# Numerical Study of Ground Vibration Due to Impact Pile Driving Essays

Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi Proceedings of the Institution of Civil Engineers http://dx. doi. org/10. 1680/geng. 11. 00094 Paper 1100094 Received 09/10/2011 Accepted 04/04/2012 Keywords: dynamics/mathematical modelling/piles & piling ICE Publishing: All rights reserved Numerical study of ground vibration due to impact pile driving 1 j Ali Khoubani MSc 2 j Mohammad Mehdi Ahmadi PhD

Senior Geotechnical Engineer, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran Associate Professor, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran 1 j 2 j 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 ? ite-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 veri? ed by comparing the computed particle velocities with those measured in the ? eld. 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 epth 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.

Notation D d E e L Lmin p r VP VR VS ? a ? t ? i i r o ocrit o pile diameter depth of penetration of pile elastic modulus deviatoric eccentricity distance between vibration source and re? ctive origin of Rayleigh waves at ground surface smallest element dimension in mesh pressure radial distance from pile centreline velocity of compression wave velocity of the Rayleigh wave velocity of shear wave Rayleigh mass proportional damping Rayleigh stiffness proportional damping stable time increment angle of deviatoric stress plane axes coef? cient of friction Poisson’s ratio density shear stress critical shear stress soil friction angle i imax omax on o1 damping ratio damping ratio in mode with highest frequency highest frequency of model natural frequency associated with 95% of modal mass of model ? st natural frequency of model 1. Introduction Pile 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 dif? cult to determine beforehand and costly to mitigate, while potentially having serious adverse effects on adjacent structures and their foundations, as well as on vibration-sensitive installations and occupants f buildings (Massarsch and Fellenius, 2008). During recent decades, several investigations have been performed to determine the characteristics of pile driving vibrations. One common method of handling vibrations is to perform ? eld measurements in terms of the peak particle velocity (PPV) during 1 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi 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 speci? c 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 ? nite-element–in? ite-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 displacement–time functions on the boundary of a model of the surrounding ground to simulate the outgoing ground waves.

The results of vibratory pile driving and impact pile driving were in acceptable agreement with ? eld data. Since this modelling was time consuming, Selby (2002) used a harmonic computation for a limited ? nite-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 ? nite-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 re? ection. The predicted vertical peak acceleration was in close agreement with ? eld data, but the predicted radial peak acceleration was more than 20% greater than ? eld data. Later, they used a similar model to study the effect of concrete-? lled 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 speci? c case study (Madheswaran et al. , 2009). Masoumi et al. (2007) developed a linear coupled ? nite-element– boundary-element approach for the prediction of free ? eld 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 strati? cation on the ground vibration for the case of a soft layer on a stiffer half space was also investigated.

Although the prediction of near-? eld vibrations was satisfactory, the far-? eld vibrations were overestimated. 2 Later, both the non-linear constitutive behaviour of the soil in the vicinity of the pile and the resulting non-linear dynamic interaction 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 ? nite-element model using Abaqus to study impact pile driving vibrations in saturated cohesive soils.

An arti? cially damped non-re? ecting boundary consisting of several soil layers with different damping ratios was de? ned at the boundary of the model to minimise the re? ection of stress waves. The Coulomb frictional contact was de? ned 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 speci? c 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 to pile 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 ? rst 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 representing particle motion in Figure 1 (Woods and Sharma, 2004).

At the tip of the pile, each impact causes a volumetric displacement 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 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi Hammer impact Particle motion (compression in pile) Shear wave front Transfer from pile to soil by friction/shear Particle motion (shear in soil) 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 Ray Figure 1. Generation mechanism of shear waves due to soil–pile friction (Woods and Sharma, 2004) Hammer impact R-wave S-wave 3. 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 fournode quadrilateral elements, with reduced integration and hourglass control. Soil ? nite-elements were biased radially towards the pile, and soil in? nite-elements were placed at the boundaries (Figure 4). During dynamic steps the in? nite-elements introduce additional normal and shear tractions on the ? nite-element boundary that are proportional to the normal and shear components of the velocity of the boundary.

These boundary damping constants are chosen by Abaqus to minimise the re? ection of compression and shear wave energy back into the ? nite-element mesh (Hibbitt et al. , 2010). The in? nite-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 re? ected waves on the PPV value, the dimensions of the ? nite-element mesh were extended 2 m beyond the distance for which the PPV values were calculated. r Ray P-wave S-wave Reflected wave

VRd V2 P V2 R Rayleigh wave d Figure 2. Combination of seismic waves resulting from impact pile driving (Woods and Sharma, 2004) L Source d2 r2 d 1 V2 R V2 P V2 R from the tip of the pile on spherical wavefronts, decaying as the ? rst 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 re? ected back into the ground as re? cted 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 Figure 3. Distance between source and re? ective origin of Rayleigh waves at ground surface (Dowding, 1996) 3 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi 10 m 12 m 12 m 27 m 27 m 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 speci? c 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 signi? cant error. 3. 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 de? ed 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 ? ow potential that has a hyperbolic shape in the meridional stress plane, and has no corners in the deviatoric stress space (Figure 6).

This ? ow potential is then completely smooth, and therefore provides a unique de? nition of the direction of plastic ? ow (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. Figure 4. Axisymmetric ? nite-element–in? nite-element mesh of model 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. Pile element Axis of symmetry Soil element 10 mm gap Figure 5. Arrangement of soil element, pile element and axis of symmetry 4 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi ? 0 Rankine (e 1/2) ? e (3 sin ? )/(3 ?/3 sin ? ) Force: MN Menetrey–Willam (1/2 e 1) 2 ? 2? /3 ? 4? /3 1) 1 Mises (e ? Figure 6. Menetrey–Willam ? ow potential in the deviatoric stress plane. (Abaqus user’s manual; Hibbitt et al. , 2010) 0 10 20 Time: ms 30 40 1a: 2io1 on ?? o1 ? on Figure 7. Force–time curve of hammer impact (Goble et al. , 1980) 1b: 2i a? o1 ? on where ? is the Rayleigh mass proportional damping, which damps the lower frequencies; a is the Rayleigh stiffness proportional damping, which damps the higher frequencies; o1 is the ? st natural frequency of the model; on is the natural frequency associated with 95% of the modal mass of the model; and i 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 ? rst 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 de? ne 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 de? nes this critical shear stress, ocrit , at which sliding of the surfaces starts as a fraction of the contact pressure, p, between the surfaces (ocrit ? ip). The fraction i is known as the coef? cient of friction (Hibbitt et al. , 2010). Kulhawy (1991) proposed a value of 0. 8–1. 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 o ? ocrit 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 5 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi 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. D 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 conditionally stable, and therefore the time increment is an important factor in obtaining accurate and reliable answers. An approximation to the stability limit is often written as the smallest transit time of a compression wave across any of the elements in the mesh 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 ? ld 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 Veri? cation 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 ? tted to the ? eld data (Figure 9). To obtain the PPV value for a speci? c 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 2a: ?t % Lmin VP 2b: s?????????????????????????????????? ? 1 A i? E VP ? ?1 ? i?? 1 A 2i? r here 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 i 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/? 2 and 1 in a two-dimensional model, and between 1/? 3 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 omax q????????????????? 2 1 ? imax A imax where omax is the highest frequency of the model, and imax is the damping ratio in the mode with the highest frequency (Hibbitt et al. , 2010). In this study, 5 3 10A5 s was used as the stable time increment. 6 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi (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 1000 Table 1. Pile properties used by Masoumi et al. (2009) PPV: mm/s

Pile type Length: m Diameter: m Density: kg/m3 Elastic modulus: MPa Poisson’s ratio Concrete 10 0. 5 2500 40 000 0. 25 PPV measured by Wiss PPV computed in this study 100 10 Soil type Density: kg/m3 Elastic modulus: MPa Poisson’s ratio Friction angle: degrees Cohesion: kPa Sandy clay 2000 80 0. 4 25 15 1 2 r: m 20 Figure 9. Comparison of computed and measured PPV values for ground surface points located at various distances from pile centreline Table 2. Soil properties used by Masoumi et al. (2009) 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 7 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi this analysis, to allow a better comparison between the results of the two studies. Masoumi et al. id 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 de? ned 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 speci? c 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 ? rst 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 40 35 Masoumi et al. This study 30 25 PPV: mm/s 20 15 10 5 0 0 5 10 r: m 15 20 25 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 2 1 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 ? eld data (Thandavamoorthy, 2004). If we de? ne 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. 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. Force: MN 0 0 25 50 Time: ms 75 100 Figure 10. Time history of hammer impact force (Masoumi et al. , 2009) Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi 0 0 1 2 3 PPV: mm/s 4 5 40 6 7 8 35 Vertical velocity: mm/s 30 25 20 15 10 5 1 2 3 4 Depth: m 0 0 1 2 3 4 5 6 7 8 9 6·00 10 5 d: m 6 7 8 9 10 Figure 14. Vertical velocity of ground surface point located at distance of 5 m from pile centreline against depth of penetration of pile Masoumi et al. This study 6·50 Critical depth of vibration: m 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 5·50 5·00 0 Vertical displacement: m 2 4 4·50 4·00 6 8 10 3·50 2 7 12 r: m 17 22 27 0 80 160 240 320 400 Time: s 480 560 640 720 Figure 15. Critical depth of vibration against distance from pile centreline Figure 13. Vertical displacement of pile toe with time 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 signi? cance of each parameter for the level of vibration of ground surface points, sensitivity analysis was performed on various parameters: hammer impact force, pile geometrical properties 9 Geotechnical Engineering

Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi 60 50 40 30 20 10 Vertical PPV: mm/s 80 70 60 50 40 30 20 10 2·0 MN 2·5 MN 3·5 MN Vertical velocity: mm/s 0 0 1 2 3 4 5 d: m 6 7 8 9 10 0 2 6 10 14 r: m 18 22 26 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 Figure 18. Vertical PPV values of ground surface points against distance from pile centreline for various hammer impacts 70 0 1 2 3 0 20 40 PPV: mm/s 60 80 100 120 r r r r r 140 60 D D D 400 mm 500 mm 600 mm

Vertical PPV: mm/s Depth: m 4 5 6 7 8 9 10 3m 5m 9m 15 m 20 m 50 40 30 20 10 0 2 6 10 14 r: m 18 22 26 Figure 17. PPV values against depth for points located at various distances from pile centreline Figure 19. Vertical PPV values of ground surface points against distance from pile centreline for impact force of 3 MN and various pile diameters (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. 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 10 rom 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 ? rst 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 constant), the transmission velocity of the stress waves decreases according to the equations Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi 100 90 80 E E E 80 MPa 60 MPa 40 MPa 70 60 ? ? ? ? 0·35 0·25 0·1 0·0 Vertical PPV: mm/s Vertical PPV: mm/s 26 70 60 50 40 30 20 10 0 2 6 10 14 r: m 18 50 40 30 20 10 22 0 2 6 10 14 r: m 18 22 26 Figure 20. Vertical PPV values of ground surface points against distance from pile centreline for impact force of 3 MN and various soil elastic moduli

Figure 21. Vertical PPV values of ground surface points against distance from pile centreline for impact force of 3 MN and various values of soil–pile friction 4a: s?????????????????????????????????? ? 1 A i? E VP ? ?1 ? i?? 1 A 2i? r every depth of penetration of the pile toe, and gives a close prediction of the measured PPV values in the ? eld. Based on this study, the following conclusions can be drawn. 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. 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. j 4b: s??????????????????? E VS ? 2(1 ? v)r 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 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 coef? cients. When the soil–pile friction coef? cient 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. Conclusion The 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

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 surrounding structures or settlement of the soil, resulting in structural damage. In urban settings, neighbouring properties are particularly 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 11 Geotechnical Engineering Numerical study of ground vibration due to impact pile driving Khoubani and Ahmadi severity of vibrations due to pile driving, and the sensitivity of the level of vibration to soil, pile and hammer properties. REFERENCES Ahmadi MM, Byrne PM and Campanella RG (2005) Cone tip resistance in sand: modelling, veri? cation, and applications.

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