12626795 Analysis of Bearing Capacity Driven Pile

ANALYSIS OF BEARING CAPACITY – DRIVEN PILE FOUNDATION

8 - 1

STRUCTURAL ENGINEER : SYAIFUL ASHARI, ST

8.1 INTRODUCTION

Driven pile is a type of the deep foundation. This foundation is driven to the ground using a hammer

which is dropped from the prescribed height. The hammer is introduces energy to push the pile to the

soil.

The followings are several reason to use the driven pile foundation (deep foundation),as follows :

� The upper soil condition is so bad so the use of spread footing is very un economically.

� Large uplift capacity is required.

� Large lateral capacity is required.

� Requirement for pier foundation and abutment foundation in bridge structure.

This chapter describes the analysis of bearing capacity for driven pile foundation based on the soil

properties and in situ test, dynamic formula to predict the bearing capacity, lateral bearing capacity and

analysis of group pile.

8.2 TYPE OF PILE FOUNDATION

8.2.1 GENERAL

Load transfer from the super structure to the pile foundation is depends to the type of soil. The bearing

capacity of pile foundation is from the end bearing capacity and skin friction capacity .

Cohesionless soil provides the end bearing capacity and cohesive soil provide skin friction

capacity . For general soil condition the bearing capacity is provided by the end bearing capacity plus

with skin friction capacity.

The ultimate bearing capacity of pile foundation can be written as :

usupu QQQ += [8.1]

where :

Qu = ultimate bearing capacity

Qup = ultimate end bearing capacity

Qus = ultimate skin friction capacity

CHAPTECHAPTECHAPTECHAPTERRRR

8888 ANALYSISANALYSISANALYSISANALYSIS OF OF OF OF BBBBEARING EARING EARING EARING

CAPACICAPACICAPACICAPACITYTYTYTY –––– DRIVEN DRIVEN DRIVEN DRIVEN PILEPILEPILEPILE

FOUNDATIONFOUNDATIONFOUNDATIONFOUNDATION


8 - 2

And the allowable bearing capacity is :

s

us

p

upa SF

QSF

QQ += [8.2]

where :

SFp = safety factor for end bearing capacity (2.0 – 4.0)

SFs = safety factor for skin friction capacity (2.0 – 4.0)

8.2.2 END BEARING PILE

End bearing pile is pile foundation that the major of bearing capacity is provided by end bearing

capacity . The skin friction capacity in end bearing pile can be neglected because it has small

influence.

End bearing capacity is calculated as follows :

pupup AqQ = [8.3]

where :


qup = ultimate end bearing pressure

Ap = end bearing contact area

8.2.3 FRICTION PILE

Friction pile is pile foundation that the major of bearing capacity is provided by skin friction capacity

(provided by adhesion) . The end bearing capacity in end bearing pile can be neglected because it

has small influence.

Ultimate skin friction capacity is calculated as follows :

∑= ssus AfQ [8.4]

where :


fs = ultimate skin friction stress

As = skin friction contact area

8.3 LOAD TRANSFER MECHANISM

8.3.1 GENERAL

Pile foundation almost to carry the moment load, this moment is transfer becomes compressive axial

load and tensile axial load . The design of bearing capacity of pile foundation must consider the type

of load acts in the pile.


8 - 3

8.3.2 COMPRESSIVE AXIAL CAPACITY

The bearing capacity of pile foundation due to axial compressive load is provided by the end bearing

capacity and skin friction capacity .

8.3.3 UPLIFT AXIAL CAPACITY

The bearing capacity of pile foundation due to axial tensile load is provided only by the skin friction

capacity .

8.4 ANALYSIS OF AXIAL BEARING CAPACITY – SOIL PROPE RTIES

8.4.1 GENERAL

Basic bearing capacity formula can be used for bearing capacity analysis for deep foundation with

several modifications. Analysis based on soil properties is using internal friction angle and

undrained shear strength .

8.4.2 CONTACT AREA

A. General

Contact area is the important thing to be considered in the pile foundation design. The contact area

may be different for different type of pile foundation.

B. Open Ended Steel Pipe Pile

When the pipe pile is driven the inside of the pipe will be plugged with the soil .

For condition of full plug , the end bearing contact area is the same with area of pipe if it is open

ended , as follows :

soilsteelp AAA += [8.5]

where :


Asteel = area of steel profile

Asoil = area of plug soil

For condition of partial plug , the end bearing contact area is half of the area of pipe if it is open

ended , as follows :

( )soilsteelp AA5.0A += [8.6]

where :




The skin friction contact area is the perimeter of the profile .


8 - 4

C. H Steel Pile

When the pipe pile is driven the inside of the pipe will be half plugged with the soil .

The end bearing contact area is :

( )soilsteelp AA5.0A += [8.7]

where :




The skin friction contact area is the perimeter of the pile with full plug .

8.4.3 END BEARING CAPACITY

A. General

The ultimate bearing capacity of pile foundation can be computed using the bearing capacity formula

as described in the previous chapter.

B. Bearing Capacity Formula

In general basic bearing capacity formula can be written as follows :

**q

*cu BNqNcNq γγ++= [8.8]

Because the width of pile foundation is small (B is small) , so the end term of the equation can be

neglected, so the end bearing pressure can be written as :

*q

*cup qNcNq += [8.9]

Ultimate end bearing capacity is computed as follows :

( ) p*q

*cup AqNcNQ += [8.10]

For the condition of cohesive soil (c=s u and φφφφ=0), the formula becomes :

uup s9q = [8.11]

where :

qp = ultimate end bearing pressure

su = undrained shear strength

*q

*c N,N = bearing capacity factor (include depth factor, inclination factor)


8 - 5

Ultimate end bearing capacity is computed as follows :

( ) puup As9Q = [8.12]

C. Vesic’s Method

Vesic propose the end bearing capacity formula based on the expansion of cavities theory .

The end bearing capacity can be calculated as follows :

( ) p*

0*cup AN'cNQ σσ+= [8.13]

where :


σ’0 = mean normal ground stress at the level of pile point

**c N,N σ = bearing capacity factor

The variables above is defined as :

'q3K21

' 00

+=σ

( )φ−= sin1K0

[8.14]

where :

q’ = effective vertical stress at the pile point

K0 = coefficient of earth pressure

φ = internal friction angle

The bearing capacity factor is defined as :

( ) ( )φ−= cot1NN *q

*c

( )0

*q*

K21

N3N

+=σ

[8.15]

D. Janbu’s Method


( ) p*q

*cup AN'qcNQ += [8.16]


8 - 6

where :



*q

*c N,N = bearing capacity factor

The bearing capacity factor is defined as :

( ) ( )φ−= cot1NN *q

*c

( ) ( ) ( )φη

φ++φ= tan'22

2*q etan1tanN

[8.17]

E. Coyle & Castello’s Method

Coyle & Castello’s method is used for cohesionless soil .


( ) p*qup AN'qQ = [8.18]

where :



*qN = bearing capacity factor

F. Meyerhof’s Method

Meyerhof proposes two formula can be used for cohesionless soil and cohesive soil.

The table below shows the Meyerhof’s end bearing capacity formula, as follows :

TABLE 8.1 END BEARING CAPACITY – MEYERHOF

COHESIONLESS

SOIL

COHESSIVE

SOIL

( ) ( )( ) p*qp

*qup AtanN50AN'qQ φ≤= ( ) pu

*cup AcNQ =

where :

cu = undrained cohesion

8.4.4 SKIN FRICTION CAPACITY

A. General

The ultimate bearing capacity of pile foundation can be computed using the bearing capacity formula

as described in the previous chapter.


8 - 7

B. αααα Method

The α method is calculates the skin friction resistance for cohesive soil based on the adhesion

factor αααα.

The skin friction capacity can be calculated as follows :

( ) suus AsQ α=

csu = [8.19]

where :


α = adhesion factor


c = cohesion


The adhesion factor α is determined based on the undrained shear strength s u usually use the

graph .

C. ββββ Method

The β method is calculates the skin friction resistance for cohesionless soil based on the coefficient

of lateral earth pressure .


( ) svus A'Q βσ=

( )stanK φ=β [8.20]

where :


σ’v = vertical effective stress at measured point

K = coefficient of lateral earth pressure

φs = friction angle of soil versus pile

Conservatively the lateral earth pressure can be computed, as follows :

Normally Consolidated Clays

( )ssin1K φ−= [8.21]

Over Consolidated Clays

( )( ) OCRsin1K sφ−= [8.22]


8 - 8

Bhushan propose the following equation to calculate β factor :

( )rD65.018.0 +=β [8.23]

where :

Dr = relative density

D. λλλλ Method

The λ method is calculates the skin friction resistance for cohesive soil based on the coefficient of

lateral earth pressure .


{ }( ) suvus As2'Q +σλ= [8.24]

where :


λ = friction capacity coefficient

v'σ = average vertical stress of ground surface and pile tip

us = average undrained shear strength of ground surface and pile tip

The factor λ is depended to the embedment length of the pile usually use the graph .

8.5 ANALYSIS OF AXIAL BEARING CAPACITY – IN SITU TE ST

8.5.1 GENERAL

Most practical method to obtain the bearing capacity is based on the in situ test such as standard

penetration test (SPT) and cone penetration test (CPT).

8.5.2 END BEARING CAPACITY – SPT

A. General

If the SPT data is used to obtain the bearing capacity it is recommended to use higher factor of safety

because inconsistency of the SPT test result.

B. Meyerhof’s Method

End bearing capacity based on the Meyerhof is :

corpcorup N400ABD

N40Q ≤

= [8.25]

where :

Qup = ultimate end bearing capacity (kPa)


8 - 9

Ncor = corrected N SPT value

D = embedment length

B = pile diameter


Ncor must be taken as average value in the range of 8B above pile tip and 3B below pile tip .

8.5.3 SKIN FRICTION CAPACITY – SPT

A. General

If the SPT data is used to obtain the bearing capacity it is recommended to use higher factor of safety

because inconsistency of the SPT test result.


The following is the skin friction capacity based on SPT test according to Meyerhof.

TABLE 8.2 SKIN FRICTION CAPACITY – MEYERHOF

LARGE DISPLACEMENT

PILE

SMALL DISPLACEMENT

PILE

( ) scorus AN2Q = ( ) scorus ANQ =

where :

Qus = ultimate skin friction capacity (kPa)

Ncor = corrected N SPT value


C. Vesic’s Method

The following is the skin friction capacity based on SPT test according to Vesic.

TABLE 8.3 SKIN FRICTION CAPACITY – VESIC

LARGE DISPLACEMENT

PILE

OPEN ENDED,

H PILE

sD54.1

us A80Q4r

= s

D54.1us A25Q

4r

=

where :


Dr = relative density



8 - 10

8.5.4 END BEARING CAPACITY – CPT

A. General

The CPT data can be used to predict the bearing capacity based on the cone resistance and side

friction .

B. LCPC’s Method

End bearing capacity based on the LCPC method is :

( ) pcceup AkqQ = [8.26]

where :

Qup = ultimate end bearing capacity (kPa)

qce = equivalent cone resistance at pile tip (kPa)

kc = cone end bearing factor


qce is taken as the average in the range of 1.5B above pile tip and 1.5B below pile tip .

The factor of cone end bearing is taken as :

TABLE 8.4 CONE END BEARING FACTOR

TYPE kc

Clay & Silt 0.600

Sand & Gravel 0.375

Chalk 0.400

8.5.5 SKIN FRICTION CAPACITY – CPT

A. General

The CPT data can be used to predict the bearing capacity based on the cone resistance and side

friction .


Skin friction capacity based on cone resistance according to the Meyerhof is :

( ) scus Aq005.0Q = [8.26]

where :


qc = cone resistance (kPa)



8 - 11

If the side friction is used the following equation can be used :

TABLE 8.5 SKIN FRICTION CAPACITY – MEYERHOF

LARGE DISPLACEMENT

PILE

SMALL DISPLACEMENT

PILE

( ) ssus Aq0.25.1Q −= ( ) ssus AqQ =

where :


qs = side friction (kPa)


C. Nottingham & Schmertmann’s Method

Skin friction capacity based on cone resistance is :

TABLE 8.6 SKIN FRICTION CAPACITY – NOTTINGHAM & SCHMERTMANN

COHESIONLESS SOIL

z < 8B z ≥≥≥≥ 8B COHESSIVE SOIL

sscsus AfBz

'Q

α= ( ) sscsus Af'Q α= ( ) ssccus Af'Q α=

where :


qs = side friction (kPa)

z = depth to mid point of soil layer

B = pile diameter

αααα’s and αααα’c is determined based on the graph.

8.6 ANALYSIS OF AXIAL BEARING CAPACITY – DYNAMIC TE ST

8.6.1 GENERAL

The pile bearing capacity can be predicted using the driving energy transferred to the pile using a

hammer. This method is known as dynamic method and can be used simply based on the final blow

count (final set) .

8.6.2 SANDER’S METHOD

Sander propose dynamic formula to predict the axial load capacity of the driven pile as follows :

( )FSshW

Q ra = [8.27]

where :

Qa = allowable axial bearing capacity


8 - 12

Wr = weight of hammer

h = hammer stroke / hammer fall distance

s = final penetration per blow at end of driving

FS = factor of safety (FS = 8)

8.6.3 ENGINEERING NEW’S METHOD

The most popular dynamic formula used is proposed by Engineering News (Wellington, 1888), as

follows :

( )( )FSCshW

Q ra +

= [8.28]

where :






C = constant (drop hammer = 25 mm)

(single acting hammer = 2.5 mm)

8.6.4 MODIFIED ENGINEERING NEW’S METHOD

The following is dynamic formula which is modification of Engineering News Formula, as follows :

( )

++

+=

pr

p2

rrha WW

WnW

CshWe

Q [8.29]

where :



Wp = weight of pile + hammer




C = constant (C = 2.5 mm)

eh = efficiency of hammer

n = coefficient of restitution

The following is the hammer efficiency and coefficient of restitution, as follows :


8 - 13

TABLE 8.7 HAMMER EFFICIENCY

HAMMER

TYPE eh

Drop Hammer 0.75 – 1.00

Single Acting Hammer 0.75 – 0.85

Double Acting Hammer 0.85

Diesel Hammer 0.85 – 1.00

TABLE 8.8 COEFFICIENT OF RESTITUTION

MATERIAL N

Wood Pile 0.00

Compact Wood On Steel Pile 0.25

Compact Wood Over Steel Pile 0.32

Steel On Steel Pile / Concrete Pile 0.50

Cast Iron Hammer On Concrete Pile 0.40

8.7 ANALYSIS OF UPLIFT CAPACITY

8.7.1 GENERAL

The uplift capacity of the driven pile is only provided by the skin friction capacity .

8.7.2 SKIN FRICTION CAPACITY

The skin friction capacity to determine the uplift capacity can be calculated with the similar procedure

as previously explained.

8.8 ANALYSIS OF LATERAL BEARING CAPACITY

8.3.4 GENERAL

During earthquake the pile foundation is take the lateral load from the result of super structure load.

When the pile subjected to lateral load the pile can be divided into two major categories, as follows :

� Rigid Pile , the pile length is short.

� Elastic Pile , the pile length is long.

8.3.5 MATLOCK & REESE’S METHOD

D. General

Matlock and Reese propose the elastic solution to analyze laterally loaded pile.

Due to the lateral load the following reactions can be calculated, as follows :

� Pile Deflection.

� Pile Slope.

� Bending Moment.

� Shear Force.

� Soil Reaction.

This method is can be used for pile embedded in granular soil .


8 - 14

E. Pile Deflection

The pile deflection at any depth of pile can be calculated, as follows :

( )

+

=

pp

2

xpp

3

x IEMT

BIE

QTAzx [8.30]

where :

x(z) = deflection at any depth of pile

Q = shear force at top of pile

M = bending moment at top of pile

Ep = modulus of elasticity of pile

Ip = moment of inertia of pile

Ax, Bx = constant

F. Pile Slope

The pile slope at any depth of pile can be calculated, as follows :

( )

+

=θ θθ

pppp

2

IEMT

BIE

QTAz [8.31]

where :

θ(z) = slope at any depth of pile





Aθ, Bθ = constant

G. Pile Bending Moment

The pile bending moment at any depth of pile can be calculated, as follows :

( ) ( ) ( )MBQTAzM mm += [8.32]

where :

M(z) = bending moment at any depth of pile





Am, Bm = constant


8 - 15

H. Pile Shear Force

The pile shear force at any depth of pile can be calculated, as follows :

( ) ( )

+=TM

BQAzV vv [8.33]

where :

V(z) = shear force at any depth of pile





Av, Bv = constant

I. Soil Reaction

The soil reaction at any depth of pile can be calculated, as follows :

( )

+

=2pp

T

MB

TQ

Azp [8.34]

where :

p(z) = soil reaction at any depth of pile





Ap, Bp = constant

J. Characteristic Length of Soil-Pile System

The T variable is the characteristic length of soil-pile system, as follows :

5

h

pp

n

IET = [8.35]

where :

T = characteristic length



nh = constant of horizontal modulus of subgrade reaction

The pile of rigid if L ≤≤≤≤ 2T and the pile is elastic if L ≥≥≥≥ 5T.


8 - 16

The value of nh is as follows :

TABLE 8.9 NH

SOIL nh

(kN/m 3)

Loose Sand 1800 – 2200

Medium Sand 5500 – 7000

Dense Sand 15000 – 18000

Loose Submerged Sand 1000 – 1400

Medium Submerged Sand 3500 – 4500

Dense Submerged Sand 9000 – 12000

K. A & B Constant

The following table shows the A and B constant.

TABLE 8.10 A CONSTANT

A COEFFICIENT z/T

Ax Ax Aθθθθ Am Av

0.0 2.435 -1.623 0.000 1.000 0.000

0.1 2.273 -1.618 0.100 0.989 -0.227

0.2 2.112 -1.603 0.198 0.956 -0.422

0.3 1.952 -1.578 0.291 0.906 -0.586

0.4 1.796 -1.545 0.379 0.840 -0.718

0.5 1.644 -1.503 0.459 0.764 -0.822

0.6 1.496 -1.454 0.532 0.677 -0.897

0.7 1.353 -1.397 0.595 0.585 -0.947

0.8 1.216 -1.335 0.649 0.489 -0.973

0.9 1.086 -1.268 0.693 0.392 -0.977

1.0 0.962 -1.197 0.727 0.295 -0.962

1.2 0.738 -1.047 0.767 0.109 -0.885

1.4 0.544 -0.893 0.772 -0.056 -0.761

1.6 0.381 -0.741 0.746 -0.193 -0.609

1.8 0.247 -0.596 0.696 -0.298 -0.445

2.0 0.142 -0.464 0.628 -0.371 -0.283

3.0 -0.075 -0.040 0.225 -0.349 0.226

4.0 -0.050 0.052 0.000 -0.106 0.201

5.0 -0.009 0.025 -0.033 0.015 0.046


8 - 17

TABLE 8.11 B CONSTANT

B COEFFICIENT z/T

Bx Bx Bθθθθ Bm Bv

0.0 1.623 -1.750 1.000 0.000 0.000

0.1 1.453 -1.650 1.000 -0.007 -0.145

0.2 1.293 -1.550 0.999 -0.028 -0.259

0.3 1.143 -1.450 0.994 -0.058 -0.343

0.4 1.003 -1.351 0.987 -0.095 -0.401

0.5 0.873 -1.253 0.976 -0.137 -0.436

0.6 0.752 -1.156 0.960 -0.181 -0.451

0.7 0.642 -1.061 0.939 -0.226 -0.449

0.8 0.540 -0.968 0.914 -0.270 -0.432

0.9 0.448 -0.878 0.885 -0.312 -0.403

1.0 0.364 -0.792 0.852 -0.350 -0.364

1.2 0.223 -0.629 0.775 -0.414 -0.268

1.4 0.112 -0.482 0.688 -0.456 -0.157

1.6 0.029 -0.354 0.594 -0.477 -0.047

1.8 -0.030 -0.245 0.498 -0.476 0.054

2.0 -0.070 -0.155 0.404 -0.456 0.140

3.0 -0.089 0.057 0.059 -0.213 0.268

4.0 -0.028 0.049 -0.042 0.017 0.112

5.0 0.000 -0.011 -0.026 0.029 -0.002

8.3.6 DAVISSON & GILL ’S METHOD

A. Pile Deflection

Davisson and Gill propose the elastic solution to analyze laterally loaded pile.

This method is can be used for pile embedded in cohesive soil .

B. Pile Deflection

The pile deflection at any depth of pile can be calculated, as follows :

( )

+

=

pp

2

xpp

3

x IEMR

'BIE

QR'Azx [8.36]

where :

x(z) = deflection at any depth of pile





A’x, B’x = constant

C. Pile Bending Moment

The pile bending moment at any depth of pile can be calculated, as follows :

( ) ( ) ( )M'BQR'AzM mm += [8.37]


8 - 18

where :

M(z) = bending moment at any depth of pile





A’m, B’m = constant

D. R Coefficient

The variable R is defined as follows :

4

s

pp

k

IER = [8.38]

where :



ks = modulus of subgrade reaction

8.3.7 BROM’S METHOD

A. General

Brom divide the condition as free head condition and restrained head condition .

Brom’s method only can be used for homogeneous soil , purely cohesive soil or purely

cohesionless soil .

B. Cohesive Soil

The following figure is the pressure diagram proposed by Brom for cohesive soil for free head

condition .

FIGURE 8.1 COHESIVE SOIL – FREE HEAD CONDITION


8 - 19

The minimum embedment depth of the pile due to shear force Q is :

( ) ( )fB5.1

Bs25.2f5.0B5.1eQFS

Du

min ++++=

( )Bs9QFS

fu

=

[8.39]

where :

Dmin = minimum embedment depth

Q = lateral shear force

e = eccentricity of lateral load

B = pile diameter


FS = safety factor (FS = 3)

The following figure is the pressure diagram proposed by Brom for cohesive soil for restrained head

condition .

FIGURE 8.2 COHESIVE SOIL – RESTRAINED HEAD CONDITION


( )B5.1

Bs9FSQ

Du

min +

= [8.39]

where :


8 - 20



B = pile diameter



C. Cohesionless Soil

The following figure is the pressure diagram proposed by Brom for cohesionless soil for free head

condition .

FIGURE 8.3 COHESIONLESS SOIL – FREE HEAD CONDITION


( )eDQ

KBD5.0FS

min

p3min

+γ

=

φ+=2

45tanK 2p

[8.40]

where :



B = pile diameter


e = eccentricity of lateral load

Kp = coefficient of passive lateral earth pressure



8 - 21

The following figure is the pressure diagram proposed by Brom for cohesionless soil for restrained

head condition .

FIGURE 8.3 COHESIONLESS SOIL – RESTRAINED HEAD CONDITION


( )p

min BK5.1FSQ

Dγ

= [8.40]

where :



B = pile diameter


Kp = coefficient of passive lateral earth pressure


8.9 GROUP PILE FOUNDATION

8.9.1 GENERAL

When the load is becomes bigger the group pile must be used to carry the load. The design of group

pile must consider the efficiency of the group and the arrangement of the pile .

8.9.2 PILE CONFIGURATION

The minimum spacing between pile in group pile is :

( )D5.35.2s −= [8.41]


8 - 22

where :

s = pile spacing

D = pile diameter

8.9.3 LOAD TRANSFER

The group pile may be subjected to centric load and eccentric load.

The load transfer to the pile due to centric load is :

nP

P1 = [8.42]

where :

P1 = vertical load in one pile

P = total centric vertical load

n = number of pile

The load transfer to the pile due to eccentric load is :

∑±

∑±=

2x

2y

1y

yM

x

xM

nP

P [8.43]

where :

P1 = vertical load in one pile

P = total centric vertical load

Mx = moment about X axis

My = moment about Y axis

x = x distance from center of pile cap

y = y distance from center of pile cap

n = number of pile

8.9.4 GROUP EFFICIENCY

The group efficiency of group pile can be calculated based on the Converse – Labarre formula, as

follows :

{ } { }

−+−θ−=mn90

n1mm1n1Eg

sD

tan 1−=θ

[8.44]

where :

Eg = efficiency of group pile

m = number of pile columns

n = number of pile rows

Documents

12626795 Analysis of Bearing Capacity Driven Pile