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Defects of concrete piles can occur at any point during the construction of piles. Most common types of pile integrity issues are; presence of voids, inconsistency in concrete mix, entrapped groundwater or slurry, and geometric dislocation. These defects can be categorized based on the place in the construction sequence at which the defect occurs. This research introduces several numerical models of defected piles with various scenarios in order to identify, locate, and quantify the necking occurring in these piles. The finite element software (ADINA) is used to simulate the studied models. The soil domain is modeled as an axisymmetric space around the concrete pile. Five diameters of piles (40, 60, 80, 100 and 120 cm) are studied. Necking is modeled at three different locations along the pile namely; upper, middle, and bottom third. Four ratios between the necking diameter and pile diameter are also studied. The dynamic force used in this research is that simulating the pile integrity test (PIT) case, with 2.5 N impact load applied at the pile head, half wave of sinusoidal pattern, and 0.5 kilo hertz frequency. The time domain of the dynamic force analysis is equal to 0.0175 sec, and applied in 450 steps.
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Vol XVI, Issue 61, July 2022 ISSN 1971 - 8993
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472;
DOI: 10.3221/IGF-ESIS.61.30
461
Locating and quantifying necking in piles through numerical
simulation of PIT
T. Salem, A. Eraky, A. Elmesallamy
Faculty of Engineering, Zagazig University, Zagazig, Egypt.
nageeb2@yahoo.com, 0020-100-7040-659
atef_eraky@yahoo.com , 0020-100-5283-557
almosllamy@gmail.com, 0020-102-2011-122
A
BSTRACT
. Defects of concrete piles can occur at any point during the
construction of piles. Most common types of pile integrity issues are;
presence of voids, inconsistency in concrete mix, entrapped groundwater or
slurry, and geometric dislocation. These defects can be categorized based on
the place in the construction sequence at which the defect occurs. This
research introduces several numerical models of defected piles with various
scenarios in order to identify, locate, and quantify the necking occurring in
these piles. The finite element software (ADINA) is used to simulate the
studied models. The soil domain is modeled as an axisymmetric space around
the concrete pile. Five diameters of piles (40, 60, 80, 100 and 120 cm) are
studied. Necking is modeled at three different locations along the pile namely;
upper, middle, and bottom third. Four ratios between the necking diameter
and pile diameter are also studied. The dynamic force used in this research is
that simulating the pile integrity test (PIT) case, with 2.5 N impact load
applied at the pile head, half wave of sinusoidal pattern, and 0.5 kilo hertz
frequency. The time domain of the dynamic force analysis is equal to 0.0175
sec, and applied in 450 steps.
K
EYWORDS
. Pile integrity test; Damage detection; Necking in piles.
Citation: Salem, T., Eraky, A., Elmesallamy,
A., Locating and quantifying necking in piles
through numerical simulation of PIT, Frattura
ed Integrità Strutturale, 61 (2022) 461-472.
Received: 09.04.2022
Accepted: 13.06.2022
Online first: 17.06.2022
Published: 01.07.2022
Copyright: © 2022 This is an open access
article under the terms of the CC-BY 4.0,
which permits unrestricted use, distribution,
and reproduction in any medium, provided
the original author and source are credited.
I
NTRODUCTION
here are many shapes of defects in concrete piles such as; cracking, honey-combing, bulges, and necking. Necking
is a reduction in cross sectional area of the pile, while bulges are increases in the pile cross sectional area. The
integral (healthy) pile is that one having constant diameter along its whole length with no cracks, necking, bulges,
or honey-combing. Non-destructive tests with dynamic loads are used to predict the location of pile defects. One of the
most familiar tests used for this target is the pile integrity test (PIT), which is fast, common, and low-cost test. The
mechanism of (PIT) is that the wave transfer from pile head to pile toe then return to the top. Although, the (PIT) is a
fast and reliable test, there are some shortcomings of this test.
T
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
462
Štrukelj et al., (2009) introduced a monitoring methodology where sensors are installed inside the pile body to measure the
pile strain under dynamic load. The results of the experiment are compared with a numerical model conducted by
PLAXIS software. Trauner (2012) studied the behavior of reinforced concrete pile inside a soil domain under dynamic
load. Sensors are installed on the steel reinforcement bars to measure the strain of the pile. Furthermore, verification is
conducted with a real PIT carried out on the field.
Ding et al., (2011) studied the PIT wave propagation in a tube section pile numerically. Models are carried out with
different wall thickness and different elastic moduli. Niederleithinger (2006) and (2008) described the CEFIT software to
simulate the PIT and the acoustic wave through the pile and the soil. Zhang et al., (2010) used ANNs software to simulate
the PIT with neural network technique. Warrington and Wynn (2000) studied the difference between the software
MAPLE, ANSYS and WEAP, in simulating wave equation through concrete piles.
Li, (2019) studied large-diameter pipe pile embedded in inhomogeneous soil to investigate the torsional
dynamic response, and presented verification of the frequency-domain analytical solution. The author
concluded that with increasing the inner radius and length of the pile or the decrease of the outer radius and
shear modulus of the pile, the oscillation amplitudes of the complex impedance and velocity admittance
decrease, denoting an increase in the resistance of the pile
to torsional dynamic loadings.
Wu et al., (2019) study the longitudinal vibration of a pile with changeable sectional acoustic impedance under
arbitrary external stimulation. The Laplace transform is used to find the analytical solution of the transfer
function, and then the residue technique of inverse Laplace transformation is used to solve the corresponding
impulse response function. The analytical solution of response at pile top may be found by convolution
computation using the impulse response function, which overcomes the limit of earlier analytical solutions
due to defined time-harmonic load.
Li and Gao, (2019) introduced better approach for describing the vertical vibration of a pipe pile while taking
into account the layered characteristics and building disturbance impact of both the outer and inner soils for
various pile specifications and soil radial inhomogeneity conditions, the impacts of the inner soil on the
dynamic response of the pipe pile were explored. The theoretical model's accuracy was confirmed by
comparing the outcomes of field measurements.
This paper studies different models of concrete piles having different necking locations and sizes using ADINA (2021)
software. Several scenarios of piles with necking defect are studied. The pile necking diameter is modeled with four
different values at three different locations along the pile length. The velocity response for an arbitrary point on the pile
surface is plotted with the time. The main objective of this study is to introduce a new methodology to locate and quantify
necking in piles with a new standard graph as a reference.
MODELING
tudied concrete piles are considered to have circular cross-sectional area and totally embedded in the soil. The pile
radii varied from 40 to 120 cm, with all having the same length of 12 meters. An axisymmetric model is used in
modeling the pile and the surrounding soils, with soil domain radius equal to 24 m plus the pile diameter, and a
height of 24 m. The same meshing pattern is used in all the models having the same incremental values, sequence, and
order, thus, avoiding the effect of meshing on the results. Tab. (1) presents the properties of the soil and the pile materials
used in the numerical analysis.
Materials Numerical model Young's Modulus
(MN/m2) Density (kg/m3) Poisson's Ratio Friction Angle (o)
Concrete Elastic isotropic 2.1 x 103 2500 0.2 N/A
Soil Mohr-Coulomb 1.0 x 102 1900 0.3 40
Table 1: Properties of the Studied Soil and Concrete Materials.
A very small value of Rayleigh damping stiffness factor β for the pile is assumed = 70 x 10-7, while Rayleigh damping mass
factor α for the pile is assumed to be zero. In addition, Rayleigh damping stiffness factor β and mass factor α for the soil is
considered = zero. These very small values are mainly chosen due to the very short duration of monitoring the incident
wave, so that it's considered that the damping effect will not affect the behavior before a relatively long duration.
S
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472;
DOI: 10.3221/IGF-ESIS.61.30
463
The dynamic load used in this research is an impact load. It modeled in ADINA software as concentrated load equal to
2.5 N applied at the pile head, with time function as presented in Fig. (1). The considered solution steps are 50 steps
during the pulse duration which equals 0.001 sec, then 400 steps from 0.001 sec to 0.017 sec. For solving the finite
element equations in a linear dynamic analysis, ADINA employed the step-by-step direct integration through implicit time
integration using the Newmark’s method.
Figure 1:
Force Time Function of Dynamic Load.
The model increases laterally every 60 cm to respect the condition (mesh side should have a maximum length
=
C
c
t
/2.5). The wave velocity (C) = E/ρ, where E is the concrete Young's modulus and ρ is the
concrete density. Therefore, the wave velocity is taken equal to 3000 m/s. The time of impact load is 0.001
sec
of a half sinusoidal wave and
frequency
0.5 kH
z
.
Lateral and cross-sectional meshes have the same
dimensions at the necking zone. The element size within the mesh surrounding the pile is equal to 5 cm in
both directions. 3D-model of the pile and the surrounding soil is shown in Fig. (2).
Figure 2: Finite Element Axisymmetric Model for the Intact Pile Case.
Regarding the boundary conditions, the bottom boundary is fixed with no movements in X, Y, and Z directions.
However, the side boundaries are rollers in the vertical directions to allow for soil settlement, as shown in Fig. (3). Larger
mesh sizes are used in the analysis to assess the effect of mesh size convergence. The chosen mesh size along with the
FEM discretization showed no difference in the results between the used mesh and the smaller ones indicating the
accuracy of the used mesh. This may be attributed to the relatively short time of solution which is 0.017 sec also the
relatively low applied point load value which is 2.5 N to the model mass.
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
464
Figure 3: Boundary conditions of the Finite Element.
STUDIED CASES
parametric study is performed in which the following parameters are studied in details:
Pile diameter varying from 40, 60, 80, 100 and 120 cm. Notch or necking in three different locations, upper,
middle third, and lower third. Four notch or necking sizes, as reduced from the pile diameter, having sizes of
12.50%, 25.0%, 37.5%, and 50.0% are deducted as notch from the pile diameter.
RESULTS
elationship between time and velocity at a specific point are studied for all cases. The location of the studied point
is at (1/3 * pile radius) from the pile center. Different parameters are studied, including pile diameter, necking
diameter, and the ratio between them. Obtained curves are compared with the PIT manual schematic diagram.
Fig. (4) shows the velocity time history at the studied point located on the surface of intact pile with diameter = 100 cm. It
is found that there are two marked parabolas (a and z). Parabola (a) is the pulse induction and named as the initial
parabola in the paper. Initial parabola is induced directly due to the impulse effect not as the same parabolas along the
response history which induced after the pulse release. Initial parabola was found as smooth peak in smaller diameters 40
cm and 60 cm and gradually noised from 60 cm then 80 cm then 100 cm then 120 cm. This declares the direct relation
between the pulse frequency effect on the PIT test and gives an obvious observation that for every pile diameter there is
an optimum frequency. parabola (z) is the terminal parabola or the end parabola, and it means that the wave has reached
the pile end and reflect. The symbol tlp in Fig. (4) expresses the time indicating the distance between the pile head and its
end bearing point along the whole pile length. The end parabola will show a conclusion as its trend is affected by necking
and also its shape changes with noisy waves in the initial parabolas. In addition, it should be noted that the responses
don’t drop down to less than zero from time 2*10-3 sec to time 8*10-3 sec.
Fig. (5) presents a comparison of velocity time history between intact pile with D = 100 cm and four different necking
values. All four necked piles have a necking at the upper third zone of the pile length. The necked pile diameters are 87.5,
75.0, 62.5 and 50.0 cm, with diameter reduction of 12.5, 25.0, 37.5, and 50.0 cm respectively. The symbol tlu in Fig. (5)
expresses the time indicating the distances between the pile head and the necking location. The symbol tlp in Fig. (5)
expresses the time indicating the distance between the pile head and its end bearing point along the whole pile length. It is
A
R
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
465
noticed that the part [Q] of the graph increases downward when the pile diameter decreases, or when the necking
increases.
Figure 4: Velocity Response for an Intact Pile of 100 cm Diameter.
Figure 5: Velocity Response for an Intact Pile 100 cm Diameter verses Four Defected Piles at Upper Third of the Pile Length.
In which:
Q : is the negative peak velocity just after the initial zone, (m/sec.);
a : is the zone of noise that took place in the initial parabola;
b : is the lowest peak in the initial noise zone;
c : is a noise point just preceding the lowest peak in the initial noise zone.
Fig. (6) presents a comparison of velocity time history between intact pile (D = 100 cm) and four necked piles. All four
necked piles have a neck at the middle of the pile length. The necked pile diameters are 87.5, 75.0, 62.5 and 50.0 cm. The
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
466
symbol tlm in Fig. (6) expresses the time indicating the distances between the pile head and the necking location. It is
noticed that part [P] of the graph increases downward when the pile diameter decreases, or when the necking increases.
Figure 6: Velocity Response for an Intact Pile 100 cm Diameter Verses Four Defected Piles at the Middle of the Pile Length.
Fig. (7) shows a comparison of velocity time history between the case of intact pile (D = 100 cm) and four necked piles
with a neck at the lower third part of the pile length. The same necking ratios are used in this case also. The symbol tlb in
Fig. (7) expresses the time that the wave travels over the first two thirds of the pile. It is noticed that the part [O] of the
graph increases downward when the pile diameter decreases, or when the necking increases.
Figure 7: Velocity Response for an Intact Pile 100 cm Diameter Verses Four Defected Piles at the Lower Third of the Pile Length.
Fig. (8) summarizes Figs. (4), (5), and (6). It is noticed that there is a time shift on the velocity time history curves when
the location of the necking moves from the pile top to the pile middle or the pile bottom. The distance between the
domain values is tlu, tlm, tlb are proportional to the physical distances between the necking in the pile to the pile length
expressed in the pile length domain value tlp.
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472;
DOI: 10.3221/IGF-ESIS.61.30
467
Figure 8:
Velocity Response for an Intact Pile 100 cm Diameter Verses Three Defected Piles of 50 cm Necking at Upper, Middle and
Lower Third of the Pile Length.
The behavior of the studied piles has a pattern which can be presented in Fig. (10). It may be compared with the known
PIT manual shape which passes through several operations of filtration and other mathematical computations to specify
the defect location, as shown in Fig. (9).
Figure 9:
The PIT Schematic Diagram and Table.
The research schematic diagram has a new conclusion that it may introduce approximately the volume of the defect. In
addition, it doesn't need any computations for filtration, but just the direct introduced response and comparing the result
with the new schematic diagram, as presented in Fig. (10). On other hand, it can be said that the ratio between the notch
diameter to the pile diameter is approximately equal to the ratio shown in the following equation:
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
468
RD = 1
23
2*
y
y
y (1)
where:
y1 : is the peak velocity of parabola [Q],
y2 : is the velocity value at point [b],
y3 : is the velocity value at point [c].
a, Q, b, and c are presented in Figs. (5) and (10).
y2 or (b) is the minimum value in the pulse parabola [a] and y3 or (c) is the maximum y value in the pulse parabola [a]. It
can be predicted whether the pile is intact or not using this formula. In addition, the location and the diameter of the
necking can also be predicted.
Figure 10: The Research Schematic Diagram.
a: Impact peak.
n: Noisy portion directly after impact peak
s: Studied portion.
d: Maximum positive amplitude along the response
whatever its duration.
L: Scoped response length
f: Minimum negative amplitude along the response whatever its
duration.
e: Noisy portion directly beyond the minimum velocity response
value.
g: Noisy portion directly after maximum velocity response value.
EFFECT OF PILE DIAMETER
he effect of pile dimeter is shown in the following figures, knowing that the figures having similar trends of that of
100 cm pile diameter. Fig. (11) presents a comparison of velocity time history between intact pile with D = 40 cm
and four piles having different necking. All four necked piles have a neck at the upper third of the pile length. The
necking (or reduction) in the pile diameter is 5, 10, 15 and 20 cm respectively. It is noticed that the part [Q] of the graph
increases downward when the pile diameter decreases, or when the necking increases.
It is noticed that for pile diameters of 40 and 60 cm, shown in Figs. (11) and (12), a separate single parabola with no
inflection point appeared below the pile tip for the intact pile only in the negative zone. On the other hand, all piles with
different necking zones are having one or more inflection points with much more distorted parabolas for larger necking
zones. However, for pile diameters of 80, 100, and 120 cm, the peak of the parabola appeared in the positive zone just
below the pile tip also. This may be attributed to that the frequency in the initial parabola induced a significant noise in
larger diameters, as shown in Figs. (5), (13), and (14).
The same trend is noticed for different pile diameters, and shown in successive figures, Fig. (12) for 60 cm diameter pile,
Fig. (13) for 80 cm diameter pile, and Fig. (14) for 120 cm diameter pile.
T
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
469
Figure 11: Velocity Response for an Intact Pile 40 cm Diameter Verses Four Defected Piles at the Higher Third of the Pile Length.
Figure 12: Velocity Response for an Intact Pile 60 cm Diameter Verses Four Defected Piles at the Upper Third of the Pile Length.
Figure 13: Velocity Response for an Intact Pile 80 cm Diameter Verses Four Defected Piles at the Upper Third of the Pile Length.
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
470
Figure 14: Velocity Response for an Intact Pile 120 cm Diameter Verses Four Defected Piles at the Upper Third of the Pile Length.
Fig. (15) presents a comparison of velocity time history between intact piles with D = 40, 60, 80, 100, and 120 cm. All five
pile diameters have a common property, the response is always positive until it reaches the end of the pile, where
reflection of the applied wave returns again. There is a relatively small shift between the end bottom parabola which may
be due to noise that took place in the initial parabola.
Figure 15: Velocity Response for Intact Piles of 40, 60, 80, 100, and 120 cm Diameter.
Fig. (16) presents a comparison of velocity time history between piles with D = 40, 60, 80, 100, and 120 cm through initial
parabolas only. As shown, pile diameter of 40 cm has the deepest response and pile diameter of 120 cm has the
shallowest. As the applied frequency is the same, the pile diameter effect is significant in the figure. The figure shows that
frequency can be increased in piles of 100 and 120 cm diameter, which means results will be better, but its barely adjusted
for piles of 40, 60 and may be present in pile diameter of 80 cm.
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
471
Figure 16: Velocity Response for Piles 40-60-80-100-120 cm Diameter Through Initial Parabola.
CONCLUSIONS
oncrete piles with and without defects under sinusoidal impact force with half kilo hertz frequency are studied
using the finite element analysis software ADINA. The following conclusions are obtained from this study:
1- There is an important zone of the velocity time history graph of the studied piles. This zone increases
downward when the pile diameter decreases, or when the necking size increases for piles necked at their lower,
middle, and upper parts.
2- There is a similar time shift on the velocity time history diagram when the location of the necking moves from the
pile top to the pile middle or the pile bottom.
3- The distances between zones (Q), (P) and (O) are equal to the physical distances between the necking zones along
the pile length.
4- A new schematic diagram with details concerning the necking location and volume is identified. The introduced
schematic diagram shows an initial parabola and a successive one. These two parabolas are the most significant ones
along the solution time, as the damping tend to affect other parabolas along the pile length.
5- For smaller pile diameters, the bottom of the parabola in the velocity time history graph is smoother with less noise
meaning that the applied force fit well with smaller diameter piles than the larger ones.
6- For intact piles, the distance between the peak of the initial parabolas and the successive one on the time domain is
equivalent to the pile length when it is multiplied by half of the wave velocity.
7- The ratio between the time difference along the peaks of the two initial parabolas, to the supposed travel time for an
intact pile, is proportional to the ratio between the distance along the pile top to the necking zone, and the pile
length. This relation could allocate the necking location along the pile length.
8- The ratio between the time indicating the distance between the pile head and the upper necking zone and the time
indicating the pile length is the same as the ratio between the time indicating distance between the first parabola and
the total pile length in the intact pile.
C
T. Salem et alii, Frattura ed Integrità Strutturale, 61 (2022) 461-472; DOI: 10.3221/IGF-ESIS.61.30
472
9- The ratio between the necking diameter to the pile diameter values, is proportional to the ratio between the velocity
value of the second parabola peak in the necked pile to the velocity value of the second one at the intact pile. The
necking diameter also can be deduced from this mentioned ratio.
REFERENCE
[1] ADINA, (2021). Automatic Dynamic Incremental Nonlinear Analysis Software, Version 9.70, ADINA R & D,
Watertown, MA, USA.
[2] Štrukelj, A., Pšunder, M., Vrecl-Kojc, H., and Trauner, L. (2009). Prediction of the Pile Behavior under Dynamic
Loading Using Embedded Strain Sensor Technology, Acta Geotechnica Slovenica, 6, pp. 65-77.
[3] Ding, X., Liu, H., Liu, J., and Chen, Y., (2011). Wave Propagation in a Pipe Pile for Low-Strain Integrity Testing,
Journal for Engineering Mechanics, 137, 9, pp.598-609.
[4] Li, Z. (2019). Torsional vibration of a large-diameter pipe pile embedded in inhomogeneous soil. Ocean
Engineering, 172, pp. 737-758.
[5] Wu, J. T., Wang, K. H., Gao, L., and Xiao, S. (2019). Study on longitudinal vibration of a pile with variable sectional
acoustic impedance by integral transformation. Acta Geotechnica, 14(6), pp. 1857-1870.
[6] Li, Z., and Gao, Y. (2019). Effects of inner soil on the vertical dynamic response of a pipe pile embedded in
inhomogeneous soil. Journal of Sound and Vibration, 439, pp. 129-143.
[7] Hou, S.W., Hu, S.J., Guo, S.P., and Zeng, Y.Q., (2016). The Research of Multi-Defective Piles for Low Strain Testing
and Numerical Simulation, In Structures Congress, 16º, Jeju Island, pp. 1-8.
[8] Cosic, M., Folic, B., and Folic, R. (2014). Numerical simulation of the pile integrity test on defected piles. Acta
Geotechnica Slovenica, 11(2), pp. 5-19.
[9] Nazir, R., and El-Hussien, O., (2014). Mathematical Simulation of Pile Integrity Test (PIT), 4th International
Conference on Geotechnique, Construction Materials and Environment, Brisbane, Australia, Nov. 19-21
[10] Niederleithinger, E., (2006). Numerical Simulation of Non-Destructive Foundation Pile Tests, The 9th European
Conference on NDT, Berlin, Germany.
[11] Niederleithinger, E., (2008). Numerical Simulation of Low Strain Dynamic Pile Test, The 8th International
Conference on the Application of Stress Wave Theory to Piles, Lisbon, Portugal, pp. 315-320.
[12] Joram M. Amir, (2009). Pile Integrity Testing, Pile test.com, 1st edition
[13] Warrington, D., Wynn, R., (2000). Comparison of Numerical Methods to Closed-Form Solution for Wave Equation
Analysis of Piling, The 13th Annual Meeting of the Tennessee Section of the American Society of Civil Engineers,
Smyrna, USA.
[14] Zhang, J., Liu, D.J., Geng, X., Gao, Z.J., Ke, Z.B., and Tao, J. (2016). Numerical Analysis of Low Strain Testing of 3-
D Axial Symmetry Viscoelastic Pile–Soil Model, Indian Geotechnical Journal, 46(2), pp. 175-182.
[15] Zhang, C., Yang, S., Zhang, J., and Xiao, N., (2010). The Numerical Simulation for the Low Strain Dynamic Integrity
Testing and Its Application in Quality Diagnosis of Foundation Pile, Journal of Xiamen University (Natural Science),
Xiamen, China.
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This paper presents an analytical solution methodology for a tubular structure subjected to a transient point loading in low-strain integrity testing. The three-dimensional effects on the pile head and the applicability of plane-section assumption are the main problems in low-strain integrity testing on a large-diameter tubular structure, such as a pipe pile. The propagation of stress waves in a tubular structure cannot be expressed by one-dimensional wave theory on the basis of plane-section assumption. This paper establishes the computational model of a large-diameter tubular structure with a variable wave impedance section, where the soil resistance is simulated by the Winkler model, and the exciting force is simulated with semisinusoidal impulse. The defects are classified into the change in the wall thickness and Young's modulus. Combining the boundary and initial conditions, a frequency-domain analytical solution of a three-dimensional wave equation is deduced from the Fourier transform method and the separation of variables methods. On the basis of the frequency-domain analytic solution, the time-domain response is obtained from the inverse Fourier transform method. The three-dimensional finite-element models are used to verify the validity of analytical solutions for both an intact and a defective pipe pile. The analytical solutions obtained from frequency domain are compared with the finite-element method (FEM) results on both pipe piles in this paper, including the velocity time history, peak value, incident time arrival, and reflected wave crests. A case study is shown and the characteristics of velocity response time history on the top of an intact and a defective pile are investigated. The comparisons show that the analytical solution derived in this paper is reliable for application in the integrity testing on a tubular structure.
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An analytical solution is proposed to investigate the torsional dynamic response of a large-diameter pipe pile embedded in inhomogeneous soil. First, both the outer and inner soils are discretized into many annular vertical zones, and their radial inhomogeneity caused by the construction disturbance effect is considered by the gradual variedness of soil parameters in the radial direction. Meanwhile, the layered properties of the soil in the vertical direction are simulated by the distributed Winkler model. Then, the analytical solution for the torsional dynamic response at the pile head is obtained by solving the pile–soil dynamic governing equations and its reliability is verified by comparing with the existing solutions. Finally, selected results for the complex impedance and velocity admittance are presented to examine the influence of the pile–soil parameters and the radial inhomogeneity of the soil on the torsional dynamic characteristics of the large-diameter pipe pile.
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This paper is concerned with the effects of inner soil on the vertical dynamic response of a pipe pile embedded in a vertically multilayered and radially inhomogeneous soil. The soil is considered a three-dimensional axisymmetric medium, the radial inhomogeneity of which (due to the construction disturbance effect) is simulated by gradually varying the soil parameters in the radial direction. The pipe pile is treated as a vertical, hollow, viscoelastic, one-dimensional bar. The velocity admittance and reflected signal at the pile head are derived by solving the equilibrium equations for the pile and soil. They are then used to obtain an insight into the coupled effects of the inner soil and several related factors, such as the pile parameters, construction disturbance effect and pile defect characteristics, on the vertical dynamic response of the pipe pile concerned in pile integrity testing. A comparison with the measured data is also presented to verify the reliability of the proposed solution.
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A standard dynamic loading test of the pile was performed on the highway section Slivnica - Hajdina near Maribor, Slovenia. Parallel to standard testing procedures the new monitoring technology based on specially developed strain sensors installed inside the pile body along the pile axis was introduced. On the basis of the measured results the normal strains along the pile axis were measured. Taking into consideration the elastic modulus of the concrete the normal stresses in the axial direction of the pile were also calculated and afterwards the shear stresses along the pile shaft have been estimated as well as the normal stresses below the pile toe. The estimation was made by considering a constant value for the pile diameter. The measured results were also compared with the computer simulation of the pile and the soil behaviour during all the successive test phases. The strain measurements inside the pile body during the standard dynamic loading test in present casedid not have the purpose of developing an alternative method of pile loading tests. It gave in the first place the possibility of a closer look at the strains and stresses of the most unapproachable parts of different types of concrete structure elements especially piles and other types of deep foundations. The presented monitoring technology proved itself as a very accurate and consistent.
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In order to study the low strain numerical simulation of piles, a three-dimensional axisymmetric viscoelastic model is established. The velocity response for transient vibration is obtained by solving the 3-D wave equations. A MATLAB program is compiled via using finite difference method. The correctness and rationality of the numerical calculation are verified by comparing theoretical result with measured curve. The characteristics of velocity response at pile top are shown through analyzing the simulated results with different viscoelastic parameters. A kind of under-reamed pile (named DX pile in China) is calculated numerically while combining with the engineering practice. And the characteristics of wave propagation in DX pile are reflected intuitively in axial plane wave field diagrams. The results have a certain guiding significance for engineering practice.
The Research of Multi-Defective Piles for Low Strain Testing and Numerical Simulation
  • S W Hou
  • S J Hu
  • S P Guo
  • Y Q Zeng
Hou, S.W., Hu, S.J., Guo, S.P., and Zeng, Y.Q., (2016). The Research of Multi-Defective Piles for Low Strain Testing and Numerical Simulation, In Structures Congress, 16º, Jeju Island, pp. 1-8.
Mathematical Simulation of Pile Integrity Test (PIT)
  • R Nazir
  • O El-Hussien
Nazir, R., and El-Hussien, O., (2014). Mathematical Simulation of Pile Integrity Test (PIT), 4th International Conference on Geotechnique, Construction Materials and Environment, Brisbane, Australia, Nov. 19-21