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SHALLOW FOUNDATIONSHALLOW FOUNDATION&&
RETAINING WALLRETAINING WALL
Part 01
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SHALLOW FOUNDATION & RETAINING WALLContents
Part one :
Shear strength of soilsShear strength of soils
Bearing capacity of soilsBearing capacity of soils
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a ow oun a ona ow oun a on
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SOIL MECHANICS & FOUNDATION ENGINEERING30 % UTS
Penilaian 40 % UAS
15 % kehadiran ≥ 9 kali
15 % keaktifan kelas/tugas
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Target
pencapaian
Mampu mendesain fondasi dangkal
Mampu mendesain dinding penahan tanah
Main References
Das, B.M. (2002). Principles of, ,
Brooks/Cole Thomson Learning
Das, B.M. (2004). Principles of FoundationEn ineerin 5th edition Brooks Cole
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Thomson Learning
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Typical Geotechnical Project
Geo-Laboratory Design Officesoil ro ertiessoil ro erties
~ for testing ~ or es gn ana ys s
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Shallow Foundations
~ for transferring building loads to underlying ground
~ mostly for firm soils or light loads
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bed rock
firm
ground
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Deep Foundations
~ for transferring building loads to underlying ground
~
P
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weak soil
I
L
E
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Shear failure
Soils generally fail in shear
strip footing
embankment
failure surface mobilised shear
resistance
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At failure, shear stress along the failure surfacereaches the shear strength.
Shear failure
The soil grains slide overeach other along the
failure surface
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a ure sur ace.
No crushing ofindividual grains.
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Shear failure
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At failure, shear stress along the failure surface(τ) reaches the shear strength (τf ).
Mohr-Coulomb Failure Criterion
τ
f
φ
cohesion friction angle
τ
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τf is the maximum shear stress the soil can take without
failure, under normal stress of σ.
σc
σ
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Mohr-Coulomb Failure Criterion
Shear strength consists of two components:
cohesive and frictional.τ
φ σ τ tan f f c +=τf
σ tan
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σc σf
c
component
c and φ are measures of shear strength.
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Higher the values, higher the shear strength.
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Transcosna Grain Elevator Canada
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West side of foundation sank 24-ft
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Bearing capacity failure
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Bearing Capacity of Soils
Shallow foundation must have two main
characteristics :
have to be safe against overall shear failure
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Failure mechanism
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Failure zone
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Physical model
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Physical model
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General shear failure
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Local shear failure
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Punching shear failure
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Vesic, 1973
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General guidelines
Footings in clays - general shear
Footings in Dense sands (Dr > 67%)- general shear
Footings in Loose to Medium dense
(30%< Dr < 67%) - Local Shear
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Footings in Very Loose Sand (Dr< 30%)- punching shear
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Bearing capacity formulas
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Soil bearing capacity
loadquq’ uQ (T, kN, Lb, Kips)
s e t t l e m e n t
A (m2, ft2)
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Ultimate bearing capacity (qu)
Allowable bearing capacity (qall)
Local shearfailure
General shearfailure
Q/A ≤ qall
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Karl Terzaghi at Harvard, 1940
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Terzaghi Bearing Capacity Formulas
q = .D
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Terzaghi’s bearing capacity equation
General shear failure
NNNq B5,0qc qcu γγ++=
NNNq B4,0qc3,1 qcu γγ++=
NNNq B3,0qc3,1 qcu γγ++=
Continuous/strip footing
square footing
Df
γ,c,φ
γ1
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circular footing
Terzaghi : BDf ≤Bearing capacity factor=
==
γ
∑γ
NNN
D
,,
.qcohesionc
qc
f 1
Terzaghi Bearing Capacity Factors
2
θ = a
N
07.5 =′= φ when Nc
)2/45(cos2 φ ′+[ ]φ φ π θ
′′−= tan)360/75.0(expa
−
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⎟⎟ ⎠
⎞⎜⎜⎝
⎛ −′
′= 1
cos2
tan2 φ
φ γ
γ
pK N
0tan >′′= φ
φ when N q
c
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Bearing Capacity Factors
40
Nγ Nq
10
20
30
( d e g r e e s )
φ
Nc
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BEARINGCAPACITYFACTORS[AfterTerzaghiandPeck(1948)]
60 50 40 30 20 10 0 20 40 60 80
N andN
0
q c Nγ
φu = 0 Nq = 1, Nγ = 0 and Nc = 5.14
Terzaghi’s bearing capacity equation
For local shear failure : 2' 2' c
3c = φ=φ tan
3tan
NNNcq ''q
'c
'u
B5,0q γγ++=
NNNcq ''q
'c
'u
B4,0q3,1 γγ++=
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NNNcq ''q
'c
'u
B3,0q3,1 γγ++=
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qallowable
(net)
=
B
Df
γ,c,φ
γ1
,,)gross(ult
qqq )gross(ult)net(ult −=
γγ+−+= NB4,0)1Nq(qcNc3,1
∑γ= Df 1.q
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FSqq )net(ult
)net(all =
General bearing capacity equationMeyerhof, 1963
FFF qiqdqs ,,FFFNFFFNFFFNq idsqiqdqsqcicdcscu
B5,0qc γγγγγ++=
: shape factor
: depth factorFFF
FFF
dqdcd
sqscs
,,
,,
γ
γ
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FFF iqici ,, γ : inclination factor
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Nc Nq N
0 5.14 1.0 0.0
5 6.5 1.6 0.5
10 8.3 2.5 1.2
15 11.0 3.9 2.6
20 14.6 6.4 5.4. . .
25 20.7 10.7 10.8
30 30.1 18.4 22.4
32 35.5 23.2 30.2
34 42.2 29.4 41.1
36 50.6 37.7 56.3
38 61.4 48.9 78.0
40 75.3 64.2 109.4
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42 93.7 85.4 155.6
44 116.4 115.3 224.6
46 152.1 156.5 330.4
48 199.3 222.3 496.0
50 266.9 319.1 762.9
Shape, depth & inclination factors
Shape
Depth
or =
Fcs 1+0.2(B/L)
Fqs=Fγs 1
For ≥10o
Fcs 1+0.2(B/L)tan2(45+φ /2)
F =F 1+0.1 B L tan2 45+ 2
or =
Fcd 1+0.2(Df /B)
Fqd=Fγd 1
For ≥10o
Fcd 1+0.2(Df /B)tan(45+φ /2)
F =F 1+0.1 D B tan 45+ 2
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q γ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −==
β
90FF o
o
qici 1
2
i 1F ⎟ ⎠
⎞⎜⎝
⎛ φβ
−=γ
InclinationInclination
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Bearing capacity-water table
γ γ N BqNqcNcqult
4,03,1 ++=D1
Case-1
Case-1
γγ −+γ=water sat2wet1 DDq
γγγ =−=γ '
water sat
Df
d
∇⊇
D2
B
∇⊇Case-2
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⊇Case-3
Case-3 : 0≤
d≤
B
Df .q γ=
( )γγγ −γ+= '' _
B
d
Case-2
γγγ =−=γ '
water sat
wetf Dq γ=
Ultimate Load for Shallow Foundationunder Eccentric Load
The eccentricity is in the X-direction (ex)
B
ex
e2BB' −=
The effective area of plate is B’ times L
Effective width
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B/2 B/2
B eff
If the eccentricity is in the Y-direction (ey)
e2LL' −=Effective length
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Foundation
Foundation is the part of structure to transmit the load
into the soil Adequate depth
Selection o f
foundation type
Soil Condition
Applied load
Bearing
capacity failure
Settlement
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Installation/cost
Quality/
adequate
strength
Cost efficiency
Shallow or Deep
Foundation
Flow chart
For designing
shallow foundationCPT, boring
start
Field investigation
Depth of Found.
Shallow foundation must have two main
characteristics :
have to be safe against overall shear failure
cannot undergo excessive settlement
Allowable bearingcapacity (qall)
.
q≤qall?
yes
no
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end
Settlement
safe?yesno
ConcreteStructure budget?
overOK
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0
1
2
3
4
qc (kg/cm2)
0
1
2
3
4
0 50 100 150 200 250 300 350 400 450 500 550 600
total friction
0
1
2
3
4
0 0,01 0,02
friction ratio (%)
Menentukankedalamanfondasi
5
6
7
8
9
10
11
D e p t h ( m )
5
6
7
8
9
10
11
qc5
6
7
8
9
10
11
D e p t h ( m )
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12
13
14
15
16
0 20 40 60 80 100 1 20 140 160 1 80 200
12
13
14
15
16
tf (kg/cm)
12
13
14
15
16
⎟⎟ ⎞
⎜⎜⎛
⎟⎟ ⎞
⎜⎜⎛
+=φ −'c1' q
tan log38.01.0
Korelasi antara qc dengan φ dan c
N
q c
k
0cu
σ−=
σ0 = tegangan total
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σ’0 = tegangan efektif
Nk = 15 for electric cone
= 20 for mechanical cone
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Footing Footing
Definition
Footings are structural members used to support
columns and walls and to transmit and distribute
their loads to the soil in such a way that the load
bearing capacity of the soil is not exceeded,
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, ,
rotation are prevented and adequate safety
against overturning or sliding is maintained.
Types of Footing Types of Footing
Wall footings are used to
support structural walls that
carry loads for other floors
or to support nonstructural
walls.
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Types of Footing Types of Footing
Isolated or single footings
are used to support single
columns. This is one of the
most economical types of
footings and is used when
columns are s aced at
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relatively long distances.
Types of Footing Types of Footing
om ne oot ngs usua y
support two columns, or
three columns not in a row.
Combined footings are used
when tow columns are so
close that single footings
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column is located at or near
a property line.
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Types of Footing Types of Footing
ant ever or strap oot ngs
consist of two single
footings connected with a
beam or a strap and support
two single columns. This
type replaces a combined
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economical.
Types of Footing Types of Footing
ont nuous oot ngs
support a row of three or
more columns. They have
limited width and continue
under all columns.
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Types of Footing Types of Footing
Ra ted or mat oundation
consists of one footing
usually placed under the
entire building area. They
are used, when soil bearing
capacity is low, column
loads are heavy single
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footings cannot be used,
piles are not used and
differential settlement must
be reduced.
Types of Footing Types of Footing
e caps are t c s a s
used to tie a group of piles
together to support and
transmit column loads to the
piles.
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Shallow foundations
S uare footin
Strip/combine footing
Rectangular footing
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Mat foundation
Distribution of Soil PressureDistribution of Soil Pressure
When the column load P is
app e on t e centr c o t e
footing, a uniform pressure is
assumed to develop on the soil
surface below the footing area.
However the actual distribution of the soil is not uniform,
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the soil and degree of flexibility of the footing.
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Distribution of Soil PressureDistribution of Soil Pressure
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Soil pressure distribution in
cohesionless soil.
Soil pressure distribution in
cohesive soil.
Mat footing
Jogja International hospital
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M
Q
B
L
M6
L.B
Q
Bq
2max +=
qmax
qmin M6Qq
2min −=
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.
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