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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
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
87
� 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
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
88
▪ *
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)
‘
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
89
② Saturated clays in undrained condition ( 0=φ )
pupucp AcAcNQ 9* ==
( uc : undrained strength)
③ Soils with 'c and 'φ ,
( )**'' qcpp NqNcAQ +=
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
90
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+
=
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
91
)',(* 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 .
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
92
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)
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
93
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
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
94
●●●● 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 :
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
95
●●●● 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 =
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
96
b) α method (undrained)
uaav scf α==
Figure. Variation of α with '/ 0σuc
∑∑ ∆=∆= LpcLfpQ us α
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
97
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
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
98
� Allowable Pile Capacity
- F.S. ranges from 2.5-4.0 depending on uncertainties of ultimate load
calculation.
� General comments
1)
2)
3)
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
99
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
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
100
(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.
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
101
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
Geotechnical Engineering
SNU Geotechnical and Geoenvironmental Engineering Lab.
102
Finally, we can get
)8.0tan('*' φσ vpqu pLKANqQ +=
↑ ↑
(obtained from Fig 11.14 and 11.19, according to given 'φ and L/D.)