12973891 Analysis of Bearing Capacity Shallow Foundation

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5.1 INTRODUCTION Bearing capacity is the maximum soil capacity to resist the load. There are two major type of failure, as

follows :

Shear Failure, the shear stress is exceed the soil shear strength. Terzaghi call this failure

stability problem.

Settlement Failure, the normal stress induced the soil to settle excessively. Terzaghi call this

failure elasticity problem.

Due to the type of failure as above the geotechnical engineer must investigate both the shear

resistance and settlement of the soil material. This investigation is called bearing capacity analysis.

The allowable bearing capacity used in the design must consider the minimum of :

Limiting the foundation settlement.

Limiting bearing capacity.

This chapter describes the basic concept of bearing capacity analysis based on the several method

proposed by several geotechnical engineer. The bearing capacity is can be calculated based on the

soil properties and also based on the in situ test result.

5.2 BEARING PRESSURE 5.2.1 GENERAL

Bearing pressure is defined as the pressure at the interface between soil and the foundation. The

pressure is the force per unit area along the bottom of the foundation. The type of bearing pressure

beneath the foundation is depended to the rigidity of the foundation. The flexible foundation

produce uniform bearing pressure and rigid foundation produce non-uniform pressure.

5.2.2 CENTRIC LOAD

The bearing pressure beneath the foundation due to centric load is :

APq = [5.1]

where :

q = bearing pressure

CHAPTER

05 ANALYSIS OF BEARING CAPACITY – SHALLOW FOUNDATION


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P = centric load

A = contact area

5.2.3 ECCENTRIC LOAD

The bearing pressure beneath the foundation due to eccentric load is :

IMy

APq ±= [5.2]

where :


P = centric load

M = bending moment

A = contact area

y = distance from center of foundation to the measured point

I = moment inertia of the foundation about axis of bending

5.3 BEARING CAPACITY 5.3.1 GENERAL

There are two types of bearing capacity, as follows :

Ultimate Bearing Capacity, maximum bearing capacity based on the geotechnical analysis result.

Allowable Bearing Capacity, design bearing capacity based on the several factors such type of soil,

type of foundation, risk etc.

5.3.2 ULTIMATE BEARING CAPACITY

Ultimate bearing capacity is computed by geotechnical analysis based on the soil properties or based

on the in situ test.

The ultimate bearing capacity is defines, as follows :

ultq [5.3]

where :

qult = ultimate bearing capacity

5.3.3 ALLOWABLE BEARING CAPACITY Allowable bearing capacity is design bearing capacity permitted used in the design.

The allowable bearing capacity is defines, as follows :

FSqq ult

a = [5.4]


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where :

qa = allowable bearing capacity


FS = factor of safety

5.4 ANALYSIS OF BEARING CAPACITY – CENTRIC LOAD 5.4.1 GENERAL Several geotechnical engineers already proposed the bearing capacity formula suh as Terzaghi,

Meyerhof, Brinch Hansen and Vesic and each formula has different assumption. During the usage of

the bearing capacity formula we must know the basic assumption used when the formula is derived.

5.4.2 TERZAGHI’S METHOD

A. General

The followings are the basic assumption used in the Terzaghi theory of bearing capacity, as follows :

Depth of foundation Df ≤ B, B = width of foundation.

No sliding between foundation and the soil.

The soil material is homogeneous.

The failure is govern by general shear failure.

No soil consolidation.

Foundation is rigid compared to the soil.

B. General Shear Failure

The bearing capacity of continuous footing when the general shear failure governs is :

( ) ( ) ( )γγγ++= sBN5.0NqscNq qccult [5.5]

where :


c = cohesion of soil

γ = unit weight of soil

q = equivalent surcharge

sc, sγ = shape factor

Nc, Nq, Nγ = bearing capacity factor

The equivalent surcharge is defined as follows :

fDq γ= [5.6]

where :

Df = depth of foundation


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The bearing capacity factor is defined as :

TABLE 5.1 BEARING CAPACITY FACTOR – TERZAGHI

Nq Nc Nγ

⎟⎠⎞⎜

⎝⎛ φ+

=

245cosa

aN2

2

q ( ) φ−= cot1NN qc ⎟⎟⎠

⎞⎜⎜⎝

⎛−

φ

φ= γ

γ 1cos

K2

tanN 2p

( )( )φ+

φ+=γ 4sin4.01

tan1N2N q

φ⎟⎠⎞⎜

⎝⎛ φ−π

=tan275.0

ea

Terzaghi never give clearly explanation how to obtain the passive pressure coefficient so the

bottom formula can be used to calculate Nγ.

The following table shows some value of bearing capacity factor from Terzaghi method.

TABLE 5.2 BEARING CAPACITY FACTOR – TERZAGHI

φ Nq Nc Nγ

0 5.7 1.0 0.0

5 7.3 1.6 0.5

10 9.6 2.7 1.2

15 12.9 4.4 2.5

20 17.7 7.4 5.0

25 25.1 12.7 9.7

30 37.2 22.5 19.7

34 52.6 36.5 36.0

35 57.8 41.4 42.4

40 95.7 81.3 100.4

45 172.3 173.3 297.5

48 258.3 287.9 780.1

50 347.5 415.1 1153.2

The shape factor is defined as :

TABLE 5.3 SHAPE FACTOR – TERZAGHI

FOUNDATION TYPE SHAPE FACTOR

STRIP ROUND SQUARE

sc 1.0 1.3 1.3

Sγ 1.0 0.6 0.8


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C. Local Shear Failure

The bearing capacity of continuous footing when the local shear failure governs is :

( ) ( ) ( )γγγ++= 's'BN5.0'Nq's'cNq qccult [5.6]

where :





s’c, s’γ = shape factor

N’c, N’q, N’γ = bearing capacity factor

The shape factor is defined as :

TABLE 5.4 SHAPE FACTOR – TERZAGHI

FOUNDATION TYPE SHAPE FACTOR

STRIP ROUND SQUARE

s’c 0.667 0.867 0.867

s’γ 1.0 0.6 0.8

The bearing capacity factor with “prime” term is calculated using the following variable, as follows :

⎟⎠

⎞⎜⎝

⎛φ=φ − tan

32tan' 1 [5.7]

5.4.3 MEYERHOF’S METHOD

A. General

Meyerhof propose the bearing capacity formula similar to the Terzaghi formula but with modification of

shape factor, depth factor and inclination factor.

( ) ( ) ( )γγγγγ++= idsBN5.0idsNqidscNq qqqqccccult [5.8]

where :





Nc, Nq, Nγ = bearing capacity factor

sc, sq, sγ = shape factor

dc, dq, dγ = depth factor

ic, iq, iγ = inclination factor


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B. Bearing Capacity Factor The bearing capacity factor proposed by Meyerhof is :

TABLE 5.5 BEARING CAPACITY FACTOR – MEYERHOF

Nq Nc Nγ

⎟⎠⎞⎜

⎝⎛ φ+= φπ

245taneN 2tanq ( ) φ−= cot1NN qc ( ) ( )φ−=γ 4.1tan1NN q

C. Shape Factor

The shape factor proposed by Meyerhof is :

TABLE 5.6 SHAPE FACTOR – MEYERHOF

sq sγ sc

φ = 0 φ > 10 φ = 0 φ > 10

⎟⎠

⎞⎜⎝

⎛+=LBK2.01s pc 0.1sq = ⎟

⎠

⎞⎜⎝

⎛+=LBK1.01s pq 0.1s =γ ⎟

⎠

⎞⎜⎝

⎛+=γ LBK1.01s p

D. Depth Factor

The depth factor proposed by Meyerhof is :

TABLE 5.7 DEPTH FACTOR – MEYERHOF

dq dγ dc

φ = 0 φ > 10 φ = 0 φ > 10

⎟⎠

⎞⎜⎝

⎛+=

BDK2.01d pc 0.1dq =

⎟⎠

⎞⎜⎝

⎛+=

BDK1.01d pq

0.1d =γ

⎟⎠

⎞⎜⎝

⎛+=γ B

DK1.01d p

E. Inclination Factor

The inclination factor proposed by Meyerhof is :

TABLE 5.7 INCLINATION FACTOR – MEYERHOF

iγ ic iq

φ = 0 φ > 10

2

o

o

c90

1i ⎟⎟⎠

⎞⎜⎜⎝

⎛ θ−=

2

o

o

q90

1i ⎟⎟⎠

⎞⎜⎜⎝

⎛ θ−=

0.0i =γ

(θ > 0)

2

o

o1i ⎟

⎟⎠

⎞⎜⎜⎝

⎛

φ

θ−=γ

5.4.4 GROUND WATER TABLE EFFECT

The location of ground water table will influence the bearing capacity of the soil.

There are three typical cases of the ground water table location, as follows :

The location of water table is less than depth of foundation.


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The location of water table is in the range of depth of foundation and depth of foundation +

foundation width.

The location of water table is more than depth of foundation + foundation width.

If the water table is less than foundation depth the design unit weight for bearing capacity analysis

is :

DDw ≤

wsat' γ−γ=γ [5.9]

If the water table is in the range of foundation depth and foundation depth + foundation width

the design unit weight for bearing capacity analysis is :

BDDD w +<<

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ −−γ−γ=γ

BDD1' w

w [5.10]

If the water table is more than foundation depth + foundation width the design unit weight for

bearing capacity analysis is :

BDDw +≥

γ=γ' [5.11]

5.5 ANALYSIS OF BEARING CAPACITY – ECCENTRIC LOAD 5.5.1 GENERAL

The load acts in foundation is not just the vertical load, because of the eccentricity super structure load

there will be moment act at the base of the foundation. Due to eccentric load we must modify some variables to obtain the bearing pressure and bearing capacity beneath the foundation.

The most commonly method used is the effective area method. This method is firstly proposed by

Meyerhof.

5.5.2 SINGLE ECCENTRIC

Single eccentric load is when the applied vertical load is eccentric in one direction.

The eccentricity of the loading is calculated as follows :

PM

e yx = [5.12]


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where :

ex = eccentricity in X axis

My = moment about Y axis

P = vertical load

The effective width of the foundation due to single eccentric load is :

xe2B'B −=

L'L = [5.13]

where :

B’ = effective foundation width

L’ = effective foundation length

B = actual foundation width

L = actual foundation length

The following figure shows the determination of the effective area.

FIGURE 5.1 EFFECTIVE AREA – SINGLE ECCENTRIC

If the moment acts at X axis Mx then effective width is calculated with the same method as above but

with different direction.

The bearing pressure due to single eccentric load will assumed as uniform stress beneath the

effective area.

The bearing pressure beneath the effective area is :


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'L'BP

'APq == [5.14]

where :


P = applied vertical load

This bearing pressure then compared to the allowable bearing capacity that is calculated also

using the effective width of the foundation.

5.5.3 DOUBLE ECCENTRIC

Double eccentric load is when the applied vertical load is eccentric in two directions.

The eccentricity of the loading is calculated as follows :

PM

e yx =

PMe x

y = [5.15]

where :

ex = eccentricity in X axis

ey = eccentricity in Y axis

Mx = moment about X axis

My = moment about Y axis

P = vertical load

The effective width of the foundation due to single eccentric load is :

xe2B'B −=

ye2L'L −= [5.16]

where :

B’ = effective foundation width

L’ = effective foundation length

B = actual foundation width

L = actual foundation length

The following figure shows the determination of the effective area.


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FIGURE 5.2 EFFECTIVE AREA – DOUBLE ECCENTRIC

The bearing pressure due to single eccentric load will assumed as uniform stress beneath the

effective area.

The bearing pressure beneath the effective area is :

'L'BP

'APq == [5.17]

where :


P = applied vertical load

5.6 ANALYSIS OF BEARING CAPACITY – IN SITU TEST 5.6.1 GENERAL The most practical of bearing capacity analysis is using the in situ test result. Based on the in situ test

we can directly obtain the ultimate bearing capacity using a simple conversion formula rather than

using complex formula as explained before.

5.6.2 STANDARD PENETRATION TEST (SPT)

A. General

The SPT is commonly used to obtain the in situ ultimate bearing capacity.

B. Meyerhof’s Method

The allowable bearing capacity based on the SPT test according to Meyerhof is :


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TABLE 5.8 SPT BEARING CAPACITY – MEYERHOF

B ≤ F4 B > F4

d1

a KFNq = d

3

2a K

BFB

FNq ⎟

⎠

⎞⎜⎝

⎛ +=

The variable above is as follows :

33.1BD33.01Kd ≤⎟⎠

⎞⎜⎝

⎛+= [5.18]

And the F factor is as follows :

TABLE 5.9 F FACTOR – MEYERHOF

F SI UNIT

F1 0.05

F2 0.08

F3 0.30

F4 1.20

C. Parry’s Method

The allowable bearing capacity based on the SPT test according to Parry for cohesionless soil is :

55a N30q = [5.19]

where :

qa = allowable bearing capacity (kPa)

N55 = N SPT with 55% efficiency

5.6.3 CONE PENETRATION TEST (CPT)

A. General The conversion of CPT test also available to obtains the allowable bearing capacity.

B. Cohesionless Soil

The ultimate bearing capacity for cohesionless soil based on CPT test is :

TABLE 5.10 CPT BEARING CAPACITY – COHESIONLESS SOIL

STRIP SQUARE

( ) 5.1cult q3000052.028q −−= ( ) 5.1

cult q3000090.048q −−=

where :

qult = ultimate bearing capacity (kg/cm2)

qc = cone resistance (kg/cm2)


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C. Clay Soil

The ultimate bearing capacity for cohesionless soil based on CPT test is :

TABLE 5.11 CPT BEARING CAPACITY – CLAY SOIL

STRIP SQUARE

( )cult q28.02q += ( )cult q34.05q +=

where :

qult = ultimate bearing capacity (kg/cm2)

qc = cone resistance (kg/cm2)

12973891 Analysis of Bearing Capacity Shallow Foundation

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Transcript of 12973891 Analysis of Bearing Capacity Shallow Foundation