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11 December 2013 Bearing Capacity 1

BEARING CAPACITY

OF SHALLOWFOUNDATIONS

4thYear Civil

FOUNDATION ENGINEERING

Dr. Tarek Nageeb Salem

Associate Professor


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DEFINITION OF SOI L

Soil is a mixture of irregularly shaped mineralparticles of various sizes containing voids between

particles. The particles are a by-product of

mechanical and chemical weathering of rock and

described as gravels, sands, silts, and clays..

Any manmade structure should, one way or

another, rest and/or transmit its load to the

underlying soil


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BEARING CAPACITY OF SOILS

Bearing capacityis the ability of soil to safely carry

the pressure placed on the soil from any engineered

structure without undergoing a shear failure with

accompanying large settlements.

Therefore,settlement analysisshould generally be

performed since most structures are sensitive to

excessive settlement.


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Bearing Capacity of Shallow

Foundations

Soil Bearing Capacity is Controlled by:

Bearing Capacity Analysis:

Terzaghis Theory (1943), based on Prandtl theory(1920).

General B.C. Equation.

Settlement Analysis:

Immediate Settlement

Consolidation Settlement


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Types of Foundations

ShallowFoundations

DeepFoundations

Spread

Mat or Raft

Friction Piles

Belled Pier


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Failure Modes for Shallow Foundations

General ShearFailure,

Zones I, II, III,

Dense Sand

Local Shear

Failure,Zones I, II,

Medium Dense

Sand


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Failure Modes, Continued

Punching Failure, Zone I Only,Loose Sand and Soft Clay



Terzaghis Assumptions

Zone I , Active.

Zones I I , Transition.

Zones I I I , Passive.



Terzaghi B/C Assumptions

Three zones do exist:1- Active zone, just below the foundation.

2- Transition zone, between the active and passive zones.

3- Passive zone, near the ground surface, just beside thefoundation.

passive act ive

Transit ion



Terzaghi Bear ing Equation for

Str ip Footing

B

qu net= c Nc + g1D(Nq- 1) + 0.5 B g2Ng

g1D

General ized so i l streng th : c,

(drainage as appli cable)

Soi l uni t weight : g2 (to tal oreffectiv e as app licab le)

Overburden

Failure Zone (depth 2B)


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Terzaghi Bear ing Equation

Nc, Nq, Ngare Terzagh i B /C Coeff ic ients , f()C, are the so i l shear streng th parameters



Bear ing Capacity Factors

0 10 20 40 60 8070 60 50 40 30 20 10

Nc andNq N g

inDegrees

40

30

20

10

0

NqNc N g

qul t = c Nc +g1 D Nq + 0.5 Bg2 Ng

5.7 1.0


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Terzaghi Bear ing Equation

B

P


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Terzaghis Equation for Different

Foundation Shapes

Continuous (Str ip) Footing:

qu = c Nc+ g1D Nq+ 0.5 B g2Ngqu-net = c Nc+ g1D (Nq - 1) + 0.5 B g2Ng

Square Footing:

qu-net = 1.3 c Nc+ g1D (Nq - 1) + 0.35 B g2NgCircular Footing:

qu-net = 1.3 c Nc+ g1D (Nq - 1) + 0.35 B g2NgN

c

, Nq

, Ng= B.C. Factors


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lc i, lq i, lg i

P

Footings with incl ined loads

Pb

Incl ined Load Facto rs


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I ncl ined Loads

Correction Factors, lci, lqi, and lgiareempir ically determined from exper iments

lc i= lq i= (1.0 - b/ 902lgi= (1.0 - b/ )2


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I ncl ined Load Factors

Inc l ined Load Factors :lc i= lq i= (1.0b/90)2lgi= (1.0b/)2

qu lt= c Nc lc lc i+ g1DNq lq lq i + 0.5B g2 Nglglgi


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Bearing Capacity of Clay, = 0qul t = c Nc +g1DNq + 0.50 Bg2NgFor Clay:

Nc= 5.70, Nq= 1.0, Ng= 0.0qul t = 5.70 cu+g1Dqul t net = 5.70 cu qall net = 1.90 cu

cu = qu/2 quUnconfined compressive strength


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Bearing Capacity of Sand, cu= 0

qul t = c Nc +g1DNq + 0.50 Bg2NgFor Sand:

Nc, Nq, Ngare determined from curve, and cu= 0,then:

qul t = g1DNq + 0.50 Bg2Ng


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Gross and Net Bearing Capacity

..

SFqq ul t

al l

qult= qul t net+ g1DD

SF

qq netul tall

..

1

g

Gross allowable bearing capacity

Gross allowable B/C

Gross ultimate B/C

..

SFqq netul tnetall Net allowable B/C

g1D is the overburden pressure


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Effect of Water Table on B/C


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Effect of Water Table on B/C

Case (a):

g1D = g

b(D

f-d ) + g

subd,

g2= gsub

qu lt= c Nc + g1DNq + 0.5B g2NgCase (b ):

g1D = gbDf,g2= gsubCase (c ):

g1D = gbDf,If , d B, then g2= gsubIf , d > B, then g

2

= gb

gb= Bulk uni t weightgsub= SubmergedUnit weigh t,gsub

= gsat

- gwater


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Settlement Analysis

Allowable bearing capacity, as calculated from the

settlement analysis, usuallycontrols the soilbearing capacity, especially in clay and silt.

The maximum allowable settlement is set f irst,then the stress (bearing pressure) that wi l l induce

that settlement wil l be the allowable bearing

capacity.

For stratif ied soils, 2:1 stress distr ibution is used to

determine the stresses at the top of each layer.


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Bearing Capacity in Stratif ied Deposits

so f t clay

st i f f c lay o r

dense sand

B1

2B

q1

q2

P P = q1A 1= q1B1L 1

B2

P = q2A 2= q2B2L 2

q1is the al lowable

bearing capaci ty

for layer 1

q2is the allowable

bearing capaci ty

fo r layer 2, andso on

The al lowable bearing capacity as determ ined from either

the shear streng th parameters or the sett lement analys is.

S


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Settlement Analysis

Total Settlement=

Immediate Settlement +

Primary Consolidation Settlement +

Secondary Consolidation Settlement

I n Sand:

Total Settlement Immediate settlement

I n Silts, Stiff and Medium Clays:

Total Settlement Immediate Settlement +

Primary Consolidation Settlement


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Settlement Analysis

I n Soft Clays, Sil ts and Organic Soils:Total Settlement = Immediate Settlement +

Primary Consolidation Settlement +

Secondary Consolidation Settlement


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Example

A footing 1.8 m x 2.5 m is located at a depth of 1.5

m below the ground surface, in an over-

consolidated clay layer. The groundwater level is

2 m below the ground surface. The unconf ined

compressive strength of that clay is 120 kPa, gbulk= 18 kN/m3, and gsat= 20 kN/m3. Determine thenet al lowable bearing capacity, assuming a factor

of safety of 3.

S l ti


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Solution

For Rectangu lar Foo t ing:

lc= 1.0 + 0.30 B /L = 1.0 + 0.30 x 1.8/2.5 = 1.22lq= 1.0qult net= c Nc lc+ g1 D (Nq -1) lq

For Clay: Nc= 5.7, Nq= 1.0, Ng= 0.0qu lt= c N

clc+ g

1D N

qlq

+ 0.5B g2Nglg

qu= 120 kPa, cu= 60 kPa


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qult net= 60 x 5.7 x 1.22 = 417.202

08.139

3

2.417

.. kN/m

SF

qq netul t

netal l

qall net= 13.91 t/m2= 1.39 kg /cm2


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11 D b 2013

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Bearing Capacity 120405032828 Phpapp01