Soil Mechanics (1) Fff
Soil Mechanics (1) Fff
Chapter (1)
Physical properties
(1)
2011
Soil Mechanics for Second Year Civil Engineering Course Content: ΔϴΎϳΰϴϔϟ ιϮΨϟ
Chapter (1): Physical Properties. Chapter (2): Grain Size Distributions.
ΕΎΒϴΒΤϠϟ ϰϤΠΤϟ ϊϳίϮΘϟ ΔΑήΘϟ ϡϮϗ
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 ιϮΨϟ 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 ΔϴΎϳΰϴϔϟ ιϮΨϟ -: 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 = ΕΎϏήϔϟ 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 ΕΎϏήϔϟ ΔΒδϧ
1) Void ratio: (e)
e
Vv
Vv Vs
Vs
ΔΑήΘϠϟ ΐϠμϟ ˯ΰΠϟ ϢΠΣ ϰϟ· ΕΎϏήϔϟ 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· ΕΎϏήϔϟ ϢΠΣ ϦϴΑ ΔΒδϨϟ ϲϫ
n
0.0 1.0 ϊΒθΘϟ ΔΟέΩ
3) Degree of saturation: (Sr)
Sr
Vw Vv
Vv
Vw
ΔΑήΘϟ ϲϓ ΓΩϮΟϮϤϟ ΕΎϏήϔϟ 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
ϲΎϤϟ 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 ΡϭήΘΗϭ
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
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2011
φΣϝ
1
J
Dr
J
mim
1
J
1
mim
o
1
J
max
n (1) Â&#x; e 1 n e ( 2) Â&#x; n 1 e (3) Â&#x; sr * e Gs * Wc ( 4) Â&#x; J d (5) Â&#x; J b
φϔΣ
φϔΣ
ΎϏΗΎΒΛ· Î?ĎŽĎ Ď„ĎŁ όϴϧÎ?ĎŽĎ˜Ď&#x;Î? ÎžĎŒÎ‘ ϙΎϨύ
Jb 1 Wc Gs sr * e ( ) *J w 1 e
Soil Mechanics (1)
Chapter (1)
Physical properties
(9)
2011
ϢΠΤĎ&#x;Î? Ď ĎĽÎŻĎŽĎ&#x;Î? όϴΑ Î”Ď—ĎźĎŒĎ&#x;Î?
φϔΣ
Vw
w
Ww
Vs
s
Ws
Ws Gs * J w *Vs Ww J w *Vw ΕΎ˰ΗΎ˰Β˰ΛϚÎ?
Prove that
Jb
§ Gs sr * e ¡ ¨ ¸ *J w Š 1 e š OR
Find the relation between
Jb, Gs, Sr, e, Jw Soil Mechanics (1)
φϔΣ
ÎŽĎ´Ď?Î˜Ďł Ďť ΖΑΎΛ Î?Ď ÎźĎ&#x;Î? ˯ΰΠĎ&#x;Î?
ÎŽĎ´Ď?Î˜Ďł Ďť ΖΑΎΛ Î?Ď ÎźĎ&#x;Î? ˯ΰΠĎ&#x;Î?
a
Chapter (1)
Physical properties
(10)
2011
ΕΎΒΛϹ ΕϮτΧ ( ϢϬϓάΣ ) ϢϬΑ ΪΒϧ ϻ ( J or Gs ) Ϫϴϓ ϥϮϧΎϘϟ ϥΎϛ Ϋ· -˺ ϢϬϴϓ ΪΣϭ 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 ÎƒÎŞÎ’Ď§ Ďť ϹΏĎ&#x;Î? ϲϓ Î˝ĎŽĎŒĎ§ -Ë˝
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 ΕΎΒΛϚÎ? ΕÎ?ώτΧ ( ϢϏϓΏΣ ) ϢϏΑ ÎƒÎŞÎ’Ď§ Ďť ( J or Gs ) ĎŞĎ´Ď“ ĎĽĎŽĎ§ÎŽĎ˜Ď&#x;Î? ĎĽÎŽĎ› Î?΍· -Ëş ΎϏΑ ÎƒÎŞÎ’Ď§ (Wc ) Ď°Ď˜Î’Î— -Ëť
Wc
Ww Ws
Soil Mechanics (1)
Chapter (1)
Physical properties
(12)
2011
1= ĎĄÎŽĎ˜Ď¤Ď&#x;Î? νΎϔϧ Assume (Ws = 1) Wc = Ww Prism ϲϓ Î˝ĎŽĎŒĎ§ -Ëź
Wc Jw 1 Gs
Wc 1
(Jd , Jb ) ϪΑ ÎƒÎŞÎ’Ď§ Ďť ϹΏĎ&#x;Î? ϲϓ Î˝ĎŽĎŒĎ§ -Ë˝
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 ΕϮτΧ ( 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 ÎƒÎŞÎ’Ď§ Ďť ϹΏĎ&#x;Î? ϲϓ Î˝ĎŽĎŒĎ§ -Ë˝ ĎŞĎ´Ď“ ÎžĎłĎŽĎŒÎ˜Ď&#x;Î? Ď˘Î˜Ďł Ďť 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 ΕΎΒΛϚÎ? ΕÎ?ώτΧ ( ϢϏϓΏΣ ) ϢϏΑ ÎƒÎŞÎ’Ď§ Ďť ( J or Gs ) ĎŞĎ´Ď“ ĎĽĎŽĎ§ÎŽĎ˜Ď&#x;Î? ĎĽÎŽĎ› Î?΍· -Ëş ϢϏϨϣ Ϲ΄Α ÎƒÎŞÎ’Ď§ (n, e ) Ď°Ď˜Î’Î— -Ëť
e
Vv Vs
Assume (Vs = 1) e = Vv
Soil Mechanics (1)
Chapter (1)
Physical properties
(15)
2011
Prism ϲϓ Î˝ĎŽĎŒĎ§ -Ëź
e
1
(n) ϪΑ ÎƒÎŞÎ’Ď§ Ďť ϹΏĎ&#x;Î? ϲϓ Î˝ĎŽĎŒĎ§ -Ë˝
vv vt
n
e 1 e
Prove that
n e 1 n OR
Find the relation between
e, n ΕΎΒΛϚÎ? ΕÎ?ώτΧ ( ϢϏϓΏΣ ) ϢϏΑ ÎƒÎŞÎ’Ď§ Ďť ( J or Gs ) ĎŞĎ´Ď“ ĎĽĎŽĎ§ÎŽĎ˜Ď&#x;Î? ĎĽÎŽĎ› Î?΍· -Ëş
Soil Mechanics (1)
Chapter (1)
Physical properties
(16)
2011
ϢϏϨϣ Ϲ΄Α ÎƒÎŞÎ’Ď§ (n, e ) Ď°Ď˜Î’Î— -Ëť
n
Vv Vt
Assume (Vt = 1) n = Vv Prism ϲϓ Î˝ĎŽĎŒĎ§ -Ëź
n 1 1-n
(e) ϪΑ ÎƒÎŞÎ’Ď§ Ďť ϹΏĎ&#x;Î? ϲϓ Î˝ĎŽĎŒĎ§ -Ë˝
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, Js Jd Jw ΕΎΒΛϚÎ? ΕÎ?ώτΧ ϢϏϨϣ Ϲ΄Α ÎƒÎŞÎ’Ď§ ( Js Jd Jw) ΔĎ&#x;ϝΪΑ ĎŞĎ Ď› ĎĽĎŽĎ§ÎŽĎ˜Ď&#x;Î? -Ëş
Js
Ws Vs
Assume (Vs = 1) Js = Ws ĎŠÎ’Î¸Î˜Ď&#x;Î? ΔĎ&#x;ÎŽÎŁ Ď°Ď“ ĎŚĎœĎ&#x; Ď Prism ϲϓ Î˝ĎŽĎŒĎ§ -Ëť
Js Jd
Js 1 Jd
w
1
S
¡ §Js ¨¨ 1 ¸¸J w š ŠJd
Js
Soil Mechanics (1)
Chapter (1)
Physical properties
(18)
2011
Jd
Ws Vt
Vt
Js Jd
Js Vt
(Wc) ϲϓ Î˝ĎŽĎŒĎ§ -Ëź
§Js ¡ ¨¨ 1 ¸¸ J w ŠJd š
Ww Ws
Wc
Js
J s
J d J w Jd *J s
Wc
Prove that
Sr
Wc Wc ( sat .) OR
Find the relation between
Sr, Wc Wc(sat) ΕΎΒΛϚÎ? ΕÎ?ώτΧ ( Wc ) ˰Α ÎƒÎŞÎ’Ď§ -Ëş
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 ήΧϷϭ ˯Ϯϫ ϲϓ ΪΣϭ ) 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 ϲΑήΗ Ϊγ
e1
e2
V1
V2
Jd2 J d1
1 e1 1 e2
V1 V2
ϞΎδϤϟ ωϮϧ Ϧϴόϣ ϢΠΣ ϭ ϥίϭ ΔϤϴϗ ΎϬΑ ΔϟΎδϣ
Ϧϴόϣ ϢΠΣ ϭ ϥίϭ ΔϤϴϗ ΎϬϴϓ ΪΟϮϳ ϻ ΔϟΎδϣ
prism ˰ϟ Ϣγέ ϢΘϳ ΔϟΎδϣ ϯ ΔϳΪΑ ϲϓ
prism ˰ϟ Ϣγέ ϢΘϳ ΔϟΎδϣ ϯ ΔϳΪΑ ϲϓ
a
a
w
w
S
S Assume
ΕΎϴτόϤϟ ϡΪΨΘγΎΑ prism ˰ϟ ˯ΰΟ ϸϤϧ
Vs = 1
ϡΪΨΘγ ϊϣ
Soil Mechanics (1)
Soil Mechanics (1) Fff
Chapter (1)
Physical properties
1
2011
όϴϧÎ?ĎŽĎ˜Ď&#x;Î? ÎşÎ¨Ď ĎŁ
1) Â&#x; e 3) Â&#x; Sr
Vv Vs Vw Vv
Vv Vt
2) Â&#x; n 4 ) Â&#x; Wc
5) Â&#x; J b
Wt Vt
6) Â&#x; J
7) Â&#x; J s
Ws Vs
8 ) Â&#x; J sat
9) Â&#x; J sub. J sat. J w 11 ) Â&#x; Dr
d
10 ) Â&#x; Gs
e max e o e max e mim
Ww Ws
Ws Vt Wt Vt
Js Jw
ΎϏΗΎΒΛ· Î?ĎŽĎ Ď„ĎŁ όϴϧÎ?ĎŽĎ˜Ď&#x;Î? ÎžĎŒÎ‘ ϙΎϨύ
e n 13) Â&#x; n 12) Â&#x; e 1 e 1 n Jb 14) Â&#x; sr * e Gs * Wc 15) Â&#x; J d 1 Wc Gs sr * e ) *J w 16) Â&#x; J b ( 1 e
Soil Mechanics (1)
Chapter (1)
Physical properties
2
2011
ϢΠΤĎ&#x;Î? Ď ĎĽÎŻĎŽĎ&#x;Î? όϴΑ Î”Ď—ĎźĎŒĎ&#x;Î?
Ws
Gs * J w * Vs
Ww
J w * Vw
( ÎŽÎ&#x;ΎΤϤĎ&#x;Î? ΔĎ&#x;΄δϣ ϲϓ ) φΣϝ
(1)
(2)
Pit ΎΠΤϣ
Embankment ϲΑÎ?ΎΗ ÎŞÎł
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 Â&#x; Ww 0.53 2.65 Ww J w * Vw Vw 1.0
Wt Jb Vt 2.65 0.53 1.97 Â&#x; 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 Â&#x; Vt Vt
Gs
0 .66 Gs
Soil Mechanics (1)
Chapter (1)
Physical properties
6
2011
Wt Vt
Jb 1 . 77
Wt Wt 0 . 66 Gs
1 . 18 Gs
Vw Sr Vv 0 . 18 Gs 0 .6 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
ΎΠΤϣ 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 Â&#x; 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 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 Ëş
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 Ëť
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 Â&#x; 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 Â&#x; 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 Jd Sr b) Wc Jsat saturated state
a 0.7
w
0.59
0.59
8.15 9.85 S
1
Wc
e
0.22
Ww Ws
Vv Â&#x; 0 .7 Vs
2.69
Ww Â&#x; Ww 2.69
Vv Â&#x; 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
ϦϴϧϮϘϟ 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
ϦϴϧϮϘϟ ϰϓ ϖϴΒτΘϟ ϦϜϤϳ
ϞΎδϤϟ 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
ίΰϫ
-:ΔΑήΠΘϟ ΕϮτΧ 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 ίΰϬϟ ϞϴϐθΗ -˽ ϞΨϨϣ Ϟϛ ϰϠϋ (ϊΟήϟ)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 ϲϤϛήΘϟ
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 ) ϲγέ ήΧ ϭ ( sieve size ) ϲϘϓ έϮΤϣ Ϣγέ ϢΘϳ -˺ Ϣγ ˺ Ϟϛ ΔϳϭΎδΘϣ ΕΎϓΎδϣ ϰϟ· ϲγήϟ 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 ϊϗϮϟ 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
ΕΎΒϴΒΤϟ Ϧϣ % ˺˹ ϩΪϨϋ ήϤϳ ϱάϟ ήτϘϟ
D 30
ΕΎΒϴΒΤϟ Ϧϣ % ˼˹ ϩΪϨϋ ήϤϳ ϱάϟ ήτϘϟ
D 60
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 ϡΪΨΘγ
Uses of grading curve: 1) Uniform coefficient (Cu) Cu
D 60 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 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 ΪΣϭ 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 ΎϬΗΎϏήϓ) 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 ΕϮτΧ ˯Ύϣ ϪΑ ˼ Ϣγ ˺˹˹˹ έΎΒΨϣ έΎπΣ· ϢΘϳ -˺ ϢΟ ˾˹ ΎϬϧίϭ ˻˹˹ Ϣϗέ ϞΨϨϤϟ Ϧϣ ΓέΎϤϟ ΔΑήΘϟ Ϧϣ ΔϨϴϋ άΧ ϢΘϳ -˻ ΙΪΤϳ ϥ ϰϟ· ήϤΘδϤϟ Νήϟ ϊϣ έΎΒΨϤϟ ϞΧΩ ΔϨϴόϟ ϊοϭ ϢΘϳ -˼ έΎΒΨϤϟ ϞΧΩ 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 ϞΎδϟ ϞΧΩ ΔϳήΪϟ 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 -˼ ϞΎδϟ ΔΟϭΰϟ = P -˽
P ( poise ) 981
V
Z t
gm . sec . / cm 2
Js Jw * D2 D 18 P ΔΒϴΒΤϟ ρϮϘγ ΔϓΎδϣ = Z ΔΒϴΒΤϟ ρϮϘγ Ϧϣί = t
Soil Mechanics (1)
Chapter (2)
11
2011
Grain Size Distribution
( N ) ÎΎϤĎ&#x;Î? ΔΒδϧ Ď°Ď Ď‹ ϞΟΤϧ Ď’Ď´Ď› 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
ΔΑΎΠΘĎ&#x;Î? ΔϳÎ?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 )Â&#x; 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 D60 D10
D10
ϲΒϴΒΤϟ ΝέΪΘϟ ϰϨΤϨϣ ϥ ϚϟΫ ϰϨόϳ ΔΑήΘϟ ϥϮϜΗ ϲϟΎΘϟΎΑϭ ΎϣΎϤΗ ϲγέ ϥϮϜϳ very uniform soil
Soil Mechanics (1)
ϲΒϴΒΤϟ ΝέΪΘϟ ϰϨΤϨϣ
Soil Mechanics (1) Fff
Zagazig University
Structural Eng. Department Ëş
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 Ëť
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 and P = 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 ΪΣϭ 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 and P = 0.01 poise. Sol.
:Ď&#x2020;ÎŁĎť ϲύ όϴϧÎ?ĎŽĎ&#x2014; Î&#x2122;ĎźÎ&#x153;Î&#x2018; Î&#x17D;ĎŹĎ ÎŁ ϢÎ&#x2DC;Ďł Ď&#x17E;Î&#x2039;Î&#x17D;δϤĎ&#x;Î? ĎŚĎŁ Ď&#x2030;ώϨĎ&#x;Î? Î?ÎŹĎŤ
C * D2 J s J w Â&#x;Â&#x; C 18P Z Â&#x;Â&#x; V t
1) Â&#x; V
2) Â&#x; J i (t 3) Â&#x; J t
0)
1 ¡ Ws § J w ¨1 ¸ Vt Š Gs š
1 ¡ N *Ws § Jw ¨1 ¸ Vt Š Gs š
Î?ϴγΎÎ&#x2DC;Ď&#x;Î? Î&#x201D;ĎłÎ?ÎŞÎ&#x2018; commencement of sedimentation Ď?Î&#x17D;Ď&#x2014; Î?ÎŤÎ? 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 Ň?0.01 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 ϡϮϗ ϞϜθΘϟ ϰϠϋ (ΔϴϴϤτϟ ϭ ΔϴϨϴτϟ) ΔϤϋΎϨϟ ΔΑήΘϟ ΓέΪϗ Ϧϋ ΓέΎΒϋ Ϯϫ (ςϟΰϟϭ Ϟϣήϟ) ΔϨθΨϟ ΔΑήΘϠϟ ϡΪΨΘδΗ ϻϭ ϡϮϘϟ 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· ΔϠΎδϟ ΔϟΎΤϟ Ϧϣ ΔΑήΘϟ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ ϲΎϤϟ ϯϮΘΤϤϟ Ϯϫ ϞϮδϟ ϙϮϠγ ΔΑήΘϟ ϚϠδΗ ϩΪϨϋ ϱάϟϭ βϜόϟ ϭ ΔϧΪϠϟ ΔϟΎΤϟ (Γήϴϐλ κϗ ΔϣϭΎϘϣ ΎϬϟ) ΔΟΰϠϟ Casagrande's method:
ΪϧήΟίΎϛ ΔϘϳήσ
ΪϧήΟίΎϛ ίΎϬΟ ΪϧήΟίΎϛ ίΎϬΟ Grooving tools ϖθϟ ΓΩ
Soil Mechanics (1)
Chapter (3)
Consistency of fine soil
3
2011
:ΔϘϳήτϟ ΕϮτΧ ˽˹ 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 ΓΩ ϡΪΨΘγΎΑ (˽ ϖθϟ Ϧϣ Ϣϣ ˺˼ ϖϠϐϟ Δϣίϼϟ ΕΎΑήπϟ ΩΪϋ ΪϳΪΤΗ ϭ ίΎϬΠϟ ϞϴϐθΗ (˾ ϯήΧ ϩΎϴϣ ΔϴϤϛ ϡΪΨΘγ ϊϣ ΔϘΑΎδϟ ΕϮτΨϟ βϔϧ έήϜΗ ϢΘϳ (˿
Wc N ΕΎΑήπϟ ΩΪϋ ϭ ϲΎϤϟ 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· ΔϠΎѧδϟ ΔѧϟΎΤϟ Ϧѧϣ ΔѧΑήΘϟ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ ϲΎϤϟ ϯϮΘΤϤϟ Ϯϫ ϞϮѧѧδϟ ϙϮϠѧѧγ ΔѧѧΑήΘϟ ϚϠѧѧδΗ ϩΪѧѧϨϋ ϱάѧѧϟϭ βѧѧϜόϟ ϭ ΔѧѧϧΪϠϟ ΔѧѧϟΎΤϟ ϖѧѧη ϖѧѧϠϏ ϦѧѧϜϤϳ ϩΪѧѧϨϋ ϱάѧѧϟ ϭ (Γήϴϐѧѧλ κѧѧϗ ΔѧѧϣϭΎϘϣ ΎѧѧϬϟ ) ΔѧѧΟΰϠϟ ΪϧήΟίΎϛ ΔϘϳήσ ϝϼΧ Ϧϣ ϚϟΫϭ ΔΑήο ˻˾ ϡΪΨΘγΎΑ Ϣϣ ˺˼ ϪϟϮσ 2) Plastic limit: (P.L.)
ΔϧϭΪϠϟ ΪΣ
ϰϟ· ΔϧΪϠϟ ΔϟΎΤϟ Ϧϣ ΔΑήΘϟ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ ϲΎϤϟ ϯϮΘΤϤϟ Ϯϫ ΔΒϠμϟ ΔΒη ΔϟΎΤϟ
:ΔϘϳήτϟ ΕϮτΧ ˽˹ 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 ΔϳΪΑ ΪϨϋ ςϴΨϟ ήτϗ ΪϳΪΤΗ (˽ ϯήΧ ϩΎϴϣ ΔϴϤϛ ϡΪΨΘγ ϊϣ ΔϘΑΎδϟ ΕϮτΨϟ βϔϧ έήϜΗ ϢΘϳ (˾
Wc d ςϴΨϟ ήτϗ ϭ ϲΎϤϟ 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 ϲΎѧϤϟ ϯϮΘΤϤϟ Ϯϫ ϕΰϤΗ ΙϭΪΣ ϥϭΩ Ϣϣ ˼ ϩήτϗ ςϴΧ ϦϳϮϜΗ ϦϜϤϳ ϩΪϨϋ ϱάϟϭ 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 ϲΎѧϤϟ ϯϮѧΘΤϤϟ Ϯϫ ϱϭΎѧѧδϣ εΎѧѧϤϜϧϻ ΔѧѧϟΎΣ ϲѧѧϓ ˯ΎѧѧϤϟ ϢѧѧΠΣ ϥϮѧѧϜϳ ϩΪѧѧϨϋ ϱάѧѧϟϭ 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.)ϡΪΨΘγΎΑ ΔΑήΘϟ ϒϴϨμΗ 1) Plasticity index ( IP )
ΔϧϭΪϠϟ ήηΆϣ
ΔϧϭΪϠΑ ϪϟϼΧ ΔΑήΘϟ ϑήμΘΗ ϱάϟ ϲΎϤϟ 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 )
ϡϮϘϟ 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 έΪϘϣ 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
Ëş
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 Ëť
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· ΔϠΎδϟ ΔϟΎΤϟ Ϧϣ ΔΑήΘϟ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ ϲΎϤϟ ϯϮΘΤϤϟ Ϯϫ κѧϗ ΔѧϣϭΎϘϣ ΎѧϬϟ ) ΔѧΟΰϠϟ ϞϮѧδϟ ϙϮϠѧγ ΔΑήΘϟ ϚϠδΗ ϩΪϨϋ ϱάϟϭ βϜόϟ ϭ ϚѧϟΫϭ ΔΑήѧο ˻˾ ϡΪΨΘѧγΎΑ Ϣϣ ˺˼ ϪϟϮσ ϖη ϖϠϏ ϦϜϤϳ ϩΪϨϋ ϱάϟ ϭ (Γήϴϐλ ΪϧήΟίΎϛ ΔϘϳήσ ϝϼΧ Ϧϣ Plastic limit: (P.L.)
ΔϧϭΪϠϟ ΪΣ
ΔΒѧη ΔѧϟΎΤϟ ϰѧϟ· ΔѧϧΪϠϟ ΔѧϟΎΤϟ Ϧѧϣ ΔѧΑήΘϟ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ ϲΎϤϟ ϯϮΘΤϤϟ Ϯϫ ϕΰϤΗ ΙϭΪΣ ϥϭΩ Ϣϣ ˼ ϩήτϗ ςϴΧ ϦϳϮϜΗ ϦϜϤϳ ϩΪϨϋ ϱάϟϭ ΔΒϠμϟ Shrinkage limit: (S.L.)
εΎϤϜϧϻ ΪΣ
ΔѧϟΎΤϟ ϰѧϟ· ΔΒϠѧμϟ ΔΒη ΔϟΎΤϟ Ϧϣ ΔΑήΘϟ ϝϮΤΘΗ ϩΪϨϋ ϱάϟ ϲΎϤϟ ϯϮΘΤϤϟ Ϯϫ ˯ϮѧϬϟ ϢѧΠΤϟ ϱϭΎѧδϣ εΎѧϤϜϧϻ ΔѧϟΎΣ ϲѧϓ ˯ΎϤϟ ϢΠΣ ϥϮϜϳ ϩΪϨϋ ϱάϟϭ 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 ϲΎѧѧϤϟ 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 WcËą 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
ÎŽÎ&#x153;Ď&#x203A;Î&#x192; clay Ď°Ď Ď&#x2039; ϹώÎ&#x2DC;ΤÎ&#x2014; ÎŽÎ&#x2019;Ď&#x203A;Î? IP Î&#x17D;ĎŹĎ&#x; ϲÎ&#x2DC;Ď&#x;Î? Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď&#x;Î? 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)
ÎŽÎ&#x2019;Ď&#x203A;Î? ĎŚĎŁ ΊΪΤϧ Ď Î&#x201D;Î&#x2018;ÎŽÎ&#x2014; Ď&#x17E;Ď&#x153;Ď&#x; Jb Jd e Î?Î&#x17D;δΣ ϢÎ&#x2DC;Ďł
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 ιϮΨϟ .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 ϱήΧϭ 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 ΔΤήϟΎΑ 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 ΩϮϤϟ 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 ϲѧΘϟϭ ΔѧϤϋΎϧ ΩϮѧϣ ϱϮѧΘΤΗ ΔϨѧθΧ ΩϮѧϣ Ϧѧϣ ωϮϧ ΓΪϋ Ϧϋ ΓέΎΒϋ ϪϧϭΪϟ
A- 4 ˻˹˹ Ϣϗέ ϞΨϨϣ Ϧϣ ήΜϛ ϭ % ̀˾ ϪϨϣ ήϤϳ silt Ϧϋ ΓέΎΒϋ A- 5 ΔΌϴγ ΩϮϣ ϭ ΔϴσΎτϣ ΩϮϣ 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 ΕήϴϴϐΗ ΎϬϟ ΙΪΤϳϭ
A-7 ΔѧϴσΎτϣ Δѧϧήϣ ιϮѧΧ ΎѧϬϟϭ ϲϟΎѧϋ liquid limit ΎѧϬϟ clay Ϧѧϋ ΓέΎѧΒϋ ΓήϴΒϛ ϪϴϤΠΣ ΕήϴϴϐΗϭ
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 ϡΪΨΘγ 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 â&#x20AC;&#x201C; 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 ΕΎϏήϔϟ 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 ΕϮτΧ .˻˹ 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 ϡΪΨΘγΎΑ ΔΑήο ˻˾ Ϣγ ˼˹̄˾ W1
ύέΎϓ ΐϟΎϘϟ ϥίϭ ΪϳΪΤΗ -˽
W2
ΔΑήΘϟ + ΐϟΎϘϟ ϥίϭ ΪϳΪΤΗ -˾ ΔΑήΘϠϟ ΔϴϠϜϟ ΔϓΎΜϜϟ ΏΎδΣ -˿
W2 W1 Vt 1000
Jb
ΔΑϮσήϟ ϯϮΘΤϣ ΪϳΪΤΗ ϭ ΐϟΎϘϟ ϞΧΩ Ϧϣ ΔΑήΘϟ Ϧϣ ˯ΰΟ άΧ -̀ W3
ϥήϔϟ ϰϓ ΎϬόοϭ ϞΒϗ ΔϨϴόϟ ϥίϭ
W4
ϥήϔϟ Ϧϣ ΎϬΟήΧ· ΪόΑ ΔϨϴόϟ ϥίϭ
Wc
W3 W4 W4
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(3)
2011
Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď Ď&#x; Î&#x201D;Ď&#x201C;Î&#x17D;Î Ď&#x;Î? Î&#x201D;Ď&#x201C;Î&#x17D;Î&#x153;Ď&#x153;Ď&#x;Î? Î?Î&#x17D;δΣ -Ě
Jd
Jb (1 Wc )
ϯΎΧÎ&#x192; ĎŠÎ&#x17D;Ď´ĎŁ Î&#x201D;Î&#x2019;δϧ ĎĄÎ?ΪΨÎ&#x2DC;ÎłÎ? Ď&#x160;ĎŁ Î&#x201D;Ď&#x2DC;Î&#x2018;Î&#x17D;δĎ&#x;Î? Î&#x2022;Î?ĎŽĎ&#x201E;ΨĎ&#x;Î? βĎ&#x201D;ϧ ÎÎ?ÎŽĎ&#x153;Î&#x2014; -Ě&#x201A;
Jd Wc Wc, Jd ĎŚĎ´Î&#x2018; Î&#x201D;Ď&#x2014;ĎźĎ&#x152;Ď&#x;Î? ϢγΠϢÎ&#x2DC;Ďł
-˺˚
Jd Jd max.
Wc O.M.C. O.M.C. = Optimum moisture content Jd max. = maximum dry density
Soil Mechanics (1)
Ď&#x17E;Î&#x153;ĎŁĎľÎ? Î&#x201D;Î&#x2018;ĎŽĎ&#x192;ÎŽĎ&#x;Î? ĎŻĎŽÎ&#x2DC;Τϣ Î&#x201D;Ď&#x201C;Î&#x17D;Î&#x; Î&#x201D;Ď&#x201C;Î&#x17D;Î&#x153;Ď&#x203A; ϲΟĎ&#x2014;Î?
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 ΕέΎτϤϟ ϕήσ ϭ
Factors affecting compaction:
1- Water content
ϚϣΪϟ ϲϓ ήΛ΄Η ϲΘϟ ϞϣϮόϟ ϲΎϤϟ ϯϮΘΤϤϟ
2- Compaction effort
ϚϣΪϟ ΪϬΟ
3- Soil type
ΔΑήΘϟ ωϮϧ
Soil Mechanics (1)
Chapter (5)
Soil Compaction
(5)
2011
ϲΎϤϟ 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 ΩΩΰΗ ϲΎϤϟ ϯϮΘΤϤϟ ΓΩΎϳΰΑ
ΔΑϮσήϟ ϯϮΘΤϣ Ϧϋ ϲΎϤϟ 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 ΕΎϏήϔϟ 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 n 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) Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď&#x;Î? Ď&#x2030;ώϧ
Gravel Sand Silt Clay
Size nÂ&#x; J d max n O .M .C p Î&#x201D;Î&#x2018;ĎŽĎ&#x192;ÎŽĎ&#x;Î? ϹώÎ&#x2DC;Τϣ Ď&#x17E;Ď&#x2DC;Ďł Ď Î&#x201D;Ď&#x201C;Î&#x17D;Î Ď&#x;Î? Î&#x201D;Ď&#x201C;Î&#x17D;Î&#x153;Ď&#x153;Ď&#x;Î? ΪϳΰÎ&#x2014; Î&#x2022;Î&#x17D;Î&#x2019;Ď´Î&#x2019;ΤĎ&#x;Î? ϢΠΣ Î&#x201C;ΊÎ&#x17D;ϳΰÎ&#x2018; Ď&#x17E;Î&#x153;ĎŁĎľÎ?
Soil Mechanics (1)
Soil Mechanics (1) Fff
Chapter (5)
Soil Compaction
(1)
2011
Compaction in field
ϊϗϮϤϟ ϲϓ ϚϣΪϟ
ϝΎѧϤϋ΄Α ΔѧτΒΗήϤϟ ϊϳέΎѧθϤϟ ϲѧϓ Δϴѧδϴήϟ ΕΎѧΒϠτΘϤϟ ΪѧΣ ΔѧΑήΘϟ ϚѧϣΩ ϞΜϤϳ .ΕѧѧθϨϤϟ ΕΎѧѧγΎγ ϭ ΔѧѧϴΑήΘϟ ΩϭΪѧѧδϟ ϭ ϕήѧѧτϟ ΎѧѧϬϤϫ Ϧѧѧϣ ϲѧѧΘϟϭ 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 ΕΎϏήϔϟ ΔΒδϧ ϞϴϠϘΗ .ΔϴηΎϤϜϧϻ ϭ ΔϴηΎϔΘϧϹ ΔΑήΘϠϟ ΔϴϤΠΤϟ ΕήϴϐΘϟ ϞϴϠϘΗ .ϩΎϴϤϠϟ ΔΑήΘϟ ΔϳΫΎϔϧ ϞϴϠϘΗ .ΔΑήΘϠϟ ϥΎϣϵ ϞϣΎόϣ ΓΩΎϳί ΔΑήΘϟ ωϮϧ ϰϠϋ ΪϤΘόΗ ΔϔϠΘΨϣ ΕΪόϣ ϡΪΨΘγΎΑ ϊϗϮϤϟ ϲϓ ΔΑήΘϟ ϚϣΩ ϢΘϳ :ϲϟΎΘϟ ΕΪόϤϟ 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 ήϴϐϟϭ ΔϜγΎϤΘϤϟ ΔΑήΘϠϟ ϡΪΨΘδϳ 3- Sheep-foot rollers
Ϧϴτϟϭ 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 ΕΎϔλϮϤϟ 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 ΕΎϔλϮϤϟ 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 ΕϮτΧ W1 ήϔΤϟ ΞΗΎϧ ϊϴϤΠΗ ϊϣ ϊϗϮϤϟ ϲϓ ΓήϔΣ ϞϤϋ ϢΘϳ -˺ Wc ϲΎϤϟ ϯϮΘΤϤϟ ΪϳΪΤΗ ϭ ϥήϔϟ ϲϓ ΔΑήΘϟ ϒϴϔΠΗ ϢΘϳ -˻ ϡΪΨΘγΎΑ ϞϣήϟΎΑ ΓήϔΤϟ ˯Ϟϣ ϢΘϳ ΔϓΎΜϜϟ ϡϮϠόϣ Ϟϣέ ϡΪΨΘγΎΑ -˼ 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 Ï°Ï Ï&#x2039; Î&#x201D;ϤδÏ&#x2DC;Ï&#x;Î&#x17D;Î&#x2018;
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 )
-: Ë°Î&#x2018; ΰϴϤÎ&#x2DC;ĎłĎ Ď&#x201A;Ď&#x2DC;Ď&#x201C; ϹΎĎ&#x2C6;ϧ ϰϨΤϨϣ ĎŽĎŹĎ&#x201C; Ď&#x17E;ϤĎ&#x152;ϤĎ&#x;Î? Ď°Ď&#x201C; ÎŞÎ&#x;ĎŽĎł Ďť ϰϨΤϨϤĎ&#x;Î? Î?ÎŹĎŤ .Ď&#x161;ĎŁÎŞĎ&#x;Î? ϰϨΤϨϣ βϤϳ Ďť -Ëş .ËŻÎ&#x17D;ϤĎ&#x;Î? Ď°Ď&#x201C; Î?Î&#x2039;Î?ÎŤ ËŻÎ?ĎŽĎŤ ΊώÎ&#x;ĎŽĎ&#x; Ď&#x161;Ď&#x;ÎŤ Ď Î&#x201D;Ď&#x152;Ď´Î&#x2019;Ď&#x201E;Ď&#x;Î? Ď°Ď&#x201C; ÎŞÎ&#x;ĎŽĎł Ďť -Ëť Ď&#x161;ĎŁÎŞĎ&#x;Î? ϰϨΤϨϣ Î&#x201D;ΤΝ Ď°Ď Ď&#x2039; ϢĎ&#x153;Î¤Ď Ď&#x; ϥΪΨÎ&#x2DC;δϳ -Ëź
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 혺혺 Ws 343 .6 196 .3 Ww 0.125 혺혺 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 â&#x20AC;&#x201C; 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 â&#x20AC;&#x201C; 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 Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď Ď&#x; Î&#x201D;Ď´Ď&#x153;Ď´Ď&#x;ĎÎÎŞĎ´ĎŹĎ&#x;Î? ΚÎ?ώΨĎ&#x;Î? Î&#x17D;ĎŹĎ&#x;ϟΧ ĎŚĎŁ ËŻÎ&#x17D;ϤĎ&#x;Î? ÎĎÎŽĎŁ ËŻÎ&#x17D;ϨÎ&#x203A;Î? Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď&#x;Î? Ď&#x2122;ĎŽĎ Îł Î&#x201D;ÎłÎ?ÎΊ ĎŽĎŤ Ď°ĎŤ ËŻÎ?ΰÎ&#x;Î? Î&#x2122;ĎźÎ&#x203A; Î&#x201D;ÎłÎ?ÎΊ ϢÎ&#x2DC;Ďł Ď
Geo-static stress
Permeability
Flow net
νÎĎľÎ? ĎĽÎŻĎ ĎŚĎŁ Î&#x17E;Î&#x2014;Î&#x17D;ϨĎ&#x;Î? ΊÎ&#x17D;ĎŹÎ&#x;ĎľÎ?
Î&#x201D;ϳ΍Î&#x17D;Ď&#x201D;ϨĎ&#x;Î?
ĎĽÎ&#x17D;ϳΎδĎ&#x;Î? Î&#x201D;Ď&#x153;Î&#x2019;Ρ
νÎĎľÎ? ĎĽÎŻĎ ĎŚĎŁ Î&#x17E;Î&#x2014;Î&#x17D;ϨĎ&#x;Î? ΊÎ&#x17D;ĎŹÎ&#x;ĎľÎ?
1) Geo-static stress
a) Effective stress: ( V )
Ď?Î&#x17D;Ď&#x152;Ď&#x201D;Ď&#x;Î? ΊÎ&#x17D;ĎŹÎ&#x;ĎťÎ?
Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď&#x;Î? Î&#x2022;Î&#x17D;Î&#x2019;Ď´Î&#x2019;ÎŁ ĎĽÎŻĎ ĎŚĎŁ Î&#x17E;Î&#x2014;Î&#x17D;ϨĎ&#x;Î? ΊÎ&#x17D;ĎŹÎ&#x;ĎťÎ? ĎŽĎŤ
ÂŚ
V ËŻÎ&#x17D;ϤĎ&#x;Î? Î&#x2013;ΤÎ&#x2014; Jsub.
Jsub. = Jsat. Jw
J *h ËŻÎ&#x17D;ϤĎ&#x;Î? Ď&#x2022;ĎŽĎ&#x201C; J ĎŠÎ&#x17D;Ď&#x201E;Ď&#x152;ϤĎ&#x;Î? Jb Jd Jsat.
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
2
2011
of soil
-:ϝΎόϔϟ ΩΎϬΟϹ ΔϴϤϫ ΔϴϤΠΤϟ ΕήϴϐΘϟ 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 Δϴγήϟ 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 Jb Jd Jsat.
V U
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
3
2011
of soil
Ď&#x17E;Î&#x2039;Î&#x17D;δϤĎ&#x;Î? Ď&#x17E;ΤĎ&#x; Î&#x17D;ĎŹĎ&#x2C6;Ď&#x201D;ÎŁ Î?ĎŽĎ Ď&#x201E;ĎŁ Ď?ĎĎľÎ? Ď&#x17E;ÎźĎ&#x201D;Ď&#x;Î? ĎŚĎŁ όϴϧÎ?ĎŽĎ&#x2DC;Ď&#x;Î? ΞĎ&#x152;Î&#x2018;
Â&#x; sr * e Gs *Wc Â&#x; Jb
§ Gs sr * e ¡ ¨ ¸ *J w Š 1 e š
Ex:Find the stress at point A, B
Jb
h1 B
Jsat.
h2 A At point (A):-
V
ÂŚJ * 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
Ď&#x2030;ίώϤĎ&#x;Î? Ď&#x17E;ϤΤĎ&#x;Î? ÎŽĎ´Î&#x203A;Î&#x201E;Î&#x2014;
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
νÎĎťÎ? ΢Ď&#x201E;Îł Ď°Ď Ď&#x2039;Î? ËŻÎ&#x17D;ϤĎ&#x;Î? Î&#x2013;ϧÎ&#x17D;Ď&#x203A; Î?ÎŤÎ?
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 (ϰσϮϟ 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 + έΪϘϤΑ ϞϘϳ
ΔϤϳΪϘϟ ΔϤϴϘϟ
V J sub. * h2 J w * H
Jw + έΪϘϤΑ Ϊϳΰϳ
ΔϤϳΪϘϟ ΔϤϴϘϟ ϝΎόϔϟ ΩΎϬΟϻ ΩΩΰϳ Ϟϔγϻ ˯ΎϤϟ ΔϛήΣ ϥ φΣϼϧ Jw + έΪϘϤΑ
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
9
2011
of soil
Ď°Ď Ď&#x2039;ϡ ĎĽÎ&#x17D;ϳΎδĎ&#x;Î?
b) Up-ward flow H
h1 Soil Jsat
h2 A
A
At point (A-A):-
V J sat. * h2 J w * h1
ÎŽĎ´Ď?Î&#x2DC;Ďł Ďť Î&#x2013;Î&#x2018;Î&#x17D;Î&#x203A;
U J w * (h1 h2 ) J w * H
Jw + ÎÎ?ÎŞĎ&#x2DC;ϤÎ&#x2018; Ϊϳΰϳ
Î&#x201D;ϤϳΪĎ&#x2DC;Ď&#x;Î? Î&#x201D;ϤϴĎ&#x2DC;Ď&#x;Î?
V J sub. * h2 J w * H
Jw + ÎÎ?ÎŞĎ&#x2DC;ϤÎ&#x2018; Ď&#x17E;Ď&#x2DC;Ďł
Î&#x201D;ϤϳΪĎ&#x2DC;Ď&#x;Î? Î&#x201D;ϤϴĎ&#x2DC;Ď&#x;Î? Ď?Î&#x17D;Ď&#x152;Ď&#x201D;Ď&#x;Î? ΊÎ&#x17D;ĎŹÎ&#x;ĎťÎ? Ď&#x17E;Ď Ď&#x2DC;Ďł Ď°Ď Ď&#x2039;Ďť ËŻÎ&#x17D;ϤĎ&#x;Î? Î&#x201D;Ď&#x203A;ÎŽÎŁ ĎĽÎ? Ď&#x2020;Σϟϧ Jw + ÎÎ?ÎŞĎ&#x2DC;ϤÎ&#x2018;
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
.......... .......... ....
ϰσϮϟ Ϧϋ ϰϟΎόϟ ˯ΎϤϟ ΏϮδϨϣ ϕήϓ ΔΑήΘϟ ϞΧΩ ˯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 ιϮΧ Ϧϣ ΔϴλΎΧ
Piping = boiling = heaving = quick sand ϥέϮϔϟ ΓήϫΎχ ϭ (shear stress ) κѧϘϟ ΕΩΎϬΟ 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
:Î?Î&#x17D;δΣ ϢÎ&#x2DC;Ďł ĎĽÎ?ÎĎŽĎ&#x201D;Ď&#x;Î? Î&#x201C;ÎŽĎŤÎ&#x17D;Ď&#x2021; Î&#x2122;ĎÎŞÎŁ Ď°Ď Ď&#x2039; ϢĎ&#x153;Î¤Ď Ď&#x;
i
H L
icr
J sub. Jw
Gs 1 1 e
i icr Â&#x; No Â&#x2DC; piping
ĎĽÎ?ÎĎŽĎ&#x201C; Î&#x2122;ΪΤϳ Ďť
icr Â&#x; critical
ĎĽÎ?ÎĎŽĎ&#x201D;Ď&#x;Î? Ď&#x161;ÎˇĎ Ď°Ď Ď&#x2039;
i ! icr Â&#x; piping
ĎĽÎ?ÎĎŽĎ&#x201C; Î&#x2122;ΪΤϳ
i
How to prevent (overcome) piping
ĎĽÎ?ÎĎŽĎ&#x201D;Ď&#x;Î? Ď&#x160;Ϩϣ
Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď&#x;Î? Ď&#x17E;ΧÎ?Ί ËŻÎ&#x17D;ϤĎ&#x;Î? ÎÎ&#x17D;δϣ Ď?ĎŽĎ&#x192; Î&#x201C;ΊÎ&#x17D;ϳί -Ëş
Sheet pile wall Î&#x201D;ϴϧΪĎ&#x152;ĎŁ ÎŽÎ&#x2039;Î&#x17D;Î&#x2DC;Îł
Soil Mechanics (1)
Chapter (6)
13
2011
Hydraulic properties of soil
΄θϨϤϟ ϒϠΧ ϥίϭ ϊοϭ -˻ Weights
filters ΕΎΤηήϣ ϡΪΨΘγ -˼
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 ϲγέ ϊϠτϧ ΎϬϨϣ ϭ (4D15) ϥΎϜϣ ΪϳΪΤΗ -˻ (D85)
85% έΎϣ ΔΒδϧ ΪϨϋ ήτϘϟ ΪϳΪΤΗ -˼
(B) ΔτϘϧ ϰϠϋ ϝϮμΤϠϟ ϲγέ ϊϠτϧ ΎϬϨϣ ϭ (4D85) ϥΎϜϣ ΪϳΪΤΗ -˽ filter ΔϘτϨϣ ϥϮϜΗ ϲΘϟ ϭ ΔΑήΘϟ ϰϨΤϨϤϟ ϥΎϳίϮϣ 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 ιϮΨϟ ΎϬϟϼΧ Ϧϣ ˯ΎϤϟ έϭήϣ ˯ΎϨΛ ΔΑήΘϟ ϙϮϠγ ΔγέΩ Ϯϫ ϰϫ ˯ΰΟ ΙϼΛ ΔγέΩ 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
ϰγέΩ 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 ϞΧΩ ˯ΎϤϟ ϥΎϳήγ Δϋήγ = V ΔϳΫΎϔϨϟ ϞϣΎόϣ = K ϰϜϴϟϭέΪϴϬϟ ϞϴϤϟ = i
i
H L
.......... .......... ....ϕήϓ ϰσϮϟ Ϧϋ ϰϟΎόϟ ˯ΎϤϟ ΏϮδϨϣ ΔΑήΘϟ ϞΧΩ ˯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 ϰγέΩ ϥϮϧΎϗ
V K *i Q A *V
K *i * A
ΕΎΒϴΒΤϟ ΔΣΎδϣ ΎϬϴϓ ΎϤΑ ΎϬϠϛ ΔΣΎδϤϟ ϰϫ = A Seepage velocity
ϥΎϳήδϟ Δϋήγ
ςϘϓ ΔΑήΘϟ ΕΎϏήϓ 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 ΕΎϏήϔϟ 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 ) ϩέΪϘϣ 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 Δϴγήϟ ΔΑϮΒϧϻ ϊτϘϣ ΔΣΎδϣ = a
(ΔϨϴόϟ ωΎϔΗέ) ϥΎϳήδϟέΎδϣ ϝϮσ = L (ΔϳΎϬϨϟ ϭ ΔϳΪΒϟ Ϧϣί ϕήϓ) ΔΑήΠΘϟ Ϧϣί = t (ήϴΒϜϟ) ΔΑήΠΘϟ ΔϳΪΑ 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
ΪΣϭ ΔψΣϼϣ ήΌΑ ΩϮΟϭ ΔϟΎΣ ϰϓ
ΪΣϭ 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
Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď&#x;Î? Ď&#x2030;ώϧ Ď°Ď Ď&#x2039; ΪϤÎ&#x2DC;Ď&#x152;Ďł
for sand
Permeability of stratified soil
Î&#x2022;Î&#x17D;Ď&#x2DC;Î&#x2019;Ď&#x201E;Ď&#x;Î? Î&#x201C;ΊΪĎ&#x152;Î&#x2DC;ĎŁ Î&#x201D;Î&#x2018;ÎŽÎ&#x2DC;Ď&#x;Î? Î&#x201D;ϳ΍Î&#x17D;Ď&#x201D;ϧ Ď°Ď&#x2DC;Ď&#x201C;ĎľÎ? ĎĽÎ&#x17D;ϳΎδĎ&#x;Î?
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
ÂŚ K1* H1 K 2 * H 2 ....... ÂŚ K * H ÂŚ H1 H 2 .........
ÂŚH Soil Mechanics (1)
H
Chapter (6)
Hydraulic properties
10
2011
b) Vertical flow
of soil
ϲγÎ&#x192;ÎŽĎ&#x;Î? ĎĽÎ&#x17D;ϳΎδĎ&#x;Î? V, q = constant K1
H1
K2
H2
K3
H3
h h1 h2 h3 V *H h Â&#x;h 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
Œ H1 H 2 ......... Œ H H § H1 H 2 ¡ ......... ¸ Œ Œ¨Š K1 K 2 K š
Soil Mechanics (1)
H
Soil Mechanics (1) Fff
Chapter (6)
Hydraulic properties
1
2011
of soil
Chapter (6) Hydraulic properties of soil ΔΑήΘϠϟ ΔϴϜϴϟϭέΪϴϬϟ ιϮΨϟ ΎϬϟϼΧ Ϧϣ ˯ΎϤϟ έϭήϣ ˯ΎϨΛ ΔΑήΘϟ ϙϮϠγ ΔγέΩ Ϯϫ ϰϫ ˯ΰΟ ΙϼΛ ΔγέΩ 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
ϞΧΩ ˯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 ϞΧΩ ˯ΎϤϟ ϥΎϳήγ Ϧϋ ήΒόΗ ϰΘϟϭ Flow lines: ϥΎϳήδϟ ρϮτΧ ΔΑήΘϟ ϞΧΩ ˯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 ΕϮτΧ 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 (ϲσϮϟ ˯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 ΕΎϣΪΨΘγ
Uses of flow net
ϑήμΘϟ ΏΎδΣ
1) Seepage discharge ( q )
q
Nf K *H * Nd
Ϣγήϟ Ϧϣ
.ϰσϮϟ Ϧϋ ϰϟΎόϟ ˯ΎϤϟ ΏϮδϨϣ ϕήϓ = H .ΔϳΫΎϔϨϟ ϞϣΎόϣ = K
φΣϻ
-:ΔΑήΘϟ ωϮϧ ϰτόϣ ϥΎϛ Ϯϟ
.ΕΎϫΎΠΗϻ ϊϴϤΟ ϰϓ ιϮΨϟ βϔϧ ΎϬϟ ΔΑήΗ ϰϫ = Isotropic soil
Kx = Kz
Soil Mechanics (1)
Chapter (6)
Hydraulic properties
6
2011
of soil
ΔϘΑΎδϟ ΕϮτΨϟ βϔϧ ϰϫ Δϟ΄δϤϟ ϞΣ .ΕΎϫΎΠΗϻ ϊϴϤΟ ϰϓ ΎϬλϮΧ ϒϠΘΨΗ ΔΑήΗ ϰϫ = In-isotropic soil
Kx z Kz -:ϰϠϳ ΎϤϛ ΎϤϫ ϦϴΰΟ 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) ĎŚĎŁ ÎşĎ Î¨Î&#x2DC;Ď Ď&#x; Î&#x201D;ĎŁÎŻĎźĎ&#x;Î? Î&#x2022;Î&#x17D;ΨĎ&#x20AC;ϤĎ&#x;Î? ΊΪĎ&#x2039;
q 1 pump Â&#x2DC; capacity
2) Seepage pressure ( Ps )
ĎĽÎ&#x17D;ϳΎδĎ&#x;Î? Ď&#x201A;Ď?Îż
n ¡ § Ps J w * H * ¨1 ¸ Š Nd š Î&#x201D;Î&#x2018;ĎŽĎ Ď&#x201E;ϤĎ&#x;Î? Î&#x201D;Ď&#x201E;Ď&#x2DC;ϨĎ&#x;Î? Ď°Î&#x2DC;ÎŁ drop head Ď°Ď&#x201C; ÎŞĎ&#x2DC;Ď&#x201D;Ď&#x;Î? Î&#x2022;Î?ÎŽĎŁ ΊΪĎ&#x2039; = 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 ΔϳΪΑ 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 safe F
For Example (2) ΔϳΎϬϧ ϭ ΔϳΪΑ 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 š Š 10 . 5 ¡ § J w * H * ¨1 Ps B ¸ 13 š Š D J sub . * D * W *1 2 § Ps A Ps B ¡ D F ¨ ¸* 2 Š š 2 W t 1 Â&#x; safe F .O . S F Ps
J
ĎĽÎ?ÎĎŽĎ&#x201D;Ď&#x;Î?
4) Piping
icr
J sub. Jw
i
'h L min .
'h
Gs 1 1 e
H Â&#x; Nd
ÎŞĎŹÎ Ď&#x;Î? ϲĎ&#x201C; ÎŞĎ&#x2DC;Ď&#x201D;Ď&#x;Î? ÎÎ?ÎŞĎ&#x2DC;ĎŁ
Soil Mechanics (1)
Chapter (6) 2011
Hydraulic properties
12
of soil
ΪϬΟ ϱϭΎδΗ ϰτΧ ήΧ ϦϴΑ Δϴγήϟ ΔϓΎδϤϟ ϰϫ = Lmin .Ϣγήϟ Ϧϣ αΎϘΗ ϭ Example (1)
Example (2)
i ! icr piping i icr 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 ωϮϧ
1- Point load = Concentrated load
ΰϛήϤϟ ϞϤΤϟ
P
2- Line load
ϰτΨϟ ϞϤΤϟ
ήϴγϮϣ ςΧ ϭ έϮγ Ϧϣ ΞΗΎϧ 3- Strip load
Δϴτϳήη ΔΣΎδϣ ϰϠϋ ϞϤΤϟ
Soil Mechanics (1)
Chapter (7)
Stresses in soil
2
2011
Î&#x201D;ÎŁÎ&#x17D;δϣ Ď°Ď Ď&#x2039; Ď&#x17E;ϤΤĎ&#x;Î?
4- Rectangle area
q
1- Point load = Concentrated load
ΰĎ&#x203A;ΎϤĎ&#x;Î? Ď&#x17E;ϤΤĎ&#x;Î? P
Z
A
Vz
r
P I* 2 Z
I = influence factor
I
3 2S
§ 1 ¨¨ 2 r z 1 ( / ) Š
¡ ¸¸ š
2.5
Soil Mechanics (1)
Chapter (7)
Stresses in soil
3
2011
ϰϨΤϨϣ ĎŚĎŁ ĎŞĎ´Ď Ď&#x2039; Ď?ώΟΤĎ&#x;Î? ĎŚĎ&#x153;Ϥϳ ĎÎ?
I
2- Line load
Vz
Ď°Ď&#x201E;ΨĎ&#x;Î? Ď&#x17E;ϤΤĎ&#x;Î?
q I* Z
q
I = influence factor
I
¡ 2§ 1 ¨¨ ¸ 2 ¸ S Š 1 ( x / z) š
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 Δϴγήϟ 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 ΔϳήΪϟϭ ΔόΑήϤϟϭ ΔϠϴτΘδϤϟ ΔΣΎδϤϠϟ ϡΪΨΘδΗ q
Z 'V Z/2
L
Z/2
ϲγέ ˻ : 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 ĎŞĎ Ď¤Î¤Ď¤Ď&#x;Î? Î&#x201D;ÎŁÎ&#x17D;δϤĎ&#x;Î? ĎĽÎ&#x17D;Ď&#x203A;ÎÎ? ĎŚĎŁ ĎŚĎ&#x203A;Î Ď&#x17E;Ď&#x201D;ÎłÎ? ΊÎ&#x17D;ĎŹÎ&#x;ĎťÎ? Î?Î&#x17D;δΤĎ&#x; ϥΪΨÎ&#x2DC;δÎ&#x2014; Ď&#x17E;ϤΤĎ&#x;Î&#x17D;Î&#x2018;
VA q*I
Chart ĎŚĎŁ ĎŞÎ&#x2018;Î&#x17D;δΣ ϢÎ&#x2DC;Ďł
Soil Mechanics (1)
Chapter (7)
Stresses in soil
10
2011
˰Α ϰϨΤϨϤϟ ϞΧΪϧ
n m
B Z L Z
ϞϤΤϟ ϥΎϜϣ ϭ ΔτϘϨϟ Ϧϣ Δϴγήϟ ΔϓΎδϤϟ = Z ϞϤΤϠϟ ήϴϐμϟ ϝϮτϟ = B ϞϤΤϠϟ ήϴΒϜϟ ϝϮτϟ = L
Soil Mechanics (1)
Chapter (7) 2011
Stresses in soil
11
:φΣϻ ΔΣΎδϤϟ ϞΧΩ 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 ϡΪΨΘγΎΑ ϞϜη ϱϵ ϡΪΨΘδΗ
Newmark chart
ϙϮϠΑ
Soil Mechanics (1)
Chapter (7)
Stresses in soil
13
2011
ϞΤϟ ΕϮτΧ 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 -˽ ήϭΪϟ ΰϛήϣ ϰϓ ΎϫΪϨϋ ΩΎϬΟϵ ΏΎδΣ (N) ΔΣΎδϤϟ ϞΧΩ 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 ϞΧΩ ΓΩϮΟϮϤϟ ΕΎϛϮϠΒϟ ΩΪϋ = N1 ΔϴϧΎΜϟ ΔΣΎδϤϟ ϞΧΩ ΓΩϮΟϮϤϟ ΕΎϛϮϠΒϟ ΩΪϋ = N2
Soil Mechanics (1)
Chapter (7)
Stresses in soil
15
2011
Contact pressure
βϣϼΘϟ ςϐο
ΔΑήΘϟϭ αΎγϷ ϦϴΑ βϣϼΘϟ τγ ϰϠϋ ϲγήϟ 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 Ëş
Soil Mechanics (1)
Chapter (7) 2011
Stresses in soil Ëť
Soil Mechanics (1)
Chapter (7) 2011
Stresses in soil Ëź
Soil Mechanics (1)
Chapter (7) 2011
Stresses in soil Ë˝
Soil Mechanics (1)
Chapter (7) 2011
Stresses in soil Ëž
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 Ě&#x20AC;
Soil Mechanics (1)
Chapter (7) 2011
Stresses in soil Ě
Soil Mechanics (1)
Chapter (7) 2011
Stresses in soil Ě&#x201A;
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 ϡΪΨΘγΎΑ 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 ΕϮτΧ ϞϜθϟΎΑ ΎϤϛ ΎϫΩΎόΑ ΔΑήΘϟ Ϧϣ ΔϠϘϠϘϣ ήϴϏ ΔϨϴϋ ΰϴϬΠΗ ϢΘϳ -˺ ˯ΎϤϟΎΑ ΎϣΎϤΗ ΓέϮϤϐϣ ϥϮϜΗ ρήθΑ ίΎϬΠϟ ϲϓ ΔϨϴόϟ ϊοϭ ϢΘϳ -˻ ˻
Ϣγ/ϢΠϛ ˹̄˻˾ ϩέΪϘϣ 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· ϡΪΨΘγΎΑ ˽ ϭ ˼ ΓϮτΨϟ έήϜΗ -˾ ˻
Ϣγ/ϢΠϛ ˹̄˻˾ ΎϫέΪϘϣ 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 ϲΘϟϭ
1- Coefficient of Compressibility (av) e eo
av
1
'e
'e 'V
2
e1 Vo
V1
'V
V
ΩΎϬΟϹ ϲϓ ήϴϐΘϟ ϰϟ· ΕΎϏήϔϟ ΔΒδϧ ϲϓ ήϴϐΘϟ ϦϴΑ ΔΒδϨϟ Ϯϫ eo = ΔϴΪΘΑϻ ΕΎϏήϔϟ 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
ΊÎ&#x17D;ĎŹÎ&#x;ĎšÎ? ϲĎ&#x201C; ÎŽĎ´Ď?Î&#x2DC;Ď&#x;Î? Ď°Ď&#x;Î&#x2021; ϰϤΠΤĎ&#x;Î? Ď?Î&#x17D;Ď&#x152;Ď&#x201D;ϧϝÎ? ĎŚĎ´Î&#x2018; Î&#x201D;Î&#x2019;δϨĎ&#x;Î? ĎŽĎŤ Hv = volumetric strain ϰϤΠΤĎ&#x;Î? Ď?Î&#x17D;Ď&#x152;Ď&#x201D;ϧϝÎ?
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
Log Vo Log V1 ' Log V
Cc
'e Log (V 1 ) Log (V 2 )
Cc
0.009( L.L 10)
Log V
ϢΘϳέΎϏϮϟ ϲϓ ήϴϐΘϟ ϲϟ· ΕΎϏήϔϟ 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
Log V1 Log V2
Log V
' Log V
Cs
'e Log (V 1 ) Log (V 2 )
ϢΘϳέΎϏϮϟ ϲϓ ήϴϐΘϟ ϲϟ· ΕΎϏήϔϟ 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
ΕϮτΨϟ (αϮϘΗ ήΒϛ ΕΫ) A ΔτϘϨϟ ΪϳΪΤΗ -˺ ϰϨΤϨϤϠϟ αΎϤϣ ςΧ ϭ ϲϘϓ ςΧ Ϣγήϧ A ΔτϘϧ Ϧϣ -˻ ϢϬϨϴΑ Δϳϭΰϟ ϒμϨϧ -˼ ΔτϘϧ ϲϓ ϒμϨϤϟ ϊτϘϴϟ ϰϨΤϨϤϟ ϲϓ ϢϴϘΘδϤϟ ςΨϟ ΪϤϧ -˽ Vc ϰϠϋ ϞμΤϨϟ ϲγέ 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 U .C .C O .C . R 1 N .C .C O .C . R ! 1 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 ËłSettlement ('H Gf
q
ϲÎ&#x2039;Î&#x17D;ϏϨĎ&#x;Î? Ď ĎŽÎ&#x2019;ĎŹĎ&#x;Î?
L h
J
H
J eo
Z 'V
Clay
L+Z ϲÎ&#x2039;Î&#x17D;ϏϨĎ&#x;Î? Ď ĎŽÎ&#x2019;ĎŹĎ&#x;Î? Î?Î&#x17D;δΤĎ&#x; όϴϧÎ?ĎŽĎ&#x2014; Î&#x201C;ÎŞĎ&#x2039; Ď&#x2122;Î&#x17D;Ϩύ
'H 'e 1) H 1 e 2 )G f ' H mv * ' V * H 3 )G f
'H
1 * 'V * H Ev Cc , eo Ď°Ď&#x201E;Ď&#x152;ĎŁ ĎĽÎ&#x17D;Ď&#x203A; Î?ÎŤÎ&#x2021;
O.C .R 1.0 4 )G f
§ V o 'V Cc * H * Log ¨¨ 1 eo Š Vo Soil Mechanics (1)
Sand
¡ ¸¸ š
Chapter (8)
(2)
2011
Consolidation
Cs , Vc Ď°Ď&#x201E;Ď&#x152;ĎŁ ĎĽÎ&#x17D;Ď&#x203A; Î?ÎŤÎ&#x2021;
O.C .R ! 1.0 V c ! V o 'V 5)G f
§ V o 'V Cs * H * Log ¨¨ 1 eo Š Vo
¡ ¸¸ š
V c V o 'V § V 'V ¡ Cs §V ¡ Cc ¸¸ * H * Log¨¨ o * H * Log¨¨ c ¸¸ 1 eo Š V c š 1 eo Š Vo š
Gf
H = Ď&#x17E;ϤΤĎ&#x;Î&#x17D;Î&#x2018; Î&#x201C;ΪϏΠϤĎ&#x;Î? Clay Ë°Ď&#x;Î? Î&#x201D;Ď&#x2DC;Î&#x2019;Ď&#x192; Ď&#x161;Ϥγ
Vo
ÂŚ J * h Â&#x;Â&#x; Chapter(6)
Clay Ë°Ď&#x;Î? Î&#x201D;Ď&#x2DC;Î&#x2019;Ď&#x192; Ď&#x2019;ÎźÎ&#x2DC;Ϩϣ Ď°Î&#x2DC;ÎŁ νÎϡÎ? ΢Ď&#x201E;Îł ĎŚĎŁ Overburden pressure ϰϤδÎ&#x2014; Ď
'V Â&#x;Â&#x; Chapter(7) Clay Ë°Ď&#x;Î? Ď&#x2019;ÎźÎ&#x2DC;Ϩϣ Ď°Î&#x2DC;ÎŁ Ď&#x17E;ϤΤĎ&#x;Î? ĎŚĎŁ Î&#x17E;Î&#x2014;Î&#x17D;ϨĎ&#x;Î? ΊÎ&#x17D;ĎŹÎ&#x;ĎšÎ? ϲĎ&#x201C; Î&#x201C;ΊÎ&#x17D;ϳΰĎ&#x;Î? Z = Clay Ë°Ď&#x;Î? Ď&#x2019;ÎźÎ&#x2DC;Ϩϣ Ď°Î&#x2DC;ÎŁ Ď&#x17E;ϤΤĎ&#x;Î? ĎĽÎ&#x17D;Ď&#x153;ĎŁ ĎŚĎŁ Î&#x201D;Ď´ÎłÎ&#x192;ÎŽĎ&#x;Î? Î&#x201D;Ď&#x201C;Î&#x17D;δϤĎ&#x;Î?
Soil Mechanics (1)
Chapter (8)
Consolidation
(3)
2011
Degree of Consolidation ( U %) ΪϠμΘϟ ΔΟέΩ ϲΎϬϨϟ ρϮΒϬϟ ϰϟ· Ϧϣί ϱ ΪϨϋ ρϮΒϬϟ ϦϴΑ ΔΒδϨϟ ϲϫ ϭ ϲΪΘΑϻ ˯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 ΪΣϭ ϩΎΠΗ ϲϓ ςϐπϟ ϭ ΔϋϮϨϤϣ ΔϴϘϓϷ ΔϛήΤϟ ϲγήϟ ϩΎΠΗϻ ϲϓ ˯ΎϤϟ ΝϭήΧ
Soil Mechanics (1)
Chapter (8)
Consolidation
(4)
2011
Gt U% Gf Uo Ut U% Uo Uo = 'V at time = zero
U%
'V U t 'V
G t = Ϧϴόϣ Ϧϣί ΪϨϋ ρϮΒϬϟ G f =
ϲΎϬϨϟ ρϮΒϬϟ
U o = Jw hw ϲΪΘΑϻ ˯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
U % 2 U % 52.6%
4 1.781 0.933Log 100 U % 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 ΓΪΣϭ 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)
ΕϮτΨϟ (αϮϘΗ ήΒϛ ΕΫ ) A ΔτϘϧ ΪϳΪΤΗ -˺ t1 Ϧϣΰϟ ϰϠϋ ϞμΤϨϟ ϲγέ ϝΰϨϧ A ΔτϘϧ Ϧϣ -˻ 4 t1 ϩέΪϘϣ Ϧϣί ϥΎϜϣ ΪϳΪΤΗ -˼ ϰϠϋ ϝϮμΤϠϟ ϰϠϋ ϲϟ· έήϜΗ ϭ X Δϴγήϟ ΔϓΎδϤϟ ΪϳΪΤΗ -˽ Ho ΔϳΪΒϟ 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
ΕϮτΨϟ ϭ Ho ΪϨϋ ϲγήϟ 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 ϲγέ 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 ϡΪΨΘγΎΑ b ΔτϘϨϟ ΪϳΪΤΗ -˼ ( ςΨϟ Ϊϣ – ϒμϨϣ – αΎϤϣ – ϲϘϓ ) ϖΒγ ΎϤϛ Vc ΩΪΣ -˽ a ϰϓ Vc Ϧϣ ϲγήϟ ϊτϘϴϟ 12 ςΨϠϟ ϱίϮϣ 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. (Vc Vo
( 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
:ϢΠΤĎ&#x;Î? Ď°Ď&#x201C; ÎŽĎ´Ď?Î&#x2DC;Ď&#x;Î? Ď Ď ĎŽÎ&#x2019;ĎŹĎ&#x;Î? ĎŚĎ´Î&#x2018; Î&#x201D;Ď&#x2014;ĎźĎ&#x152;Ď&#x;Î? -Ëź
G H
'H 'e 'V H 1 e V :Jsat ĎĄÎŻĎť Gs , Wc ϲĎ&#x201E;Ď&#x152;ĎŁ ĎĽÎ&#x17D;Ď&#x203A; Î?ÎŤÎ? -Ë˝
eo
J sat
Gs *Wc Â&#x; Sr 1 Â&#x; sarurated Sr
(Gs Sr * eo )J w Â&#x; 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)