Numerical Study of Ground Vibration Due to Impact Pile Driving

Proceedings of the Institution of Civil Engineers

Geotechnical Engineering 167 February 2014 Issue GE1

Pages 28–39 http://dx.doi.org/10.1680/geng.11.00094

Paper 1100094

Received 09/10/2011 Accepted 04/04/2012

Published online 03/09/2012

Keywords: dynamics/mathematical modelling/piles & piling

ICE Publishing: All rights reserved

Geotechnical EngineeringVolume 167 Issue GE1

Numerical study of ground vibration due toimpact pile drivingKhoubani and Ahmadi

Numerical study of groundvibration due to impact piledrivingj1 Ali Khoubani MSc

Senior Geotechnical Engineer, Department of Civil Engineering,Sharif University of Technology, Tehran, Iran

j2 Mohammad Mehdi Ahmadi PhDAssociate Professor, Department of Civil Engineering, SharifUniversity of Technology, Tehran, Iran

j1 j2

Ground vibration due to pile driving is a long-lasting concern associated with the foundation construction industry. It

is of great importance to estimate the level of vibration prior to the beginning of pile driving, to avoid structural

damage, or disturbance of building occupants. In this study, an axisymmetric finite-element model that utilises an

adaptive meshing algorithm has been introduced, using the commercial code Abaqus, to simulate full penetration of

the pile from the ground surface to the desired depth by applying successive hammer impacts. The model has been

verified by comparing the computed particle velocities with those measured in the field. The results indicate that the

peak particle velocity at the ground surface does not occur when the pile toe is on the ground surface; as the pile

penetrates into the ground, the particle velocity reaches a maximum value at a critical depth of penetration. Some

sensitivity analyses have been performed to evaluate the effect of soil, pile and hammer properties on the level of

vibrations. The results show that increase in pile diameter, hammer impact force, soil–pile friction and reduction in

soil elastic modulus can increase the peak particle velocity.

NotationD pile diameter

d depth of penetration of pile

E elastic modulus

e deviatoric eccentricity

L distance between vibration source and reflective origin

of Rayleigh waves at ground surface

Lmin smallest element dimension in mesh

p pressure

r radial distance from pile centreline

VP velocity of compression wave

VR velocity of the Rayleigh wave

VS velocity of shear wave

Æ Rayleigh mass proportional damping

� Rayleigh stiffness proportional damping

˜t stable time increment

¨ angle of deviatoric stress plane axes

� coefficient of friction

� Poisson’s ratio

r density

� shear stress

�crit critical shear stress

� soil friction angle

� damping ratio

�max damping ratio in mode with highest frequency

ømax highest frequency of model

øn natural frequency associated with 95% of modal mass

of model

ø1 first natural frequency of model

1. IntroductionPile driving is an age-tested method of constructing foundations

where adequate ground support is not directly available. However,

it is also a source of negative environmental effects. Noise and

air pollution are the most commonly expressed concerns, but

these are also relatively easily alleviated. By contrast, vibrations

originating from impact pile driving are both difficult to deter-

mine beforehand and costly to mitigate, while potentially having

serious adverse effects on adjacent structures and their founda-

tions, as well as on vibration-sensitive installations and occupants

of buildings (Massarsch and Fellenius, 2008).

During recent decades, several investigations have been per-

formed to determine the characteristics of pile driving vibrations.

One common method of handling vibrations is to perform field

measurements in terms of the peak particle velocity (PPV) during

28

pile driving, to determine the soil attenuation properties. The

PPV is the maximum velocity that a soil particle experiences

during the driving of a pile from the ground surface to the desired

depth. The attenuation properties are then used in vibration

attenuation equations to estimate the distance from the vibration

source beyond which structural damage is unlikely to occur for

that specific site. Extensive work in this area has been carried out

by Wiss (1981), Woods and Jedele (1985), Uromeihy (1990),

Massarsch and Fellenius (2008).

As an alternative method, numerical analysis can be performed to

evaluate the severity of vibrations prior to the beginning of a pile

driving project. In this context, Ramshaw et al. (2000) developed a

finite-element–infinite-element model using the commercial code

Abaqus to predict the time history of the vibration velocity due to

impact and vibratory pile driving. Elastic behaviour was assumed

for both the pile and the soil. The overall problem was broken

down into three separate stages: a hammer impact model to

simulate the force imposed onto the pile head; a model of the

propagation of the impact waves down the pile shaft (soil response

modelled by springs and dashpots); and imposition of the displace-

ment–time functions on the boundary of a model of the surround-

ing ground to simulate the outgoing ground waves. The results of

vibratory pile driving and impact pile driving were in acceptable

agreement with field data. Since this modelling was time consum-

ing, Selby (2002) used a harmonic computation for a limited

finite-element mesh, which was executed rapidly on a PC using the

commercial code Strand7. The results for vibratory pile driving

were given in terms of the radial and vertical components of

ground vibration that gave acceptable correlations with site data.

Madheswaran et al. (2005) used the finite-element code Plaxis to

investigate ground acceleration time history due to impact pile

driving in sand. The pile and the soil were modelled by means of

elastic and the elastic–plastic models respectively. Absorbent

boundaries were used at the bottom and side boundaries to avoid

wave reflection. The predicted vertical peak acceleration was in

close agreement with field data, but the predicted radial peak

acceleration was more than 20% greater than field data. Later,

they used a similar model to study the effect of concrete-filled

trenches on the screening of ground peak particle acceleration

(PPA) due to impact pile driving. Optimum trench dimensions,

concrete strength and distance from source of vibration to trench

were proposed, so that the trench was most effective in screening

of vibrations for that specific case study (Madheswaran et al.,

2009).

Masoumi et al. (2007) developed a linear coupled finite-element–

boundary-element approach for the prediction of free field

vibrations in terms of PPV due to vibratory and impact pile

driving. A linear elastic constitutive behaviour was considered for

the soil and the pile. The effect of soil stratification on the ground

vibration for the case of a soft layer on a stiffer half space was

also investigated. Although the prediction of near-field vibrations

was satisfactory, the far-field vibrations were overestimated.

Later, both the non-linear constitutive behaviour of the soil in the

vicinity of the pile and the resulting non-linear dynamic inter-

action between the pile and the soil were accounted for. It was

shown that considering non-linear behaviour for the soil adjacent

to the pile will lead to a better estimation of the level of vibration

(Masoumi et al., 2009).

Recently, Serdaroglu (2010) developed a non-linear finite-element

model using Abaqus to study impact pile driving vibrations in

saturated cohesive soils. An artificially damped non-reflecting

boundary consisting of several soil layers with different damping

ratios was defined at the boundary of the model to minimise the

reflection of stress waves. The Coulomb frictional contact was

defined at the soil–pile interface. This model underestimated the

measured peak vertical and radial velocities.

In all of these analyses, the pile was initially placed at a specific

depth, and hammer impact was then applied on the pile head; so

that soil deformations around the pile and contact stresses

between the pile and the soil were not realistic. In the current

study, penetration of the pile from the ground surface to the

desired depth is modelled using the commercial code Abaqus.

This model takes into account the effects of plastic deformations

in the soil adjacent to the pile and large slip frictional contact

between the pile and the soil on the amplitude of vibrations. The

model also enables vibrations to be predicted at all depths of

penetration of the pile. Moreover, sensitivity analysis was

performed to determine the effect of hammer, pile and soil

properties on the level of vibrations.

2. Mechanism of wave propagation due topile driving in homogeneous soils

Just as the support of piles comes about through two mechanisms

– skin friction and end bearing – seismic waves are generated by

piles through the same two mechanisms. Shear waves (S-waves)

are generated along the surface or skin of the pile by relative

motion between the pile and the surrounding soil as the pile is

driven. Shear waves enter the soil first near the upper contact point

between soil and pile. As the compression waves in the pile travel

down the pile, the shear waves propagate out from the pile shaft

on a conical wavefront (Figure 1). The cone angle is quite shallow,

because the compression wave velocity in the pile is much larger

than the shear wave velocity in the soil; so, as an approximation,

the wavefront emanating from the pile shaft can be assumed to be

cylindrical in homogeneous soils. The direction of wave travel is

perpendicular to the wavefront – in other words, radially away

from the pile for a cylindrical wavefront. Particle motion in this

wavefront is parallel to the pile, as shown by the arrows represent-

ing particle motion in Figure 1 (Woods and Sharma, 2004).

At the tip of the pile, each impact causes a volumetric displace-

ment in the ground, which results in both primary waves

(P-waves, also called compression waves) and shear waves

travelling outwards from the pile tip (here idealised as a spherical

cavity; Figure 2). Both P-waves and S-waves travel outwards

29


Numerical study of ground vibration dueto impact pile drivingKhoubani and Ahmadi

from the tip of the pile on spherical wavefronts, decaying as the

first power of distance. The P-wave travels faster than the S-wave,

so its wavefront precedes the shear wave at any given point in the

ground. When the P-wave and S-wave encounter the surface of

the ground, part of their energy is converted to surface waves

(Rayleigh waves, or R-waves), and part is reflected back into the

ground as reflected P- and S-waves. The Rayleigh wave is the

most damaging to nearby structures. Even if the energy is

inserted at a depth in the ground, the Rayleigh wave develops

quickly at the surface, as shown in Figure 3. The newly formed

R-wave then travels along the surface with the characteristic of

Rayleigh waves, so some distant surface locations will experience

three waves: P-wave, S-wave and R-wave. The amplitude of the

energy associated with each wave will depend on many factors,

including the depth of the pile into the ground, the stiffness of the

ground, the uniformity of the ground, and the energy delivered to

the pile (Woods and Sharma, 2004).

3. Numerical simulation of pile driving

3.1 Mesh and geometry

An axisymmetric model was assumed about the centreline of the

pile. The length and the diameter of the pile were 10 m and 0.5 m

respectively. Both the pile and the soil were discretised into four-

node quadrilateral elements, with reduced integration and hour-

glass control. Soil finite-elements were biased radially towards

the pile, and soil infinite-elements were placed at the boundaries

(Figure 4). During dynamic steps the infinite-elements introduce

additional normal and shear tractions on the finite-element

boundary that are proportional to the normal and shear compo-

nents of the velocity of the boundary. These boundary damping

constants are chosen by Abaqus to minimise the reflection of

compression and shear wave energy back into the finite-element

mesh (Hibbitt et al., 2010). The infinite-elements provide perfect

transmission of energy out of the mesh just for the case of plane

body waves impinging orthogonally on the boundary in an

isotropic medium. To reduce the effect of the probable reflected

waves on the PPV value, the dimensions of the finite-element

mesh were extended 2 m beyond the distance for which the PPV

values were calculated.

Hammer impact

Particle motion(compression in pile)

Shearwave front

Particle motion(shear in soil)

Ray

Transfer frompile to soil byfriction/shear

Figure 1. Generation mechanism of shear waves due to soil–pile

friction (Woods and Sharma, 2004)

Hammer impact

S-wave

Ray

P-wave

S-wave

R-wave

Reflected wave

Figure 2. Combination of seismic waves resulting from impact

pile driving (Woods and Sharma, 2004)

V 2P � V 2

R�

V dRr �

Rayleigh wave

d

SourceL d r� �� 2 2 � d� V 2

R

V 2P � V 2

R

1 �

Figure 3. Distance between source and reflective origin of

Rayleigh waves at ground surface (Dowding, 1996)

30



Numerical simulation of pile driving using the Lagrangian–

Eulerian analysis introduced in Abaqus is feasible only by

considering a conical end for the pile, and a gap between the soil

elements and the axis of symmetry of the model (Figure 5).

When the cone angle is larger than 908, the pile cannot be

pressed into the soil in the numerical analysis using Abaqus,

owing to numerical convergence and mesh distortion. On the

other hand, as Sheng et al. (2005) stated, ‘the numerical analysis

for cone angles less than 608 requires very small time steps and

the execution time will be increased.’ They used a cone angle of

608 in their numerical analyses. In this study, the same cone angle

was used.

As mentioned before, a gap is placed on the axis of symmetry.

This causes the pile to push the soil elements sideways and

downwards, and open its way into the ground. Considering a

smaller gap leads to a better simulation of the real condition;

however, using a gap with a diameter less than a specific value

terminates the analysis owing to excessive distortion of the soil

elements. The required minimum gap distance to maintain

numerical stability is dependent on hammer impact force and

cone angle. In this study, a gap of 10 mm seemed adequate for

most of the analyses. For a pile with a diameter of 500 mm, this

gap corresponds to an area equal to 0.16% of the pile toe area,

which is not a significant error.

3.2 Material properties

Precast concrete piles are commonly used as driven piles. Since

the elastic modulus of the precast concrete (typically about

30 GPa) is much larger than that of the surrounding soil, and

calculation of vibrations in the surrounding soil is the subject of

this study, the pile was considered as a rigid body. A rigid body

is a collection of nodes, elements and/or surfaces whose motion

is governed by the motion of a single node, called the rigid body

reference node. The motion of a rigid body can be prescribed by

applying boundary conditions at the rigid body reference node

(Hibbitt et al., 2010). A reference node was introduced at the pile

head. Applying hammer impact on the pile head is a wave

problem, but here the transmission of the compression wave

along the pile shaft is neglected, and the pile was used just as a

medium to transmit the impact force to the surrounding soil

through two mechanisms: the pile toe force and the shaft friction.

It has been shown that considering non-linear behaviour for the soil

in the vicinity of the pile will lead to a reduction of the level of

vibration (Masoumi et al., 2009), so the soil behaviour was defined

by means of the Mohr–Coulomb model to take into account

dissipation of vibrations due to plastic deformations in the soil

adjacent to the pile. The Mohr–Coulomb model used in Abaqus is

an extension of the classical Mohr–Coulomb failure criterion

proposed by Menetrey and Willam (1995). It is an elastic–plastic

model that uses a yield function of the Mohr–Coulomb form; this

yield function includes isotropic cohesion hardening/softening.

However, the model uses a flow potential that has a hyperbolic

shape in the meridional stress plane, and has no corners in the

deviatoric stress space (Figure 6). This flow potential is then

completely smooth, and therefore provides a unique definition of

the direction of plastic flow (Pan and Selby, 2002).

As the seismic waves, including surface and body waves, travel

outwards from the source of vibration, they encounter larger

volumes of ground, resulting in a reduction of energy per unit

volume in the ground. This phenomenon is known as geometric

or radiation damping. The ground itself has some damping

capacity, known as material or hysteretic damping (Woods and

Sharma, 2004). Material damping has a great effect on the

attenuation of seismic waves. In this study, Rayleigh damping

(Equation 1) was used to model this kind of damping.

10 m

12 m

12 m

27 m 27 m

Figure 4. Axisymmetric finite-element–infinite-element mesh of

model

Pile element

Axis of symmetry

Soil element

10 mm gap

Figure 5. Arrangement of soil element, pile element and axis of

symmetry

31



Æ ¼ 2�ø1øn

ø1 þ øn1a:

� ¼ 2�

ø1 þ øn1b:

where Æ is the Rayleigh mass proportional damping, which

damps the lower frequencies; � is the Rayleigh stiffness propor-

tional damping, which damps the higher frequencies; ø1 is the

first natural frequency of the model; øn is the natural frequency

associated with 95% of the modal mass of the model; and � is

the damping ratio. Frequency analysis was done for the model

containing the soil elements to obtain the natural frequencies of

the soil model. In this study, values of 4.3 and 0.00095 were used

for the Rayleigh mass and stiffness parameters respectively,

corresponding to a value of 10% for the damping ratio.

3.3 Loading and boundary conditions

The gravity load was first applied to the soil elements to establish

the initial in situ stress states prior to pile driving. The pile toe

was initially located at the ground surface, and successive

hammer impacts were applied to the pile head through the

reference node. The horizontal and rotational degrees of freedom

of the pile reference node were constrained to guide the pile

vertically into the soil elements. Hammer impact was modelled

as a transient concentrated force, varying according to the force–

time curve shown in Figure 7, which has been reported by Goble

et al. (1980). The time between applying two successive hammer

impacts should be large enough that the resulting vibration from

one impact does not affect the next one. On the other hand, it

should not be too large, because computational effort will be

increased. In this study, one second was assumed as the time

between applying two successive hammer impacts.

3.4 Soil–pile interaction

The pure master–slave, kinematic contact algorithm was used to

define the interaction between the pile and the soil. The outward

surface of the pile was selected as the master surface, and a

region containing soil nodes was chosen as the slave surface.

The Coulomb friction model was assumed for the tangential

behaviour of the soil–pile interface. According to this model,

two contacting surfaces can carry shear stresses up to a certain

magnitude across their interface before they start sliding relative

to one another; this state is known as sticking. The Coulomb

friction model defines this critical shear stress, �crit, at which

sliding of the surfaces starts as a fraction of the contact

pressure, p, between the surfaces (�crit ¼ �p). The fraction � is

known as the coefficient of friction (Hibbitt et al., 2010).

Kulhawy (1991) proposed a value of 0.8–1.0 for the ratio of the

soil–pile friction angle to the internal friction angle of the soil

for smooth concrete. In this study, a value of 0.8 was chosen for

the aforementioned ratio.

The hard contact model was considered for the normal behaviour

between the pile and the soil. According to this model

(a) the surfaces transmit no contact pressure unless the nodes of

the slave surface contact the master surface

(b) no penetration is allowed at any constraint location

(c) there is no limit to the magnitude of contact pressure that can

be transmitted when the surfaces are in contact (Hibbitt et al.,

2010).

The Coulomb friction model and the hard contact model were

numerically imposed by means of the kinematic method. This

method enforces exactly that there is no slip between two

surfaces until � ¼ �crit and no penetration of the master surface

into the slave surface is allowed.

3.5 Arbitrary Lagrangian–Eulerian (ALE) adaptive

meshing

ALE adaptive meshing is a tool that makes it possible to

maintain a high-quality mesh throughout an analysis, even when

large deformation such as penetration occurs, by allowing the

mesh to move independently of the material. In problems where

large deformation is anticipated, the improved mesh quality

resulting from adaptive meshing can prevent the analysis from

Θ 0�

Θ � 4 /3πΘ 2� π/3

Θ /3� π

Mises ( 1)e �

Menétrey–Willam(1/2 1)� �e

Rankine ( 1/2)e �

e (3 sin )/(3 sin )� � �φ φ

Figure 6. Menetrey–Willam flow potential in the deviatoric stress

plane. (Abaqus user’s manual; Hibbitt et al., 2010)

3

2

1

0

Forc

e: M

N

10 20 30 40

Time: ms

Figure 7. Force–time curve of hammer impact (Goble et al.,

1980)

32



terminating as a result of severe mesh distortion. In these

situations adaptive meshing can be used to obtain faster, more

accurate and more robust solutions than with pure Lagrangian

analyses (Hibbitt et al., 2010).

Experimental results obtained by van den Berg (1994) show that

outside a region of about 1.5D in clay and 2D in sand around the

cone no visible deformation can be distinguished. Moreover,

numerical results obtained by Ahmadi et al. (2005) indicate that

penetration of a cone into the sand does not affect the soil located

beyond a distance of 4D from the cone. In this study, ALE

adaptive meshing was used for the soil elements whose distances

from the pile centreline were less than six times the pile diameter.

This can also reduce the execution time in comparison with using

adaptive meshing for the whole model.

3.6 Stable time increment

The explicit time integration method was used to solve the

equations of motion. The central-difference operator is condition-

ally stable, and therefore the time increment is an important

factor in obtaining accurate and reliable answers. An approxima-

tion to the stability limit is often written as the smallest transit

time of a compression wave across any of the elements in the

mesh

˜t � Lmin

VP2a:

VP ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� �ð ÞE

1þ �ð Þ 1� 2�ð Þr

s2b:

where Lmin is the smallest element dimension in the mesh, VP is

the velocity of the compression wave, E is the soil elastic

modulus, r is the soil density and � is the soil Poisson’s ratio.

This estimate for ˜t is only approximate, and in most cases is not

safe. In general, the actual stable time increment chosen by

Abaqus will be less than this estimate by a factor between 1/ˇ2

and 1 in a two-dimensional model, and between 1/ˇ3 and 1 in a

three-dimensional model. Moreover, introducing damping to the

solution reduces the stable time increment chosen by Abaqus

according to the equation

˜t <2

ømax

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ �2

max

q� �max

� �3:

where ømax is the highest frequency of the model, and �max is the

damping ratio in the mode with the highest frequency (Hibbitt et

al., 2010). In this study, 5 3 10�5 s was used as the stable time

increment.

4. Results and discussion

4.1 Driving mechanism

In this study, the process of pile driving has been modelled

completely. This means that the pile toe is initially on the ground

surface, and it is driven into the ground by means of applying

successive hammer impacts. Figure 8 shows the deformed mesh of

the surrounding soil with the pile at three different depths, which

have been obtained in one analysis process. For example, Figure

8(a) shows the pile when it has been driven from the ground

surface to a depth of 2.5 m. By applying more hammer impacts,

the pile toe moves down to depths of 5 m and 10 m, as shown in

Figures 8(b) and 8(c). This process can be continued until any

desired depth is reached. One advantage of this kind of modelling

is the ability to record the particle velocity continuously, similar to

field measurements of vibrations during pile driving.

As can be seen, the ground surface is curved, owing to friction

force between the pile shaft and the soil, which is also observed

in the experimental results (van den Berg, 1994). Adaptive

meshing is used for the eight columns of the soil elements

adjacent to the pile. In this region, the mesh moves independently

of the soil material, so the element shape is not representative of

the displacements occurring within the soil. In fact, Abaqus

changes the size of the elements in a way that avoids excessive

distortion of the soil elements. Outside the adaptive meshing

region, the elements’ deformations are due only to the increased

stresses caused by the penetration of the pile, but, as stated in

Section 3.5, these deformations are very small.

When the pile is driven into the ground, it displaces the soil

elements encountered on its way. In the radial direction, the

points located at the soil–pile interface are displaced by a radial

distance equal to the pile radius. Radial displacement decreases

with distance from the pile. In the vertical direction, soil elements

near the ground surface are pushed upwards, whereas elements at

greater depths are pushed downwards. An important feature of

this modelling is the use of adaptive meshing to avoid termination

of the analysis due to excessive distortion of the elements. Test

runs showed that numerical modelling of pile driving by means

of applying hammer impacts (stress-controlled driving) is hardly

achievable without the use of adaptive meshing.

4.2 Verification of the model

Masoumi et al. (2009) used the properties presented in Tables 1

and 2 for the pile and the soil in their numerical simulation to

predict the measured PPV values due to impact pile driving

reported by Wiss (1981). The same parameters were used in this

study in order to compare the results with those of Masoumi et al.

PPV values were computed for the ground surface points located

at various distances from the pile centreline, and were compared

with the line fitted to the field data (Figure 9). To obtain the PPV

value for a specific point, the velocity–time history of that point

was depicted during the penetration of the pile from the ground

surface to a depth of 10 m. The maximum velocity on the time

33



history graph was introduced as the PPV. Computed PPV values

are in good agreement with those measured by Wiss (1981).

The PPV values computed in this study were also compared with

the numerical results obtained by Masoumi et al. (2009).

Masoumi et al. used the force–time history shown in Figure 10

as the hammer impact force, which has been obtained from a two

degrees of freedom model developed by Deeks and Randolph

(1993). The same impact force–time history was used just for

(a) (b) (c)

Figure 8. Deformed mesh of model during pile installation. Pile

toe at depths of: (a) 2.5 m; (b) 5 m; (c) 10 m

Pile type Concrete

Length: m 10

Diameter: m 0.5

Density: kg/m3 2500

Elastic modulus: MPa 40 000

Poisson’s ratio 0.25

Table 1. Pile properties used by Masoumi et al. (2009)

1

10

100

1000

2 20

PPV:

mm

/s

r : m

PPV measured by WissPPV computed in this study

Figure 9. Comparison of computed and measured PPV values for

ground surface points located at various distances from pile

centreline

Soil type Sandy clay

Density: kg/m3 2000

Elastic modulus: MPa 80

Poisson’s ratio 0.4

Friction angle: degrees 25

Cohesion: kPa 15

Table 2. Soil properties used by Masoumi et al. (2009)

34



this analysis, to allow a better comparison between the results of

the two studies. Masoumi et al. did not simulate the full

penetration of the pile: they considered the pile toe only at three

depths, of 2.5 m, 5 m and 10 m. Therefore the results were

compared for the case of applying a hammer impact on the pile

head when the pile toe was at a depth of 5 m. Here, the PPV was

defined as the maximum velocity that particles experienced just

as a result of applying this hammer impact. Considering Figure

11, it can be seen that the computed results in this study

overestimate the results obtained by Masoumi et al. at distances

of 5–9 m from the pile centreline, and underestimate them at

distances of 9–23 m from the pile centreline. Moreover, in

comparison with the results of Masoumi et al., the computed

PPV values are smaller near the ground surface, and are larger at

greater depths (Figure 12).

4.3. Further investigation of the results

The vertical displacement of the pile toe is shown against time in

Figure 13. As the pile penetrates more into the ground, lateral

pressure at the pile toe and also the shaft area in contact with the

soil, and consequently the frictional force on the pile shaft, are

increased, so more hammer blows are required for a specific

value of penetration of the pile. For example, whereas 1 m of

penetration at a depth of 4 m is achievable by applying 23

hammer blows, 172 hammer blows are required for the same

value of penetration at a depth of 7 m. The reduction in the slope

of the curve conforms to this fact.

This numerical model is capable of predicting the velocity of soil

particles during penetration of the pile. The velocities of two

points, both located at a distance of 5 m from the pile centreline,

but with the first point on the surface and the second one at a

depth of 5 m below the ground surface, were calculated for each

0.1 m of penetration of the pile toe. Figure 14 shows the vertical

velocity of the ground surface point against the depth of

penetration of the pile. As the pile penetrates further into the

ground the particle velocity increases, and reaches a maximum

value at a depth of 4.8 m. The velocity then decreases and

becomes constant, with some slight variations. This trend was

also observed in the reported field data (Thandavamoorthy,

2004). If we define the depth of the pile toe at which the PPV at

the ground surface occurs as the critical depth of vibration,

Figure 15 shows the variations of critical depth of vibration with

distance from the pile centreline. It can be seen that the critical

depth of vibration changes with distance from the pile, but these

changes are negligible. In other words, for all ground surface

points with radial distances from the pile centreline greater than

5 m, the critical depth of vibration falls within two limits of

4.5 m and 5.5 m, as shown in Figure 15. This trend was also

observed for piles with other diameters and different hammer

impacts.

The variations of the vertical velocity for the point located

5 m below the ground surface are shown in Figure 16. As the

pile is driven into the ground the particle velocity increases,

and reaches a maximum value at a depth of about 6 m. With

further penetration of the pile toe, the particle velocity

decreases.

2

1

0

Forc

e: M

N

0 25 50 75 100

Time: ms

Figure 10. Time history of hammer impact force (Masoumi et al.,

2009)

2520151050

5

10

15

20

25

30

35

40

0

PPV:

mm

/s

r : m

Masoumi .et al

This study

Figure 11. Comparison of PPV values computed in this study with

results of Masoumi et al. (2009) for ground surface points located

at various distances from pile centreline when pile toe is at depth

of 5 m

35



PPV values for points located at different depths are depicted in

Figure 17. The PPV values shown in Figure 17 are the maximum

velocity that points experience during the full penetration of the

pile, and do not necessarily occur at the same time. It can be seen

that for points located at distances of 3 m and 5 m from the pile

centreline the PPV value is maximum at a depth of about 8 m,

whereas for points located at distances of 9 m, 15 m and 20 m

from the pile centreline the PPV value is maximum at a depth of

about 1 m.

4.4 Sensitivity analysis

To determine the effect of and the degree of significance of

each parameter for the level of vibration of ground surface

points, sensitivity analysis was performed on various para-

meters: hammer impact force, pile geometrical properties

876543210

1

2

3

4

5

6

7

8

9

10

0

Dep

th: m

PPV: mm/s

Masoumi .et al

This study

Figure 12. Comparison of PPV values computed in this study with

results of Masoumi et al. (2009) for points located at various

depths at distance of 20 m from pile centreline when pile toe is at

depth of 5 m

�10

�8

�6

�4

�2

0

0 80 160 240 320 400 480 560 640 720

Vert

ical

dis

plac

emen

t: m

Time: s

Figure 13. Vertical displacement of pile toe with time

109876543210

5

10

15

20

25

30

35

40

0

Vert

ical

vel

ocity

: mm

/s

d: m

Figure 14. Vertical velocity of ground surface point located at

distance of 5 m from pile centreline against depth of penetration

of pile

2722171273·50

4·00

4·50

5·00

5·50

6·00

6·50

2

Crit

ical

dep

th o

f vi

brat

ion:

m

r : m

Figure 15. Critical depth of vibration against distance from pile

centreline

36



(including diameter and length), soil elastic modulus and soil–

pile friction.

4.4.1 Hammer impact force

Vertical PPV values against distance from the pile centreline are

shown in Figure 18 for hammer impacts of 2, 2.5 and 3.5 MN . It

can be seen that an increase in the hammer impact force increases

the resultant vibration. When the hammer impact force changes

from 2 MN to 3.5 MN, the mean increase in the vertical PPV

values is 24%.

4.4.2 Pile geometrical properties

The effect of pile diameter on the level of vibrations was also

investigated. The results obtained imply that the pile diameter is

an important factor in determining the severity of the vibrations.

An increase in the pile diameter leads to a substantial increase in

the PPV values (Figure 19). When the pile diameter changes

from 400 mm to 600 mm, the mean increase in the vertical PPV

values is 34%.

As previousely mentioned, the level of vibration for points

on the ground surface first increases and then decreases with

further penetration of the pile toe, so installing longer piles

does not increase the PPV value at the ground surface, as

long as the length of the pile is longer than the critical

depth of vibration, and the pile does not penetrate another

soil layer.

4.4.3 Soil elastic modulus

Figure 20 shows the sensitivity of the level of vibrations to the

elastic modulus of the soil. When the soil elastic modulus

decreases (assuming all the other soil parameters remain con-

stant), the transmission velocity of the stress waves decreases

according to the equations

109876543210

10

20

30

40

50

60

0

Vert

ical

vel

ocity

: mm

/s

d: m

Figure 16. Vertical velocity of point located 5 m below ground

surface at distance of 5 m from pile centreline against depth of

penetration of pile

140120100806040200

1

2

3

4

5

6

7

8

9

10

0

Dep

th: m

PPV: mm/s

r 3 m�r 5 m�r 9 m�r 15 m�r 20 m�

Figure 17. PPV values against depth for points located at various

distances from pile centreline

262218141060

10

20

30

40

50

60

70

80

2

Vert

ical

PPV

: mm

/s

r : m

2·0 MN2·5 MN3·5 MN

Figure 18. Vertical PPV values of ground surface points against

distance from pile centreline for various hammer impacts

262218141060

10

20

30

40

50

60

70

2

Vert

ical

PPV

: mm

/s

r : m

D 400 mm�

D 500 mm�

D 600 mm�


distance from pile centreline for impact force of 3 MN and various

pile diameters

37



VP ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� �ð ÞE

1þ �ð Þ 1� 2�ð Þr

s4a:

VS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

E

2(1þ v)r

s4b:

However, the stress waves cause higher vibratory strains in the

soil mass when they pass through the soil, and therefore the level

of vibration increases. When the soil elastic modulus changes

from 80 MPa to 40 MPa, the mean increase in the vertical PPV

values is 26%; so for loose soils, higher PPV values can be

expected.

4.4.4 Soil–pile friction

Part of the vibration of soil particles is due to the passage of

shear waves transmitting on a cylindrical wavefront. These waves

are generated by soil–pile friction. So, if the friction between the

soil and the pile reduces, the resultant vibration will be reduced.

Figure 21 shows a comparison of the vertical PPV values for

different soil–pile friction coefficients. When the soil–pile

friction coefficient changes from 0.1 to 0.35, the mean increase

in the PPV values is 34%. It can be concluded that, for concrete

piles, a higher level of vibration can be expected than for steel

piles, because the soil–concrete friction is greater than the soil–

steel friction.

5. ConclusionThe installation of piles by means of applying successive hammer

impacts was modelled. Adaptive meshing was used to maintain a

high-quality mesh during penetration of the pile. The improved

mesh prevents the analysis from terminating as a result of severe

mesh distortion, and also increases the stable time increment.

This modelling is able to compute the velocity of particles at

every depth of penetration of the pile toe, and gives a close

prediction of the measured PPV values in the field. Based on this

study, the following conclusions can be drawn.

j The PPV at the ground surface does not occur when the pile

toe is on the ground surface; as the pile penetrates into the

ground, the particle velocity reaches a maximum value at a

critical depth of penetration.

j For points below the ground surface, the particle velocity

increases as the pile toe penetrates closer to the point, and

then decreases as the pile toe moves further away from the

point.

j For points located close to the pile, the PPV value is larger at

greater depths, whereas for points located far from the pile,

the PPV value is larger near the ground surface.

j The level of vibrations is dependent on the properties of the

pile, hammer and soil. An increase in the pile diameter, soil–

pile friction and impact force increase the PPV value,

whereas an increase in the soil elastic modulus reduces the

PPV value. Installing longer piles does not increase the PPV

value at the ground surface, as long as the length of the pile

is greater than the critical depth of vibration, and the pile

does not penetrate another soil layer.

Piles are used to support many major structures, including large

railroad and highway bridges and high-rise building throughout

the world. Installing a pile in the ground causes the ground

surrounding the pile to shake. Depending on the intensity of

ground shaking, vibrations may cause direct damage to surround-

ing structures or settlement of the soil, resulting in structural

damage. In urban settings, neighbouring properties are particu-

larly vulnerable to ground shaking due to pile driving, because of

the proximity of structures to the pile driving location. It is

therefore necessary to evaluate the level of vibration prior to

beginning of pile driving project. The numerical simulation of

pile driving introduced in this study can be used to determine the

262218141060

10

20

30

40

50

60

70

80

90

100

2

Vert

ical

PPV

: mm

/s

r : m

E 80 MPa�

E 60 MPa�

E 40 MPa�



soil elastic moduli

262218141060

10

20

30

40

50

60

70

2

Vert

ical

PPV

: mm

/s

r : m

0·35�μ0·25μ �0·1μ �0·0μ �



values of soil–pile friction

38



severity of vibrations due to pile driving, and the sensitivity of

the level of vibration to soil, pile and hammer properties.

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Numerical Study of Ground Vibration Due to Impact Pile Driving