pile driveability

Pile Driveability analysis

PILE DRIVEABILITY ANALYSIS

5/24/2014 Dr. S. NallayarasuDepartment of Ocean Engineering

Indian Institute of Technology Madras-36

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Pile Driveability analysisMAIN PILE PILE MAKE UP FOR PILE

INSTALLATION AT ROW B



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STEP 1 : P1 ADD

SELF PENETRATION

STEP 2 : P2 ADD ON P1

STAB AND WELD

SELF PENETRATION AGAIN

STEP 3 : START HAMMERING AND SO ON



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Pile Driveability analysisINTRO FULL SEQUENCES



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TO DETERMINE THE ABILITY TO DRIVE TO TARGET PENETRATIONTo determine whether or not the proposed pile can be driven to the final target penetration to achieve the required ultimate soil capacity

TO ASSESS THE HAMMER CAPACITYTo assess the hammer capacity in terms of its driving energy and efficiency

TO ASSESS THE STRESSES INDUCED ON PILE Static and dynamic stresses induced during the driving process TO ASSESS THE DRIVEN PILE CAPACITY

To back calculate the ultimate capacity of driven piles

PILE DRIVEABILITY ANALYSIS

PURPOSE



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USING DYNAMIC FORMULAPile driving dynamic formula were used to assess the driveability of the driven piles. Even now, for onshore works, this approach is used.In this method, final set at target penetration is used as a criteria to determine the stresses developed in the pile

WAVE EQUATION ANALYSISFor long piles, wave equation analysis is used. Typically offshore piles, this is used to assess the stresses developed during the driving process and the effort required to achieve the final penetration, and make a decision when to stop the driving process (Pile refusal Criteria)

Pile termination criteria is based on number of blows required for depth of penetration typically say 1m. Some times called Pile Refusal Crieteria. This needs to be set so that the field engineers can decide to stop driving any further.

ASSESSMENT METHODOLOGY



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DYNAMIC PILE DRIVING FORMULA



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Pile Driveability analysisHAMMER TYPES

DIESEL HAMMERS OPEN ENDED CLOSE ENDED

HYDRAULIC HAMMERS SINGLE ACTING DOUBLE ACTING

STEAM HAMMERS DROP HAMMERS VIBRATORY HAMMERS



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Pile Driveability analysisPARTS OF A DIESEL HAMMER

PISTON CYLINDER RAM PILE CAP BLOCK PILE CAP PILE CUSHION



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Pile Driveability analysisSIMPLIFIED ENERGY BALANCE

.h d R P s uE E E R s

.

h d h u u p i l e u s o i lW H R s R k R k

Energy Imparted = Work done + Losses

Losses include

Loss in impact system Loss in Pile Loss in Soil

Ru S ER R



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Pile Driveability analysisSIMPLEST FORM OF SET Vs IMPACT

hu

W HRS

Ru= load capacity of pile



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Pile Driveability analysisOTHER SIMPLER FORMS SET Vs RESISTANCE

hu

W HRS

Sanders

1

hu

W HRS C

Engineering News

1

h hu

h p

W H WRS C W W

Eytelwein

C1 = Temporary Compression allowance for pileC2 = Temporary Compression allowance for pile cushion / followerC3 = Temporary Compression allowance for soil

2

1 2 31

2

h ph hu

h p

W n WW HRW WS C C C

Hiley



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Pile Driveability analysisDerivation of General Formula Pile Driving

S = pile penetration for last blow, or setSpp = plastic deformation of pileSep = elastic deformation of pileSes = elastic deformation of soilS0 = S - SppWh = weight of hammerH = drop of hammeref = efficiency factor for hammereiv = efficiency factor for impactWp = weight of pileA = cross section of pileL = pile lengthEp = modulus of elasticity of pilevh = hammer velocity before impactuh = hammer velocity after impactvp = pile velocity before impactup = pile velocity after impact



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Pile Driveability analysisg = gravitational accelerationRu = load capacity of pile (just after driving)E1 = energy reaching pileE2 = energy left after impact

The energy reaching the pile is

2

1 2h h

h hW vE W H

g

The energy efficiency of impact is

2 22

2 21

( / 2 ) ( / 2 )( / 2 ) ( / 2 )

h h p pi

h h p p

W g u W g u EW g v W g v E

5/24/2014 Dr. S. Nallayarasu

Department of Ocean EngineeringIndian Institute of Technology Madras-36

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Pile Driveability analysisThe law of impulse gives

( ) ( )ph h h p pWW v u v u

g g

Thus, the coefficient of elastic restitution, n, is

Velocity of pile after impact - velocity of hammer after impactVelocity of hammer before impact - velocity of pile before impact

p h

h p

u un

v v

Assuming vp = 0, and eliminating, uh, up, and vh,2

h pi

h P

W n WW W

The energy left after impact is

2

2h p

h i h h hh p

W n WE W H W H

W W



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Pile Driveability analysisThe work done during impact is approximately

21( )2u pp ep

E R S S S Neglecting the elastic deformation of the soil, and introducing Hookes law for the pile

uep

p

R LS CAE

Where C = ratio between actual displacement at pile top and that given by Hookes Law. From the above equations, the following equation is obtained

2

2

h ph hu

h pupp

p

W n WW HRW WCR LS S

AE



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Pile Driveability analysisMODIFIED ENGINEERING NEWS (ENR) FORMULA

2h ph h

uh p

W n WW HRs C W W

Where

Ru = Ultimate pile capacity (RS+RE).h = Hammer efficiency.Wh = Weight of Ram.Wp = Weight of pile including pile cap, cab block.H = Height of fall of ram.s = Set, amount of point penetration per blow.n = Co-efficient of restitution.C = Temporary compression allowance.



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Type Efficiency

Drop Hammers 0.75-1.00

Single-acting hammers 0.75-0.85

Double-acting or Differential 0.85

Diesel Hammers 0.85-1.00

EFFICIENCY OF HAMMERS



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Material n

Broomed wood 0

Wood piles (non-deteriorated end) 0.25

Compact wood cushion on steel pile 0.32

Compact wood cushion over steel pile 0.40

Steel-on-steel anvil on either steel or concrete pile 0.50

Cast-iron hammer on concrete pile without cap 0.40

COEFFICIENT OF RESTITUTION OF MATERIALS



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Pile Diameter Nominal Wall Thickness, t

in. mm in. mm

24 610 1/2 13

30 762 9/16 14

36 914 5/8 16

42 1067 11/16 17

48 1219 19

60 1524 7/8 22

72 1829 1 25

84 2134 11/8 28

96 2438 11/4 31

108 2743 13/8 34

120 3048 11/2 37

MINIMUM PILE WALL THICKNESS



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Pile Driveability analysisGUIDELINE ON HAMMER ENERGY

Consider a hammer of 100 Tonnes Ram weight and a stroke height of 1.5m will give a hammer energy of 150 Tm or 1500 kNm or 1500 kJ



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WAVE EQUATION ANALYSIS OF PILE DRIVING



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Pile Driveability analysisNotation

w0 = Displacement of pile topwtip = Displacement of pile tip

= W0+elastic compression of pile

= w0 + wcw = Displacement of the small

elementw = Elastic compression of small

elementF = Impact force applied at the

pile topP = Compression force on the

small elementP = Initial force on the elementfs = Frictional resistance of soilQtip = End bearing resistance of

soil at the tip



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Pile Driveability analysisConsider a small element of thickness y located at a depth of y from the pile top, the force on the segment can be calculated using Hooks Law.

Strain in the element due to elastic compression () =

Stress in the element () =

Force acting on the element (P) =

yw

ywEP

PA

P PwP E Ay



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Pile Driveability analysisThe above equation can be written as (after taking limit of = 0)

( 1 )P PwP E Ay

Due to impact force applied at the top of the pile, the stress wave travels along the pile and causes the element accelerate downwards. The velocity and acceleration the element can be found as

2

2 and (2)w wat t

where w is the instantaneous displacement of the element. The acceleration of the element causes the inertial force developed on the element equal to

2

2 (3)P P swP A y - f yt



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From equation (1),

2

P P 2E A ( 5 )P wy y

Substitution on (4) in (5), yields,

2

P P 2= A (4 )P w - Ry t

Dividing by y and taking limit y = 0, yields

2 2

2 2 (6 )P P P Pw wA R E At y



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Pile Driveability analysisDivide by EpAp, we get

2 2

2 2 (7)P

P P P

w R wE t E A y

Where defined as velocity of stress wave and R is the soil

frictional resistance and hence the above equation can be written as

P

P

Ec

2 2

2 2 2

1 ( 8 )P P

w w Ry c t E A

The above equation is the one dimensional wave equation and can be solved using method of separation of variables or numerical methods



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CLOSED FORM SOLUTIONS METHOD OF SEPARATION OF VARIABLES METHOD OF LAPLACE TRANSFORM

FINITE DIFFERENCE METHOD By dividing the pile / soil interface into the several sub

segments and solving the system of equations in time domain. Smith simplified the finite difference scheme by a set of

equations describing the relationship between mass, displacement, acceleration and velocity.

SOLUTIONS



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Pile Driveability analysisSOLUTION FOR SHOCK WAVES FOR FINITE PILEUsing the method of separation of variables, solution to the finite pile can be obtained

The differential equation can be written as2 2

22 2 where c = w w Ect y

With the boundary conditions

0

0, 0 : 0,

, 0 :

wy ty

y h t w w

The solution to the problem in the form of

0+Y(y) T(t)w w

y

y

y



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Pile Driveability analysisThe basic assumption here is that solutions can be written as a product of two function Y(y), which depends upon y only and another function T(t), which depends only on t. Substitution of the above equation with differential equation gives

2 2

2 2 2

1 1 1d T d Yc T dt Y dy

The left hand side of this equation depends upon t only, the right hand side depends upon y only. Therefore the equation can be satisfied only if both sides are equal to a certain constant. This constant may be assumed to be negative or positive. If it is assumed that this constant is negative one may write

22

2

1 ,d YY dy

Where is an unknown constant. The general solution is

Y=A cos (y)+ B sin (y),5/24/2014 Dr. S. Nallayarasu


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Pile Driveability analysisWhere A and B are constants. They can be determined from the boundary conditions Because dY / dy must be 0 for y=0 it follows that B=0. If now it is required that y=0 for y=h, in order to satisfy the boundary condition it follows that either A=0, which leads to the useless solution w=0, or cos (h)=0, which can be satisfied if

2 1 , 0,1, 2,.....2k

k kh

On the other hand, one obtains for the function T2

2 22

1 d T cT dt

With the general solution

T=A cos (ct)+ B sin (ct).The solution for the displacement w can be written as

00

cos sin cosk k k k kk

w w A ct B ct y



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Pile Driveability analysisThe velocity now is

0

sin cos cosk k k k k k kk

w A c ct B c ct yt

Because this must be zero for all values of y (this is an initial condition) it follows that Bk=0. On the other hand, the initial condition that the displacement must also be zero for t=0, now leads to the equation

00

cos ,k kk

A y w

Which must be satisfied for all values of y in the range 0


NUMERICAL SOLUTION



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PILEPile is treated as an elastic element with specified stiffness and may move with displacement, velocity and acceleration during an impact by external energy

SOILSoil is characterized by static and dynamic resistance

PILE - SOIL MODEL



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Pile Driveability analysisSOIL RESISTANCE STATIC RESISTANCE (Rs) -- (-Ru < Rs < Ru)

Static resistance of soil is a function of displacement of the pile to the soil and is therefore present during static and dynamic loading. This varies with time. It achieves a maximum limit (Ru) which is the ultimate soil resistance for maximum displacement.

DYNAMIC RESISTANCE (DAMPING RESISTANCE) (Rd)Dynamic resistance related to the velocity of the pile and only present during dynamic loading.

Dynamic resistance can be approximated as fraction of static resistance using the relationship with velocity (V) of pile and a empirical constant (Js) Rd = JsVRu

TOTAL RESISTANCE (Rt)The sum of Static and Dynamic Resistances in the soil and varies with time.



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Pile Driveability analysisLoad deformation relationship for soil

t s dR R R

for < q

R for > q

s u

s u

R RqR

d s uR J VR

t u s uR R J VRq

1t u sR R J V



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Pile Driveability analysisPile Soil Model



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Pile Driveability analysisNOTATIONS

i = element numbert = timet = time intervalC = compression of pile element i at time t = displacement of pile element i at time t = plastic displacement of soil spring i at time tF = force in pile element i at time tg = acceleration caused by gravity JS = soil damping constant at element iK = spring constant for pile element iK = spring constant for soil at element iR = force exerted by soil spring i on element i at time tV = velocity of pile element i at time tW = weight of pile element iq = quake of the soil (displacement up to elastic stage)



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The equations to update the displacement, velocity and acceleration at each time step for each element is given below. Initial velocity of Ram (Vr) shall be used to start with for the pile element at the top. The initial displacement of the pile segment at the top shall be assumed zero. The acceleration of the hammer can be taken as equal to gravitation acceleration (g).

11 1

1.t t t t t ti i i i i ii

a a F F R Rm

1 1t t ti i iV V a t

Acceleration

Velocity of pile



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1 1.t t ti i it V Pile Displacement1t

i rV V Initial Condition 1 0ti 1tia g

NUMERICAL PROCEDURE

/i im W g


1 .t t ti i i iF K 1' ' 1t t t ti i i i i iR K J V

Force on the Pile Spring

Force on the Soil Spring



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Force on the pile spring can be calculated once the displacements of the pile segments are evaluated

The force on the soil spring can be calculated using the relative displacement of pile and soil together with the soil spring values and damping

Smith (1960) notes that the equation produces no damping when - becomes zero, and suggests an alternate equation to be used after first becomes equal to q, where q is the quake for element i.

1' . ' .t t t ti i i i i u i iR K J R V Where Ru is the ultimate static soil-resistance of element i.




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Time IncrementSmiths lumped mass model is mathematically stable only if the computational time increment is chosen shorter than the shortest (critical) wave travel time of any segment l. The critical time increment is the time that it takes the stress wave to travel through the pile segment.

/cri i it L c or for a lumped mass element

12/cri i it m K Where mi, Ki, Li and ci are the segment mass, stiffness, length and stress wave speed in segment l respectively. The wave speed of the segment is 12/i i ic E With i being unit mass of the segment. Where pile properties change within a segment length, all segment properties are averaged.




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In order to avoid instability, the computational time increment, t is chosen as

min /crit t Where min (tcri) stands for the minimum critical time increment ofall hammer and pile segments and is a number greater than 1.the program defaults to = 1.6.

While the critical time of the hammer-driving system pile model isnormally determined from the stiffest segment in hammer or drivingsystem, the program also checks the pile segments, considering theeffects of soil resistance on the stiffness of the pile segments. As aconsequence, GRLWEAP may select the computational time incrementwith smaller values from high capacities than for low capacities.




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Corrector Integration

After the acceleration value has been calculated for a segment, its velocity and displacement values are corrected by integration under the assumption of a linearly varying acceleration:

1 2t t t ti i i i tv v a a and

21 1 12 6t t t t ti i i i i tv t a a Since the displacements are now more accurately known than after

initial prediction, the spring forces and are recalculated. Thus

for the calculation of spring forces on the next lower segment, i+1

updated force values are available.

tiR1

tiR

Pile Driveability analysisThe initial velocity of the ram at initial impact, Vr, which can be calculated as

2r h

h

gVW

Where

h = hammer efficiencyWh = weight of hammer

Values of the pile element spring constants, Ki, of the pile and other elements, where

i ii

i

A EKL

Where

Ai = cross sectional area of element iEi = Youngs modulus of element iLi = length of element i



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In performing the computations, the following sequence of operations is carried out:

1. The initial velocity, Vr, is calculated. Other time-dependent quantities are initialized at zero or to produce equilibrium of forces under gravity.

2. The displacement are calculated where for the first time-step, V is the initial velocity of the ram.

3. The total plastic deformation of the soil, , remains constant [starting at =0] unless it is changed by the following condition

' t tm m mq ' t tm m mq

COMPUTATIONAL STEPS



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Ultimate Pile Resistance Ru Quake q

Usually empirically based, 2.5 mm commonly used for all soil types

Damping Factor JS Empirically based. Typically, 0.5-0.6 sec/m for

base; 1/3 of this value for shaft

SOIL PARAMETERS

Soil Type Damping Coefficients (sec./m)

Quake (mm)

Side (Shaft) Point (Toe) Side (Skin) Point (Toe)Clay 0.65 0.50 2.54 2.54Sand 0.15 0.50 2.54 2.54



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Clay Silt Sand

Soft Firm Stiff Very stiff

Hard

Quake mm

Qs 5.08 3.81 2.54 2.54 2.54 2.54 2.54

Qp 5.08 3.81 2.54 2.54 2.54 2.54 2.54

Damping factor m/s

Js 0.36 0.23 0.20 0.16 0.10 0.223 0.26

Jp 0.66 0.50 0.50 0.50 0.50 0.50 0.50

ROUSSEL, 1979 Based on Experiments



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Pile Driveability analysisSoil Resistance to Driving (SRD) (Ru)

SRD profiles are assessed using the procedures recommended by Stevens et al. (1982). Upper and lower bound values of SRD are computed for both coring and plugged pile conditions for continuous driving. Four cases are assessed.

Case 1 lower bound, coring pile (1.5Rs + Ran) in sand and clayCase 2 upper bound, coring pile (2Rs + Ran) in sand and clayCase 3 lower bound, plugged pile (Rs + Re) in sand and clayCase 4 upper bound, plugged pile (1.3 Rs + 1.5 Re) in sand

(Rs + 1.67 Re) in clay

Where

Rs is outside shaft resistance

Ran is end bearing on pile annulus

Re is full pile end bearing



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Pile Driveability analysisTime Dependent effect of Clay on SRD and RuThe method adopted to calculate variable soil setup is referenced inRausche et al, 2009 which assumes gain in the pile bearing as afunction of logarithmic time. With a specified soil setup factor the longterm capacity is:

u si uQ f RWhereQu = the long term pile capacity capacityfsi = the specified soil setup factorRu = the Soil Resistance to Driving in each soil layerAfter a certain time delay (tw), which is less than the full setup time, the capacity in each soil layer is:

100

100

111( ) log

log

wsiu w u

si si

tfR t Qf tt

t

Wheretw = the time delayt0 = a reference time (full setup time)



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Pile Driveability analysisA setup factor of 2 was assumed as full setup achieved after 4 weeks. Although a setup factor of 2 may be considered low, it is consistent with the fairly large Fp factor of 0.65 considered for continuous driving. The estimated setup factor for 7 days and 48 hours are 1.88 and 1.76 respectively, accordingly to the equation above.

To apply the variable setup factor to the SRD method, the pile capacity factor Fp is:

0.3pF OCRWhere = 0.5 for no setupFp has been modified to allow for setup according to the following:

= 0.88 for 48 hour set-up = 0.94 for 7 days set-up.



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The estimation of SRD for regional projects in India is based on a simple concept of combination of friction and end bearing may be adopted for continous driving

Standard SRD Criteria

Soil Type Skin friction End bearing

Sand 100% 100%

Clay 50% 0%

Continuous Driving

Soil Type Skin friction End bearing

Sand 100% 100%

Clay 75% 0%

Restart Driving

For restart driving, following criteria may be employed



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Pile refusal criteria shall be as per API RP 2A and repeated here for clarity.

300 blows / 0.3m for 5 consecutive 0.3m (for continuous driving)800 blows / 0.3m800 blows / 0.152m (Setup case)

The most stringent of the above shall be applied to determine the pile refusal.

Many times, the hammer manufacturer recommendation will be final.

Pile Refusal Criteria



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GRLWEAP is a finite difference based numerical analysis software to simulate the pile driveability using wave equation

The input to the program requires the following data.

Pile properties along its length Soil skin friction and end bearing data Quake and Damping characteristics of the soil Pile Stoppage and Re-start information Hammer weight, drop height and energy information Hammer and pile cushion data

GRLWEAP from Pile Dynamics Inc, USA



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56




57




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60




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Pile Driveability analysisPile Driveability Results



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Pile Driveability analysisPILE DRIVING FATIGUE Stress Range Computation Stress Concentration Factor Fatigue Evaluation Factor of Safety



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= Stresses in each segment of pile

N = Number of blows

L = Depth of penetration

Notation



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Pile Driveability analysisSTRESS AT WELD LOCATION



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1 max minlog log . .k

allowref

tlogN k m SCFT

1

max min

allow mk

ref

kNtSCF

T

STRESS CYCLE (S-N) CURVE

Nallow = Predicted number of cycles to failure for stress rangem = Negative inverse slope of S-N curvemin = Minimum stress (tensile)max = Maximum stress (compressive)logk1 = intercept of log N-axis by S-N curvet = Thickness of pipe wall (mm)Tref = Reference thickness (25mm)m = slope of S-N curve = 3k1 = constant = 11.61 (log k1 = 3.572 x 1011)SCF = Stress Concentration Factor



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Pile Driveability analysisS-N CURVES FROM DNV RP C203



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68




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6( ) 111

t m oSCF et T

t

1.82 1.

1

LDt T

t

2

1.0 3.01.5D DLog Logt t

1 ( )2tT t

SCF on single sided circumferential butt welds can be estimated using following relationship

;

D = Outer Diameter; T = Larger thickness ; t = smaller thickness ; L = Length of transitio

WELDED FROM OUTSIDE SCF FOR OUTSIDE



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6( ) 111

t mSCF et T

t

1.82 1.

1

LDt T

t

2


1 ( )2tT t


D = Outer Diameter; T = Larger thickness ; t = smaller thickness ; L = Length of transition;

WELDED FROM OUTSIDE SCF FOR INSIDE



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6 111

tSCF et T

t

1.82 1.

1

LDt T

t

2


1 ( )2tT t


;

D = Outer Diameter; T = Larger thickness ; t = smaller thickness ; L = Length of transition;

WELD FROM OUTSIDE SCF FOR OUTSIDE



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Pile Driveability analysisFATIGUE DAMAGE COMPUTATION

blowsp

n allow

NDN

Cumulative Fatigue damage can be calculated using Miners rule

In which

n represents the number subdivisions of penetration to monitor the blows



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pile driveability

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