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Bearing Capacity of Shallow
Foundations
Design Components
• Design is divided into two parts;
• GEOTECHNICAL DESIGN:-
• The design that takes into account only the properties of soil is called as Geotechnical Design.
• SCOPE OF DESIGN:-
• The scope of geotechnical design is;
• a) Df =?
• b) B =?
• c) L =?
• GOAL:-
• The goal of geotechnical design is;
• Bearing capacity.
• Settlement should be within permissible limits.
SPECIFIC DESIGN OF FOUNDATION:-
• Design means the determination of;
• Df =?
• t =?
• B =?
• L =?
• As =?
P
G.S.L
Df
BXL
B
L
FOOTINGS WITH One Way
Eccentricity
eL eB
Q
B
L
Stability Problem
Bearing Capacity Failure
Bearing Capacity Analysis
•How do we estimate the maximum bearing pressure that the soil can withstand before failure occurs?
West side of foundation sank 24-ft
Bearing Capacity Failures
Types/Modes of Failure general shear failure local shear failure
punching shear failure
B.C. Failures
Local shear
Intermediate case +/- gradual failure
Punching
Loose sands, weak clays (dr.) F. surf. not defined Gradual failure
General shear
Dense soils, Rock, NC clays Defined failure surf.
Fast failure
General Shear Failure
B.C. Failures
(Vesic, 1963 and 1973)
Deep
foundations
We design for the general shear case (for shallow foundations)
Bearing Capacity Theory LIMIT EQUILIBRIUM
1. Define the shape of a failure surface
2. Evaluate stresses vs. strengths along this surface
BC Factor
Bearing Capacity Theory LIMIT EQUILIBRIUM
Ultimate bearing capacity = qult = ?
(Bearing press. required to cause a BC failure)
Moments about point A
( ) ( )
⋅
−
⋅
−
⋅
= ( ) 2
) 2
( B
Bb B
Bb B s
Bb q
M A ult uπ σzD
zD u
c
ult
N s
q = + σ
zD u
ult s
q = 2⋅π ⋅ +σ
Terzaghi’s Bearing Capacity Theory
Terzaghi’s Bearing Capacity Theory
Terzaghi’s Bearing Capacity Theory
Terzaghi developed the theory for continuous foundations (simplest, 2D problem).
γ
γσ N BN
N c
q
ult= '
c+ '
zD q+ 0 . 5 '
γ
γσ
N BNN c
qult = 1.3 ' c + 'zD q + 0.4 '
γ
γσ N BN
N c
q
ult= 1 . 3 '
c+ '
zD q+ 0 . 3 '
From model tests, he expanded the theory to:
N
c= cohesion factor N
q= surcharge factor
N
γ= self wt factor
Terzaghi’s Bearing Capacity Theory
= f ( φ ’) for values
See Extra Handout
Further Developments
• Skempton (1951)
• Meyerhof (1953)
• Brinch Hanson (1961)
• De Beer and Ladanyi (1961)
• Meyerhof (1963)
• Brinch Hanson (1970)
• Vesic′ (1973, 1975)
Shape factors….…
Depth Factors …….
Load Inclination Factors ….
Base Inclinations factors ..
Ground Inclination Factors….
Bearing Capacity Factors ….
γ γ γ γ γ
γ γ
σ N s d i b g BN s d i b g
g b i d s N c
qult = ′ c c c c c c + zD′ q q q q q q + 0.5 ′
CONTOH
B Df = 0,7 m
β= 200
φ= 300 c = 0
γ = 18 kN/m3 Q = 150 kN
Berapakah B dengan SF = 3
6 , 12 18
7 , 0 .
4 , 22
; 4 , 18
nilai diperoleh 1973
Vesic, tabel
Dari
2 1
=
×
=
=
=
=
+
=
γ
γ
γ
γ γ γ γ
f q
i d s qi
qd qs q u
D q
N N
F F F BN F
F F qN q
( )
1
20207 ,
1 0
7 , 30 0
sin 1
30 tan 2 1 1 /
2
= +
=
− +
=
≤
γd qd
F
B F B
B Df
11 , 20 0
1 1
605 , 90 0
1 20 1 90
0 2 0 2
2 0 2 0
0 0
=
− φ
=
φ
− β
=
=
−
=
− β
=
γi qi
F F
m B
B B B
B qall Q
283 , 1 48
, 902 4
, 745 14
, 150 73
2
2
=
→ +
+
=
= 6
, 0 4 , 0 1 4
, 0 1
577 , 1 30 tan 1
tan 1
L 1 sangkar, B
bujur Fondasi
Dengan
=
−
=
−
=
= +
= φ +
=
=
→
γ L
F B
L B L
F B
s qs
[ ]
3 1
3
2 1
i d s qi
qd qs q all
u u
all
F F F BN F
F F qN q
q SF
q q
γ γ γ
γ γ
+
=
=
=
B B q
B B q
all all
48 , 902 4
, 745 14
, 73
441 , 705 13
, 235 44
, 3 221 1
+ +
=
+ +
=
Groundwater Table Effect
Groundwater Table Effect;
Case I
1. Modify σ′zD
2. Calculate γ′ as follows:
w
b
γ γ
γ
γ ′ = = −
Groundwater Table Effect;
Case II
1. No change in σ′zD
2. Calculate γ′ as follows:
−
−
−
′ =
B D Dw
w 1
γ γ
γ
Groundwater Table Effect;
Case III
1. No change in σ′zD 2. No change in γ′
γ
γ ′ =
