2 2 (z q) K a 2C K a
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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
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:
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
2C q z0 Ka
Pa Pa
(c)
(d)
If Z0>0, then case (c);
1 Pa ( H z0 ) 2 K a 2
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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
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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
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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
2
rHKp
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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
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.

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 )
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
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2 2
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(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
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1 Pp H 2 K p qHK p 2CH K p 2
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
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第一节 概述 Introduction

What is earth pressure?
Earth pressure: The pressure applied on a retaining wall from soil
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第一节 概述 Introduction

Types of earth pressure?
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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 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
Passive pressure
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第一节 概述 Introduction
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
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
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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:
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
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p2
第二节 朗肯土压力理论

Passive earth pressure
Rankine’s theory
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

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.