Geotechnical Engineering-II [Lec #26: Slope Stability]

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

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STABILITY OF SLOPES
Slope
An exposed ground surface that stands at an angle with the
horizontal is called an unrestrained slope.

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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

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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

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TYPES OF SLOPES
C) w.r.t. Slope Material
1. Cohesionless
2. Cohesive
Cohesionless Cohesive

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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

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TYPES/MODES OF SLOPE FAILURE
Toe Failure
 Failure surface passing through
toe of slope
 Material of slope is
homogeneous
 Relatively steep slope angles

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TYPES/MODES OF SLOPE FAILURE
Base Failure
 Failure surface passing through foundation
 Foundation soil somehow weaker than slope material
 Relatively gentle slopes

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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

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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

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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

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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

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Infinite Slope
𝐹𝑂𝑆 =
𝑐′ + 𝜎 𝑛′ ∙ tan 𝜙′
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′
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

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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 #26: Slope Stability]

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