土压力理论与挡土墙设计.ppt
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6.2.1 Limit state/极限状态 -Active limit equilibrium/主动极限平衡 -Passive limit equilibrium/被动极限平衡
x K0 z
6.2.2 Rankine active earth pressure/主动土压力
•In Non-Cohesive soils (soil surface horizontal)/地表水平无粘性土
§6 Earth Pressure and Retaining Wall
土压力理论与挡土墙设计
• Introduction/引言
• Rankine’s earth pressure theory / 朗肯土压力理论 • Coulomb’s earth pressure theory / 库仑土压力理论 • Discuss / 讨论 • Retaining wall design / 挡土墙设计
Let, dEa 0
d
Ea
1 2
H
2
cos2
cos
cos2
1
sin cos
sin cos
i i
2
where,
cos2
cos
cos2
1
sin cos
sin i 2
cos
i
, active
pressure
coefficient
Ea
1 H 2
2
a
If i=0,α=0,δ=0, Then
A0
tg
B0
G A0tg B0
where,
A0
1 2
(H
a)2
B0
1 2
(H
a)2
tg
1 2
a2
tg
1源自文库2
ab
Ea
G
sin 90
sin
A0tg
B0
cos sin
where,
Let, dEa 0
d
then,
A0tg
B0
sin
sin
sin 2
cos
Ea
1 2
H
2
1
cos2 sin
2
1
2
H 2 1 sin 1 sin
1
2
H 2tg2 45
2
Ea
1
2
H2
a
where
a
tg2 45
2
• Complex boundary conditions/复杂边界条件
S
1 2
H
a2
tg
1 2
H
a2
tg
1 2
ab
1 2
a2
tg
1
3
tg2
45
2
3
K
p
where
Kp
tg2 45
2
,
passive
pressure
coefficient
Ep
1 H 2
2
tg 2 45
2
1 H 2
2
Kp
•In Cohesive soils (soil surface horizontal)/ /地表水平粘性土
1
3
tg2
45
2
cos
A0 cos sin cos2
0
tg 2 2tg tg ctg tg B0 ctg tg 0
A0
tg tg
tg
ctg tg
B0 A0
where,
-Coefficient of active earth pressure /主动土压力系数λa
a
a h
A retaining wall of embankment is 6m high. And the relative parameters are c=0,φ=30。,α=14 。 00’,δ=φ/3, as well as shown in Fig. below. Calculate the active earth pressure and draw the distribution.
-Assuming
-Active earth pressure
E
G
sin 90
sin
dEa 0
d
-Passive earth pressure
sin 90
Ep G sin
Ea f ( ) Ep f ( )
6.3.2 Active Case/主动情形
Ka
tg2 45
2
•For sloping soil surface(β) /地表倾斜
Ea
1
2
H
2
cos
cos cos
cos2 cos2 cos2 cos2
6.2.3 Rankine passive earth pressure/被动土压力
•In Non-Cohesive soils (soil surface horizontal) /地表水平无粘性土
2c
tg
45
2
3
K
p
2c
Kp
3 H
where
Kp
tg2 45
2
,
passive
pressure
coefficient
Ep
1 H 2 2
tg 2 45
2c H 2
tg 45
2
1 H 2 2
Kp
2cH
Kp
6.3 Coulomb’s Earth Pressure theory / 库仑土压力理论 6.3.1Basic concept
Ea
A0
tg
B0
cos sin
Ea
A0tg B0 tg tg
tg
tg
cos sin
A0tg B0 tg tg
a
a
tg
tg
cos sin
where,
-Distribution of active earth pressure /土压力的分布
-Example
3
1
tg2 45
2
where 1 H
45
2
E
1 H 2 tg2 45
2
2
Ea
1
2
H
2
Ka
where
Ka
tg2 45
2
, active
pressure
coefficient
•In Cohesive soils (soil surface horizontal)/地表水平粘性土
3
1
tg 2 45
2
2c tg 45
2
45
2
Z0
2c
tg 45
2
, vertical
wall
depth
Ea
1 H
2
Z0 2
tg 2 45
2
1 H 2
2
tg 2 45
2cHtg 45
2
2
2c 2
E
1 H 2
2
K
2cH
K
2c 2
where
6.1 Introduction/引言
x k0 z
k0 1
-Coefficient of earth pressure at rest 静止土压力
k0 1 sin ' Bishop, 1958
E0
1
2
H
2
K0
主动土压力
被动土压力
6.2 Rankine Earth Pressure theory /朗肯土压力理论
• General solution
AB H cos
AD AB sin
BC
AB
sin sin
90 90
i i
then,G
1 2
H
2
sin
sin 90 cos2 cos i
i
E
1 2
H
2
sin
cos2
sin 90
cos i
i
sin 90
sin
x K0 z
6.2.2 Rankine active earth pressure/主动土压力
•In Non-Cohesive soils (soil surface horizontal)/地表水平无粘性土
§6 Earth Pressure and Retaining Wall
土压力理论与挡土墙设计
• Introduction/引言
• Rankine’s earth pressure theory / 朗肯土压力理论 • Coulomb’s earth pressure theory / 库仑土压力理论 • Discuss / 讨论 • Retaining wall design / 挡土墙设计
Let, dEa 0
d
Ea
1 2
H
2
cos2
cos
cos2
1
sin cos
sin cos
i i
2
where,
cos2
cos
cos2
1
sin cos
sin i 2
cos
i
, active
pressure
coefficient
Ea
1 H 2
2
a
If i=0,α=0,δ=0, Then
A0
tg
B0
G A0tg B0
where,
A0
1 2
(H
a)2
B0
1 2
(H
a)2
tg
1 2
a2
tg
1源自文库2
ab
Ea
G
sin 90
sin
A0tg
B0
cos sin
where,
Let, dEa 0
d
then,
A0tg
B0
sin
sin
sin 2
cos
Ea
1 2
H
2
1
cos2 sin
2
1
2
H 2 1 sin 1 sin
1
2
H 2tg2 45
2
Ea
1
2
H2
a
where
a
tg2 45
2
• Complex boundary conditions/复杂边界条件
S
1 2
H
a2
tg
1 2
H
a2
tg
1 2
ab
1 2
a2
tg
1
3
tg2
45
2
3
K
p
where
Kp
tg2 45
2
,
passive
pressure
coefficient
Ep
1 H 2
2
tg 2 45
2
1 H 2
2
Kp
•In Cohesive soils (soil surface horizontal)/ /地表水平粘性土
1
3
tg2
45
2
cos
A0 cos sin cos2
0
tg 2 2tg tg ctg tg B0 ctg tg 0
A0
tg tg
tg
ctg tg
B0 A0
where,
-Coefficient of active earth pressure /主动土压力系数λa
a
a h
A retaining wall of embankment is 6m high. And the relative parameters are c=0,φ=30。,α=14 。 00’,δ=φ/3, as well as shown in Fig. below. Calculate the active earth pressure and draw the distribution.
-Assuming
-Active earth pressure
E
G
sin 90
sin
dEa 0
d
-Passive earth pressure
sin 90
Ep G sin
Ea f ( ) Ep f ( )
6.3.2 Active Case/主动情形
Ka
tg2 45
2
•For sloping soil surface(β) /地表倾斜
Ea
1
2
H
2
cos
cos cos
cos2 cos2 cos2 cos2
6.2.3 Rankine passive earth pressure/被动土压力
•In Non-Cohesive soils (soil surface horizontal) /地表水平无粘性土
2c
tg
45
2
3
K
p
2c
Kp
3 H
where
Kp
tg2 45
2
,
passive
pressure
coefficient
Ep
1 H 2 2
tg 2 45
2c H 2
tg 45
2
1 H 2 2
Kp
2cH
Kp
6.3 Coulomb’s Earth Pressure theory / 库仑土压力理论 6.3.1Basic concept
Ea
A0
tg
B0
cos sin
Ea
A0tg B0 tg tg
tg
tg
cos sin
A0tg B0 tg tg
a
a
tg
tg
cos sin
where,
-Distribution of active earth pressure /土压力的分布
-Example
3
1
tg2 45
2
where 1 H
45
2
E
1 H 2 tg2 45
2
2
Ea
1
2
H
2
Ka
where
Ka
tg2 45
2
, active
pressure
coefficient
•In Cohesive soils (soil surface horizontal)/地表水平粘性土
3
1
tg 2 45
2
2c tg 45
2
45
2
Z0
2c
tg 45
2
, vertical
wall
depth
Ea
1 H
2
Z0 2
tg 2 45
2
1 H 2
2
tg 2 45
2cHtg 45
2
2
2c 2
E
1 H 2
2
K
2cH
K
2c 2
where
6.1 Introduction/引言
x k0 z
k0 1
-Coefficient of earth pressure at rest 静止土压力
k0 1 sin ' Bishop, 1958
E0
1
2
H
2
K0
主动土压力
被动土压力
6.2 Rankine Earth Pressure theory /朗肯土压力理论
• General solution
AB H cos
AD AB sin
BC
AB
sin sin
90 90
i i
then,G
1 2
H
2
sin
sin 90 cos2 cos i
i
E
1 2
H
2
sin
cos2
sin 90
cos i
i
sin 90
sin