### Single-Pile

```8. Axial Capacity
of Single Piles
CIV4249
©1998 Dr. J.P. Seidel
Modified by J.K. Kodikara, 2001
Methods
•
•
•
•
Pile driving formulae
Dynamic or Statnamic load test
Static formulae
Pile driving formulae
• e.g. Hiley formula (Energy balance)
Q=
e.W.h .
F (set + tc / 2)
• Ru= working load, W=weight of the
hammer, h= height of the hammer drop
(stroke), F=factor of safety
F
• tc= elastic (temporary) compression
Ru
• e = efficiency
tc
s
D
Plunging failure
What is the distribution
of resistance?
Approximate methods
Instrumentation
contract requirement
What is the
Davisson’s Method
Butler and Hoy
Chin’s Method
Brinch Hanson
etc. etc.
Deflection
Dynamic and Statnamic
Testing Methods
•
•
•
•
Rapid alternatives to static testing
Cheaper
Separate dynamic resistance
Correlation
Pu
Axial Capacity
W
Qs
Qb
Pu = Qb + Qs - W
Base Resistance
Qb = Ab [cbNc + P’ob(Nq-1) + 0.5gBNg + Pob]
minus weight of pile, Wp
but Wp  Ab.Pob
Qb
and as L >>B, 0.5gBNg << Wp
and for f > 0, Nq - 1  Nq
Qb = Ab [cbNc + P’obNq]
Shaft Resistance
Due to cohesion or friction
As
Cohesive component : Qsc = As . a . cs
Frictional component : Qsf = As .K P’ostan d
P’os
K.P’os
Qs = Qsc + Qsf = As [ a .cs + K P’ostan d ]
Total Pile Resistance
Qu = Qb + Qs
Qu = Ab [cbNc+P’obNq] + As [ a .cs+K P’otan d ]
How do we compute Qu when shaft resistance
along the pile is varying?
Mobilization
10 - 20% diam
2 - 5mm
Total
Base
Shaft
Settlement
Piles in Clay
Qu = Ab [cbNc+P’obNq] + As [ a .cs+K P’otan d ]
Qu = AbcbNc + Asa .cs
Undrained
Qu =
=A
Ab [c
[cbN
Nc+P’
+P’obN
Nq]] +
+A
As [[ a
a .c
.cs+K
+K P’
P’otan
tan dd ]]
Q
u
b
b c
ob q
s
s
o
Qu = Ab P’obNq + AsK P’ostan d
Drained / Effective
Qu = A
+ cA+sK
tan
d
Qbu P’
= ob
AbNcqbN
AsP’
ao.c
s
Driven Piles in Clay
2.0
1.5
Du
vo
Average curve for sensitivea
marine clay
1.0
Average curve for clays of
low-medium sensitivity
0.5
0
10
20
30
r
a
40
50
60
Bearing capacity in kN
300
30
200 x 215mm conrete
250
25
(Gothenberg)
200
20
150
15
300 x 150mm tapered timber (Drammen)
100
300 x 125mm I-Beam 150mm (8 in) steel tube (San Francisco)
50
0
(Gothenberg)
1
5
10
50
100
Time after driving in days
500
10
5
1000
Bearing capacity in tons
Driven Piles in Clay
Nc Parameter
Nc
Bending capacity factor Nc
10
9
8
7
6
5
0
1
2
3
4
5
L/d B
Compare Skempton’s Nc for shallow foundations
Nc= 5(1+0.2B/L)(1+0.2D/ B)
Aust. Piling Code,
AS159 (1978)
1.0
50
100
150
200
250
2.0
1.5
1.0
0.5
Figures denote penetration ratio =
Depth of penetration in clay
Key:
Pile diameter
49 49
Steel tube piles
19 49 56
Precast concrete
13 15
piles
17 27
13
Design curve for
44 39
33
39
44
27 33
penetration ratio > 20
19
17
38
15
0
1000
2000
10
8
40
5
3000
44
35
4000
Undrained shear strength (cu ) lb/ft
Reduction Factor , a
Undrained shear strength (cu )
kN/m2
0.8
0.6
0.4
0.2
5000
2
0
100
200
Average Undrained Shear Strength, cu , kPa
Bored Piles in Clay
• Skempton’s recommendations for side
resistance
– a =0.45
– acu =100 kPa
for cu <215 kPa
for cu>215 kPa
– Nc is limited to 9.
– A reduction factor is applied to account for
likely fissuring (I.e., Qb = Ab  cb Nc)
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
Piles in Sand
Qu = Ab [cbNc+P’obNq] + As [ a .cs+K P’ostan d ]
Qu = Ab [cbNc+P’obNq] + As [ a .cs+K P’ostan d ]
Qu = Ab P’obNq] + AsK P’ostan d ]
Overburden Stress P’ob
Qu = Ab P’obNq] + AsK P’ostan d ]
Meyerhof Method : P’ob = g’z
Vesic Method : critical depth, zc
for z < zc : P’ob = g’z
for z > zc : P’ob = g’zc
zc/d is a function of f after installation
- see graph p. 24
Critical Depth (zc)
20
15
zc

vc
zc / d
W.T.
10
L
5
d
0
28
33
f
38
43
Bearing Factor, Nq
Qu = Ab P’obNq] + AsK P’ostan d ]
NTotal
function
of :may
friction
f
q is aend
bearing
alsoangle,
be limited:
Layered soils :
Nqaffects
may bef reduced
if penetration
What
• In-situ
density
Meyerhof
: Qb?< A
50N
tanf
b
q
insufficient. e.g.
Meyerhof
(p 21)
• Particle properties
• Installation
procedure
Beware if f is preor post-installation:
Nq determined from graphs appropriate
to each particular method
Nq factor (Berezantzev’s Method)
1000
If D/B <4
Nq
reduce
proportionately
to Terzaghi and
Peck values
100
For driven piles :
For bored piles :
10
25
30
35
f
40
45
f ' = 0.75 f '1 +10
f   f1  3
Overburden Stress P’os
Qu = Ab P’obNq] + AsK P’ostan d ]
Meyerhof Method : P’os = g’zmid
Vesic Method : critical depth, zc
for zmid < zc : P’ob = g’z
for zmid > zc : P’ob = g’zc
zc/d is a function of f after installation
- see graph p. 24
Lateral stress parameter, K
• A function of Ko
– 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 / Ko:
Pile Type
K / Ko
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 / Ko
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.tand
• The K and tand values are often combined
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 concrete
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 = 40o ; g = 21kN/m3)
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 = 44o ; g = 21.7 kN/m3
Compute modified capacity using Meyerhof
Example
•
•
•
•
•
•
•
Bored pile
900mm diameter
Uniform medium dense sand (f = 35o ; g = 19.5kN/m3)
Water table at 1m
Pile length 20m
Check shaft capacity with Vesic and Meyerhof Methods
By comparsion, check capacity of 550mm diameter
screwed pile
Lateral load on single 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)
```