Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
1. 1
Geotechnical EngineeringโII [CE-321]
BSc Civil Engineering โ 5th Semester
by
Dr. Muhammad Irfan
Assistant Professor
Civil Engg. Dept. โ UET Lahore
Email: mirfan1@msn.com
Lecture Handouts: https://groups.google.com/d/forum/geotech-ii_2015session
Lecture # 27
15-Dec-2017
2. 2
SLOPE STABILITY ANALYSIS
Infinite Slope
Applied Shear Stress (t)
๐ =
๐
( ๐ฟ cos ๐ผ)(1)
๐ =
๐พ๐ป๐ฟ sin ๐ผ
( ๐ฟ cos ๐ผ)(1)
๐ = ๐พ๐ป sin ๐ผ cos ๐ผ
๐น๐๐ =
๐โฒ + ๐พ๐ป๐๐๐ 2 ๐ผ โ tan ๐โฒ
๐พ๐ป sin ๐ผ cos ๐ผ
Factor of Safety (FOS)
Case-A: c-f Soil (c>0; f>0) L
H h
a
W
a
b
c
d
T
N
a
tr
๐ญ๐ถ๐บ =
๐จ๐๐๐๐๐๐๐๐ ๐บ๐๐๐๐ ๐บ๐๐๐๐๐๐๐ ๐๐ ๐บ๐๐๐
๐จ๐๐๐๐๐๐ ๐บ๐๐๐๐ ๐บ๐๐๐๐๐
Available Shear Strength of Soil (tr)
๐ ๐ = ๐โฒ + ๐พ๐ป๐๐๐ 2 ๐ผ โ tan ๐โฒ
Without considering the effect of WT
3. 3
SLOPE STABILITY ANALYSIS
Infinite Slope
๐น๐๐ =
๐โฒ + ๐ ๐โฒ โ tan ๐โฒ
๐พ๐ป sin ๐ผ cos ๐ผ
Case-A: c-f Soil (c>0; f>0)
๏ฑ cโ & fโ; effective strength parameters
๏ฑ Obtained through drained triaxial test
๐ ๐ = ๐ ๐
โฒ
=
๐ด๐ต = โ
๐ด๐ถ =
L
H
h
a
W
a
b
c
d
T
N
a
tr
A
C
B
D
a
๐ด๐ท = โ ๐ค =
๐ข =
โ ๐ค =
๐ข = ๐พ ๐คโ ๐๐๐ 2 ๐ผ
๐น๐๐ =
๐โฒ + (๐พ๐ป โ ๐พ ๐คโ) โ ๐๐๐ 2 ๐ผ tan ๐โฒ
๐พ๐ป sin ๐ผ cos ๐ผ
๐พ๐ป๐๐๐ 2
๐ผ ๐ ๐ โ ๐ข
โ cos ๐ผ
๐ด๐ถ cos ๐ผ = โ ๐๐๐ 2 ๐ผ
๐พ ๐คโ ๐ค
๐ด๐ท = โ ๐๐๐ 2
๐ผ
Pore water pressure, u
Considering
presence of WT
4. 4
SLOPE STABILITY ANALYSIS
Infinite Slope
Case-B: Cohesive soil (f=0)
L
H h
a
W
a
b
c
d
T
N
a
tr
๐น๐๐ =
๐โฒ
๐พ๐ป sin ๐ผ cos ๐ผ
Case-C: Granular soil (c=0)
๐น๐๐ =
(๐พ๐ป โ ๐พ ๐คโ) โ ๐๐๐ 2
๐ผ โ tan ๐โฒ
๐พ๐ป sin ๐ผ cos ๐ผ
๐น๐๐ = 1 โ
๐พ ๐คโ
๐พ๐ป
tan ๐โฒ
tan ๐ผ
๐น๐๐ =
๐โฒ
+ (๐พ๐ป โ ๐พ ๐คโ) โ ๐๐๐ 2
๐ผ tan ๐โฒ
๐พ๐ป sin ๐ผ cos ๐ผ
(For c-f soil)
๐น๐๐ = ๐พ๐ป 1 โ
๐พ ๐คโ
๐พ๐ป
๐๐๐ 2
๐ผ โ tan ๐โฒ
๐พ๐ป sin ๐ผ cos ๐ผ
5. 5
SLOPE STABILITY ANALYSIS
Infinite Slope
Case-C: Granular soil (c=0)
For critical case; FOS = 1
๐น๐๐ =
tan ๐
tan ๐ผ
tan ๐ผ = tan ๐โฒ
i.e. the slope is only stable up to the angle of friction of soil.
๐น๐๐ = 1 โ
๐พ ๐คโ
๐พ๐ป
tan ๐โฒ
tan ๐ผ
For dry slope, h=0
๐ผ = ๐โฒ
L
H h
a
W
a
b
c
d
T
N
a
tr
6. 6
SLOPE STABILITY ANALYSIS
Infinite Slope
Case-C: Granular soil (c=0)
For fully saturated slope, h=H
๐น๐๐ = 1 โ
๐พ ๐คโ
๐พ๐ป
tan ๐โฒ
tan ๐ผ
๐น๐๐ =
๐พ โ ๐พ ๐ค
๐พ
tan ๐โฒ
tan ๐ผ
๐น๐๐ = 0.5
tan ๐โฒ
tan ๐ผ
For critical case; FOS = 1
1 = 0.5
tan ๐โฒ
tan ๐ผ
tan ๐ผ = 0.5 โ tan ๐โฒ
i.e. a fully saturated slope will be stable only up to half of its
friction angle
๐ผ = 0.5 โ ๐โ
L
H h
a
W
a
b
c
d
T
N
a
tr
7. 7
Practice Problem #1
Calculate the maximum permissible slope angle for a sandy soil
having gsat = 20 kN/m3, fโ =30ยฐ, to give a FOS of 1.5 when;
a. the slope is dry
b. the slope is fully saturated with water table at the ground
surface
8. 8
Practice Problem #2
An infinite slope is shown in the figure. The position of water
table is 2m below the ground surface. Determine the change in
FOS of the slope if WT is brought to a depth of 4m below the
surface.
gsat = 18 kN/m3
cโ= 10 kPa
fโ = 20ยฐ
H = 6m
a = 15ยฐ
9. 9
CONCLUDED
REFERENCE MATERIAL
Principles of Geotechnical Engineering โ (7th Edition)
Braja M. Das
Chapter #13
Essentials of Soil Mechanics and Foundations (7th Edition)
David F. McCarthy
Chapter #17
Geotechnical Engineering โ Principles and Practices โ (2nd Edition)
Coduto, Yueng, and Kitch
Chapter #17