5) Equations for Estimation of Pile Capacity

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5) Equations for Estimation of Pile Capacity

Ultimate bearing capacity of pile is given as,

spu QQQ +=

i) Point Bearing Capacity

For a shallow foundation with vertical loading,

dsqdqsqcdcscu FFBNFFqNFFcNq γγγγ2

1++=

⇒ for pile

γγ ***'' DNNqNcq qcp ++=

where *

cN , *

qN and *

γN include the necessary shape and

depth factors, D is width of pile and q’ is effective

vertical stress at the level of pile tip.

⇒ Width of pile, D is relatively small

qcp NqNcq**

'' +=

Therefore, )''(**qcpppp NqNcAqAQ +=⋅=

4

dA

2

p

π= 21p ddA ⋅=

d

Pipe Pile

d1

d2

H-Section pile

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� Determination of Bearing Capacity Factors *

cN and *

qN

a) Meyerhof’s Method

-

▪ lp qq ≤

▪ ( )crb DL / is a function of friction angle.

Figure. Variation of (Lb/D)cr with soil friction angle

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▪ *

cN and *

qN reach the maximum values at ( )crb DL /

2

1

(in most cases, ( )crbb DLDL /

2

1/ ≥ )

Figure. Variation of the maximum values of *

cN and *

qN with 'φ

① Sand

( )'tan5.0'** φqalpqpp NpqANqAQ =≤=

where, ap = atmospheric pressure ( 2/100 mkN= )

- Based on field tests (SPT) for homogeneous granular soil

601ab601a2

)(N4p/DL)(N4p.0)(kN/m ≤=pq

( 601 )(N = average corrected value of the SPT number about D10

above and D4 below the pile point)

‘

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② Saturated clays in undrained condition ( 0=φ )

pupucp AcAcNQ 9* ==

( uc : undrained strength)

③ Soils with 'c and 'φ ,

( )**'' qcpp NqNcAQ +=

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b) Vesic’s method

- Based on the theory of expansion of cavities

l : zone of compression

ll : radial zone

lll : plastic zone

- )''(**σσ NNcAqAQ ocpppp +==

where, o'σ = mean effective normal stress at pile tip

'3

21q

K o+=

( 'q = vertical effective stress at pile tip)

0K = earth pressure coefficient at rest ( 'sin1 φ−= )

** '' qo NqN =σ σ

**

'

'q

o

Nq

Nσ

=σ

*

21

3q

o

NK+

=

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)',(* φσ rrIfN =

)'sin3

'sin4(

2'tan)'2/( )2/'4/(tan'sin3

3 φφ

φφπ φπφ

+− +−

= rrIe

)12/)ln1(3

4,0'('cot)1( *** +++==−= πφφσ rrcc INForNN

where, ∆+

=r

rrr

I

II

1=reduced rigidity index

=φ+

=φ+µ+

='tan'')tan'')(1(2 qc

G

qc

EI s

s

s

r rigidity index

(Refer to Table p.494)

=∆ Average volumetric strain in plastic zone

( 0=∆ For dense sand or saturated clay, II rr =⇒ )

- **

cNandNσ can be obtained from Table 11.4 (p.495), with 'φandI rr .

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c) Janbu’s method

'cot)1(

)'tan1'(tan

)''(

**

'tan'222*

**

φ

φφ φη

−=

++=

+=

qc

q

qcpp

NN

eN

NqNcAQ

η’ = 70o (soft clays) – 105o (dense sands)

*

qN and *

cN are given in Table 11.5 (p.499)

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ii) Frictional Resistance

∑=

=

)( pLf

AfQ

s

sss

where, p : perimeter of pile

L : pile length

δ+= tan'sas qcf

where, ac = adhesion between soil and pile

sq' = effective stress normal to side of pile

δ = interface friction angle

where '

vσ = vertical effective stress prior to installation

K = earth pressure coefficient

= f(friction angle, method of installation, pile length, ….)

At top, pKK ≈ and at tip, oKK ≈ � For driven pile

'

vs Kq σ=

uQ

sq

ac

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●●●● For sands

δtan'ss qf =

δσ tanK '

v=

'3/2 φδ ≈ (sand with concrete)

'2/1 φδ ≈ (sand with steel)

� Alternative way to get frictional resistance

Bhusen⇒ for high-displacement driven piles

rD0065.018.0tanK +=δ

rD008.05.0K +=

(Dr in %)

Meyerhof⇒ for high-displacement driven piles

601 )(02.0 Npf aav =

for low-displacement driven piles

601 )(01.0 Npf aav =

where, ap = atmospheric pressure ( 2/100 mkN≈ )

601 )(N = average corrected value of 녰

Note :

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●●●● For clays

a) λ method

Based on the assumption that the displacement of soil caused by pile

driving results in passive lateral pressure at any depth.

)2( '0 uav cf += σλ

'0σ = mean effective vertical stress for the entire embedment depth

uc : mean undrained shear strength ( 0=φ )

λ : decreases with embedment pile length (use average value).

Figure. Variation of λ with pile embedment length

(redrawn after Mc Clelland, 1974)

avs pLfQ =

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b) α method (undrained)

uaav scf α==

Figure. Variation of α with '/ 0σuc

∑∑ ∆=∆= LpcLfpQ us α

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c) β method

(Excess pore pressures developed during driving piles dissipate within a

month or so. Frictional resistance can be determined on the basis of effective

stress in a remolded state.)

'0βσ=f

where, 'tan RK φβ =

'Rφ : (Drained) friction angle of remolded clay

'0σ : vertical effective stress

'sin1 RK φ−= ⇒ For NC clay

OCRK R )'sin1( φ−= ⇒ For OC clay

')'(tan)'sin1( 0σφφ RR OCRf −=

With the value of f , the total frictional resistance may be evaluated as

∑ ∆= LfpQs

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� Allowable Pile Capacity

- F.S. ranges from 2.5-4.0 depending on uncertainties of ultimate load

calculation.

� General comments

1)

2)

3)

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6) Coyle and Castello Design Correlations

� Based on 24 large-scale field load tests of driven piles in sand.

pLfANqQQQ avpqspu +=+= *'

where, δσ tanKf '

)ave(vav =

↑ average effective stress along shaft � Typical results of instrumented pile load tests

(a)

(b)

strain gauge

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(a)

(b)

(c)

i) Point resistance, pQ

pqp ANqQ *'=

pQ , 'q , pA : known ⇒ *

qN can be computed.

⇒ Fig 11.14 shows *

qN with varying L/D and 'φ .

*

qN increases, reaches maximum and decreases thereafter with L/D.

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ii) Frictional resistance, sQ

pLfQ avs =

LpQs ,, : known ⇒ avf can be computed.

δσ tanKf '

)ave(vav =

δ : assumed as '8.0 φ

'

)ave(vav ,f σ : known

Fig 11.19 shows K with varying L/D and 'φ .

� K can be computed

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Finally, we can get

)8.0tan('*' φσ vpqu pLKANqQ +=

↑ ↑

(obtained from Fig 11.14 and 11.19, according to given 'φ and L/D.)