1. 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 # 26
13-Dec-2017
2. 2
STABILITY OF SLOPES
Slope
An exposed ground surface that stands at an angle with the
horizontal is called an unrestrained slope.
3. 3
TYPES OF SLOPES
A) w.r.t. Method of Construction
1. Natural Slopes
2. Man-made / Engineered Slopes
Embankments, earthen dams, river dikes, excavation trenches, etc.
Engineered SlopeNatural Slope
4. 4
TYPES OF SLOPES
B) w.r.t. Extents
1. Infinite Slopes
Having constant slope of infinite extent, e.g. long slope of a mountain
face.
2. Finite Slopes
Slopes of limited heights and extents, e.g. typical man-made slopes
Finite SlopeInfinite Slope
5. 5
TYPES OF SLOPES
C) w.r.t. Slope Material
1. Cohesionless
2. Cohesive
Cohesionless Cohesive
6. 6
STABILITY OF SLOPES
A slope is said to be stable if
it meets a prescribed need for
a fixed period of time with a
suitable safety factor (FOS).
Nova Frebergo, Brazil
January 13, 2011
California, USA
January, 1997
10. 11
TYPES/MODES OF SLOPE FAILURE
Toe Failure
Failure surface passing through
toe of slope
Material of slope is
homogeneous
Relatively steep slope angles
11. 12
TYPES/MODES OF SLOPE FAILURE
Base Failure
Failure surface passing through foundation
Foundation soil somehow weaker than slope material
Relatively gentle slopes
15. 16
LIMIT EQUILIBRIUM ANALYSIS
Most common quantitative measure of slope stability
Stability of slope expressed in terms of factor of safety just
before failure
𝐹𝑂𝑆 =
𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒
𝐷𝑖𝑠𝑡𝑢𝑟𝑏𝑖𝑛𝑔 𝐹𝑜𝑟𝑐𝑒
𝐹𝑂𝑆 =
𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑆𝑜𝑖𝑙
𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠
Failure Surface
FOS < 1
FOS = 1
FOS > 1
Typical design criterion for stable slope; FOS > 1.5
→ Failure
→ Verge of failure/Just stable
→ Stable
16. 17
SLOPE STABILITY ANALYSIS
Infinite Slope
Assumptions:
1. Slope face is planar and
of infinite extent
2. Failure surface is║to
slope face
3. Water surface is║to
slope face
𝐹𝑂𝑆 =
𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑆𝑜𝑖𝑙
𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠
L
H h
a
a
b
c
d
17. 18
SLOPE STABILITY ANALYSIS
Infinite Slope
Case-A: c-f Soil (c>0; f>0) L
H h
a
W
a
b
c
d
T
N
a
Available Shear Strength
of Soil (tr) tr
𝜏 𝑟 = 𝑐′
+ 𝜎 𝑛′ ∙ tan 𝜑′
Normal stress on the
failure plane
𝜎 𝑛 =
𝑁
( 𝐿 cos 𝛼)(1)
=
𝛾𝐻𝐿 cos 𝛼
( 𝐿 cos 𝛼)(1)
= 𝛾𝐻𝑐𝑜𝑠2
𝛼
𝑊 = 𝛾𝐻𝐿
𝑁 = 𝑊 cos 𝛼 = 𝛾𝐻𝐿 cos 𝛼
𝑇 = 𝑊 sin 𝛼 = 𝛾𝐻𝐿 sin 𝛼
𝑭𝑶𝑺 =
𝑨𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑺𝒐𝒊𝒍
𝑨𝒑𝒑𝒍𝒊𝒆𝒅 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒔𝒔
18. 19
SLOPE STABILITY ANALYSIS
Infinite Slope
Applied Shear Stress (t)
𝜏 =
𝑇
( 𝐿 cos 𝛼)(1)
𝜏 =
𝛾𝐻𝐿 sin 𝛼
( 𝐿 cos 𝛼)(1)
𝜏 = 𝛾𝐻 sin 𝛼 cos 𝛼
𝐹𝑂𝑆 =
𝑐′ + 𝛾𝐻𝑐𝑜𝑠2 𝛼 ∙ tan 𝜙′
𝛾𝐻 sin 𝛼 cos 𝛼
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
𝑭𝑶𝑺 =
𝑨𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑺𝒐𝒊𝒍
𝑨𝒑𝒑𝒍𝒊𝒆𝒅 𝑺𝒉𝒆𝒂𝒓 𝑺𝒕𝒓𝒆𝒔𝒔
Available Shear Strength of Soil (tr)
𝜏 𝑟 = 𝑐′ + 𝛾𝐻𝑐𝑜𝑠2 𝛼 ∙ tan 𝜙′
Without considering the effect of WT
19. 20
SLOPE STABILITY ANALYSIS
Infinite Slope
𝐹𝑂𝑆 =
𝑐′ + 𝜎 𝑛′ ∙ tan 𝜙′
𝛾𝐻 sin 𝛼 cos 𝛼
Case-A: c-f Soil (c>0; f>0)
c’ & f’; effective strength parameters
Obtained through drained triaxial test
𝜎 𝑛 = 𝜎 𝑛
′
=
𝐴𝐵 = ℎ
𝐴𝐶 =
L
H
h
a
W
a
b
c
d
T
N
a
tr
A
C
B
D
a
𝐴𝐷 = ℎ 𝑤 =
𝑢 =
ℎ 𝑤 =
𝑢 = 𝛾 𝑤ℎ 𝑐𝑜𝑠2 𝛼
𝐹𝑂𝑆 =
𝑐′ + (𝛾𝐻 − 𝛾 𝑤ℎ) ∙ 𝑐𝑜𝑠2 𝛼 tan 𝜙′
𝛾𝐻 sin 𝛼 cos 𝛼
𝛾𝐻𝑐𝑜𝑠2
𝛼 𝜎 𝑛 − 𝑢
ℎ cos 𝛼
𝐴𝐶 cos 𝛼 = ℎ 𝑐𝑜𝑠2 𝛼
𝛾 𝑤ℎ 𝑤
𝐴𝐷 = ℎ 𝑐𝑜𝑠2
𝛼
Pore water pressure, u
Considering
presence of WT
20. 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