# 8. Axial Capacity

Urban and Civil

Nov 29, 2013 (4 years and 5 months ago)

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8. Axial Capacity

of Single Piles

CIV4249

Modified by J.K. Kodikara, 2001

Methods

Pile driving formulae

Static formulae

Pile driving formulae

e.g. Hiley formula (Energy balance)

Q

=

e
⹗⹨.†‮

††††††††††††††
䘠⡳整‫⁴挠㈩

R
u
= working load, W=weight of the
hammer, h= height of the hammer drop
(stroke), F=factor of safety

tc= elastic (temporary) compression

e

= e
fficiency

F

D

s

tc

R
u

Plunging failure

contract requirement

What is the

Davisson’s Method

Butler and Hoy

Chin’s Method

Brinch Hanson

etc. etc.

What is the distribution

of resistance?

Approximate methods

Instrumentation

Deflection

Dynamic and Statnamic

Testing Methods

Rapid alternatives to static testing

Cheaper

Separate dynamic resistance

Correlation

Axial Capacity

W

P
u

Q
s

Q
b

P
u

= Q
b

+ Q
s

-

W

Base Resistance

Q
b

= A
b

[
c
b
N
c

+ P’
ob
(
N
q
-
1)

+ 0.5
g

g

+
P
ob
]

minus weight of pile, W
p

but W
p

A
b
.P
ob

and as L >>B,
0.5
g

g
<<
W
p

Q
b

= A
b

[
c
b
N
c

+ P’
ob
N
q
]

and for

f

㸠〬
N
q

-

1

N
q

Q
b

Shaft Resistance

Due to cohesion or friction

Cohesive component : Q
sc

= A
s

.
a

⸠.
s

Frictional component : Q
sf

= A
s

.K P’
os
tan
d

P’
os

K.P’
os

Q
s

= Q
sc

+ Q
sf

= A
s

[
a

.c
s

+ K P’
os
tan
d
]

A
s

Total Pile Resistance

Q
u

= Q
b

+

Q
s

Q
u

=
A
b

[
c
b
N
c
+P’
ob
N
q
]

+ A
s

[
a

.c
s
+K P’
o
tan
d
]

How do we compute Q
u

when shaft resistance
along the pile is varying?

Mobilization

Shaft

2
-

5mm

Base

10
-

20% diam

Total

Settlement

Piles in Clay

Q
u

= A
b

[
c
b
N
c
+P’
ob
N
q
]

+ A
s

[
a

.c
s
+K P’
o
tan
d
]

Q
u

= A
b

[
c
b
N
c
+P’
ob
N
q
]

+ A
s

[
a

.c
s
+K P’
o
tan
d

]

Q
u

= A
b
c
b
N
c

+ A
s
a

.c
s

Q
u

= A
b

[
c
b
N
c
+P’
ob
N
q
]

+ A
s

[
a

.
c
s
+K P’
o
tan
d
]

Q
u

= A
b

P’
ob
N
q

+ A
s
K P’
o
tan
d

Q
u

= A
b
c
b
N
c

+ A
s
a

.c
s

Q
u

= A
b

P’
ob
N
q

+ A
s
K P’
os
tan
d

Undrained

Drained / Effective

Driven Piles in Clay

2.0
1.5
1.0
0.5
0
10
20
30
40
50
60
r
a
D
u

vo
Average curve for sensitivea
marine clay
Average curve for clays of
low-medium sensitivity
Driven Piles in Clay

300
250
200
150
100
50
0
1
5
10
50
100
500
1000
Time after driving in days
Bearing capacity in kN
200 x 215mm conrete
(Gothenberg)
300 x 150mm tapered timber (Drammen)
150mm (8 in) steel tube (San Francisco)
300 x 125mm I-Beam
(Gothenberg)
30
25
20
15
10
5
Bearing capacity in tons
N
c

Parameter

N
c

Compare Skempton’s N
c

for shallow foundations

N
c
= 5(1+0.2B/L)(1+0.2D/ B)

10
9
8
7
6
5
0
1
2
3
4
5
L/d
B
Bending capacity factor N
c
a

50
100
150
200
250
1000
2000
3000
4000
5000
2.0
1.5
1.0
0.5
0
Figures denote penetration ratio =
Depth of penetration in clay
Pile diameter
Key:
Steel tube piles
Precast concrete
piles
Design curve for
penetration ratio >
49
49
49
56
13
15
17
27
33
40
10
5
8
15
38
33
27
39
44
44
39
19
17
19
13
35
44
Undrained shear strength (c ) lb/ft
2
u
Undrained shear strength (c ) kN/m
2
u
20
1.0
0.8
0.6
0.4
0.2
0
100
200
Average Undrained Shear Strength, c , kPa
u
Reduction Factor ,
a
Aust. Piling Code,
AS159 (1978)

Bored Piles in Clay

Skempton’s recommendations for side
resistance

a

=0.45

for c
u

<215 kPa

a
c
u

=100 kPa

for c
u
>215 kPa

N
c

is limited to 9.

A reduction factor is applied to account for
likely fissuring (I.e., Q
b

= A
b

b

N
c
)

Soil disturbance

sampling
attempts

to establish in
-
situ
strength values

soil is failed/remoulded by driving or
drilling

pile installation causes substantial
disturbance

bored piles : potential loosening

driven piles : probable densification

Scale effects

Laboratory samples or in
-
situ tests
involve small volumes of soil

Failure of soil around piles involves much
larger soil volumes

If soil is fissured, the sample may not be
representative

Q
u

= A
b

[
c
b
N
c
+P’
ob
N
q
]

+ A
s

[
a

.c
s
+K P’
os
tan
d
]

Piles in Sand

Q
u

= A
b

[
c
b
N
c
+P’
ob
N
q
]

+ A
s

[
a

.
c
s
+K P’
os
tan
d
]

Q
u

= A
b

P’
ob
N
q
]

+ A
s
K P’
os
tan
d
]

Overburden Stress P’
ob

Q
u

= A
b

P’
ob
N
q
]

+ A
s
K P’
os
tan
d
]

Meyerhof Method : P’
ob

=
g

z

Vesic Method : critical depth, z
c

for z <

z
c :

P’
ob

=
g

z

for z >

z
c :

P’
ob

=
g

z
c

z
c
/d is a function of
f

after installation

-

see graph p. 24

Critical Depth (z
c
)

L
z
c

vc
W.T.
d
20
15
10
5
0
28
33
38
43
f
z / d
c
Bearing Factor, N
q

N
q

is a function of :

friction angle
,
f

N
q

is a function of :

Q
u

= A
b

P’
ob
N
q
]

+ A
s
K P’
os
tan
d
]

What affects
f

?

In
-
situ density

Particle properties

Installation procedure

N
q

determined from graphs appropriate

to each particular method

Total end bearing may also be limited:

Meyerhof : Q
b

< A
b
50N
q
tan
f

䉥睡B攠楦i
f

-

-

䱡祥牥搠獯楬s›

N
q

may be reduced if penetration

insufficient. e.g. Meyerhof
(p 21)

N
q

factor (Berezantzev’s Method)

1000
100
10
25
30
35
40
45
f
N
q
If D/B <4

reduce
proportionately
to Terzaghi and
Peck values

For driven
piles :
10
+
'

75
.
0
=
'
1
f
f
For bored piles :

f
f
1
3
Overburden Stress P’
os

Q
u

= A
b

P’
ob
N
q
]

+ A
s
K
P’
os
tan
d
]

Meyerhof Method : P’
os

=
g

z
mid

Vesic Method : critical depth, z
c

for z
mid

<

z
c :

P’
ob

=
g

z

for z
mid

>

z
c :

P’
ob

=
g

z
c

z
c
/d is a function of
f

after installation

-

see graph p. 24

Lateral stress parameter, K

A function of K
o

normally consolidated or overconsolidated
-

see Kulhawy properties manual

see recommendations by Das, Kulhawy (p26)

A function of installation

driven piles (full, partial displacement)

bored piles

augercast piles

screwed piles

Das (1990) recommends the following values for
K / K
o
:
Pile Type
K / K
o
Bored or Jetted piles
1
Low-displacement, driven piles
1 to 1.4
High-displacement, driven piles
1 to 1.8
Kulhawy (1984) makes the following similar recommendations:
Pile Type
K / K
o
Jetted piles
1/2 to 2/3
Drilled shaft, cast-in-place
2/3 to 1
Driven pile, small displacement
3/4 to 5/4
Driven pile, large displacement
1 to 2
K.tan
d

The K and tan
d

into a single function

see p 28 for Vesic values from Poulos and
Davis

Pile
-
soil friction angle,
d

A function of
f

See values by Broms and Kulhawy (p26)

A function of pile material

steel, concrete, timber

A function of pile roughness

precast concrete

Cast
-
in
-
place concrete

Pile
-
soil friction angle

Broms (1966) suggests the following
Pile Material
d
/
f
'
Steel
d  

Concrete
0.75
Timber
0.66
Kulhawy (1984)
Pile Material
d
/
f
'
Typical analogy
Rough concrete
1.0
Cast-in-place
Smooth c
oncrete
0.8 to 1.0
Precast
Rough steel
0.7 to 0.9
Corrugated
Smooth steel
0.5 to 0.7
Coated
Timber
0.8 to 0.9
Pressure-treated
Example

Driven precast concrete pile

350mm

square

Uniform dense sand
(
f
㴠=0
o
;

g

= 21kN/m
3
)

Water table at

1m

Pile length

15m

Check end bearing with Vesic and Meyerhof Methods

Pile is driven on
2m

further into a very dense layer

f

44
o

;
g

㴠=ㄮ㜠歎⽭
3

Compute modified capacity using Meyerhof

Example

Bored pile

900mm

diameter

Uniform medium dense sand
(
f
㴠=5
o
;

g

= 19.5kN/m
3
)

Water table at

1m

Pile length

20m

Check shaft capacity with Vesic and Meyerhof Methods

By comparsion, check capacity of 550mm diameter

screwed pile

Calculation of ultimate lateral resistance
(refer website/handouts for details)

Lateral pile deflection (use use subgrade
reaction method, p
-
y analysis)

Rock socketed pile (use rocket, Carter et
al. 1992 method)