Upload
lenka
View
58
Download
1
Embed Size (px)
DESCRIPTION
Lateral Earth Pressure. E. E. E. E. Tunnel. Dock. Abutment. 6.1 General - PowerPoint PPT Presentation
Citation preview
6.1 General
Conditions of plane strain are assumed, i.e. strains in the longitudinal direction of the structure are assumed to be zero. It is assumed that the stress–strain behavior of the soil can be represented by the rigid–perfectly plastic idealization.
E
Dock Tunnel
EE
Abutment
E
Lateral Earth Pressure
加筋土挡墙
挖孔桩支护
钢筋混凝土挡土墙
Lateral Earth Pressure
完工
完工
Lateral Earth Pressure
钢筋混凝土挡土墙
Rigid earth retaining wall
扶壁式
刚性加筋
预应力
板桩变形
板桩上土压力 实测
计算
锚杆
板桩
Flexible earth retaining wall
Lateral Earth Pressure
retaining and protection of foundation excavation
Lateral Earth Pressure
• There are 3 states of lateral earth pressureKo = At Rest
Ka = Active Earth Pressure (wall moves away from soil)
Kp = Passive Earth Pressure (wall moves into soil)
Passive is more like a resistance
Lateral Earth Pressure
Relation among three earth pressures
-△ +△
+△-△
E
o△a △p
Ea
Eo
Ep
Lateral Earth Pressure
6.2 At Rest Earth Pressure
One common earth pressure coefficient for the “at rest” condition in granular soil is:
Ko = 1 – sin(φ)
Where: Ko is the “at rest” earth pressure coefficient and φ is the soil friction value.
K0h
h
z
K0z
oo KhE 2
2
1
z
h/3
Lateral Earth Pressure
Retaining wall between the slope
Lateral Earth Pressure
Failured earth retaining wall
Lateral Earth Pressure
Failured reinforced earth retaining wall
Lateral Earth Pressure
6.2 Rankine Theory of Earth Pressure
If the soil mass as a whole is stressed such that the principal stresses at every point are in the same directions, theoretically, there will be a network of failure planes equally inclined to the principal planes.
The Rankine Theory assumes: There is no adhesion or friction between the wall and soil Lateral pressure is limited to vertical walls Ground surface is horizontal.
Lateral Earth Pressure
pa pp
f
zK0z
f =c+ tan
伸展 压缩45o-/2 45o + /2
If there is a movement of the wall away from the soil, the value of x decreases as the soil dilates or expands outwards, the decrease in x being an unknown function of the lateral strain in the soil. If the expansion is large enough, the value of x decreases to a minimum value such that a state of plastic equilibrium develops. Since this state is developed by a decrease in the horizontal stress x, this must be the minor principal stress ( 3). The vertical stress z is then the major principal stress ( 1).
Lateral Earth Pressure
1) Active Earth Pressure
45o + /2
h
z(σ1)
pa(σ3)
z
245tan2
245tan2
13
oo c
aaa KczKp 2
When the horizontal stress becomes equal to the passive pressure the soil is said to be in the passive Rankine state, there being two sets of failure planes each inclined at 45o + /2 to the vertical (the direction of the major principal plane)
Lateral Earth Pressure
For cohesive soil
This means that in active case the soil is in a state of tension between the surface and depth z0. In practice, however, this tension cannot be relied upon to act on the wall, since cracks are likely to develop within the tension zone and the part of the pressure distribution diagram above depth z0 should be neglected.
For sandy soil
h/3
Ea
hKa
aa zKp
h
aKh2)2/1(
Lateral Earth Pressure
2) Passive Earth Pressure
The maximum value 1 is reached when theMohr circle through the point representing the fixed value 3 touches the failure envelope for the soil. In this case, the horizontal stress is defined as the passive pressure ( pp) representing the maximum inherent resistance of the soil to lateral compression.
ppp KczKp 2
ppp KchKhE 2)2/1( 2
The force due to the passive pressure distribution is referred to as the total passive resistance (Pp). For a vertical wall surface of height H:
Lateral Earth Pressure
Example 1Lateral Earth Pressure
Example 2
h=5m
1=17kN/m3
c1=0
1=34o
2=19kN/m3
c2=10kPa
2=16o
h 1 =
2mh 2
=3m
A
B
C
Lateral Earth Pressure
A
B
C
h=5m
h 1=
2mh 2
=3m
011 aaA zKp kPaKhp aaB 4.10111 =上
kPaKcKhp aaaB 2.42 22211 =-下
kPaKcKhhp aaaC 6.362)( 2222211
mkNEa /6.712/3)6.362.4(2/24.10 =
10.4kPa4.2kPa
36.6kPa
Solution:Lateral Earth Pressure
6.3 Coulomb Theory of Earth Pressure
Coulomb’s theory (1776) involves consideration of the stability, as a whole, of the wedge of soil between a retaining wall and a trial failure plane. The force between the wedge and the wall surface is determined by considering the equilibrium of forces acting on the wedge when it is on the point of sliding either up or down the failure plane, i.e. when the wedge is in a condition of limiting equilibrium.
αβ
δ
G
h
A
C
B E R
Active earth pressure:
h
hK
a
Lateral Earth Pressure
α=10oβ=15o
δ=20o
4.5
m
A
B
α=10o
Ea
h/3
In terms of α=10o , β=15o , =30o , δ=20o
480.0aK
mkNKhE aa /1.852
1 2 =
Solution:
The point of application of the total active thrust is not given by the Coulomb theory but is assumed to act at a distance of 1/3 H above the base of the wall.
Lateral Earth Pressure
6.4 the comparison of Rankine Theory and Coulomb Theory
1 analysis theory
Rankine theory Coulomb theoryLimit stress method
Slide wedge method
Solve the Soil pressure intensity p at
first
Solve the total earth pressure E at first
αβ
δE
Limit equilibrium condition
Lateral Earth Pressure
3 calculating error ——Rankine theory
WR
Ea'
Ea
δ0
WR
Ep
Ep'
Active pressureLarge
Passive pressuresmall
Lateral Earth Pressure
2 calculating error ——Rankine theory
Active pressureLarge
Passive pressuresmall
the actual slip surface may not be a plane
Sliding surface
Lateral Earth Pressure
3 calculating error ——Coulumb theory
Sliding surface
Passive pressuresmall
Active pressureLarge
2 calculating error ——Coulumb theory
Active pressure coefficient Ka (α=β=0)
δ=0 δ= /2 δ=
20 40 20 40 20 40
Sokolovsky
0.49 0.22 0.45 0.20 0.44 0.22
Rankine 0.49 0.217 0.49 0.217 0.49 0.217
Conlomb 0.49 0.22 0.45 0.20 0.43 0.21
Lateral Earth Pressure
3 calculating error ——compare with the exact value2 calculating error ——compare with the exact value
Passive pressure coefficient Kp (α=β=0)
δ=0 δ= /2 δ=
20 40 20 40 20 40
Sokolovsky 2.04 4.60 2.55 9.69 3.04 18.2
Rankine 2.04 4.60 2.04 4.60 2.04 4.60
Conlomb 2.04 4.60 2.63 11.8 3.52 92.6
Lateral Earth Pressure
2 calculating error ——compare with the exact value
1. Load on filling2. Stratified filling3. Water in filling
4 several kinds of active pressure
Lateral Earth Pressure
1 Rankin theory
1=z+q
pa= 3=qKa+zKa
HZ
1
3
qKaHKa
zKa
1. Load on filling
Lateral Earth Pressure
1. Load on filling
Lateral Earth Pressure
2. Coulomb theory
21 cos
2 cosa a aE H K qHKα
α β
Lateral Earth Pressure
1. Load on filling
3. Local loads—Rankin
theory
Lateral Earth Pressure
1. Load on filling
C
B
A
1 1 c1
2 2 c2 H2
H1
Rankin theory
)2
45(2)2
45(2 ooha tgcztgp
Lateral Earth Pressure
2. Stratified filling
earth pressure Pa=Kaszwater pressure pu=u
3. Water in filling
Lateral Earth Pressure
Impermeable foundation
朗肯理论
KaH2
KaH1
H2
水压力土压力
Lateral Earth Pressure
3. Water in filling
H2
H1
δ
Ea pw
Earth pressure Water pressure
Ea
pw
Coulombs theory
Lateral Earth Pressure
Impermeable foundation
3. Water in filling
Permeability coefficient of the filling is much smaller than of the foundation
H2
H1
saH2
H1
Effective stress
=total stress
u=0
Pore water
pressure
KasaH2
KaH1
Earht
pressure
透水地基
Lateral Earth Pressure
3. Water in filling
The flow net is needed to calculate the pore water pressure
Lateral Earth Pressure
3. Water in filling
Permeability coefficient of the filling is much smaller than of the foundation