soilmechs_effectivestress_2014
DESCRIPTION
soil mechanicsTRANSCRIPT
-
Maria M
avro
ulidou, 2
014
1
The principle of
Effective Stress
Karl Terzaghi
(1883-1963)
All measurable
effects in soils
are associated
with changes in
effectivestress
Maria M
avroulidou, 2
014
Maria M
avro
ulidou, 2
014
2
Lecture Plan
Defin
itions
The concept o
f effe
ctiv
e
stress
Pore pressure
Effe
ctiv
e stress calculatio
n
Effe
ct o
f static
water above
ground level
Effe
ct o
f capilla
ry rise
Summary
-
Maria M
avro
ulidou, 2
014
3
Questio
n
uw
uw
w
W,
If stress has not changed in problem
2, why these
changes in the soil?
Problem
1
Problem
2
Maria M
avro
ulidou, 2
014
4
Defin
itions
Total Stress
Force
CrossSectio
nalArea
=
Effective stress
wu
'=
Note:
The dash is not optional !!!!!!
The effective stress cannot be m
easured directly,
it is calculated by Eqn (2)
Since, according to Terzaghi soil behaviour
(strengths and deformations) is related to effective stresses
it is important to decide if stress is total or effective
where
uw
: Pore w
ater pressure , i.e. the pressure of the water
in the pore spaces
(2)
(1)
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Maria M
avro
ulidou, 2
014
5
The concept o
f effe
ctiv
e stress
is transmitte
d by:
1)Interpartic
lecontacts
2)Pore water pressure actin
g in
pore voids (of equal intensity in all directions)
uwarising in pores does not
contribute to
the soils
shear
resistance =>(neutral)
Only 1) gives m
echanical resistance
to shearing=> effe
ctiv
e in
mobilisin
g sh
ear resistance
govern
ing vo
lume ch
ange /d
eform
ation
Maria M
avro
ulidou, 2
014
6
What is
effe
ctiv
e stress?
=
N
A=PA
A
Aw =
area of water (w
hile A is total area)
A
=N
A
PA+uw
=
+uw
The particle contact area is relatively very sm
all A~
Aw
For equilibrium
normal to x-x: Load P
=
N+
uw A
Particle contact area A
s
We can represent
the principle as:
-
Maria M
avro
ulidou, 2
014
7
Answer
It is the norm
al force
carried by the soil skeleto
n,
divided by the w
hole
cross sectional area of the soil
It does not represent the exact contact stress between
particles but the distribution of load carried by the soil
solids (skeleton) over the cross-sect area considered.
ie:
It is the averageinterparticle
stress on the x-x plane
=>
not to be confused with intergranular
contact stress:
NB: T
he effe
ctiv
e stre
ss is a prin
ciple and
not a
law:
i.e. It is
an empiric
al, w
orking hypothesis
Effective stress cannot be m
easured directly=>
always
through uw
and m
easurements
Advan
tage o
f the p
rincip
le:in the lab there is no
need to apply field uw
and values.
Only the difference (
-u
w) needs to be considered
Maria M
avro
ulidou, 2
014
8
Now we can note th
at
uw
uw
w
W,
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Maria M
avro
ulidou, 2
014
9
Pore pressure (1)
Reminder: soils contain water in
pores(voids)
Water exerts isotropic stress
(i.e
. the same in
all d
irectio
ns)
This is th
e pore pressure
Groundwater level
Ground level
hw
borehole
Groundwater level : level o
f water in
open
borew
hole
Pore p
ressure u
w = (level o
f water in
open
borew
hole)
x (unit w
eight o
f water)
uw = h
w
w g
=hw x
w
w =9.81kN
/m3
z
Maria M
avro
ulidou, 2
014
10
Pore pressure (2)
If th
ere is no flo
w, u
wis
hydrostatic
uw
uw 1
1.Piezo
meter: p
lastic tube m
easurin
g th
e pressu
re head
at a specific p
oint
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Maria M
avro
ulidou, 2
014
11
Pore pressure (3)
Pore pressure m
ay not b
e
hydrostatic
Artesian pressure
e.g
. assum
e a
sand la
yer o
verla
in b
y c
lay
(clay confines sand as it has low perm
eability):
The level of w
ater in the borehole rises higher than
the layers surface (can be higher than ground surface)
Underdrainage (dow
nward flow
)
Pore pressure changes due to
external lo
ads (=>flo
w)
In th
is lecture we will m
ainly fo
cus
on hydrostatic
conditio
ns
Maria M
avro
ulidou, 2
014
12
Calculatio
n of T
otal V
ertic
al S
tress
Example: W
hat is
vat th
e base?
q v
z1
z2
zz
v= q
+
1z1+
2z2+
3( z -
z1 -z2)
Questio
n:
Which
are w
e talking about?
1.If so
il is totally
dry, =
d
2.If so
il is fully satu
rated =
sat
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Maria M
avro
ulidou, 2
014
13
Calculatio
n of p
ore water pressure
Example: W
hat is
uwat p
oint A
?
Soil w
ith a static
water ta
ble
Uw(A
)=
w g
z =
w
z
Wate
r table
z
A
: uw= 0
Using hydrostatic
s prin
ciples,
water p
ressure at A
is:
w
:m
ass d
ensity
of w
ate
r
g: a
ccele
ratio
n d
ue to
gra
vity
w
: unit w
eig
ht o
f wate
r
Where:
Maria M
avro
ulidou, 2
014
14
Calculatio
n of v
ertic
al effe
ctiv
e stress
Example: W
hat is
vat th
e base?
2m
6m
wt
d
d =15.6kN/m
3
sat =
19.56kN/m
3
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Maria M
avro
ulidou, 2
014
15
Pore pressure and stress profile
s
050
100
150
0m
2m
4m
6m
8m
kP
a
pore
wate
r
pre
ssure
Effe
ctiv
e
stre
ss
Tota
l
Stre
ss
Depth
Vertical stress an
d pore p
ressure v
ariation
Maria M
avro
ulidou, 2
014
16
Effe
ct o
f water above soil s
urface
(For hydrostatic
conditio
ns)
Questio
ns:
1. A sand of 20kN
/m3
lies under a 1m deep river. W
hat is the vertical effective stress 4m
below the top of the sand?
2. The N
orth Sea is 200m
deep. The sea bed consists of sand of
20kN/m
3. What is the vertical effective stress 4m
below the top
of the sand?
3. Consider a soil m
ass with the w
ater table at surface level. The
soil is a sand of 20kN/m
3. What is the vertical effective stress
4m below
the top of the sand?
uw
uw
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Maria M
avro
ulidou, 2
014
17
Water ta
ble (w.t.)
:level at w
hich pore
pressure is atm
ospheric, ie
uw=0
Below th
e water ta
ble, p
ore pressures are
positiv
e.
Above th
e water ta
ble,pore pressure are
negativ
e: u
w= -
w*hc
Capilla
ry rise: th
e height a
bove th
e water
table to
which th
e soil is
saturated
Effe
ct o
f capilla
ry rise
uw=0
uw
uw
Maria M
avro
ulidou, 2
014
18
Why is water rising above w.t.?
=>surface te
nsion
(visualise void spaces as capilla
ry tu
bes of
varia
ble cross-sectio
n)
The sm
aller the voids, the higher the capillary rise
in coarse sands: 0
.12-0.18m
in fin
e sands:
0.3-1.2m
in silts
:0.76-7.6m
in clays : 7
.6-23m
Effe
ct o
f capilla
ry rise
a) Rise of w
ater in capillary tube b) Pressure w
ithin the capillary rise height)
-
Maria M
avro
ulidou, 2
014
19
Effe
ct o
f capilla
ry rise
uw
z
2m8m
Assume
1.a soil la
yer where water ta
ble is at th
e
ground surface (fully saturated)
2.The same soil la
yer with
the water ta
ble
2m below ground surface, and a capilla
ry
rise of 2
m
In both cases, soil is
fully saturated.
Diffe
rence in to
tal stress= NONE (as unit
weight is
the same, ie
sat )
Diffe
rence in pore pressure:In 2, a reductio
n
by 20kN/m
2( w*2m).
This m
eans th
at effective stress is increased
by th
e
same am
ount, ie. b
y 20kN/m
2
Maria M
avro
ulidou, 2
014
20
Summary
To calculate th
e effe
ctiv
e stress in
hydrostatic
conditio
ns:
1. C
alculate to
tal vertic
al stress
Be careful about selectio
n of
if a
bove th
e saturated zone:
=
=
=
=d
if b
elow th
e saturated zone:
=
=
=
=sat
2. C
alculate hydrostatic
water
pressure:uw
=zw w
3. C
alculate effe
ctiv
e vertic
al stress:
=
=
=
=
z
=
=
=
=
uw
NB:T
he latter is not affected by static water above ground surface
-
Maria M
avro
ulidou, 2
014
21
Tutorial
Exercise 1
Aconfin
edaquife
rconsists
ofa5m
layerofsand
overla
inby
a4m
layer
of
clay.
The
sand
isunderla
inbyim
perm
eable
rock.Thewaterlevelin
astandpipedriv
eninto
thesandlayeris
3m
above
thesoil(clay)surfa
ce.Thebulk
unitweighsofthe
clay
and
sand
are
18kN/m
3and
20kN/m
3
respectiv
ely.
Determ
ine
the
vertic
al
effe
ctiv
estre
ssatthe
top
and
botto
mofthe
sand
layer.
(Take
w=9.81kN/m
3)
NB: In
this case th
e water in
the sand is
under
arte
sian pressure (ie
. not h
ydrostatic
)
(Answ
er: A
t the top of the sand:v =3.33kN
/m2
At the bottom
of the sand:v =54.28kN
/m2
)
Exercise 2
A la
yer o
f fine sand 3m th
ick overlie
s a th
ick clay
layer. T
he w
ater ta
ble is in
the sand, a
t a depth of
1.8m below th
e surfa
ce. In
the zone above th
e
water ta
ble th
e average degree of s
aturatio
n of th
e
sand is 70%. T
he porosity
of th
e sand is 35% and
its specific
gravity
is 2.65. T
he w
ater c
ontent o
f the
clay is 40% and its
specific
gravity
is 2.7. C
alculate
the vertic
al to
tal a
nd effe
ctiv
e stre
ss at a
depth of
6.7m below th
e clay surfa
ce. (T
ake w=9.81kN/m
3)
(Answ
er: total stress: 178.98kN/m
2 ; effective stress: 99.98kN
/m2)
Maria M
avro
ulidou, 2
014
22
Tutorial
Exercise 3
A soil profile consists o
f three layers. T
he soil is su
bject to
a uniformly distrib
uted load of q=80kPa. Layer I w
hose
depth is 3
m is fu
lly dry above the water ta
ble. Layers II
and III, w
hose depths are 3m and 6m respectiv
ely are
fully saturated, lying below the water ta
ble (i.e
. the w.t. is
at 3m below ground level).T
he properties of th
e three
layers a
re:
Layer I:
Dry unit w
eight
d = 17 kN/m
3
Layer II:
Saturated unit w
eight
sat=19.5 kN/m
3.
Layer III:
Saturated unit w
eight
sat =18 kN/m
3
Determine the pore pressure and the total and effectiv
e
stresses at 0m, 3m, 6m and 12m below the ground
surface. Ta
ke the unit w
eight of water
w=9.81 kN/m
3
-
Maria M
avro
ulidou, 2
014
23
Tutorial
Exercise 4
A soil profile consists o
f two layers: a
layer of silty
sand 5m
deep, underlain by a 4m layer of sa
turated clay. T
he
properties of th
e two layers a
re:
Layer I (silty
sand):
Saturated unit w
eight
sat=18.5 kN/m
3. Layer II (cla
y):
Saturated unit w
eight
sat =17.7 kN/m
3
Determine and plot th
e pore pressure and the total and
effectiv
e stre
sses against d
epth for th
e following two cases: a
) the water ta
ble is a
t the surface; b) th
e water ta
ble is a
t 2.5m
below surface but th
e silty
sand is sa
turated with capillary
water to
a height up to the soil su
rface. (Ta
ke w=9.81kN/m
3)
Exercise 5
A soil profile consists o
f two layers: a
layer of sa
nd 5m deep,
underlain by a 4m layer of sa
turated cla
y. The water ta
ble is
at 3m below the ground surface. The properties of th
e two
layers a
re:
Layer I (sa
nd):
Dry unit w
eight
d = 17 kN/m
3
Saturated unit w
eight
sat=20 kN/m
3.
Layer II (cla
y):
Saturated unit w
eight
sat =19 kN/m
3
Determine and plot th
e pore pressure and the total and
effectiv
e stre
sses against d
epth for th
e following two cases: a
) capillary rise
in the sand above the water ta
ble is n
egligible; b)
there is ca
pillary water to
a height of 1m above the water
table. (Ta
ke w=9.81kN/m
3)