河海大学土力学课件
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2 2
岩土工程研究所
(z q) K p 2C K p
第二节 朗肯土压力理论
Passive earth pressure
Rankine’s theory
in cohesive soils
1 2 Pp H K p 2CH K p 2
岩土工程研究所
1 Pp H 2 K p qHK p 2CH K p 2
主动土压力 Active earth pressure 被动土压力 Passive earth pressure 静止土压力 Earth pressure at rest
Active pressure
At-rest pressure
Fra Baidu bibliotek
Passive pressure
岩土工程研究所
第一节 概述 Introduction
Rankine’s theory
The line of action of Pp passes through the center of the area of the pressure distribution diagram
岩土工程研究所
1
Pp
H
qKp
rHKp
1 p p (z q)tg 2 (45 ) (z q) K p
Pa=rH2Ka/2+qHKa
The resultant thrust is equal to the area of the pressure distribution diagram, I.e. the area of trapezia The line of action of Pa passes through the center of the area of the trapezia
passive pressure. The soil is in passive state.
静止土压力 Earth pressure at rest:The wall is rigid and does not yield, that is there is no movement taking place, the horizontal soil pressures are said to
岩土工程研究所
3 pa (z q)tg 2 (45 ) (z q) K a
2
第二节 朗肯土压力理论
Active earth pressure
Surcharge
Rankine’s theory
in cohesionless soils
1 z q
3
A uniform surcharge load (q) is applied over the whole surface
1 z q
1 z q
3
Pa=rH2Ka/2+qHKa
Pressure distribution
Pa H
Surcharge
3
qKa
2
rHKa
f 45
Types of earth pressure?
主动土压力 Active earth pressure: The wall moves away from the supported soil, and the horizontal soil pressures are refereed to as active pressure.
岩土工程研究所
Passive earth pressure
Rankine’s theory
in cohesive soils
Surcharge
3
1 p p ztg (45 ) 2Ctg (45 )
2
2
2
1
Pp
H
zK p 2C K p
rHKp
1 p p (z q)tg 2 (45 ) 2Ctg (45 )
1 z
Soil in state of plastic equilibrium
Pa=rH2Ka/2
3
Pa H/3 pa=rHKa
H
Smooth vertical back, horizontal surface
3 pa ztg (45 ) zK a
2
2
岩土工程研究所
第二节 朗肯土压力理论
Active earth pressure
( pa ) B H1Ka
Rankine’s theory
in case of ground water
( pa )C H1Ka 2 Ka H
1 2 Pw w H 2 2 1 1 Pa H12 K a H1 H 2 K a 2 K a H2 2 2
Active earth pressure
Rankine’s theory
in cohesive soils
Assuming: pa (z q) K a 2C K a 0 Tension crack depth:
z0
(c)
2
2C q Ka
(d)
3 pa (z q)tg (45 ) 2Ctg (45 )
2
rHKp
岩土工程研究所
1 p p ztg (45 ) zK p
2
第二节 朗肯土压力理论
Passive earth pressure in cohesionless soils The resultant thrust is equal to Vertical stress is minor principal stress the area of the Surcharge pressure distribution Pp=rH2Kp/2+qHKp 3 z q diagram
The soil is in active state.
被动土压力 Passive earth pressure:The wall is caused to move towards the soil being supported, and the horizontal soil pressures are refereed to as
2
Kp is coefficient of passive earth pressure
第二节 朗肯土压力理论
Active earth pressure
1
Rankine’s theory
in cohesive soils
Assuming: pa zK a 2C K a 0
3
Tension crack depth:
2C q z0 Ka
Pa Pa
(c)
(d)
If Z0>0, then case (c);
1 Pa ( H z0 ) 2 K a 2
岩土工程研究所
If Z0<0, then case (d);
1 Pa H 2 K a qHK a 2CH K a 2
第二节 朗肯土压力理论
2 2 (z q) K a 2C K a
岩土工程研究所
If Z0<0, then case (d); If Z0>0, then case (c);
第二节 朗肯土压力理论
Active earth pressure
Rankine’s theory
in cohesive soils
p1
Pa
H
qKa
rHKa
P h H
2 p1 p2 h H 3( p1 p2 )
3 pa (z q)tg 2 (45 ) (z q) K a
2
岩土工程研究所
p2
第二节 朗肯土压力理论
Passive earth pressure
Rankine’s theory
岩土工程研究所
第一节 概述 Introduction
At-rest earth pressure? Under natural conditions of deposition, with semi-infinite extent, there is a negligible amount of horizontal strain, the soil is said to be in an at-rest state (or K0 state), and the horizontal effective stress is:
第六章 土压力
Chapter 6 Earth Pressure
河海大学 岩土工程研究所 Research Institute of Geotechnical Engineering, Hohai University
岩土工程研究所
第一节 概述 Introduction
土压力概念 What is earth pressure? 土压力种类： Types of earth pressure 静止土压力： Earth pressure at rest
z0 2C Ka
3 pa ztg (45 ) 2Ctg (45 )
2
Total passive resistance force:
1 Pa ( H z0 ) 2 K a 2
2
2
zK a 2C K a
岩土工程研究所
第二节 朗肯土压力理论
in cohesionless soils
The wall moves towards the earthfill, Vertical stress is minor principal stress
3 z
Pp=rH2Kp/2
1
Pp
H
H/3 Passive earth pressure
Kp is coefficient of passive earth pressure
Ka is coefficient of active earth pressure
第二节 朗肯土压力理论
Active earth pressure
Rankine’s theory
in cohesionless soils
Surcharge
The wall moves away from the earthfill, Vertical stress is major principal stress
h K0 v
Where K0=coefficient of earth pressure at rest .
The resultant thrust is equal to the area of the pressure distribution diagram, I.e.
1 P0 H 2 K 0 2
be at-rest pressure. The soil is in at-rest state.
主动极限平衡状态: Active state: plastic equilibrium with lateral expansion taking place.
被动极限平衡状态: Passive state: plastic equilibrium with lateral compression taking place. 静止平衡状态: At-rest state: elastic equilibrium with no lateral strain taking place.
岩土工程研究所
第二节 朗肯土压力理论
Active earth pressure
Rankine’s theory
in cohesionless soils
The wall moves away from the earthfill, Vertical stress is major principal stress
岩土工程研究所
第一节 概述 Introduction
What is earth pressure?
Earth pressure: The pressure applied on a retaining wall from soil
岩土工程研究所
第一节 概述 Introduction
Types of earth pressure?
岩土工程研究所
(z q) K p 2C K p
第二节 朗肯土压力理论
Passive earth pressure
Rankine’s theory
in cohesive soils
1 2 Pp H K p 2CH K p 2
岩土工程研究所
1 Pp H 2 K p qHK p 2CH K p 2
主动土压力 Active earth pressure 被动土压力 Passive earth pressure 静止土压力 Earth pressure at rest
Active pressure
At-rest pressure
Fra Baidu bibliotek
Passive pressure
岩土工程研究所
第一节 概述 Introduction
Rankine’s theory
The line of action of Pp passes through the center of the area of the pressure distribution diagram
岩土工程研究所
1
Pp
H
qKp
rHKp
1 p p (z q)tg 2 (45 ) (z q) K p
Pa=rH2Ka/2+qHKa
The resultant thrust is equal to the area of the pressure distribution diagram, I.e. the area of trapezia The line of action of Pa passes through the center of the area of the trapezia
passive pressure. The soil is in passive state.
静止土压力 Earth pressure at rest:The wall is rigid and does not yield, that is there is no movement taking place, the horizontal soil pressures are said to
岩土工程研究所
3 pa (z q)tg 2 (45 ) (z q) K a
2
第二节 朗肯土压力理论
Active earth pressure
Surcharge
Rankine’s theory
in cohesionless soils
1 z q
3
A uniform surcharge load (q) is applied over the whole surface
1 z q
1 z q
3
Pa=rH2Ka/2+qHKa
Pressure distribution
Pa H
Surcharge
3
qKa
2
rHKa
f 45
Types of earth pressure?
主动土压力 Active earth pressure: The wall moves away from the supported soil, and the horizontal soil pressures are refereed to as active pressure.
岩土工程研究所
Passive earth pressure
Rankine’s theory
in cohesive soils
Surcharge
3
1 p p ztg (45 ) 2Ctg (45 )
2
2
2
1
Pp
H
zK p 2C K p
rHKp
1 p p (z q)tg 2 (45 ) 2Ctg (45 )
1 z
Soil in state of plastic equilibrium
Pa=rH2Ka/2
3
Pa H/3 pa=rHKa
H
Smooth vertical back, horizontal surface
3 pa ztg (45 ) zK a
2
2
岩土工程研究所
第二节 朗肯土压力理论
Active earth pressure
( pa ) B H1Ka
Rankine’s theory
in case of ground water
( pa )C H1Ka 2 Ka H
1 2 Pw w H 2 2 1 1 Pa H12 K a H1 H 2 K a 2 K a H2 2 2
Active earth pressure
Rankine’s theory
in cohesive soils
Assuming: pa (z q) K a 2C K a 0 Tension crack depth:
z0
(c)
2
2C q Ka
(d)
3 pa (z q)tg (45 ) 2Ctg (45 )
2
rHKp
岩土工程研究所
1 p p ztg (45 ) zK p
2
第二节 朗肯土压力理论
Passive earth pressure in cohesionless soils The resultant thrust is equal to Vertical stress is minor principal stress the area of the Surcharge pressure distribution Pp=rH2Kp/2+qHKp 3 z q diagram
The soil is in active state.
被动土压力 Passive earth pressure:The wall is caused to move towards the soil being supported, and the horizontal soil pressures are refereed to as
2
Kp is coefficient of passive earth pressure
第二节 朗肯土压力理论
Active earth pressure
1
Rankine’s theory
in cohesive soils
Assuming: pa zK a 2C K a 0
3
Tension crack depth:
2C q z0 Ka
Pa Pa
(c)
(d)
If Z0>0, then case (c);
1 Pa ( H z0 ) 2 K a 2
岩土工程研究所
If Z0<0, then case (d);
1 Pa H 2 K a qHK a 2CH K a 2
第二节 朗肯土压力理论
2 2 (z q) K a 2C K a
岩土工程研究所
If Z0<0, then case (d); If Z0>0, then case (c);
第二节 朗肯土压力理论
Active earth pressure
Rankine’s theory
in cohesive soils
p1
Pa
H
qKa
rHKa
P h H
2 p1 p2 h H 3( p1 p2 )
3 pa (z q)tg 2 (45 ) (z q) K a
2
岩土工程研究所
p2
第二节 朗肯土压力理论
Passive earth pressure
Rankine’s theory
岩土工程研究所
第一节 概述 Introduction
At-rest earth pressure? Under natural conditions of deposition, with semi-infinite extent, there is a negligible amount of horizontal strain, the soil is said to be in an at-rest state (or K0 state), and the horizontal effective stress is:
第六章 土压力
Chapter 6 Earth Pressure
河海大学 岩土工程研究所 Research Institute of Geotechnical Engineering, Hohai University
岩土工程研究所
第一节 概述 Introduction
土压力概念 What is earth pressure? 土压力种类： Types of earth pressure 静止土压力： Earth pressure at rest
z0 2C Ka
3 pa ztg (45 ) 2Ctg (45 )
2
Total passive resistance force:
1 Pa ( H z0 ) 2 K a 2
2
2
zK a 2C K a
岩土工程研究所
第二节 朗肯土压力理论
in cohesionless soils
The wall moves towards the earthfill, Vertical stress is minor principal stress
3 z
Pp=rH2Kp/2
1
Pp
H
H/3 Passive earth pressure
Kp is coefficient of passive earth pressure
Ka is coefficient of active earth pressure
第二节 朗肯土压力理论
Active earth pressure
Rankine’s theory
in cohesionless soils
Surcharge
The wall moves away from the earthfill, Vertical stress is major principal stress
h K0 v
Where K0=coefficient of earth pressure at rest .
The resultant thrust is equal to the area of the pressure distribution diagram, I.e.
1 P0 H 2 K 0 2
be at-rest pressure. The soil is in at-rest state.
主动极限平衡状态: Active state: plastic equilibrium with lateral expansion taking place.
被动极限平衡状态: Passive state: plastic equilibrium with lateral compression taking place. 静止平衡状态: At-rest state: elastic equilibrium with no lateral strain taking place.
岩土工程研究所
第二节 朗肯土压力理论
Active earth pressure
Rankine’s theory
in cohesionless soils
The wall moves away from the earthfill, Vertical stress is major principal stress
岩土工程研究所
第一节 概述 Introduction
What is earth pressure?
Earth pressure: The pressure applied on a retaining wall from soil
岩土工程研究所
第一节 概述 Introduction
Types of earth pressure?