CE 632 Bearing Capacity PPT
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Transcript of CE 632 Bearing Capacity PPT
CE-632CE 632Foundation Analysis and DesignDesign
Ultimate Bearing CapacityThe load per unit area of the foundation at which shear failure in soil
i ll d th lti t b i it
Ultimate Bearing Capacity
1
occurs is called the ultimate bearing capacity.
Foundation Analysis and Design: Dr. Amit Prashant
Principal Modes of Failure:Principal Modes of Failure:
General Shear Failure: Load / AreaLoad / Areaq
men
t qu
Set
tle
Sudden or catastrophic failureWell defined failure surfaceWell defined failure surfaceBulging on the ground surface adjacent to foundationCommon failure mode in dense sand
2
Foundation Analysis and Design: Dr. Amit Prashant
Principal Modes of Failure:Principal Modes of Failure:
Local Shear Failure: Load / Areaqq
qu1
ttlem
ent
qu
Set
Common in sand or clay with medium compactionSignificant settlement upon loadingFailure surface first develops right below the foundation and then p gslowly extends outwards with load incrementsFoundation movement shows sudden jerks first (at qu1) and then after a considerable amount of movement the slip surface may
h th d
3
reach the ground.A small amount of bulging may occur next to the foundation.
Foundation Analysis and Design: Dr. Amit Prashant
Principal Modes of Failure:Principal Modes of Failure:
Punching Failure:Load / Area
q
q
qu1
ttlem
ent qu
Set
Common in fairly loose sand or soft clay Failure surface does not extends beyond the zone right beneath the foundationExtensive settlement with a wedge shaped soil zone in elastic equilibrium beneath the foundation. Vertical shear occurs around the edges of foundation.Aft hi f il l d ttl t ti t l
4
After reaching failure load-settlement curve continues at some slope and mostly linearly.
Foundation Analysis and Design: Dr. Amit Prashant
Principal Modes of Failure:Principal Modes of Failure:Relative density of sand, Dr
0 0 5 1 0Vesic (1973)
Local General shearn, D
f/B* 00 0.5 1.0
* 2BLB =shear
unda
tion B
B L=
+
Circular Foundation
pth
of fo
u
5
Punchingativ
e de
p
Long Rectangular Foundation
Punching shear
Rel
a
5
10
Foundation Analysis and Design: Dr. Amit Prashant
Terzaghi’s Bearing Capacity Theoryg g p y yB
Eff ti b d
Strip Footing
j k
Rough Foundation Surface
Df
neglected Effective overburdenq = γ’.Df
a b
qu
φ’ φ’45−φ’/2 45−φ’/2
Shear
g i
c’- φ’ soilB
I
II IIIII III
Assumption
Planes de fc φ soilII
Assumption L/B ratio is large plain strain problemDf ≤ BShear resistance of soil for D depth is neglected
6
Shear resistance of soil for Df depth is neglectedGeneral shear failureShear strength is governed by Mohr-Coulomb Criterion
Foundation Analysis and Design: Dr. Amit Prashant
Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity TheoryB
21. 2. 2. .sin tan4u p aq B P C Bφ γ φ′ ′ ′= + −
21. 2. . .sin tan4u pq B P B c Bφ γ φ′ ′ ′ ′= + −
qu
4p
Iφ’ φ’
ab
C = B/2 P P P P= + +I
dφ’ φ’
Ca= B/2cosφ’
Ca B.tanφ’Ppγ = due to only self weight of soil
in shear zone
p p pc pqP P P Pγ + +
dφ φPp Pp
in shear zone
Ppc = due to soil cohesion only (soil is weightless)
7
Ppq = due to surcharge only
Foundation Analysis and Design: Dr. Amit Prashant
Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity Theory
⎛ ⎞
Weight term Cohesion term
( )21. 2. tan 2. . .sin 2.4u p pc pqq B P B P B c Pγ γ φ φ⎛ ⎞′ ′ ′ ′= − + + +⎜ ⎟
⎝ ⎠SSurcharge term
( ). 0.5 .B B Nγγ ′ . . cB c N . . qB q N
. . 0.5 .u c qq c N q N B Nγγ ′= + +Terzaghi’s bearing capacity equation
1 PK⎡ ⎤2aeN
Terzaghi’s bearing capacity factors
2
1 tan 12 cos
PKN γ
γ φφ
⎡ ⎤′= −⎢ ⎥′⎣ ⎦ 22cos 45
2
qNφ
=′⎛ ⎞+⎜ ⎟
⎝ ⎠⎛ ⎞
8
3 in rad. tan4 2
a π φ φ′⎛ ⎞ ′= −⎜ ⎟
⎝ ⎠( )1 cotc qN N φ′= −
Foundation Analysis and Design: Dr. Amit Prashant
9
Foundation Analysis and Design: Dr. Amit Prashant
Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity Theory
Local Shear Failure:Local Shear Failure:Modify the strength parameters such as: 2
3mc c′ ′= 1 2tan tan3mφ φ− ⎛ ⎞′ ′= ⎜ ⎟
⎝ ⎠2 . . 0.5 .3u c qq c N q N B Nγγ′ ′ ′ ′ ′= + +
⎝ ⎠
Square and circular footing:Square and circular footing:
1.3 . . 0.4 .u c qq c N q N B Nγγ′ ′ ′= + + For square
1.3 . . 0.3 .u c qq c N q N B Nγγ′ ′ ′= + + For circular
10
Foundation Analysis and Design: Dr. Amit Prashant
Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity TheoryEffect of water table:
Dw
Case I: Dw ≤ Df
Surcharge, ( ). w f wq D D Dγ γ ′= + −
DfCase II: Df ≤ Dw ≤ (Df + B)
Surcharge, . Fq Dγ=
BIn bearing capacity equation replace γ by-
( )fD D−⎛ ⎞B
Li it f i fl
( )w fD DB
γ γ γ γ⎛ ⎞
′ ′= + −⎜ ⎟⎝ ⎠
Case III: Dw > (Df + B)Limit of influenceNo influence of water table.
Another recommendation for Case II:d D D=
11
( ) ( )22 22 w
w sat wdH d H dH H
γγ γ′
= + + −w w fd D D= −
( )0.5 tan 45 2H B φ′= +Rupture depth:
Foundation Analysis and Design: Dr. Amit Prashant
Skempton’s Bearing Capacity Analysis for p g p y ycohesive Soils
~ For saturated cohesive soil, φ‘ = 0 1, and 0qN Nγ= =
For strip footing: 5 1 0.2 with limit of 7.5fc c
DN N
B⎛ ⎞
= + ≤⎜ ⎟⎝ ⎠⎝ ⎠
For square/circular footing:
6 1 0.2 with limit of 9.0fc c
DN N
B⎛ ⎞
= + ≤⎜ ⎟⎝ ⎠g
For rectangular footing: 5 1 0.2 1 0.2 for 2.5fc f
D BN DB L
⎛ ⎞⎛ ⎞= + + ≤⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
7.5 1 0.2 for 2.5c fBN DL
⎛ ⎞= + >⎜ ⎟⎝ ⎠
.u cq c N q= +q c N
12
Net ultimate bearing capacity, .nu u fq q Dγ= − .u cq c N=
Foundation Analysis and Design: Dr. Amit Prashant
Effective Area Method for Eccentric LoadingEffective Area Method for Eccentric Loading
Dy
x
Me =
In case of Moment loading
B
Dfx
VF
xMeBB’=B-2ey
AF=B’L’x
yV
eF
=
I f H i t l F t
eyex
L’=L-2ey
In case of Horizontal Force at some height but the column is
centered on the foundationx
.y Hx FHM F d=
M F d=
13
.x Hy FHM F d=
Foundation Analysis and Design: Dr. Amit Prashant
General Bearing Capacity Equation: (Meyerhof, 1963)
0 5q c N s d i q N s d i B N s d iγ= + +. . . . . . . . 0.5 . . . . .u c c c c q q q qq c N s d i q N s d i B N s d iγ γ γ γγ+ +
Shape f t
Depth factor
inclination f t
Empirical correction factor factor factor
pfactors
2 φφ ′′⎛ ⎞ ( )1N N φ′ ( ) ( )1 1 4N N φ′2 .tantan 45 .2qN eπ φφ ′⎛ ⎞= +⎜ ⎟
⎝ ⎠( )1 cotc qN N φ′= − ( ) ( )1 tan 1.4qN Nγ φ′= −
( ) ( )1.5 1 tanqN Nγ φ′= −[By Hansen(1970):
( ) ( )2 1 tanqN Nγ φ′= +
( ) ( )qγ φ
[By Vesic(1973):
[ y ( )
. . . . . . . . . . . . 0.5 . . . . . . .u c c c c c c q q q q q qq c N s d i g b q N s d i g b B N s d i g bγ γ γ γ γ γγ= + +
14Ground factor Base factor
Foundation Analysis and Design: Dr. Amit Prashant
15
Foundation Analysis and Design: Dr. Amit Prashant
M h f’ C i FMeyerhof’s Correction Factors:
2B φ′⎛ ⎞ B φ′⎛ ⎞for 10oφ′ ≥
Shape Factors
21 0.2 tan 452c
BsL
φ⎛ ⎞= + +⎜ ⎟⎝ ⎠
21 0.1 tan 452q
Bs sLγ
φ′⎛ ⎞= = + +⎜ ⎟⎝ ⎠
φ
for lower valueφ′
1qs sγ= =for lower valueφ
Depth Factors 1 0.2 tan 45
2f
c
Dd
Lφ′⎛ ⎞= + +⎜ ⎟
⎝ ⎠ 1 0.1 tan 452
fq
Dd d
Lγφ′⎛ ⎞= = + +⎜ ⎟
⎝ ⎠
for 10oφ′ ≥
2L ⎝ ⎠
1d dγ= =for lower valueφ′
1qd dγ
Inclination 2
1o
i i β⎛ ⎞⎜ ⎟
2
1i β⎛ ⎞⎜ ⎟
16
Factors 190c qi i β
= = −⎜ ⎟⎝ ⎠
1iγβφ
= −⎜ ⎟′⎝ ⎠
Foundation Analysis and Design: Dr. Amit Prashant
Hansen’s Correction Factors:( ) 1/2
⎡ ⎤1 for 0
2 .H
cFiBL c
φ′= − =′
( ) 1/211 1 for 0
2 .H
cu
Fi
BL sφ
⎡ ⎤−′= + >⎢ ⎥
⎣ ⎦Inclination Factors
50 5F⎡ ⎤ 5
0 7F⎡ ⎤
For 0φ = For 0φ >
0.51. .cot
Hq
V
FiF BL c φ
⎡ ⎤= −⎢ ⎥′ ′+⎣ ⎦
0.71. .cot
H
V
FiF BL cγ φ
⎡ ⎤= −⎢ ⎥′ ′+⎣ ⎦
For 0
0.4 for fc f
Dd D B
B
φ =
⎡= ≤⎢
⎢
For 0
1 0.4 for fc f
Dd D B
B
φ >
⎡= + ≤⎢
⎢
Depth Factors
10.4 tan for fc f
Dd D B
B−
⎢⎢
= >⎢⎣11 0.4 tan for f
c f
Dd D B
B−
⎢⎢
= + >⎢⎣
For D B< For D B>For fD B< For fD B>1dγ =( )21 2 tan . 1 sin f
q
Dd
Bφ φ
⎛ ⎞′ ′= + − ⎜ ⎟
⎝ ⎠( )2 11 2 tan . 1 sin tan f
q
Dd
Bφ φ − ⎛ ⎞
′ ′= + − ⎜ ⎟⎝ ⎠
Shape Factors 0.2 . for 0c c
Bs iL
φ′= =
( )1 i φ′
( )0.2 1 2 . for 0c cBs iL
φ′= − >
( )1 0 4( )1 . sinq qs i B L φ′= + ( )1 0.4 .s i B Lγ γ= −
Hansen’s Recommendation for cohesive saturated soil, φ'=0 ( ). . 1u c c c cq c N s d i q= + + + +
Foundation Analysis and Design: Dr. Amit Prashant
Notes:Notes:
1. Notice use of “effective” base dimensions B‘, L‘ by H b t t b V iHansen but not by Vesic.
2. The values are consistent with a vertical load or a vertical load accompanied by a horizontal load HB.
3. With a vertical load and a3. With a vertical load and a load HL (and either HB=0 or HB>0) you may have to compute two sets of shape and depth factors s sand depth factors si,B, si,Land di,B, di,L. For i,Lsubscripts use ratio L‘/B‘ or D/L‘.
4. Compute qu independently by using (siB, diB) and (siL, diL) and use min value for
18
design.
Foundation Analysis and Design: Dr. Amit Prashant
Notes:Notes:
1. Use Hi as either HB or HL, or both if HL>0.
2. Hansen (1970) did not give an ic for φ>0. The value given here is from Hansen (1961) and also used by Vesic.
3. Variable ca = base adhesion, on the order of 0.6 to 1.0 x base cohesion.
4. Refer to sketch on next slide for identification ofslide for identification of angles η and β, footing depth D, location of Hi (parallel and at top of base slab; usually also produces eccentricity)also produces eccentricity). Especially notice V = force normal to base and is not the resultant R from combining V
19
and Hi..
Foundation Analysis and Design: Dr. Amit Prashant
20
Foundation Analysis and Design: Dr. Amit Prashant
N tNote:
1. When φ=0 (and β≠0) use Nγ = -2sin(±β) in Nγ term.γ ( β) γ
2. Compute m = mB when Hi = HB (H parallel to B) and m = mL when Hi = HL (Hm mL when Hi HL (H parallel to L). If you have both HB and HL use m = (mB
2 + mL2)1/2. Note use
of B and L not B’ L’of B and L, not B , L .
3. Hi term ≤ 1.0 for computing iq, iγ (always).
21
Foundation Analysis and Design: Dr. Amit Prashant
Suitability of MethodsSuitability of Methods
22
Foundation Analysis and Design: Dr. Amit Prashant
IS:6403-1981 RecommendationsNet Ultimate Bearing capacity: ( ). . . . . 1 . . . 0.5 . . . . .nu c c c c q q q qq c N s d i q N s d i B N s d iγ γ γ γγ= + − +
q c N s d i= 5 14NFor cohesive soils where. . . .nu u c c c cq c N s d i= 5.14cN =For cohesive soils where,
, ,c qN N Nγ as per Vesic(1973) recommendations
Shape Factors
1 0.2cBsL
= + 1 0.2qBsL
= + 1 0.4 BsLγ = −For rectangle,
1 3 1 2
D φ′⎛ ⎞
1.3cs = 1.2qs =0.8 for square, 0.6 for circles sγ γ= =
For square and circle,
1 0.2 tan 452
fc
Dd
Lφ′⎛ ⎞= + +⎜ ⎟
⎝ ⎠fD φ′⎛ ⎞
Depth Factors
1 0.1 tan 452
fq
Dd d
Lγφ⎛ ⎞= = + +⎜ ⎟
⎝ ⎠for 10oφ′ ≥
1qd dγ= = for 10oφ′ <
23
Inclination Factors
q γ φ
The same as Meyerhof (1963)
Foundation Analysis and Design: Dr. Amit Prashant
Bearing CapacityBearing Capacity Correlations with SPT-valueS a ue
Peck, Hansen, and Thornburn (1974)Thornburn (1974)
&
IS:6403-1981 Recommendation
24
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity Correlations with SPT-valueBearing Capacity Correlations with SPT value
Teng (1962):1 ( )2 21 3 . . 5 100 . .6nu w f wq N B R N D R⎡ ⎤′′ ′ ′′= + +⎣ ⎦
For Strip Footing:
1F S d ( )2 21 . . 3 100 . .3nu w f wq N B R N D R⎡ ⎤′′ ′ ′′= + +⎣ ⎦
For Square and Circular Footing:
For Df > B take Df = BFor Df > B, take Df B
Water Table Corrections: Dw
[0.5 1 1ww w
DR RD
⎛ ⎞= + ≤⎜ ⎟⎜ ⎟
Water Table Corrections: w
Df
[w wfD⎜ ⎟
⎝ ⎠
[0.5 1 1w fD DR R
⎛ ⎞−′ ′= + ≤⎜ ⎟⎜ ⎟ B
B
25
[0.5 1 1w wf
R RD
+ ≤⎜ ⎟⎜ ⎟⎝ ⎠
B
Limit of influence
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity Correlations with CPT-valueBearing Capacity Correlations with CPT-value0. 2500IS:6403-1981 Recommendation:
0.1675nuq
Cohesionless Soil
0.1250
nu
qc
D0.5
0
0.06251fD
B=
1.5B to
Bqc value is taken as
0 100 200 300 4000
to 2.0B
taken as average for this zone
B (cm)Schmertmann (1975):
kgq
26
2
kg in 0.8 cm
cq
qN Nγ ≅ ≅ ←
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity Correlations with CPT-valueBearing Capacity Correlations with CPT-value
IS:6403-1981 Recommendation:
Cohesive Soil
q c N s d i= . . . .nu u c c c cq c N s d i=
Soil Type Point Resistance Values( qc ) kgf/cm2
Range of Undrained Cohesion (kgf/cm2)
Normally consolidated clays qc < 20 qc/18 to qc/15
Over consolidated clays qc > 20 qc/26 to qc/22
27
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footing on Layered SoilDepth of rupture zone tan 45
2 2B φ′⎛ ⎞= +⎜ ⎟
⎝ ⎠or approximately taken as “B”
Case I: Layer-1 is weaker than Layer-2Design using parameters of Layer -1
B 1
Case II: Layer-1 is stronger than Layer-2Distribute the stresses to Layer-2 by 2:1 method and check the bearing capacity at this level forB
2
1
Layer-1
L 2
and check the bearing capacity at this level for limit state.
Also check the bearing capacity for original foundation level using parameters of Layer-1
B Layer-2 foundation level using parameters of Layer 1
Choose minimum value for design
4B φ′⎛ ⎞Another approximate method for c‘-φ‘ soil: For effective depth tan 45
2 2B Bφ⎛ ⎞+ ≅⎜ ⎟
⎝ ⎠Find average c‘ and φ‘ and use them for ultimate bearing capacity calculation
28
1 1 2 2 3 3
1 2 3
........av
c H c H c HcH H H
+ + +=
+ + +1 1 2 2 3 3
1 2 3
tan tan tan ....tan....av
H H HH H H
φ φ φφ + + +=
+ + +
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Stratified Cohesive Soilg p yIS:6403-1981 Recommendation:
29
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footing on Layered Soil:g y g yStronger Soil Underlying Weaker Soil
Depth “H” is relatively smallPunching shear failure in top layerGeneral shear failure in bottom
Depth “H” is relatively largeFull failure surface develops in top layer itselfGeneral shear failure in bottom
layery
30
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of F ti L d S ilFooting on Layered Soil:Stronger Soil Underlying Weaker Soilea e So
31
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footing on Layered Soil:St S il U d l i W k S ilStronger Soil Underlying Weaker Soil
Bearing capacities of continuous footing of with B under vertical load on the surface of homogeneousunder vertical load on the surface of homogeneous thick bed of upper and lower soil
32
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footing on Layered Soil:Stronger Soil Underlying Weaker Soil
For Strip Footing: 2 122 tan1 fa sDc H Kq q H H qφγ γ′ ′⎛ ⎞
+ + + ≤⎜ ⎟For Strip Footing:
Where, qt is the bearing capacity for foundation considering only the top layer to infinite depth
11 11 fa s
u b tq q H H qB H B
γ γ= + + + − ≤⎜ ⎟⎝ ⎠
only the top layer to infinite depth
For Rectangular Footing:
2 22 tanfDc H KB B φ′ ′⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞2 11 1
22 tan1 1 1 fa su b t
Dc H KB Bq q H H qL B L H B
φγ γ⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞= + + + + + − ≤⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠Special Cases:p
1. Top layer is strong sand and bottom layer is saturated soft clay
2 0φ =1 0c′ =
2. Top layer is strong sand and bottom layer is weaker sand
1 0c′ = 2 0c′ =2 Top layer is strong saturated clay and bottom layer is weaker saturated clay
33
2. Top layer is strong saturated clay and bottom layer is weaker saturated clay
2 0φ =1 0φ =
Foundation Analysis and Design: Dr. Amit Prashant
Eccentrically Loaded FoundationsyM
QMeQ
=
Bmax 2
6Q MqBL B L
= +
Q
max61Q eq
BL B⎛ ⎞= +⎜ ⎟⎝ ⎠B BL B L
min 2
6Q MqBL B L
= −
BL B⎝ ⎠
min61Q eq
BL B⎛ ⎞= −⎜ ⎟⎝ ⎠
e
⎝ ⎠
16
eB
>For There will be separation e 6B
of foundation from the soil beneath and stresses will be redistributed.
Use for , and B, L for to obtain qu, ,c qd d dγ2B B e′ = −
L L′ =, ,c qs s sγ
34.u uQ q A′=
The effective area method for two way eccentricity becomes a little more complex than what is suggested above.
It is discussed in the subsequent slides
Foundation Analysis and Design: Dr. Amit Prashant
Determination of Effective Dimensions for Eccentrically L d d f d ti (Hi ht d A d 1985)Loaded foundations (Highter and Anders, 1985)
C I 1 1e eCase I: 1 1 and 6 6
L Be eL B
≥ ≥
33 BeB B ⎛ ⎞⎜ ⎟1
332
BeB BB
⎛ ⎞= −⎜ ⎟⎝ ⎠
33⎛ ⎞eB
B1
133
2LeL L
L⎛ ⎞= −⎜ ⎟⎝ ⎠eL
eB
L1L
1 112
A L B′ = ( )1 1max ,L B L′ =
ABL
′′ =
′B
35
Foundation Analysis and Design: Dr. Amit Prashant
Determination of Effective Dimensions for Eccentrically Loaded foundations (Highter and Anders 1985)
Case II: 10.5 and 0L Be e< < <
foundations (Highter and Anders, 1985)
0.5 and 06L B
< < <
eL2
eL
eB
L1
2
L
B
( )1 212
A L L B′ = + AB′
′ =
36
BL′( )1 1max ,L B L′ =
Foundation Analysis and Design: Dr. Amit Prashant
Determination of Effective Dimensions for Eccentrically Loaded foundations (Highter and Anders 1985)foundations (Highter and Anders, 1985)
Case III: 1 and 0 0.56
L Be eL B
< < <6L B
B1
eB
eL
L
B
( )1 21A L B B′ = + A′
B2
37
( )1 22 ABL
′′ =
′L L′ =
Foundation Analysis and Design: Dr. Amit Prashant
Determination of Effective Dimensions for Eccentrically Loaded foundations (Highter and Anders 1985)foundations (Highter and Anders, 1985)
Case IV: 1 1 and 6 6
L Be eL B
< <
B1
e
eB
eL
L
B
BB2
( )( )2 1 2 212
A L B B B L L′ = + + +
38
ABL
′′ =
′L L′ =
2
Foundation Analysis and Design: Dr. Amit Prashant
Determination of Effective Dimensions for Eccentrically Loaded foundations (Highter and Anders 1985)foundations (Highter and Anders, 1985)
Case V: Circular foundationCase V: Circular foundation
eRR
R
A′′ AL
B′ =
′
39
Foundation Analysis and Design: Dr. Amit Prashant
Meyerhof’s (1953) area correction based on empirical l ti (A i P t l I tit t 1987)correlations: (American Petroleum Institute, 1987)
40
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of F ti SlFootings on SlopesMeyerhof’s (1957) SolutionSolution
0 5q c N BNγ′ + 0.5u cq qq c N BNγγ= +
0c′ =Granular Soil
0.5u qq BNγγ=
41
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of F ti SlFootings on SlopesMeyerhof’s (1957) SolutionSolution
Cohesive Soil
0φ′ =
u cqq c N′=u cqq
H
42s
HNc
γ=
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footings on SlopesFootings on SlopesGraham et al. (1988), Based on method of characteristics
1000
For
0fDB
=100 B100
43
100 10 20 30 40
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footings on SlopesFootings on SlopesGraham et al. (1988), Based on method of characteristics
1000
100
For
0fDB
=100 B
44
100 10 20 30 40
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footings on SlopesG h t l (1988) B d th d f h t i tiGraham et al. (1988), Based on method of characteristics
For
D0.5fD
B=
45
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footings on SlopesG h t l (1988) B d th d f h t i tiGraham et al. (1988), Based on method of characteristics
For
D1.0fD
B=
46
Foundation Analysis and Design: Dr. Amit Prashant
Bearing Capacity of Footings on SlopesB l (1997) A i lifi d hBowles (1997): A simplified approach
B α = 45+φ’/2B
'
Df a
fqu
gα = 45+φ /2
a' c'
g'qu
f'
α α45−φ’/2a c
eα α
45−φ’/2b'
c
e' rorbd
B
b
d'
Compute the reduced factor Nc as:
. a b d ec c
LN NL
′ ′ ′ ′′ =
Bg'
quf'
Compute the reduced factor Nq as:
c cabdeL
α α45−φ’/2
a' c'e'
47
. a e f gq q
aefg
AN N
A′ ′ ′ ′′ =b'
d'
Foundation Analysis and Design: Dr. Amit Prashant
Soil Compressibility Effects on Bearing CapacityVesic’s (1973) ApproachUse of soil compressibility factors in general bearing capacity equation.These correction factors are function of the rigidity of soilThese correction factors are function of the rigidity of soil
tans
rvo
GIc σ φ
=′ ′ ′+
Rigidity Index of Soil, Ir:
BCritical Rigidity Index of Soil, Icr:
3.30 0.45
tan 452
BL
φ
⎧ ⎫⎛ ⎞−⎜ ⎟⎪ ⎪⎪ ⎪⎝ ⎠⎨ ⎬′⎡ ⎤⎪ ⎪−⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭
B/2
( ). / 2vo fD Bσ γ′ = +
20.5.rcI e⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭=
Compressibility Correction Factors, cc, cg, and cq ( )vo fγr rcI I≥For 1c qc c cγ= = =
( )103.07.sin .log 2.0.6 4.4 .tan rIB φ
φ′⎡ ⎤⎛ ⎞ ′− +⎢ ⎥⎜ ⎟ ′⎝ ⎠
r rcI I< 1 sin 1Lqc c e
φφ
γ
⎢ ⎥⎜ ⎟ ′+⎝ ⎠⎣ ⎦= = ≤For
For 0 0.32 0.12 0.60.logc rBc IL
φ′ = → = + +
48
L1
For 0 tan
qc q
q
cc c
Nφ
φ−
′ > → = −′