
Consolidation
(6)
2011
3- Constrain Modulus = Compression Modulus
e
(Ev)
eo
1
'e
2
e1
Vo
V1
V
'V
Ev
Ev
'V
Hv
1
mv
ϰϤΠΤϟ΍ ϝΎόϔϧϻ΍ ϰϟ· ΩΎϬΟϹ΍ ϲϓ ήϴϐΘϟ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
Soil Mechanics (1)
Chapter (8)
Consolidation
(7)
2011
4- Compression Index (Cc)
e
eo
1
'e
2
e1
LogVo
LogV1
' LogV
Cc
'e
Log (V 1 ) Log (V 2 )
Cc
0.009( L.L 10)
Log V
ϢΘϳέΎϏϮϟ ϲϓ ήϴϐΘϟ΍ ϲϟ· ΕΎϏ΍ήϔϟ΍ ΔΒδϧ ϲϓ ήϴϐΘϟ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
ΩΎϬΟϹ΍
Soil Mechanics (1)
Chapter (8)
Consolidation
(8)
2011
5- Recompression Index (Cr)
ςϐπϟ΍ ΓΩΎϋ·
= Swelling Index (Cs)
= Expansion Index (Ce)
εΎϔΘϧϻ΍
ΩΪϤΘϟ΍
e
12 ςΨϟ΍ Ϟϴϣ Ϯϫ
'e
e1
e2
1
2
LogV1 LogV2
Log V
' LogV
Cs
'e
Log (V 1 ) Log (V 2 )
ϢΘϳέΎϏϮϟ ϲϓ ήϴϐΘϟ΍ ϲϟ· ΕΎϏ΍ήϔϟ΍ ΔΒδϧ ϲϓ ήϴϐΘϟ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
Loop ˰ϟ΍ ΔϘτϨϣ ϰϓ ΩΎϬΟϹ΍
Soil Mechanics (1)
Chapter (8)
Consolidation
(9)
2011
Preconsolidation pressure (Max. past stress)
Vc , Pc )
ϲοΎϤϟ΍ ϲϓ ΔΑήΘϟ΍ Ϫϟ ΖοήόΗ ΩΎϬΟ· ϲμϗ΃ Ϯϫ
e
A
ϲϘϓ΃
ϒμϨϣ
αΎϤϣ
Log V
Log Vc
Ε΍ϮτΨϟ΍
(αϮϘΗ ήΒϛ΍ Ε΍Ϋ) A ΔτϘϨϟ΍ ΪϳΪΤΗ -˺
ϰϨΤϨϤϠϟ αΎϤϣ ςΧ ϭ ϲϘϓ΃ ςΧ Ϣγήϧ A ΔτϘϧ Ϧϣ -˻
ϢϬϨϴΑ Δϳϭ΍ΰϟ΍ ϒμϨϧ -˼
ΔτϘϧ ϲϓ ϒμϨϤϟ΍ ϊτϘϴϟ ϰϨΤϨϤϟ΍ ϲϓ ϢϴϘΘδϤϟ΍ ςΨϟ΍ ΪϤϧ -˽
Vc ϰϠϋ ϞμΤϨϟ ϲγ΃έ ϝΰϨϧ ΔϘΑΎδϟ΍ ϊσΎϘΘϟ΍ ΔτϘϧ Ϧϣ -˾
Soil Mechanics (1)
Chapter (8)
Consolidation
(10)
2011
Over consolidation ratio (O.C.R)
Vc
O.C.R
Vo
ϖΑΎδϟ΍ ΩΎϬΟϹ΍
..........
......
ϲϟΎΤϟ΍ ΩΎϬΟϹ΍
ϲϓ ϡΪΨΘδϳ ϭ ϲϟΎΤϟ΍ ΩΎϬΟϹ΍ ϰϟ· ϖΑΎδϟ΍ ΩΎϬΟϹ΍ ϦϴΑ ΔΒδϨϟ΍ Ϯϫ
ΔϴϨϴτϟ΍ ΔΑήΘϟ΍ ϒϴϨμΗ
O .C . R 1 Ÿ U .C .C
O .C . R 1 Ÿ N .C .C
O .C . R ! 1 Ÿ O .C .C
1- Under consolidation clay (U.C.C)
O .C . R 1
Vc Vo
2- Normal consolidation clay (N.C.C)
O .C . R
Vc
1
Vo
3- Over consolidation clay (O.C.C)
O .C . R ! 1
Vc !Vo
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (8)
Consolidation
(1)
2011
Final ˳Settlement ('HGf
q
ϲ΋ΎϬϨϟ΍ ρϮΒϬϟ΍
L
h
J
H
J
eo
Z
'V
Clay
L+Z
ϲ΋ΎϬϨϟ΍ ρϮΒϬϟ΍ ΏΎδΤϟ Ϧϴϧ΍Ϯϗ ΓΪϋ ϙΎϨϫ
'H
'e
1)
H
1 e
2 )G f ' H mv * ' V * H
3 )G f
'H
1
* 'V * H
Ev
Cc , eo ϰτόϣ ϥΎϛ ΍Ϋ·
O.C .R 1.0
4 )G f
§ V o 'V
Cc
* H * Log ¨¨
1 eo
© Vo
Soil Mechanics (1)
Sand
·
¸¸
¹
Chapter (8)
(2)
2011
Consolidation
Cs , Vc ϰτόϣ ϥΎϛ ΍Ϋ·
O.C .R ! 1.0
V c ! V o 'V
5)G f
§ V o 'V
Cs
* H * Log ¨¨
1 eo
© Vo
·
¸¸
¹
V c V o 'V
§ V 'V · Cs
§V ·
Cc
¸¸ * H * Log¨¨ o
* H * Log¨¨ c ¸¸
1 eo
© V c ¹ 1 eo
© Vo ¹
Gf
H = ϞϤΤϟΎΑ ΓΪϬΠϤϟ΍ Clay ˰ϟ΍ ΔϘΒσ ϚϤγ
Vo
¦ J * h ŸŸ Chapter(6)
Clay ˰ϟ΍ ΔϘΒσ ϒμΘϨϣ ϰΘΣ νέϷ΍ ΢τγ Ϧϣ
Overburden pressure ϰϤδΗ ϭ
'V ŸŸ Chapter(7)
Clay ˰ϟ΍ ϒμΘϨϣ ϰΘΣ ϞϤΤϟ΍ Ϧϣ ΞΗΎϨϟ΍ ΩΎϬΟϹ΍ ϲϓ ΓΩΎϳΰϟ΍
Z = Clay ˰ϟ΍ ϒμΘϨϣ ϰΘΣ ϞϤΤϟ΍ ϥΎϜϣ Ϧϣ Δϴγ΃ήϟ΍ ΔϓΎδϤϟ΍
Soil Mechanics (1)
Chapter (8)
Consolidation
(3)
2011
Degree of Consolidation ( U %)
ΪϠμΘϟ΍ ΔΟέΩ
ϲ΋ΎϬϨϟ΍ ρϮΒϬϟ΍ ϰϟ· Ϧϣί ϱ΃ ΪϨϋ ρϮΒϬϟ΍ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
ϭ΃
ϲ΋΍ΪΘΑϻ΍ ˯ΎϤϟ΍ ςϐο ϰϟ· ˯ΎϤϟ΍ ςϐο ϲϓ ήϴϐΘϟ΍ ϦϴΑ ΔΒδϨϟ΍ ϲϫ
νϭήϔϟ΍ ξόΑ ΎϬϟ ϭ ϪΑΎδΤϟ Δϳήψϧ Terzaghi ϢϟΎόϟ΍ ϡΪϗ ΪϘϟ ϭ
Terzaghi Assumptions
ΔόΒθϣ ϭ ΔδϧΎΠΘϣ ΔΑήΘϟ΍
ρΎϐπϧϼϟ ΔϠΑΎϗ ήϴϏ ˯ΎϤϟ΍ ϭ ΔΑήΘϟ΍ ΕΎΒϴΒΣ
Darcy ϥϮϧΎϗ ϖϴΒτΗ
ΖΑΎΛ ΔϳΫΎϔϨϟ΍ ϞϣΎόϣ
ΪΣ΍ϭ ϩΎΠΗ΍ ϲϓ ςϐπϟ΍ ϭ ΔϋϮϨϤϣ ΔϴϘϓϷ΍ ΔϛήΤϟ΍
ϲγ΃ήϟ΍ ϩΎΠΗϻ΍ ϲϓ ˯ΎϤϟ΍ ΝϭήΧ
Soil Mechanics (1)
Chapter (8)
Consolidation
(4)
2011
Gt
U%
Gf
Uo Ut
U%
Uo
Uo = 'Vat time = zero
U%
'V U t
'V
G t = Ϧϴόϣ Ϧϣί ΪϨϋ ρϮΒϬϟ΍
G f =
ϲ΋ΎϬϨϟ΍ ρϮΒϬϟ΍
U o = Jw hw ϲ΋΍ΪΘΑϻ΍ ˯ΎϤϟ΍ ςϐο
U f =
Ϧϴόϣ Ϧϣί ΪϨϋ ˯ΎϤϟ΍ ςϐο
Ϧϴόϣ Ϧϣί ΪϨϋ ρϮΒϬϟ΍ ΏΎδΤϟ
Gt U % *G f
U% ΏΎδΣ ϲϫ ΔϠϜθϤϟ΍
Soil Mechanics (1)
Chapter (8)
(5)
2011
Consolidation
U % ΏΎδΤϟ
ϲϫ ΕϻΩΎόϣ ϝϼΧ Ϧϣ
TV
TV
S
2
U % Ÿ U % 52.6%
4
1.781 0.933Log 100 U % Ÿ U % ! 52.6%
U% , TV ϦϴΑ ΔϗϼόϠϟ ϰϨΤϨϣ ϦϜϤϳ ϭ΃
ϻϭ΃ TV ΏΎδΣ Ϧϣ ΪΑϻ U% ΏΎδΣ ϦϜϤϳ ϰΘΣ
TV
CV *t
2
d
Soil Mechanics (1)
Chapter (8)
Consolidation
(6)
2011
7 V = Time factor Ϧϣΰϟ΍ ϰϠϋ ΪϤΘόϳ ϞϣΎόϣ
C V = Coeff. of consolidation ΪϠμΘϟ΍ ϞϣΎόϣ
t = time ΪϠμΘϟ΍ ϩΪϨϋ ΏΎδΣ ΏϮϠτϤϟ΍ Ϧϣΰϟ΍
d = effective depth ΝϭήΨϟ΍ ˯ΎϨΛ΃ ˯ΎϤϟ΍ έΎδϣ ϝϮσ
Double drainage = two way drainage
ϦϴΘϬΟ Ϧϣ ϑήλ
Sand
d
H
2
Clay
H
Sand
Single drainage = One way drainage
ΓΪΣ΍ϭ ΔϬΟ Ϧϣ ϑήλ
Sand
d
H
Clay
Rock
Soil Mechanics (1)
H
Chapter (8)
Consolidation
(7)
2011
Cv ΏΎδΣ
Coefficient of Consolidation ΪϠμΘϟ΍ ϞϣΎόϣ
ϦϴΘϘϳήτΑ ϞϤόϤϟ΍ Ϧϣ ϪϴϠϋ ϝϮμΤϟ΍ ϢΘϳ
1- Cassagrand method (Log time method)
2- Taylor method (Root time method)
1- Cassagrand method (Log time method)
U% = 50 % ΪϨϋ Cv ΏΎδΤΑ ϡϮϘϳ
Tv = 0.197
At U% = 50 %
0.197
H
H0
A
ϰϨΤϨϤϟ΍ Ϧϣ t50 ΐδΤϧ ϡίϻ
H50
H100
CV * t50
d2
B
t1 4t1
Soil Mechanics (1)
Chapter (8)
2011
Consolidation
(8)
Ε΍ϮτΨϟ΍
(αϮϘΗ ήΒϛ΍ Ε΍Ϋ ) A ΔτϘϧ ΪϳΪΤΗ -˺
t1 Ϧϣΰϟ΍ ϰϠϋ ϞμΤϨϟ ϲγ΃έ ϝΰϨϧ A ΔτϘϧ Ϧϣ -˻
4 t1 ϩέ΍ΪϘϣ Ϧϣί ϥΎϜϣ ΪϳΪΤΗ -˼
ϰϠϋ ϝϮμΤϠϟ ϰϠϋ΃ ϲϟ· έήϜΗ ϭ X Δϴγ΃ήϟ΍ ΔϓΎδϤϟ΍ ΪϳΪΤΗ -˽
Ho Δϳ΍ΪΒϟ΍ ϲϓ Γ˯΍ήϘϟ΍
ϦϴτΨϟ΍ ΪϤΑ ϚϟΫ ϭ B ΔτϘϧ ϰϠϋ ϝϮμΤϟ΍ -˾
H100 ΔϳΎϬϨϟ΍ ϲϓ Γ˯΍ήϘϟ΍ ϰϠϋ ϞμΤϧ B ΔτϘϧ Ϧϣ -˿
H50 ϰϠϋ ϞμΤϨϟ Ho , H100 ϦϴΑ ΔϓΎδϤϟ΍ ϒμϨϧ -̀
t50 ϰϠϋ ϞμΤϨϟ ϰϘϓ΍ ϝΰϨϧ H50 Ϧϣ -́
Cv ΏΎδΤϟ ϥϮϧΎϘϟ΍ ϰϓ ϖΒτϧ -̂
2- Taylor method (Root time method)
U% = 90 % ΪϨϋ Cv ΏΎδΤΑ ϡϮϘϳ
At U% = 90 %
Tv = 0.848
0.848
CV * t90
d2
ϰϨΤϨϤϟ΍ Ϧϣ t90 ΐδΤϧ ϡίϻ
Soil Mechanics (1)
Chapter (8)
2011
Consolidation
(9)
H
H0
A B
Ε΍ϮτΨϟ΍
ϭ Ho ΪϨϋ ϲγ΃ήϟ΍ έϮΤϤϟ΍ ϊτϘϴϟ ϢϴϘΘδϤϟ΍ ςΨϟ΍ ΪϤϧ -˺
A ΪϨϋ ϲϘϓϷ΍ έϮΤϤϟ΍
L ΔϓΎδϤϟ΍ ΪϳΪΤΗ -˻
1.15
L ΪόΑ ϰϠϋ ϥϮϜΗ ϲΘϟ΍ ϭ B ΔτϘϧ ΪϳΪΤΗ -˼
ϰϓ ϰϨΤϨϤϟ΍ ϊτϘϴϟ H50 ΔτϘϧ ϭ B ΔτϘϧ ϦϴΑ ςΨϟ΍ Ϟμϧ -˽
t90 ϰϠϋ ϞμΤϨϟ ϲγ΃έ ϝΰϨϧ ΎϬϨϣ ΔτϘϧ
Cv ΏΎδΤϟ ϥϮϧΎϘϟ΍ ϰϓ ϖΒτϧ -˾
Soil Mechanics (1)
Chapter (8)
Consolidation
(10)
2011
Field curves
ϊϗϮϤϟ΍ ΕΎϴϨΤϨϣ
ϊѧѧϗϮϤϟ΍ ΕΎѧѧϴϨΤϨϣ Ϧѧѧϋ ήѧѧΒόΘϟ ϞѧѧϤόϤϟΎΑ ΪϠѧѧμΘϟ΍ ΕΎѧѧϴϨΤϨϣ ΢ϴΤѧѧμΗ ϲѧѧϫ
΄ѧѧτΨϟ΍ ΍άѧѧϫϭ .ϊѧѧϗϮϤϟ΍ ϲѧѧϓ ΏέΎѧѧΠΗ Ϧѧѧϣ ΎѧѧϬϴϠϋ ϝϮѧѧμΤϟ΍ ΐόѧѧμϳ ϲѧѧΘϟ΍
ϊѧϗϮϤϟ΍ ϲѧϓ ΔѧϨϴόϟ΍ ϕϮѧϓ ΔѧΑήΘϟ΍ ϥίϭ Ϧѧϣ ΔΠΗΎϧ ϝΎϤΣ΃ ΩϮΟϭ Ϧϣ ΞΗΎϧ
.ϞϤόϤϟ΍ ϲϓ ΓΩϮΟϮϣ ήϴϏ
1- N.C.C. (Vc Vo ( ςΨϟ΍ Ϊϣ – ϒμϨϣ – αΎϤϣ – ϲϘϓ΃ ) ϖΒγ ΎϤϛ Vc ΩΪΣ -˺
ϞϤόϤϟ΍ Ϧϣ eo ΩΪΣ -˻
(eo , Vo ϊσΎϘΗ ) a ΔτϘϨϟ΍ ΪϳΪΤΗ -˼
f ϰϠϋ ϝϮμΤϠϟ ϰϨΤϨϤϟ΍ ϰΘΣ ϲϘϓ΃ ϝΰϨϧ 0.42 eo ϥΎϜϣ ΩΪΣ -˽
ϊϗϮϤϟ΍ ϲϨΤϨϣ ϲϠϋ ϞμΤϨϟ eo , a , f ΔτϘϧ ϦϴΑ Ϟμϧ -˾
Soil Mechanics (1)
Chapter (8)
Consolidation
(11)
2011
2- O.C.C. (Vc!Vo 2
1
Vo ΩΪΣ -˺
ϞϤόϤϟ΍ Ϧϣ eo ΩΪΣ -˻
eo , Vo ϡ΍ΪΨΘγΎΑ b ΔτϘϨϟ΍ ΪϳΪΤΗ -˼
( ςΨϟ΍ Ϊϣ – ϒμϨϣ – αΎϤϣ – ϲϘϓ΃ ) ϖΒγ ΎϤϛ Vc ΩΪΣ -˽
a ϰϓ Vc Ϧϣ ϲγ΃ήϟ΍ ϊτϘϴϟ 12 ςΨϠϟ ϱί΍Ϯϣ Ϣγήϧ b ΔτϘϧ Ϧϣ -˾
f ϰϠϋ ϝϮμΤϠϟ ϰϨΤϨϤϟ΍ ϰΘΣ ϲϘϓ΃ ϝΰϨϧ 0.42 eo ϥΎϜϣ ΩΪΣ -˿
ϊϗϮϤϟ΍ ϲϨΤϨϣ ϲϠϋ ϞμΤϨϟ eo , a , b , f ΔτϘϧ ϦϴΑ Ϟμϧ -̀
Soil Mechanics (1)
Chapter (8)
Consolidation
(12)
2011
3- U.C.C. (VcVo ( ςΨϟ΍ Ϊϣ – ϒμϨϣ – αΎϤϣ – ϲϘϓ΃ ) ϖΒγ ΎϤϛ Vc ΩΪΣ -˺
ϞϤόϤϟ΍ Ϧϣ eo ΩΪΣ -˻
(eo , Vo ϊσΎϘΗ ) b ΔτϘϨϟ΍ ΪϳΪΤΗ -˼
ϲϨΤϨϤϟ΍ ϊϣ Vo ϊσΎϘΗ a ΔτϘϧ ΪϳΪΤΗ -˽
f ϰϠϋ ϝϮμΤϠϟ ϰϨΤϨϤϟ΍ ϰΘΣ ϲϘϓ΃ ϝΰϨϧ 0.42 eo ϥΎϜϣ ΩΪΣ -˾
ϊϗϮϤϟ΍ ϲϨΤϨϣ ϲϠϋ ϞμΤϨϟ eo , a , b , f ΔτϘϧ ϦϴΑ Ϟμϧ -˿
Soil Mechanics (1)
Chapter (8)
Consolidation
(13)
2011
Isochrones
q
q
U
Pore water pressure
V
u
V
Effective stress
ϲΟέΎΨϟ΍ ϞϤΤϟ΍ ΔϣϭΎϘϤΑ ΎϬΑ ΩϮΟϮϤϟ΍ ˯ΎϤϟ΍ ϭ ΔΑήΘϟ΍ ΕΎΒϴΒΣ ϡϮϘΗ
ΔΑήΘϟ΍ Ϧϣ ˯ΎϤϟ΍ ΝήΨΗ Ϧϣΰϟ΍ έϭήϣ ϊϣ ϦϜϟϭ
:Isochrones
effective stress, pore water pressure ϦϴΑ Δϗϼόϟ΍ ΢οϮϳ Ϣγέ ϲϫ
ϝΎόϔϟ΍ ςϐπϟ΍ Ϊϳΰϳ ϭ ˯ΎϤϟ΍ ςϐο ϞϘϳ ΎϬϴϓ ϲΘϟ΍ ϭ ΔϔϠΘΨϣ ΔϨϣί΃ ΪϨϋ
Soil Mechanics (1)
Chapter (8)
Consolidation
(14)
2011
ΕΎψΣϼϣ
:ΔϳΫΎϔϨϟ΍ ϞϣΎόϣ ΪϳΪΤΗ -˺
K mv *Cv *J w
:Field , Lab. ϊϗϮϤϟ΍ ϭ ϞϤόϤϟ΍ ϦϴΑ Δϗϼόϟ΍ -˻
ΔΑήΘϠϟ ΓΰϴϤϣ Δϔλ ΎϬϧϷ ΔΘΑΎΛ ϥϮϜΗ Cv ϥΎϓ Clay βϔϨϟ
CV ( Lab) CV ( Field)
§ Tv* d
¨¨
© t
2
·
¸¸
¹Lab
§ Tv* d
¨¨
© t
2
·
¸¸
¹Field
U% = degree of consolidation ΪϠμΘϟ΍ ΔΟέΩ βϔϧ ΪϨϋ
ϲϠϳ ΎϤϛ ϥϮϧΎϘϟ΍ ΢Βμϳ ϭ ΖΑΎΛ Tv ϥϮϜϳ
§d
¨¨
© t
2
·
¸¸
¹Lab
§d
¨¨
© t
2
·
¸¸
¹ Field
Soil Mechanics (1)
Chapter (8)
(15)
2011
Consolidation
:ϢΠΤϟ΍ ϰϓ ήϴϐΘϟ΍ ϭ ρϮΒϬϟ΍ ϦϴΑ Δϗϼόϟ΍ -˼
G
H
'H 'e 'V
H 1 e V
:Jsat ϡίϻ Gs , Wc ϲτόϣ ϥΎϛ ΍Ϋ΍ -˽
eo
J sat
Gs *Wc
Ÿ Sr 1 Ÿ sarurated
Sr
(Gs Sr * eo )J w
Ÿ Sr 1
1 eo
Soil Mechanics (1)
Soil Mechanics
(1)
Fff
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Chapter (8)
Consolidation
2011
Soil Mechanics (1)
Part(2)
Soil Mechanics
(1)
Fff
Final Exam
ϯήψϧ
Final Exam
˺
ϯήψϧ
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Soil Mechanics (1)
Part(4)
Soil Mechanics
(1)
Fff
Final Exam
2011
Final Exam
˺
2011
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Soil Mechanics (1)
Part(1)
Soil Mechanics
(1)
Fff
Final Exam
2011
Final Exam
˺
2011
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Soil Mechanics (1)
Part(3)
Soil Mechanics
(1)
Fff
Final Exam
2011
Final Exam
˺
2011
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Soil Mechanics (1)