Download Chapter2 permeability and stress in soil

Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
§3 permeability in soil
土的渗透性
•土的渗透性 Permeability
•有效应力 Effective stress
3.1 土的渗透性 Permeability
1 达西定律Darcy Law
This states that discharge velocity, v of water is proportional to
the hydraulic gradient, i .
v=q/A= k i
H1  H 2
i
L
where :
K=Darcy coefficient of permeability ,m/s
The hydraulic gradient i is the ratio of the head loss h over a distance L
The discharge velocity v is defined as the quantity of water , q
percolating through a cross-sectional area A in unit time .This is not the
sane as the velocity of the water percolating through the soil which is
known as the seepage velocity .
n
Vv
V
,
As  nA
q v 1 e
v0 
 
v
As n
e
Constant head permeameter
Falling head permeameter
Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
2 粘性土的渗透性 Permeability of Clay
(C
la
y)
v=
k(
i-i
b'
)
v=
ki
(s
an
d)
v
i
ib
ib'
3 渗透性力 Force of permeability
 w h1 F   w LF cos    w h2 F  TLF  0
Z1  Z 2
cos  
L
 wh1   w Z1   w Z 2   wh2  TL  0
 w h1  Z1  Z 2  h2   TL  0
h1  Z1  h2  Z 2   H1  H 2
H1  H 2
i
L
T   wi
j  T   wi
j   wi    
d s  1
1 e
 w  1  nd s  1 w
4 流砂与管涌 Running Sand, Heaving or Piping
解 水头差：h=1.5+2.5=4m
流径长L=2.5+2d
细砂的浮容重:
 s 
26.8  10
 

 9.6 KN / m3
1 e
1  0.75
'
临界水力梯度
考虑安全系数后,实有的水力梯度为:
h
'
K1 

2.5  2d  
4
9.6
1.5 

2.5  2d 10
d  1.88m
'
icr 

h
i  K1 
2.5  2d
5 临界水力梯度 Critical hydraulic gradient
 '  s  w
icr 

 w  w (1  e)
Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
• Calculate
the Force of
permeability applied on sand
γs=26.8kN/m3, e=0.72,
Determine
whether
will
running sand occur?
• If
• If the running sand occurs,
calculate the necessary water
head difference.
L=25cm
For the seepage situations
shown in Fig below, the
length of the sand sample
L=25cm and water head
difference h=20cm.
h=20cm
Exercise 3-1
Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
3.2 有效应力Effective stress
1.The Principle of Effective Stress
♦ The importance of the forces transmitted through the
soil skeleton from particle to particle was recognized in
1923 when Terzaghi presented the principle of effective
stress, an intuitive relationship based on experimental
data. The principle applies only to fully saturated soils
and relates the following three stresses:
(1) 总应力 the total normal stress (σ)
(2) 孔隙水压力 the pore water pressure (u)
(3) 有效应力 the effective normal stress (σ’ )
总应力 the total normal stress (σ) on a plane within
the soil mass, being the force per unit area transmitted
in a normal direction across the plane, imaging the soil
to be a solid (single-phase) material.
孔隙水压力 the pore water pressure (u), being the
pressure of the water filling the void space between the
solid particles.
有效应力 the effective normal stress (σ’ ) on the
plane, representing the stress transmitted through the
soil skeleton only.
Civil Engineering Department of Shanghai University


Soil Mechanics Chapter 2
 A  A  Ns  uAw
 
Ns
Aw
u
  '  1   u
A
A
♦ The relationship is :
σ = σ’ +u
The Principle of Effective Stress
-Un-Saturated soil
Bishop,1959
    ua  xua  uw 
'
x  Aw
A
For Saturated soil: x=1
For completely dried soil x=0
 '    uw
 '    ua
Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
Skempton A W, 1961
 a  tg u 
uw
 '    1 
tg ' 

 a  tg u 
 S xuw
 '    1 
tg ' 

(For Completely Saturated soil)
(For Partly Saturated soil)
Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
-静水条件下的有效应力
hydrostatic
Total stress at a-a plane
   w h1   sat h2
pore water pressure
u   w hw   w h1  h2 
effective normal stress at a-a
plane
’
＝－u   w h1   sat h2   w h1  h2    'h2
Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
-自上而下的稳定渗流
Seepage to the down
Total stress at a-a plane
   w h1   sat h2
pore water pressure
u   w h1  h2  h   w hw
effective normal stress at a-a
plane
 '    u   w h1   sat h2   w h1  h2  h 
  ' h2   w h   ' w i h2
i=h/h2
Civil Engineering Department of Shanghai University
Soil Mechanics Chapter 2
-自下而上的稳定渗流
Seepage to the upper
Total stress at a-a plane
   w h1   sat h2
h
h1
hw
b
pore water pressure
u   w h1  h2  h   whw
b
h2
a
a
u
effective normal stress at a-a
plane
 '    u   w h1   sat h2   w h1  h2  h 
  ' h2   w h   ' wi h2
i=h/h2
γwh
σ'
Civil Engineering Department of Shanghai University
Example
For sand, e=0.6, Sr=35% (above
water table)
γs=27kN/m3,
For clay, γsat=21kN/m3
Calculate the total stress, pore
water pressure and the effective
stress in 9m depth. Plot the
distribution.
Soil Mechanics Chapter 2