phase-system-of-soil-ppt.pptx

• V.Nageshwaran, M.E.,
Assistant Professor,
Department of Civil Engineering,
UCET
CE6405 SOIL MECHANICS

Key: C J air C J water . . solids
o Soil - 3 Phase System - Partial
o Soil - 2 Phase System - Dry or Wet System
SOIL PHASE SYSTEM
root
soi I part icIe-----¥

3 PHASE SYSTEM PARTIALLY SATURATED
o Ws - Weight of Solids
o Vs - Volume of Solids
o Vw - Volume of Water
o Va - Volume of Air
o Vv - Volume of Voids
o V - Total Volume of Soil
Volume Relationships
o V = Vs+Vw+Va
o Vv = Vw+Va
Weight Relationships
o W = Ws+Ww+Wa
o Wv=Ww+Wa
o Wv = Ww [Since, Wa = O]
Note: Wd - Weight of Solids
w.:of
v. Air 1
1
v.
t _
-
..-
.
-
..-
.-
.-
..
-
-
..
-
-
-
..-
..---
-
-
--
--
.--
_
.
V
w ..
-.:.:
..:--
:
-
..W
-
..-
..a
.
-
.t.
-
e
..-
r
.;
.-
..-
:-.
:.
:-- ""j_
..,
.
.
. .....
-
o Ww - Weight of Water
o Wa - Weight of Air = 0
o Wv - Weight of Voids
o W - Total Weight of Soil
)Vounas
Solds
(a) Elenw.t a
C
NaturalSol
(b}Element Sepafilled
IntoThnle Phasea
PHASE SYSTEM
SOIL AS A m1w
w
w
(l)Wagtus

2 PHASE SYSTEM DRY (COMPLETELY) SYSTEM
o Vw - Volume of Water = 0
o Va - Volume of Air
o V = Vs+Vw+Va
o Vv = Vw+Va [Since, Vw = O]
o W = Ws+Ww+Wa
o Wv=Ww+Wa
o Wv = 0 [Since, Ww & Wa =O]
o Ww - Weight of Water = 0
..olid
v
AJr
v• w
w
( • ) eights

2 PHASE SYSTEM WET {COMPLETELY) SYSTEM
o Vw - Volume of Water
o Va - Volume of Air = 0
o V = Vs+Vw+Va
o Vv = Va+Vw [Since, Va = O]
o W = Ws+Ww+Wa
o Wv=Ww+Wa
o Ww - Weight of Water
o Wv = Ww [Since, Wa =O]
v
(i)'olume
w
Y
.J
(M)'eiPbf
Saldi

VOLUME-MASS/WEIGHT RELATIONSHIPS

VOLUME-MASS/WEIGHT RELATIONSHIPS
o Water Content, w - Ratio of Weight of Water, Ww to the
Weight of Solids, W5 or Wd- Expressed as a /o.
0
w
ws
w
w
d
w =
= w x 100 or w =
= w x 100
w =
=
W - W x 100=
=
s
ws
M
w =
= w xlOO or w =
=
Ms
_W l xlOO
ws
M
w xlOO
Md
w =
=
M - M
s x 100=
=
Ms
Where,
M
- 1 x 100
Ms

CONT ...
Density of Soil - Ratio of Mass of Soil, M to the Unit Volume
of Soil, V.
o Bulk Density, p - M/V [Total Vol.]
o Dry Density, Pci- Md/V [Vol. prior to drying]
o Density of Solids, Ps- MdNs [Vol. of Solids]
o Saturated Density, Psat- Msat/V
o Submerged Density, Psub- (Md)sat/V
P sub = Psat - Pw

CONT ...
Unit Weight of Soil - Ratio of Weight of Soil, W to the Unit
Volume of Soil, V.
o Bulk Unit Weight, y - W/V [Total Vol.]
o Dry Unit Weight, Yci- WdN [Vol. prior to drying]
o Unit Weight of Solids, Vs- Wd/V5
o Saturated Unit Weight, Ysat - Wsat/V
[Vol. of Solids]
o Submerged Unit Weight, Ysub - (Wd)satN
Ysub = Ysat - Yw
o Conversion between Density &Unit Weight
...............- = 9.81 k / m
tlc:n

CONT ...
o Specific Gravity, G5 - Ratio of Weight of a given Volume of
Soil Solids at a given temperature to the Weight of an equal
volume of distilled water at that temperature, both Weights
being taken in air.
o Indian Standard specifies 27°C as the Standard Temperature
for reporting the Specific Gravity.
G = Ys
Y
w
s
o Apparent or Mass or Bulk Specific Gravity, Gm - Specific
Gravity of Soil Mass.
G = y
Y
w
m

CONT ...
2
.•
I. Araplte
3
.
e· 1
1
2.94
2.J
O
-
3
.
3. 3.1
2,72
2.H.9
2.-
J2.
13.
J4. m
o
n
lS. M1gne1
1
1e
J6. Monooorillonite
1
7
, M ltc
18.
19.
20
21. Q
u
a
m
2
2
. u
23. T
alc
Na.
C Feld -_
0
yllite
I
•
S
.
2
3.2l,S
2.64.16
.
6
4
.
5
4 5
7
]
.
8
S.17
2,7 . 78
.13J
-.62 -.76
.
'6
I_ .84
2.6S
2.221
I
5. Cllc le
6.
7.
8.
9.
IO
.
lblloys
ite
H mile
(2
11
IJ Horftb
ltNJe

SUMMARY OF VOLUME-MASS/WEIGHT RELATIONSHIPS
Densities
M
p
=
=
v
M s a t
Psat =
=
Psub
v
Unit Weights
w
y
=
=
v
w s a t
Ysat =
=
Ysub
v
Ysub Ysat Yw
G = Ys
Y
w
s
G = y
Y
w
m

VOID RATIO, POROSITY & DEGREE OF SATURATION
o Void Ratio, e - Ratio of Volume of Voids to the Volume of
Soil Solids in the given Soil mass.
o Porosity, n - Ratio of Volume of Voids to the Total Volume of
the given Soil mass.
o Degree of Saturation, S - Ratio of Volume of Water presen
in a given Soil mass to the Total Volume of Voids in it.
..,
.,
"
>
-
! 1
e ==
vv
-
Vs
n ==
vv
-
V
S= Vw
vv
e V
oida Volds n
(a)
y
S
;
o
,,
i
•
l
•
E
•
lement In
o f •
• (b) Sol Element In
T1
1
1w
.s n
AND POROSl'l'Y
VOIDS RA
TIO

DEGREE OF SATURATION
1 - - - - - - - - - - - - - •
t
Wet
----- ----------
Air
•
•
"
•
•
•
C
>
•
HIM1id
0 ................................................................... _._. ..._Dry
Water t:Orllln w
•
•tmtMS OP SOIL STATS
FIG. Z.3 DESC1tlmVE WITH
VARIOUS VAIJIPS OP S '
o Fully Saturated Soil - Vw = Vv ---i) = 1
o Perfectly Dry Soil - Vw = 0 - - S = 0

0
/o AIR VOIDS & AIR CONTENT
o 0
/o Air Voids, n3
- Ratio of Volume of Air Voids to the Total
Volume of Soil mass.
o Air Content, ac - Ratio of Volume of Air Voids to the Volume
of Voids.
o Degree of Saturation, S - Ratio of Volume of Water presen
in a given Soil mass to the Total Volume of Voids in it.
V
a
n = = -
a V ._....
"
v
a == a •
v
a = 1 - Vw = 1 - S
c v
v
• Volds n
VOida
(a) Soll E'8mentIn
. ,••• ol •
•
(b) Sol Element In
Ter1e•otn
VOIDS RA110 AND PORMl'rY
...
1
i
-i
(1-n)

emax e
PlG. 1A. lo ' llU!LA
TIONSHIP
CONT ...
o 1
0 = O; When e = emax; i.e. Soil is in its Loosest State.
o 1
0 = 1; When e = emin; i.e. Soil is in its Densest State.
o 1
0 = 0 to 1; When e # emaxor emin; i.e. Soil is not in its Loosest
or Densest State.
r - - - - - - - - - - - - - - - - I L
Density at Most Loosest tate
Density at Most Compact State
-a
:IC
f
emax
I Yd Yd .min Yd .max
D - - - - - - .
Yd.max Yd.min
D - - - - - - - - -
llmax - n m i n 1 -n
Yd.min
Yd.max
. 1
0 •

CONT ...
TABLE 2.l. CIIAllACIERIS11CS OF G sons IN DEMD AND IOOSE STA'll:S
Vd.6 llatlo
,.
. •
26,0
2'
29
23
17
29
12
( ,,) (T l ,
..
0.92 0.35
0.40
0.40
0.30
0.20
O.
«>
O.J4
47.6
50
S2
47
49
"
- •
..,
I 00 13
l2.6
18.J
18.,
20.0
21.7
18.8
23 0
..
1.10
0.90 13.6
13.l
12.0
14.0
0 95
1.20
0.85
l. Unform sp.-aercs
2..
3. Uniform inorganic stlt
4, Silt)' sand
S. Fine10co•nc sml
6. Micaceoussand
7. Sil sand1111 ravel
TABLE 2.3. RELAnVE DENSITY
Very loose
MedWm
as--,100
0 ''
''
3J
a3
6
'

(a ) Loosest state· ('b ) Densest state
F i g u r e 3 . 8 P a c k i n g o f g r a in s o f u n i'f o r r n s i z e
Ta b l e .
3 . B C a s s 4
fic .a t i o n o f s a n r
d y so8"ts
R e a t i v e d e n s "'t y D,..,. % T y p e o f
:
s o 'm
l
0-15
.S- 5 0
50-70
7 0 - 8 5
.8 5- 1 0 0
Ve:ry Jo o s e
Loose
Medi u i n dense
D e n s e
Very d e n s e

RELATIVE COMPACTION
o Relative Compaction/Degree of Compaction, Re - Rati0
of Dry Density of Soil at Natural State to the Dry Density of
Soil at its Compact State.
R e - -Y
-
a-
Yd .max
Re
1+ emin
l + e
Ro
Re
1 1
Ro I
D
R
_ Yd.min
Yd.max
o Lee & Singh (1971) approximate eqn.
0
Re 80 +0. =-n

SUMMARY OF TERMS AND TERMINOLOGIES
I _ Yd-yd.min Yd.max
.
Y d . m a x - y d. m i n Yd
D -
I - emax - e
D -
emax - e m i n
R
_ Y
a
C -
yd.max
R
_ l+emin
c -
l + e
Re =80+0.2In
a = 1 - Vw
c vv
a ==1-S
c

FUNCTIONAL RELATIONSHIPS
(i) Relation between e, G5 , w & S
vv
ew - e.S
ew Water Void Ratio
e
w== W
W ewY
w
Wd Ys·l
Gs -
Yw
w== ew·Yw
Gs·Yw
ew -w.G s e =
w.Gs
s
- - -
- - -
Air
1
AG. 2.5. SOIL PI ,BIENT IN
T.E•M.S OP •- AND e '!
e w s a t · G s

CONT ...
(ii) Relation between e, S & n3
na =
=
V
a
v
V
a Vv Vw e ew
V Vs+ Vv l+e
e e
- -
- - - -
Air
+e
e 1 S
na =
l+e
1
PIG. 2.5. SOIL PI,BMBNT IN
OP f '4J AND .
TERMS

CONT ...
(iii) Relation between n3 , ac & n
ac =
=
V
a
vv
n== vv
v
-
- - - -
Air
1
PIG. 2.5. SOIL PI,BMBNT IN
f'4] AND .
TERMS OP

CONT...
{iv} Relation between d,"P5 & e {or n}
- Wa Ys·
Vs l & V - l + e
d
d
e Gs·Yw
Y
a
- 1 n & V - 1 -
V
d
T
- • Voids
•
+
-
"
j
1
!
(a)SoHElement In
Ten••ot•
VOIDS RATIO
•
AND POROSl1TY
T
n
-
I
J
i
-i
(1-n) {!.
PJG. 2.,.. SOIL ET
.ENENT
I
N
TERMS
OP t•· AND ' •

CONT ...
(v} Relation between Y
,sG5 & e (or n}
wsat wd +WW
-
Y s · +yw.vw
Vs 1,Vw ew , & V 1+ e
-
Gs ·Yw+Yw.e
l+e
sat
Gs+e ·Yw
l+e -
- 1 n, Vw n, & V 1
n +yw.n
-Ys·
1
'Ysat
·
-
-
t
-
-
·
-·
-1
.
·
-
-
-
,
·
-
·
- -
·
- -
- -
-
. .
· e
.
,.
I
----) - - -
. .. . ..
• UJ..e
J.
1
:M
m
:1
.
1
r - - : a i - . i A
. - i . . . _ ,
---• •
- --iiiiW
!
iI
i!
i
!!
o
._
.
.
I!
_
!!!
.-
l
--
_
-
.
-
.
-
.
-
_ , .·
-M
!Im
1
"
i
! 9
i
!
i
.
*
,
. ..
. .
. . . '
1

CONT ...
(vi} Relation between , 5 , e, & S
w wd+WW Y s · +yw.vw
-
v
vs - 1, v w - ew' & v 1+ e
_ Gs·Yw+Yw·e.S _
l+e
Gs+e.S ·Yw
l+e
d
AG. 2.S. SOIL m ;EMBNT IN
TERMS OF t'4J AND e

'
, s & e
Y Ysat Yw
CONT ...
(vii) Relation between
'
y' Gs+e.yw
l + e Y
w
G s l .yw
y'
l+ e

CONT ...
(viii) Relation between
w
W -
-
w
-
d
l + w
l + w
d _ - - - -
v l + w .V
'Y
+ w
w

CONT ...
, Y'
r& n
(ix) Relation between
W d sub 1.Ys 1.Yw
G s 1 ·Yw
G s •Yw Yw
and V l+e
y'
w d sub
W d sub - or y' = Gs·Yw - Y
w
l + e l + e
v
and
l+e
Y'
Y
a - 1 n w

CONT ...
(x} Relation between Y,sat; Y '&IS
Gs+ e.S ·'Yw or
y 'Yd+
l+e
Y-
l+e l+e

CONT ...
(xi} Relation between
yd==
Gs·Yw
- - l + e -
Gs·Y
w
s

CONT ...
(xii) Relation between ;YG
5 , w & n3
V -Va+ Vw +Vs or V a+ +
Y
w Ys
- +
+
- + + -
Ys·V V Y
w Ys
v Yw·V
Y
w Gs
1-na .Gs·'Yw
l+w.Gs
'Yd
'Yd 1
or

SUMMARY OF FUNCTIONAL RELATIONSHIPS
s= vw = ew = ew
vv ev e
Gs= Ys
Y
w
or Ys = Gs·Yw
w.Gs
e = = - -
S
v
a =
= a
c vv
n ==
vv
-
V
na =
=
V
a =
=n.ac
v
n =
=
e - e w
a 1+ e
e l - S
n = = - -
a l+e
Y-
G +e.S.y
l+e
s w
y
l+w
Yd -Gs·Yw(l n)
yd
Y
a -
yd
G .y
s w
l+e
G .y
s w
w.G
I+ s
s

G +e .y
s w
Ysat = l+e
CONT ...
1 - na .Gs·Yw
1+ w.G s
1 - na .yw
yd==
1
w +
Gs
Y =
=Ysat Yw
'
y' ya - 1 n .yw
yd==
y'

phase-system-of-soil-ppt.pptx

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