Depth of Fixity of Piles in Clay Under Dynamic Lateral Load.pdf

7/25/2019 Depth of Fixity of Piles in Clay Under Dynamic Lateral Load.pdf

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O R I G I N A L P A P E R

Depth of Fixity of Piles in Clay Under Dynamic Lateral

Load

R. Ayothiraman A. Boominathan

Received: 19 May 2011 / Accepted: 17 November 2012 / Published online: 15 December 2012

Springer Science+Business Media Dordrecht 2012

Abstract Dynamic experiments were carried out on

instrumented model aluminium single piles embedded

in clay of different consistencies to study its bending

behaviour under lateral loads. Piles with different

length to diameter ratios were used. Dynamic lateral

load of different magnitudes ranging from 7 to 30 N at

wide range of frequencies from 2 to 50 Hz were

applied. The load transferred to the pile, pile head

displacement and the strain variation along the pile

length were measured using a dedicated data acqui-

sition system. Static lateral load tests were alsoperformed to investigate the magnification of dynamic

response of piles in clay. It is found that the maximum

bending moment due to dynamic load is magnified by

about 1.54 times in comparison to the static load for

short piles but about 9 times for long piles. Depth of

fixity and effective pile length is also largely amplified

under dynamic loads, thus indicating that a pile which

behaves as a flexible pile under static load, may not

exhibit flexible behaviour under dynamic load.

Keywords Bending moment Clay DynamicsDepth of fixity Magnification Pile

List of symbols

d Outer diameter of pile

Ep Youngs modulus of pile material

f Frequency of excitation

fn Natural frequency of soil-pile system

F0 Magnitude of dynamic load

Gs Maximum dynamic shear modulus of soil

Ic Consistency index of clay

L Pile length

Lf Depth of fixityLfd Depth of fixity under dynamic loads

Lfs Depth of fixity under static loads

Md Dynamic Magnification Factor

Vs Shear wave velocity

Z Depth along the pile length

q Saturated soil density

1 Introduction

The lateral capacity and stiffness of piles are mainly

dependent upon characteristics of top soil layers

present within a few meter depths, which are generally

soft clay or loose sand that exhibit nonlinear behav-

iour. In addition to the static loads, piles are also

subjected to earthquakes, bomb blasts, operation of

machines and hammers, construction operations,

quarrying, fast moving traffic, wind, or loading due

to wave action of water, which are dynamic in nature

R. Ayothiraman (&)

Department of Civil Engineering, Indian Institute

of Technology Delhi, New Delhi 110016, India

e-mail: [email protected]

A. Boominathan

Department of Civil Engineering, Indian Institute

of Technology Madras, Chennai, India

1 3

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DOI 10.1007/s10706-012-9597-z


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and predominantly acting in lateral direction. Design

of pile foundations to resist lateral loads is primarily

based on the limiting deflection criteria considering

the safe operation of the superstructure. The deflection

may be amplified or de-amplified under dynamic

loads, which depends on the dynamic characteristics

of the soilpile system. Consequently, a carefulengineering analysis of lateral pile deflections under

anticipated static and dynamic loads become a crucial

step in the satisfactory design and performance of pile

foundations.

A number of rigorous mathematical solutions for

static soilpile interaction problems have been

reported in Poulos and Davis (1980). The dynamic

response analysis of pile foundations is a problem of

wave propagation in soil media, which has two

important aspects: wave reflection/refraction phenom-

ena and radiation damping, which is quiet complex tosimulate in the model. Additionally the development of

gaps at pilesoil interface during dynamic loading

increases the complexity. With these difficulties, a

comprehensive rigorous solution, which could take

into account all these aspects, is highly intricate.

However, in the last few decades, significant research

has been undertaken in understanding the fundamental

characteristics of pile foundation behaviour under

lateral loads. Various methods were developed assum-

ing linear soil behaviour, among which, the semi-

analytical elastic continuum approach (Novak1974;Novak and El-Sharnouby1983) is commonly used in

practice to determine the stiffness and damping

constants of single piles. However, the field and

laboratory investigations carried out on piles embed-

ded in clay, sand and sandy clay sites by various

authors (Prakash and Chandrasekaran 1973; Novak

1985; Blaney and ONeill 1986,1989; El-Marsafawi

et al.1992; Han and Vaziri1992; Nogami et al.1992;

Puri and Prakash1992; Crouse et al. 1993; Dou and

Byrne 1996; Halling et al. 2000; Anandarajah et al.

2001; Boominathan et al. 2002; Pak et al. 2003;Boominathan and Ayothiraman2005,2006,2007a,b)

show large difference between observed and estimated

values due to nonlinear behaviour of soil and gapping

at the pilesoil interface. Kuhlemeyer (1979) was one

of the first who attempted to study the dynamic soil

pile interaction adopting simple 2D finite element

method, but recently Wu and Finn (1997) and Sawant

and Dewaikar (1999) developed quasi-3D FEMand 3D

FEM respectively for analyzing the seismic/cyclic

response by using simple nonlinear models like bi-

linear model or equivalent linear models. In recent

years, Gazetas and Dobry (1984), Saha and Ghosh

(1986), Nogami et al. (1992), Badoni and Makris

(1996), El Naggar and Novak (1996), El Naggar

(1997), El Naggar and Bentley (2000), Arduino et al.

(2002), Mostafa and El-Naggar (2002) and Kucukar-slan and Banerjee (2003) developed models by

accounting nonlinear behaviour of soil and gapping.

Except a few models, the rest have mainly focused on

the estimation of dynamic constants (namely, stiffness

and damping constants) of the soilpile system. But, it

is well known that the depth of fixity is an important

parameter in the analysis/design of laterally loaded

piles (Konagai 2005), which is solely dependent on the

bending behaviour of piles. More recently, Kavvadas

and Gazetas (1993), Mylonakis (1995), Gazetas and

Mylonakis (1998), Mylonakis (2001), Gerolymos andGazetas (2005) developed simplified models to study

the kinematic bending behaviour of piles based on

BeamonDynamicWinklerFoundation (BDWF)

models with linear behaviour of soil. The use of these

simplified models is restricted to the situation where

linear soil behaviour prevails, and not appreciable to use

where the soil nonlinearity governs the pile response.

Makris and his co-workers approximately accounted

the soil nonlinearity in their simplified models to study

the pile response including bending behaviour of piles

subjected to seismic loading. Therefore, use of theirmodels to study the dynamic soilpile interaction to the

inertial loads (particularly, machine-induced dynamic

loads) may result in large discrepancy in the predicted

response. More importantly, the validity of these

simplified models needs to be re-looked.

Literature on the experimental studies exclusively

on model piles embedded in clays under lateral

dynamic loads and parametric studies are very limited

(Agarwal1973; Novak and Grigg1976; Hassini1990;

Finn and Gohl 1992; Georgiadis et al. 1992). This

available limited experimental data on dynamic pileresponse of piles in clay does not provide a good basis

for calibration and validation of the available nonlin-

ear models. Boominathan and Ayothiraman (2005,

2007a) carried out experiments on model piles in clay

subjected dynamic lateral loads and Boominathan and

Ayothiraman (2007a) proposed an equation to predict

the depth of fixity (depth of maximum bending

moment) under dynamic loads. Comparison of static

and dynamic bending behaviour of piles embedded in

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soft clay is also presented by Boominathan and

Ayothiraman (2007b) and found that the response of

piles under dynamic loads is largely amplified for piles

in soft clay. However, it is known that effect of soil

pile parameters on amplification of pile response

including depth of fixity is important to understand for

generalizing the solution. Therefore, there is a need toaddress this issue by carrying out experimental

investigations in understanding the bending behavior

of piles under static and dynamic lateral loads for piles

embedded in different consistencies of clay and

accordingly the controlled experimental investigations

were carried out in a laboratory. This paper presents

magnification of pile behaviour in clay under dynamic

lateral loads by comparing the static and dynamic

response measured from respective experiments.

2 Materials Used

2.1 Soil

Clay collected from a site in Chennai city was used in

the study. The physical and engineering properties of

the clay samples were determined through laboratory

tests as per standard procedures. The undrained shear

strength of clay was determined by conducting

laboratory vane shear test and unconfined compression

(UCC) test on remoulded soil sample prepared atdifferent consistency indices (Ic) of clay as per the

procedure recommended by ASTM standards. The

laboratory vane shear test was used for all consistency

indices, but the UCC test was used only for consis-

tency indices, Ic = 0.30 and 0.60. The summary of

index and engineering properties of clay are presented

in Table1. The soil is classified as Fat clay with sand

(CH) in accordance with D2487 (ASTM 2003). The

water content determined at different consistencies of

clay is also given in Table 1.

2.2 Pile

2.2.1 Pile Modelling and Fabrication

Aluminium pipes having an outer diameter of 25 mm

and wall thickness of 3 mm were used. Length to

diameter ratio (L/d) of pile (10, 20, 30 and 40) was

considered so as to cover the behaviour of both short

rigid piles and long flexible piles based on the relative

stiffness of the soilpile system. The various criterions

normally adopted to classify the rigid pile behaviour

and flexible pile behaviour is summarized in Boomi-

nathan and Ayothiraman (2007b) and accordingly it isfound that piles having L/d= 10 and 20 behaves as

rigid piles embedded in very soft and medium stiff

clay, but L/d= 20 as intermediate piles in medium

stiff clay. However piles having L/d[ 28 behave as

flexible piles at all consistencies of clay considered.

The model pile of required L/dratio was fabricated. A

conical driving shoe was fixed at the pile tip to

facilitate easy installation of piles and to prevent soil

plugging into the hollow model piles. A pile cap

weighing 3.1 N was attached to the pile head to

simulate the static vertical load on piles.

2.2.2 Pile Instrumentation and Calibration

Pile was instrumented using foil-type electrical strain

gauges having resistance 120 1.2 X fixed in quar-

ter-bridge arrangement along the pile length to record

the pile deflection and bending moment. The strain

gauges were fixed using adhesives at the marked

locations after cleaning the surface. The Teflon wires

Table 1 Properties of clay

Properties Value

Grain size distribution

Gravel (%) 1.0

Sand (%) 25.0

Silt (%) 32.5

Clay (%) 41.5

Specific gravity 2.54

Atterberg limits

Liquid limit (%) 74.0

Plastic limit (%) 26.0

Plasticity index (%) 48.0

Water content(%) for

Ic & 0.0 75

Ic = 0.15 67

Ic = 0.30 60

Ic = 0.60 45

Undrained shear strength (kN/m2

) for

Ic & 0.0 3.5

Ic = 0.15 9.3

Ic = 0.30 13.7

Ic = 0.60 31.6

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were connected to the strain gauges and taken through

the pile. A multi-meter is used to check the resistance

values to ensure proper connection. Then a thin elastic

membrane was wound at each location of strain

gauges to ensure the strain gauges are waterproof.

Details of a typical instrumented model pile are shown

in Fig.1. Instrumented model piles were calibrated byperforming simple bending test and the relation

between the bending moment and measured strain

values for each depth location on the pile were

correlated. The calibration constant of strain gauges

for all piles was found as 0.051 Nm/unit strain and

almost same for all strain gauges, except in few cases

with an error of1.0 %, which is negligible.

3 Experimental Setup and Instrumentation

3.1 Static Experiments

For pile foundations subjected to lateral loads, it is

observed from the literature that boundary effect is

more predominant within 10 times the pile diameter

from pile periphery (Narasimha Rao et al. 1998).

Hence, the static lateral load tests were conducted by

conventional method (rope and pulley arrangement) in

a model test container having circular cross-section of

diameter 600 mm and height of 1,200 mm. Two dial

gauges: one placed at pile cap measured the pile head

deflection and another one close to the soil surface

measured the ground level deflection. The instru-

mented pile measured the static bending momentvariation along the pile length.

3.2 Dynamic Experiments

In order to minimize the reflection of waves from

conventionally used rigid square tanks in lab experi-

ments, Elastic Half Space Simulation (EHSS) was

developed at Soil Dynamics laboratory of IIT Madras to

conduct dynamic lateral load tests on model piles, by

applying the analogy given by Stokoe and Woods

(1972). The simulated Elastic Half Space testing facilityconsists of a test tank of size 2.0 9 2.0 9 .5 m,

boundary element and an absorbing element, which is

shown in Fig.2. The tank wall was made of hollow

cement blocks of about 250 mm thickness. The bound-

ary element consists of mild steel basket in logarithmic

arc spiral shape and wrapped around with a geomem-

brane sheet, which separates the soil from the absorbing

element as well as maintains the constant moisture

content of clay. The geomembrane was made to the

required logarithmic arc shape with the mildsteel basket

by hot air welding.After welding, fiberglass coating wasapplied to bond the mild steel basket with welded

geomembraneand it was checked forwater leakage.The

space between the masonry wall and the boundary

element was tightly packed with sawdust. The efficacy

of the EHSS was verified and it is found that the

simulated EHSS is every efficient in minimizing the

wave reflection and representing the ideal elastic half

space conditions prevailing in the field (Boominathan

and Ayothiraman 2007b). A 100 N capacity electro-

dynamic exciter was attached to the pile cap such that it

produced steady-state sinusoidal dynamic lateral load.A 2 kN capacity Hottinger Baldwin Measurement

(HBM) load cell attached between the pile cap and

exciter was used to measure the load transferred to the

pile head and HBM Linear variable differentiable

transformers (LVDT) capable of measuring the differ-

ent range of displacements:2 and5 mmfixed onthe

pile cap were used to measure the time history of pile

head displacement (Fig.3). The instrumented model

pile measured the bending moment along the pile length

STRAIN GAUGEWIRES

100

750

5

100

50

100

CONICALSHOE

B

8

7

6

200

100

100

100

100

PILE CAP

ALUMINIUMPILE OF

25mm O.D.

4

3

2

1

A

OD = 25mm

ID = 19mmID

PILE WALL3 mm THICK

ALL DIMENSIONS ARE IN mm

DETAILS AT B

60

25

25

15

PILE WALL

STRAIN GAUGE

K=2.0R=120

STRAIN GAUGE

WIRES

DETAILS AT A

OD

Fig. 1 Typical instrumented model pile (after Boominathan

and Ayothiraman2007b)

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under dynamic lateral load. A data acquisition system

(DAS) consisting of HBM MGC plus multichannel

digital carrier frequency amplifiersystem and a PentiumII PC with DAS card and software GeniDAQ was

used to observe and measure automatically the load

transferred to the pile head, pile head displacement, and

the strain along the pile length.

4 Test Procedure

4.1 Clay Bed Preparation and Pile Installation

Clay was mixed with required amount of water to getthe particular consistency index. Uniformly mixed

clay was placed and hand-packed in the test tank in

several layers of 15 cm thick, and each layer was

tamped with a needle-like wooden template to remove

the entrapped air and 100 % degree of saturation was

ensured. Soil samples were collected from the test tank

(EHSS) at various depths as well as in the radial

directions for confirming the homogeneity of clay bed

as adopted by Katagiri and Imai (1994). Water content

test was carried out on collected soil samples and it

was found that the water content was almost constant,which ensured the homogeneity of clay.

Cross-hole test was carried out in the EHSS to

determine the shear wave velocity of clay (Vs). The

tests were conducted at various depths of EHSS: 0.25,

0.50, 0.75 and 1.00 m. The measured shear wave

velocity ranges from 39 m/s for very soft clay to

129.4 m/s for medium stiff clay. The dynamic shear

modulus of clay was evaluated using the equation:

Gs qV2s where q is the mass density of soil

determined in situ (EHSS) using cylindrical barrelmethod. The in situ density measured at different

depths of soil bed is nearly same, which confirms the

homogeneity of the prepared clay bed. The average

dynamic shear modulus of clay at different consisten-

cies of clay ranges from 3 to 36 MPa and it was found

that the shear modulus of clay remains almost constant

with the depth of EHSS, which also proves the

homogeneity of prepared clay bed.

The instrumented pile was installed into the

prepared homogeneous clay bed by gently pushing it

vertically. This generally disturbs and reduces the soilstrength in the vicinity of pile due to thixotropic nature

of clay and hence sufficient time must be allowed for

the soil to regain its strength. In the present study, vane

shear tests were carried out on remoulded clay samples

immediately after the disturbance and, 1, 2, 3, 4 and

5 h after the disturbance to examine the thixotropic

nature of clay. It is found that the remoulded clay

sample gains its strength with time and the strength

remain constant with time after 3.04.0 h for different

Fig. 2 Elastic half space simulation (EHSS)

10 11

12

1 2

3 46 5

7

9

8

SawDust

Clay

80 Test Tank

Not to Scale

(2.0 2.0 1.5 m)

1. Loading Frame

2. MS Angle

3. Electro-Dynamic Exciter

4. Load Cell5. Displacement Transducer (LVDT)

6. Pile Cap

7. Aluminium Model Pile

8. Strain Gauges

9. MS Basket covered with Impermeable Geomembrane

10. Excitation Amplifier

11. Multi-Channel Carrier Frequency Amplifier System

12. Data Acquisition System

Fig. 3 Dynamic lateral load test setup with Data Acquisition

System (after Boominathan and Ayothiraman2007b)

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consistencies of clay and hence, each test was carried

out after 5 h of installation of the pile.

4.2 Static Tests

The static lateral load was applied in increments up to

ultimate stage and the lateral deflection of the pile wasmeasured. Strain gauge readings were recorded for

each increment of load by the DAS. Vertical settle-

ment of pile was also measured by the dial gauges

positioned at the pile cap for few tests and was found to

be negligible. The tests were conducted on piles with

length to diameter ratios (L/d) of 10, 20, 30 and 40,

embedded at different consistencies of clay.

4.3 Dynamic Tests

Steady-state sinusoidal lateral vibration was applied tothe pile head using the electro-dynamic exciter. The

magnitude of the load was controlled and varied using

theexcitation amplifier.Undertheconstant magnitude of

dynamic load, the frequency of excitation (f) was varied

from 2 to 50 Hz. The load transferred to thepilehead, the

pile head displacement, anddynamic strainalong the pile

length was measured using the data acquisition system.

An AGILENT digital storage oscilloscope was used to

cross- check the load and amplitude measurements.

After the completion of one test on pile, the pile was

pulled out from the EHSS. The clay was excavated forabout 30 cm (12 times pile diameter) distance from the

center of the pile and up to 10 cm (4 times pile diameter)

below the pile tip. The clay was refilled in the EHSS with

same moisture content so as to ensure and maintain

constant consistency of clay through out the testing

phase. As reported by Prakash and Puri (1998), the

magnitude of unbalanced dynamic forces resulting from

machineries is usually in 2030 % of the static forces.

Hence the magnitude of dynamic forces considered in

the study (F0: 7, 14, 21, and 30 N) was arrived from the

safe/working static forceson thepiles.Tests were carriedout at these magnitudes of lateral vibration.

5 Analysis and Discussion of Results

5.1 Static Pile Response

Lateral loaddeflection behaviour is measured from

static experiments and typical behaviour is shown in

Fig.4for pile at medium stiff clay (Ic = 0.60). It is to

be reminded here that the static lateral load tests were

conducted with an objective of determining the

magnification of pile response to dynamic lateral load.

It is seen from Fig.4that there exists an ambiguity of

determining the pile deflection corresponds to a load

equal to dynamic load (F0 = 730 N). Therefore, the

loaddeflection curves are expanded up to the range

of magnitude of dynamic load and the expandedcurves are shown in Fig.5. It is depicted from the

figure that the loaddeflection curves are steadier

within the dynamic load compared to the load

deflection curve shown up to the ultimate load. The

static deflection values obtained from this figure for

different piles embedded at various consistencies were

measured to determine the dynamic amplification

factor under dynamic load. A typical variation of static

bending moment of piles with L/d= 10 at Ic = 0.30

and L/d= 40 at Ic = 0.15 and Ic = 0.60 plotted

against the normalized depth (z/d) is shown inFig.6. The normalized depth (z/d) is the ratio of the

depth (z) at which strain is measured to the pile

diameter (d). Though the bending moment was

measured at different load intervals up to the ultimate

load, the BM up to applied maximum dynamic load is

only given with an intention for comparison with the

bending moment under dynamic loads. It is observed

from Fig.6 that the bending moment increases

gradually with depth to the maximum value and then

0 4 8 12 16

Deflection, mm

0

350

700

1050

1400

LateralLoa

d,

N

Ic = 0.60; Ep/Gs = 1983

L/d = 10

L/d = 20

L/d = 30

L/d = 40

Fig. 4 Loaddeflection curves for different pile length atIc = 0.60

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tends to zero, close to or above the pile tip. It is found

that the maximum static bending moment occurs at a

depth of about 415 times the pile diameter from thesurface of the clay bed for piles embedded at different

consistencies of clay.

5.2 Dynamic Pile Response

5.2.1 Frequency Response Curve

The compliance (i.e. the ratio of the displacement to

the force applied or also known as inverse of stiffness)

at all dynamic force values were calculated and a

typical compliance versus frequency plot for a pile

(L/d= 30) embedded in soft clay (Ic = 0.15) is

presented in Fig.7. For a typical linear system, the

displacement is linearly proportional to the force and

hence the variation of compliance with frequency at

all forces must become a single curve. It is very clear

Deflection, mm

0

15

30

45

60

LateralLoad,

N

Ic = 0.15; Ep/Gs = 10319

L/d =10

L/d = 20

L/d = 30

L/d = 40

(a)

0.0 0.2 0.3 0.5 0.6

0.00 0.10 0.20 0.30

Deflection, mm

0

15

30

45

60

LateralLoad,N

Ic = 0.30; Ep/Gs = 4275

L/d = 10

L/d = 20

L/d = 30

L/d = 40

(b)

Fig. 5 Expanded loaddeflection curve for different pile length

ata Ic = 0.15 and b Ic = 0.30

8

Bending Moment, N - m

0

8

16

24

32

40

NormalizedDepth(z/d)

Ic = 0.15; L/d=40

Fo=7N

Fo =14N

Fo =21N

Fo =30N

(b)


0

8

16

24

32

40


Ic = 0.60; L/d=40

Fo =7N

Fo =14N

Fo =21N

Fo =30N

(c)

0 2 4 6

0 4 8 12 16

0 2 4 6


0

5

10


Ic = 0.30; L/d=10

Fo =7 N

Fo =14 N

Fo =21 N

Fo =30 N

(a)

Fig. 6 Typical variation of static bending moment with

normalized depth for a pile a L/d = 10 at Ic = 0.30; b L/d =40 at Ic = 0.15; c L/d = 40 at Ic = 0.60

Geotech Geol Eng (2013) 31:447461 453

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from Fig.7 that the occurrence of distinguishable

compliance curves and peaks at different natural

frequencies prove the prevalence of nonlinear

response of the soil particularly in the low frequency

to resonance region. A similar finding was also

reported by Badoni and Makris (1996) based on the

nonlinear spring-dashpot model. However, it isobserved from the present study that for piles embed-

ded at medium stiff clay, compliance at all magnitudes

of force tend to merge and the peaks occur more or less

at one frequency, which indicates that the degree of

nonlinearity decreases with increase in the modulus of

clay.

5.2.2 Natural Frequency

The natural frequency of the soilpile system (fn)

obtained from the frequency response curves atvarious consistencies of clay varies from 11.5 to

30.0 Hz. The variation of natural frequency of the

soilpile system with modulus ratio (Ep/Gs) at low

magnitude of force F0 = 7 N is shown in Fig. 8. The

modulus ratio is defined as the ratio of Youngs

modulus of the pile material to the maximum dynamic

shear modulus of clay. Fig. 8clearly indicates that the

natural frequency of the soilpile system increases

significantly with the decrease in the modulus ratio

(Ep/Gs), i.e. with an increase in the shear modulus of

clay. This is mainly attributed to the increase ofstiffness of the soilpile system with an increase in the

shear modulus of clay. However, at very high modulus

ratio, i.e. for piles embedded in very soft clay

(Ic & 0.0), the variation of natural frequency with

length to diameter ratio of piles is constant, which

reflects that the soilpile system vibrates practically atsame frequency irrespective of the pile length. This is

mainly attributed to the stiffness degradation resulting

from the strong nonlinear behaviour at very soft

consistency of the clay. It can also be depicted from

the figure that the measured natural frequency of the

soilpile system is about 30 Hz for the pile with L/d=

40, embedded in medium stiff clay. The natural

frequency of full-scale soilpile system measured by

Puri and Prakash (1992) ranges from 27.5 to 34 Hz, for

the pile with L/d= 42 embedded in stiff clay. This

indicates that the natural frequencies obtained fromthe lab experiments conducted on model piles nearly

simulate the field conditions.

5.2.3 Dynamic Magnification Factor

The static deflection of the pile corresponding to the

magnitudes of dynamic load was obtained from the

loaddeflection curve and the dynamic magnification

factor, (Md), i.e. the ratio of dynamic displacement

amplitude to the static deflection for the respective

lateral load was evaluated. A typical variation ofdynamic magnification factor with frequency for a pile

(L/d= 20)embedded in soft clay (Ic = 0.15)isgivenin

Fig.9. The figure shows that for the piles embedded in

soft clay, the peak amplitude is magnified by about 1.8

times than the static displacement at low magnitude of

the dynamic load, F0 = 7 N and about 0.7 times at

F0 = 30 N. It indicates the reduction in the rate of

increase of magnification with an increase in the

magnitude of dynamic load due to the occurrence of

0 10 20 30 40 50

Frequency, Hz

0.000

0.005

0.010

0.015

Compliance,

mm/N

Ic = 0.15; L/d = 30

Fo = 7N

Fo = 14N

Fo = 21N

Fo = 30N

Fig. 7 Typical compliance versus frequency plot for a pile with

L/d= 30 at Ic = 0.15

1000 10000 100000

Modulus Ratio (Ep / Gs)

0

10

20

30

40

NaturalF

requency,

Hz

L/d = 10

L/d = 20

L/d = 30

L/d = 40

Fig. 8 Measured natural frequency of soilpile system at

different consistencies of clay

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large hysteretic damping resulting from the strong

nonlinear behaviour of soft clay. This finding isconsistent with the observations made on all piles. The

variation of peak dynamic magnification factor with the

modulus ratio for piles withL/d= 10 and 40at low and

high magnitude of dynamic load (F0 = 7 and 30 N) is

given in Fig.10. The figure shows that for the piles

embedded in very soft clay, the peak amplitude is

magnified by about 7 times the static displacement at

low magnitude of the dynamic load, F0 = 7 N and

about 5 times at F0 = 30 N. It is very interesting to

observe from the figure that the peak dynamic magni-

fication factor drastically decreases with the decrease inthe modulus ratio (i.e. with an increase in the shear

modulus of clay) for all piles. This is attributed to the

combined effect of increase in the stiffness and damping

of the clay. This shows that even slight changes in

consistency of clay (natural moisture content of clay) in

field by any suitable method, the DMF could be reduced

significantly. It could also be inferred from Fig. 10that

the reduction in the rate of increase of magnification

with an increase in themagnitude of dynamic load dueto

the occurrence of large hysteretic damping resulting

from strong nonlinear behaviour of very soft clay (highmodulus ratio). However, as the consistency increases

from soft to medium stiffclay, theeffect of magnitude of

dynamic load on the rate of reduction of peak magni-

fication factor decreases.

5.2.4 Bending Moment Profile

It is found from the experimental study that the

maximum dynamic strain/BM occurs at fundamental

natural frequency of the soilpile system (Boomina-

than and Ayothiraman2007a). It is also found that thefrequency dependency of dynamic strain or bending

moment (BM) is more predominant at depths close to

depth of maximum BM. This is due to the fact that

large inertial forces are mobilized near the resonance

region because of large amplitude of vibration. The

occurrence of maximum dynamic BM at the funda-

mental frequency of the system is also reported based

on various studies: finite element studies by Krishnan

et al. (1983) and Beamon DynamicWinklerFoun-

dation (BDWF) approach by Kavvadas and Gazetas

(1993) and Mylonakis (2001).The BM under dynamic load was obtained from the

measured strain at the natural frequency of the soil

pile system by multiplying the calibration factor

obtained from calibration of strain gauges. The typical

variation of BM with normalized depth for a piles with

L/d= 10 at Ic = 0.30 andL/d= 40 at Ic = 0.15 and

Ic = 0.60 is given in Fig.11. It is worthy of note from

Fig.11a&b that the dynamic BM towards the pile tip

does not attain zero, because of vibration of pile even

near the pile tip. But, it is seen from Fig. 6a that the

BM under static lateral load attains maximum andreduces towards zero near the pile tip. This indicates

that even the lower parts of the pile can affect the pile

head response due to dynamic nature of lateral load.

However, it is inferred from Fig. 11c that for long

piles embedded in medium stiff clay, the BM reaches

zero value well above the pile tip. This leads to a

conclusion that as the stiffness of clay increases, effect

of inertial interaction due to dynamic nature of loading

reduces on the behaviour of piles.

0 10 20 30 40 50

Frequency, Hz

0.0

0.5

1.0

1.5

2.0

DynamicMagnificationFactor

Ic = 0.15; L/d = 20

Fo = 7N

Fo = 14N

Fo = 21N

Fo = 30N

Fig. 9 Typical dynamic magnification factor versus frequency

plot for L/d = 20 at Ic = 0.15

1000 10000 100000


0

2

4

6

8

PeakDynamicMagnificationFactor

L/d = 10; Fo = 7 N

L/d = 40; Fo = 7 N

L/d = 10; Fo = 30 N

L/d = 40; Fo = 30 N

Fig. 10 Peak dynamic magnification factor versus modulus

ratio plot for L/d= 10 and 40

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5.2.5 Maximum Bending Moment

In general, it is known that the pile deflections and

bending moments are magnified under dynamic load.

To determine the magnification of bending moment,

the bending moment profile obtained for dynamic

lateral loads is compared with the bending momentprofile obtained for static loads in respective soilpile-

loading conditions. A typical bending moment profile

for a pile with L/d= 40 embedded in medium stiff

clay and subjected to a load of magnitude, F0 = 30 N

is shown in Fig. 12. It can be easily inferred from the

figure that the bending moment under dynamic lateral

load is magnified at all depths. Also maximum

dynamic BM occurs at much deeper depth, compared

to depth of maximum static bending moment, which

indicates that the depth of fixity is amplified under

dynamic load.The maximum BM ratio, i.e. the ratio of maximum

dynamic BM to the maximum static BM calculated for

all piles embedded at different consistencies of clay

are presented in Table 2. It is found from the table that

the maximum BM moment under dynamic load is

always magnified for all tested piles embedded at very

soft to medium stiff consistencies of clay. It could be

seen from Table2that the BM under dynamic loads is

magnified by about 1.65 times the static BM for piles

embedded in very soft clay. The maximum BM ratio

of long piles is much higher than that of short piles andthe maximum dynamic BM is magnified as high as

about 9 times for piles embedded at a consistency

index,Ic = 0.30. The magnification of maximum BM

under dynamic load is mainly because of large inertial

force mobilized and passive resistance along the

increased active pile length under dynamic loads.

The variation of maximum bending moment ratio with

pile length and modulus ratio is shown in Fig. 13. It

can be easily depicted from the figure that the

maximum bending moment ratio increases signifi-

cantly with an increase in pile length and the modulusof clay (i.e. as the modulus ratio reduces) up to the

consistency index, Ic = 0.30. Figure13 also shows

that the maximum dynamic BM is magnified by about

1.54 times the maximum static BM for short piles

(L/dB 20), whereas for long piles (L/d= 30 and 40),

the maximum dynamic BM is magnified significantly

by about 9 times. It is due to the fact that larger passive

resistance is mobilized along the increased active

length of the pile under dynamic loads. The rate of

magnification of maximum bending moment under

dynamic load reduces at high magnitude of dynamic

load and for piles embedded in medium stiff clay

because of the higher rate of increase in the maximum

static bending moment. Similar observation on mag-

nification of bending moment under cyclic/dynamic

loading were reported by many authors (Kagawa and


0

2

4

6

8

10


Ic = 0.30; L/d=10; f = 18 Hz

Fo=7N

Fo =14N

Fo =21N

Fo =30N

(a)


0

8

16

24

32

40

NormalizedDepth(z

/d)

Ic=0.15; L/d=40; f=22Hz

Fo=7N

Fo =14N

Fo =21N

Fo =30N

(b)

0 5 10 15 20 25

0 10 20 30 40

0 40 80 120


0

8

16

24

32

40


Ic = 0.60; L/d=40; f = 30 Hz

Fo=7N

Fo =14N

Fo =21N

Fo =30N

(c)

Fig. 11 Typical variation of dynamic bending moment with

normalized depth of pileaL/d = 10 at Ic = 0.30; bL/d = 40atIc = 0.15; c L/d = 40 at Ic = 0.60

456 Geotech Geol Eng (2013) 31:447461

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Kraft 1980; Krishnan et al. 1983; Kavvadas and

Gazetas1993; Sawant and Dewaikar1999) based on

analytical/semi-analytical/numerical studies. Thus,

the results of this study based on experimental

investigation on instrumented piles provide a good

basis for validating these analytical/semi-analytical/

numerical models.

5.2.6 Depth of Fixity

Depth of fixity (Lf) is defined as length of pile

measured from the ground surface at which bending

moment is maximum. It should also be noted that the

depth of fixity is very important for long flexible piles

only. Hence, in the present study, it is assumed that the

depth of maximum bending moment measured for

long piles (L/d= 30 and 40) are discussed. The

variation of depth of fixity with modulus ratio for all

piles subjected both static and dynamic load is shownin Fig.14. It is clearly seen from the figure that the

depth of fixity under dynamic load (Lfd) varies from 6

to 24 times the pile diameter, but for static loads the

effective pile length (Lfs) ranges from 4 to 15 times the

pile diameter from the surface of the clay bed. This

indicates an increase of depth of fixity length under

dynamic loads. This is mainly because of large inertial

components mobilized under dynamic loads near

resonance that need to be transferred to deeper depth,

which necessitates the requirement of additional pile

length under dynamic loads. It can be concluded here

that many piles, which exhibit a flexible (length-

independent) static behaviour cannot be considered as

flexible under dynamic loads at frequencies near

resonance. Similar observation was reported based on

numerical studies by Velez et al. (1983) and Krishnan

et al. (1983). It is found that the depth of fixity isalways lesser than the effective pile length (i.e. pile

length from surface at which deflection is zero) (Dou

and Byrne 1996; Boominathan and Ayothiraman

2007a). There is no equation available in literature

for estimation of depth of fixity under dynamic loads,

but there are equations for estimating effective pile

length under static and dynamic loads based on

analytical/semi-analytical methods (Krishnan et al.

1983; Velez et al.1983; Gazetas1991). For compar-

ison, it is assumed that the depth of fixity is approx-

imately equal to effective pile length and results ofpresent study are compared with equations reported in

literature. Figure14presents the variation of normal-

ized depth of fixity (i.e. ratio of depth of fixity, Lfto

pile diameter, d) with modulus ratio. It is found from

Fig.14 that the existing equations fairly predict the

depth of fixity under static lateral loads. It is also

inferred from the figure that though these equations

estimate depth of fixity under dynamic loads with a

fair accuracy for piles in medium stiff/stiff clay, they

0 100 200

Bending Moment, N-m

0

10

20

30

40


L/d = 10 (Dynamic)

L/d = 20 (Dynamic)

L/d = 30 (Dynamic)

L/d = 40 (Dynamic)

L/d = 10 (Static)

L/d = 20 (Static)

L/d = 30 (Static)

L/d = 40 (Static)

Fig. 12 Comparison of static and dynamic bending moment

profile for piles in medium stiff clay

Table 2 Maximum bending moment ratio

Modulus

ratio

L/

d

Maximum BM ratio

F0 = 7 N F0 = 14 N F0 = 21 N F0 = 30 N

24278 10 1.45 1.38 1.48 1.53

20 1.25 1.31 1.37 1.34

30 1.65 1.49 1.42 1.24

40 1.38 1.33 1.27 1.18

10319 10 2.23 1.96 1.67 1.68

20 2.13 1.69 1.57 1.39

30 4.03 3.43 3.32 2.88

40 3.95 3.56 3.46 2.92

4275 10 3.70 4.07 4.77 4.95

20 3.64 3.90 3.95 4.03

30 8.79 7.70 7.32 6.81

40 7.95 7.58 7.53 7.09

1983 10 3.16 3.08 3.05 3.14

20 3.16 3.15 3.22 3.66

30 7.13 6.86 6.66 6.64

40 6.95 6.23 6.07 5.99

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significantly underestimate the depth of fixity for pilesin soft to very soft clay. Hence the following empirical

equation is proposed by curve fitting method and

multiple regression analysis for estimation of depth of

fixity under dynamic loads:

Lfd

d1:24

Ep

Gs

0:291

whereLfdis the depth of fixity under dynamic lateral

load,dis the pile diameter,Epis the Youngs modulus

of pile material,Gsis the low-strain shear modulus of

clay. The regression coefficient (R2

) of 0.8484 wasobtained for the above equation. Also, it is to be noted

that the above equation is developed based on the

experimental results of hollow piles and as a function

of outer pile diameter and hence respective correction

factor must be applied when it is used for solid piles.

The depth of fixity ratio, i.e. the ratio of depth of

fixity length under dynamic loads (Lfd) to depth of

fixity under static loads (Lfs) is calculated for long piles

embedded at different consistencies of clay and its

variation with modulus ratio is shown in Fig.15. It is

seen from the figure that the depth of fixity underdynamic loads is 1.6 times higher than the effective

pile length under static loads for piles in very soft clay,

whereas 22.5 times higher for piles in medium stiff

clay. Although the depth of fixity under dynamic loads

is less for piles in medium stiff to stiff clay compared

to piles in soft clay, the depth of fixity ratio, i.e. the

magnification of depth of fixity under dynamic loads is

larger for piles in medium stiff clay. This could be due

to the fact that the depth of fixity of piles in soft clay

under static loads increases drastically and thus

bringing down the magnification effect for pilesembedded in very soft clay. The effective pile length

(depth of fixity) ratio determined using empirical

equations proposed by Krishnan et al. (1983) and

Velez et al. (1983) is also plotted in Fig.15. It is found

from the figure that though these equations show

similar trend, i.e. reduction of depth of fixity ratio with

increase of modulus ratio, they underestimate the

magnification of depth of fixity/effective pile length

under dynamic loads for all consistencies of clay.

Hence the following empirical equation is proposed by

multiple regression analysis for estimation of ratio ofeffective pile length under dynamic and static lateral

loads:

Lfd

Lfs5:91

Ep

Gs

0:122

whereLfsis the depth of fixity under static loads, and

other parameters are as defined earlier. The regression

coefficient (R2) of only 0.485 was obtained for the

above equation, which means that the above equation

Length to Diameter Ratio (L/d)

0

4

8

12

Maximu

mBMRatio

Ic=0.60; Ep/Gs= 1983

Fo = 7 NFo = 14 NFo = 21 NFo = 30 N

(a)

0 10 20 30 40 50

1000 10000 100000


0

5

10

MaximumBMRatio

L/d = 10

L/d = 20

L/d = 30

L/d = 40

(b)

Fig. 13 Effect of a pile length and b modulus ratio on

maximum bending moment ratio

1000 10000 100000 1000000

Modulus Ratio (Ep/Gs)

0

10

20

30

40

Norm.D

epthofFixity

L/d = 30 (Dynamic)

L/d = 40 (Dynamic)

L/d = 30 (Static)

L/d = 40 (Static)

Proposed Eqn (1)

Gazetas (1991) (dynamic)

Krishnan et al. (1983) (dynamic)

Velez et al. (1983) (dynamic)

Krishnan et al. (1983) (static)

Velez et al. (1983) (static)

Broms (1964) (static)

Fig. 14 Effect of modulus ratio on depth of fixity under static

and dynamic lateral loads

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of maximum bending moment, effective pile length and

the proposed empirical equations may be verified further

and modified accordingly as and when a more reliable

data is made available based on either centrifuge or full-

scale experiments on instrumented piles.

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