5) Equations for Estimation of Pile Capacity

Geotechnical Engineering

SNU Geotechnical and Geoenvironmental Engineering Lab.

86

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.)

5) Equations for Estimation of Pile Capacity

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