Geotechnical Engineering-II [Lec #23: Rankine Earth Pressure Theory]

1
Geotechnical Engineering–II [CE-321]
BSc Civil Engineering – 5th Semester
by
Dr. Muhammad Irfan
Assistant Professor
Civil Engg. Dept. – UET Lahore
Email: mirfan1@msn.com
Lecture Handouts: https://groups.google.com/d/forum/geotech-ii_2015session
Lecture # 23
29-Nov-2017

2
RANKINE THEORY OF ACTIVE EARTH
PRESSURE
ASSUMPTIONS
1. The soil is homogeneous and isotropic.
2. The most critical shear surface is a plane. In reality, it is
slightly concave upward, but this is a reasonable assumption
(especially for the active case) and it simplifies the analysis.
3. The backfill surface is planar (although it does not necessarily
need to be horizontal).
4. There is no friction between wall and soil.
5. The wall is infinitely long so that a representative two-
dimensional section of the wall may be analyzed,
assuming there is no strain in the direction perpendicular
to the section. We refer to this as a plane strain condition.

3
PRESSURE
If wall AB is not allowed to move 
Shearstress,t
Effective Normal
stress, s’so’Koso’sa’
a
sh’
b
c
s’h = Ko s’o
Stress condition in soil  Mohr’s circle a
If wall is allowed to move away from soil mass
 horizontal principal stress will decrease 
 Circle b  Circle c

4
PRESSUREShearstress,t
Effective Normal
stress, s’so’
Koso’
sa’A O
D
C
f c

5
PRESSURE

6
PRESSURE

7
PRESSURE
For cohesionless soils, c’ = 0

8
PRESSURE
f
ff
s
s







 




sin1
sin1
2
45tan2
o
a
aK
aaa KczK  2s





 





 

2
45tan'2
2
45tan2 ff
s cza

9
RANKINE ACTIVE PRESSURE
DIAGRAM
aa K2c-Kz
z
zC
aK2c-aK2c-
Kz a
WALL
WALL
WALL

10
RANKINE ACTIVE PRESSURE
DIAGRAM
aa K2c-Kz
z
zC
aK2c-
WALL

11
RANKINE THEORY OF ACTIVE EARTH PRESSURE
-- DEPTH OF UNSUPPORTED CUT --
aa K2c-Kz
z
zC
aK2c-
General Case
(c-f soil) 0Cz
aac KcKz  20 
At zC
a
a
c
K
Kc
z



2
a
c
K
c
z



2
Cohesionless Soils
(c’=0)
Cohesive Soils
(f=0)
Ka =
Height of unsupported cut (hC)
 Zero Net force acting on wall

c
zc


2
WALL
hC = Ht. of
Unsupported
Cut
CC zh  2
 s’a = 0
1

12
RANKINE THEORY OF PASSIVE
EARTH PRESSURE
Wall movement
towards soil
Shearstress,t
Effective Normal
stress, s’so’Koso’ sp’A O
D
C
f c

13
EARTH PRESSURE
Derivation: similar to that for active state
For cohesionless soils, c’ = 0

14
EARTH PRESSURE
f
ff
s
s







 




sin1
sin1
2
45tan2
o
p
pK





 





 

2
45tan'2
2
45tan2 ff
s czp
ppp KczK  2s

15
EARTH PRESSURE

17
RANKINE THEORY
ACTIVE PRESSURE -- SUMMARY --
f
ff
s
s







 




sin1
sin1
2
45tan2
o
a
aK
a
c
K
c
z



2

18
RANKINE THEORY
PASSIVE PRESSURE -- SUMMARY --
f
ff
s
s







 




sin1
sin1
2
45tan2
o
p
pK

19
RANKINE THEORY
-- INCLINATION OF FAILURE PLANE --





 

2
45tan
f
ninclinatioplaneFailure 




 

2
45tan
f
ninclinatioplaneFailure
Active Case Passive Case

20
Practice Problem #3
f
ff
s
s







 




sin1
sin1
2
45tan2
o
a
aK

21
CONCLUDED
REFERENCE MATERIAL
Principles of Geotechnical Engineering – (7th Edition)
Braja M. Das
Chapter #13
Essentials of Soil Mechanics and Foundations (7th Edition)
David F. McCarthy
Chapter #17
Geotechnical Engineering – Principles and Practices – (2nd Edition)
Coduto, Yueng, and Kitch
Chapter #17

Geotechnical Engineering-II [Lec #23: Rankine Earth Pressure Theory]

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Geotechnical Engineering-II [Lec #23: Rankine Earth Pressure Theory]