Experimental study of near-shore pile-to-pile interaction

Soil Dynamics and Earthquake Engineering 48 (2013) 282–293

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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn

Experimental study of near-shore pile-to-pile interaction Francesca Dezi a,n, Fabrizio Gara b, Davide Roia b a b

Department of Economics and Technology, University of San Marino, Via Salita alla Rocca, 47890, San Marino Department of Civil and Building Engineering and Architecture, Universita Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 August 2012 Received in revised form 6 January 2013 Accepted 12 January 2013 Available online 19 March 2013

This paper presents the results of lateral impact load field tests carried out on a system of three steel pipe piles vibro-driven into soft clay in a near-shore marine environment, with the aim of evaluating the pile–soil–pile dynamic interaction. Piles are arranged in an ‘‘L’’ shaped horizontal layout and are instrumented with accelerometers at their free heads. The obtained results show the complex dynamic behaviour at very small strain of the vibrating soil–water–piles system. The role of different type of waves in the pile to pile interaction is investigated by analyzing the results in the time and frequency domains and by means of a time–frequency analysis. The effects of the pile spacing and input direction on these interaction mechanisms are also presented. Finally, important dynamic parameters of the soil, such as the velocities of the shear waves and surface waves (Scholte waves) of the upper soil are directly estimated from the time delays between signals recorded at the pile heads. & 2013 Elsevier Ltd. All rights reserved.

1. Introduction The pile–soil–pile dynamic interaction is a complex mechanism affecting the performance of many structures founded on piles such as off-shore and near-shore platforms, wind turbines, docks, jetties, wharfs, mooring structures and bridge piers. For these structures, the dynamic effects caused by current, wind, wave, boat mooring, boat impact and also earthquakes, in some cases may lead to early failure and must be carefully evaluated. In pile foundations subjected to dynamic excitation due to seismic waves propagating through the soil or any dynamic load applied to the superstructure, each pile is first excited and, then, due to its motion, becomes itself a source of new waves (source pile) that propagate until encountering adjacent piles (receiver piles). From a theoretical viewpoint, the soil–pile interaction may be approached with numerical methods, modelling the whole soil– pile system with the Finite Element Method (FEM) and the Boundary Element Method (BEM), and analytical models. Among others, [1–6] used the FEM, whereas [7–13] implemented the BEM for the dynamic response analysis of piles. In some cases, the limitation of the FEM in modelling far fields is overcome coupling FEM with BEM. Both FEM and BEM consider soil as a continuum and give the advantage of making it possible to perform fully coupled seismic soil–pile–structure interaction analyses. Analytical approaches are based on different assumptions on wave propagation through the soil from pile to pile, which can reach a satisfying

n

Corresponding author. Tel.: þ39 549 888111; fax: þ39 549 888113. E-mail addresses: [email protected], [email protected] (F. Dezi), [email protected] (F. Gara), [email protected] (D. Roia). 0267-7261/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.soildyn.2013.01.025

degree of refinement. In particular, Berger et al. [14] presented a simplified analytical procedure based on the assumption that a pile, subjected to horizontal vibration, generate 1D P-waves travelling in the direction of shaking only and 1D SH-waves travelling in the direction perpendicular to shaking only; Gazetas and Dobry [15] presented an approximate 2D plane-strain model in which compression–extension waves propagate in the two quarterplanes along the direction of loading while shear waves are generated in the two quarter-planes perpendicular to the direction of loading; and an alternative 2D solution was developed by Novak et al. [16] by solving the problem of a soil slice of infinite extent subjected to horizontal oscillations from a rigid circular inclusion, the model was verified by means of 3D FE formulation by Roesset et al. [17,18]. A comprehensive review on the subject is in [19]. Experimental results carried out on full- or small-scale in-situ and laboratory tests are essential for accurate calibration and validation of these models. Petrovski and Jurukovski [20], Blaney and O’Neill [21], Kobori et al. [22], Tuzuki et al. [23], Mizuno and Iiba [24], Imamura et al. [25], Shimomura et al. [26] conducted forced vibration tests. As regards impact load tests, an experimental campaign, including also other types of tests, were carried out by Halling et al. [27], on a 3  3 concrete pile group in soft clay; from the results of impact load tests the natural frequencies and damping ratios of the soil–pile system at low strains were evaluated. It is worth noting that all the experimental studies reported above deal with groups of piles fixed at the head (connected with a cap) and, to the authors’ knowledge, there are no scientific works on the interaction between systems of near-shore free-head piles. The lack of experimental evidences on the dynamic soil–pile interaction and, particularly for near-shore piles, was the main

F. Dezi et al. / Soil Dynamics and Earthquake Engineering 48 (2013) 282–293

motivation of the experimental programme carried out at the ‘‘Mirabello’’ harbour in La Spezia (Italy) on near-shore steel pipe piles which were installed by vibro-driving for a depth of 9.5 m into soft marine clay and tested under dynamic lateral loads, e.g., impact load tests, free and forced vibration tests. The main objective of this experimentation is to study the dynamic behaviour, at both small and large strain, of a single pile and a system of piles. The response of the single pile to horizontal impact load tests has been already discussed in [28]. This paper deals with the horizontal impact load tests carried out on a system of three steel pipe piles arranged in an ‘‘L’’ shape

283

horizontal layout with different spacing to study the pile–soil– pile dynamic interaction. Tests were carried out in two different series, one performed 1 week after pile vibro-driving and the other after 10 weeks. The paper is divided into three parts. In the first section the geotechnical site characterization and the test field are described, together with the instrumentation and test configurations. The second part outlines the experimental results, analyzed in both time and frequency domains to identify the fundamental frequencies of the system and to investigate the contribution of different wave types to pile motion varying the test configuration (i.e. spacing between loaded and receiver

TEST FIELD

Fig. 1. Test site.

0 A B

mud and loose clayey silt normal consolidated slightly silty clay

5

C

slightly sandy, silty clay

10

E D E

overconsolidated silty clay and clayey silt sand and dense silty sand with heterogeneous coarse lenses overconsolidated silty clay and clayey silt

15

D

sand and dense silty sand with heterogeneous coarse lenses

C

slightly sandy, silty clay

D

sand and dense silty sand with heterogeneous coarse lenses

0

CPT q c [MPa] pile

10 ~2.0 1.5

S1

z [m]

~9.5m

mud

25 30 35

0

20

40

60

80 100

( ) NSPT [blows/foot] Fig. 2. Subsoil profile.

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pile and impact direction). A time–frequency analysis, created by computing the Fourier spectra using a sliding temporal window, is also presented to describe how the spectral content of the signal changes with time. The remaining part of the paper presents a procedure for the evaluation of the wave velocity of superficial deposits. The approach is based on the calculation of the difference between the arrival times of waves recorded at the head of piles and involves the performance of two impact tests varying the direction of loading. The standard measurement instrumentation and the basic understanding of signal processing required in this procedure make this method for the evaluation of in situ shear wave and surface wave velocities promising for practical purposes.

2. Site and setup of tests 2.1. Site characterization The test site is located in the tourist port ‘‘Mirabello’’ in La Spezia (North-West Italy), where a foundation of about 500 vibrodriven steel pipe piles, with diameters ranging between 609– 711 mm, and embedded length from 20 to 45 m, was realized for a new sector of the arbour (Fig. 1). Several site explorations (1973, 1981, 1991, 1992 and 2008) were carried out before the construction of this new section of the harbour. A large volume of soil was investigated by means of Table 1 Geotechnical parameters. Soil type

Borehole P.P. [kPa]

A B C D E

CPT V.T. [kPa]

68

22 44

120

50

DMT

FVT

qc [MPa]

fs [kPa]

cu [kPa]

OCR cu [kPa]

cur [kPa]

0.37 0.45 0.82 7.90 2.25

13 14 18 100 120

14 19 40

3.00

20 25 47

5 8 12

82

5.00 108

22

P.P. ¼ resistance to penetration measured by pocket penetrometer, V.T. ¼ shear strength measured by pocket scissometer, qc ¼ cone resistance, fs ¼ sleeve friction, cu ¼ undrained shear strength, OCR ¼ over consolidation ratio, cur ¼ undrained residual shear strength.

laboratory tests and in-situ tests conducted up to a maximum depth of about 50 m. The soil stratigraphy and a CPT profile representative of soil conditions in the proximity of the test site is reported in Fig. 2 while the main soil properties of each soil layer, derived by the geotechnical investigations, are presented in Table 1. Based on these results the soil strength profile can be reasonably considered as uniform over the pile embedment length. A more detailed description of the geotechnical investigations is reported in [28]. 2.2. Test field The test field consists of three steel pipe piles, 15.5 m long, vibro-driven for a depth of 9.5 m into the soft marine clay and with pile head elevation 1.0 m above the mean sea level (m.s.l.) (Figs. 2 and 3a). The piles are arranged in an ‘‘L’’ shaped horizontal layout characterized by different distances between pile P1, located at the ‘‘L’’ corner, and piles P2 and P3 (Fig. 3a and b). The test field layout allows studying the pile-to-pile interaction in two orthogonal directions and for two pile spacings. Pile P1 has a diameter of 711 mm and thickness of 11 mm whereas piles P2 and P3 have a diameter of 609 mm and thickness of 10 mm. The head of the piles are kept free and the head of pile P1 is stiffened with two steel profiles, welded in a crux shape (Fig. 3c). 2.3. Instrumentation To measure the horizontal acceleration at the head of each pile uniaxial piezoelectric accelerometers (A) are used. In particular, accelerometer 4370 Bruel & Kjær with nominal sensitivity 80 mV/ g and frequency range 0.1–4800 Hz is used at the head of the loaded pile, while accelerometers PCB 353B43 with sensitivity 300 mV/g and frequency range 1–2000 Hz are used at the head of the receiver piles. The accelerometers (yellow circles of Fig. 4(a)) are located at 0.3 m from the top of each pile and are conveniently moved in different positions to measure acceleration in different directions. Magnetic mounting adapters are used to attach the accelerometers to the pile surface; this connection system has the advantage of ensuring a cut-off frequency much higher than the frequencies of interest and permits to move the accelerometers quickly from place to place according to different test configurations. For the loaded pile, a mechanical filter is

Fig. 3. (a) Test field; (b) horizontal layout of test field; and (c) plan view of pile P1.

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285

P3 P2

P1

Fig. 4. Instrumentation: (a) accelerometers and instrumented hammer; (b) measuring chain.

Fig. 5. Impact load: (a) time history; (b) frequency spectrum (semi-log plot).

Hx-x

Hy-y

A3y

Hxy-x

Instrumented hammer Uniaxial accelerometer

A3x A2x

A1x

A3x Hx

A2y

A1y

A2x

A1xy Hxy

Hy

Hx-y

A3y

Hxy-y

Hy-x

A3y

A3x A2y

A1y

Hx

A2x

A2y

A1x

A1xy Hxy

Hy Fig. 6. Test configurations.

interposed between accelerometer and pile surface to prevent insignificant very high frequency vibration, which can cause overloads. In addition, the pile P1 is instrumented with 19 strain gauges to measure the longitudinal strains along the pile and capture the cross section average strains (elongation and curvatures of the pipe) with the aim of studying the response of the single pile to dynamic lateral loads. For details on the strain gauges position along the pile, on the trasducers and cables protection from the marine environment and vibro-driving, and on the results of the impact load tests carried out on the single pile (in terms of natural frequencies, damping, mode shapes, and horizontal dynamic impedance function of the soil–water–pile system), readers may refer to [28]. The measuring chain also includes amplifiers, signal conditioners, one spectrum analyzer, two data acquisition systems, and a computer with dedicated software (Fig. 4b). The characteristics of the measuring instruments are chosen according to preliminary

approximate finite element analyses [28] which were performed to estimate frequencies and amplitudes (magnitude order) of both accelerations and strains. A sampling rate of 10 kHz is chosen to achieve high resolution in time domain and an acquisition time duration of 2 s with a 100 pre-trigger samples (0.01 s) is considered to catch the entire duration of the pile oscillation and to capture the beginning part of the hammer impulse. An instrumented hammer (equipped with a load cell) having a mass of 5.5 kg is adopted for the tests (Fig. 4(a)). Several preliminary in situ tests were performed to choose the properties of the hammer and the stiffness of the hammer tip in such way that the impacts could induce accelerations at the pile heads within the transducers measuring ranges and greater than the noise due to both the ambient and the electrical measuring chain. During the tests, a maximum impact force of about 50 kN is reached with the used hammer equipped with a medium-low hard tip. A typical time history recorded by the load cell of the hammer for a medium intensity impact is reported in Fig. 5(a)

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(pre-trigger starts the acquisition data 0.01 s before the impact) whereas the corresponding frequency spectrum is shown in Fig. 5(b). This spectrum is characterized by a constant force level up to about 100 Hz and then decreases up to nearly zero at 1000 Hz; therefore, this hammer permits to investigate the dynamic behaviour of the whole system in a wide range of frequencies. 2.4. Test configurations Tests were carried out considering six different test configurations, varying the direction (x, y, or diagonal, identified with xy index) of the horizontal impact at the head of pile P1 and the measuring direction of the accelerometers at the head of each pile, as illustrated in Fig. 6. In particular, Hi–j denotes a test in which the hammer impacts the pile along the i direction while the acceleration is measured in the j direction. These configurations permit studying the propagation of the dynamic input, from pileto-pile through the soil–water system, for different directions (parallel, orthogonal and diagonal to the impact direction) and different pile spacing. For each test configuration, a set of 10 horizontal hammer impacts are given and the time histories of the impact load and of

the acceleration at the head of each pile are recorded. A total of 60 tests are carried out for each of the two test series which are conducted: the first, 1 week after the pile installation and the second after 10 weeks. The tests are repeated to evaluate differences with time in the dynamic behaviour of the pile–soil– pile system. Before the tests, the sea water and soil levels inside and outside each pipe are measured. Furthermore, the ambient noise mainly due to marine waves is registered (0.0067 g RMS), and preliminary tests are conducted in order to set up the data acquisition system and proper gains for the accelerometer signals. In all tests the seabed inside and outside the piles is at the same level and approximately at 1.5 m depth below the sea level (Fig. 2).

3. Experimental results 3.1. Time domain response In this section the dynamic response of the near-shore piles under impact loads is presented in terms of time histories of the horizontal accelerations measured at the head of each pile.

Fig. 7. Time histories of accelerations on loaded pile: Tests Hx–x and Hx–y.

Hx-x A3x

Raw signal Filtered signal A2x

0.6

Hy-y A3y

Raw signal Filtered signal

A1y

A2y

A1x

A2x

A2y

A3x

A3y

Acceleration [ms-2]

0

-0.6 0.6

0

-0.6 0 0.01

0.2

t [s]

0.4

0.6 0 0.01

0.2

t [s]

0.4

Fig. 8. Time histories of accelerations on receiver piles: Tests Hx–x and Hy–y.

0.6

F. Dezi et al. / Soil Dynamics and Earthquake Engineering 48 (2013) 282–293

Hy-x

A2x

Acceleration [ms-2]

0.6

Hx-y A3x

Raw signal Filtered signal

287

A3y

Raw signal Filtered signal

A1y

A2y

A1x

A2x

A2y

A3x

A3y

0

-0.6 0.6

0

-0.6 0 0.01

0.2

0.6 0 0.01

0.4

t [s]

0.2

0.4

t [s]

0.6

Fig. 9. Time histories of accelerations on receiver piles: Tests Hy–x and Hx–y.

Hxy-y

Hxy-x A3x

Raw signal Filtered signal

A1xy

A2x

Acceleration [ms-2]

0.6

A3y

Raw signal Filtered signal

A1xy

A2y

A2x

A2y

A3x

A3y

0

-0.6 0.6

0

-0.6

0 0.01

0.2

0.4

t [s]

0.6 0 0.01

0.2

0.4

0.6

t [s]

Fig. 10. Time histories of accelerations on receiver piles: Tests Hxy–x and Hxy–y.

Accelerations are denoted by Aij, where i represents the pile monitored and j the direction of the measured acceleration. The qualitative features of the signals, recorded from the loaded and the receiver piles during different test configurations, are discussed. In Figs. 7–10, graphs refer to one of the ten impacts impressed for each test configuration of the second series; raw signals and filtered signals (Butterworth low-pass filter with a cut-off frequency of 100 Hz) are reported with light grey and black lines, respectively; 0.01 s on the abscissa represents impact time. The upper graphs of Fig. 7 show the acceleration time histories recorded on the loaded pile during the test Hx–x. A1x is the acceleration registered in the same direction of the impact load and A1y is the acceleration orthogonal to the direction of the impact load. The signals are characterized by very high frequency

content; amplitudes are significant in the first part of the signals and rapidly decrease after 0.05 s. Such features are due to pipe cross-sectional deformations which are predominant near the hammer impact point and are no more evident in the filtered signal. In the lower graphs of Fig. 7, a low-pass filter, with a cutoff frequency of 20 Hz, is applied to the acceleration time histories of the loaded pile. In the test Hx–x, a low amplitude damped harmonic oscillation at the frequency of the first bending mode of the soil–water–pile system is observed; while in the test Hx–y no regular oscillation is clearly evident. In Fig. 8 the acceleration time histories of the receiver piles recorded during tests Hx–x (A2x and A3x>) and Hy–y (A2y and A3y) are reported. Peak values are always two orders of magnitude smaller than those of the loaded pile. The signals are characterized by an initial time delay followed by a first part

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with high frequency content, a second transitory part, with minor high frequency content, and a final part with a damped harmonic oscillation at the first dominant frequency of the system. The first part is due to the faster waves that firstly arrive to the receiver piles, i.e., P-waves propagating through the sea water and through the saturated clay seabed; their effects are more significant in the pile disposed along the impact direction (A2x and A3y in tests Hx–x and Hy–y, respectively). P-waves travelling through the sea water and those through the soil are characterized by not clearly distinguishable arrival times. This is probably due to the fact that, in fully saturated soil P-waves are essentially transmitted through the liquid phase (water) and the velocity is of the same order of the sound speed in water [29]. The high frequency content of the first part of the signals, which almost disappears after a low-pass signal filtering, is primarily due to the radial circumferential modes of the loaded pile. These modes are predominant at the pile head close to the hammer impact point and over the pipe length in water but significantly reduce over the embedded part of the loaded pile. Consequently, from the cross-sectional deformations of the submerged pile portion a large amount of high frequency P-waves, travelling through the water, is generated, whereas from the cross-sectional deformations of the embedded pile portion only a small amount of high frequency waves (P-, S- and surface waves), travelling through the seabed soil, is generated. The second part of the signals is characterized by the arrival of waves travelling slower through the soil: primarily surface waves (Scholte waves) when the receiver pile is along the impact direction or shear waves (S-waves) for a pile disposed orthogonally to the impact direction. Comparison between raw and lowpass filtered signals shows that the high-frequency content is much lower in the second part of signals than in the first part. However, looking at various impacts, the high frequency content in the second part is not always the same. This may be due to the contribution of the pile cross-sectional modes that can be different because of the variability of the hammer impact point with respect to the stiffeners location at the pile head. Furthermore, some considerations can be made on the attenuation of these waves with distance. Pile P2 in test Hx–x and pile P3 in test Hy–y are both disposed along the impact direction but at a different distance from the loaded pile; it can be observed from the raw signals that the first part (P-waves) attenuates rapidly with distance while the second part of signals (mainly due to surface waves) less rapidly. On the other hand, signals recorded from pile P3 in test Hx–x and pile P2 in test Hy–y, both disposed orthogonally to the impact direction, exhibit maximum values in the second part mainly due to S-waves; despite the different distance of these piles from the loaded pile, the attenuation is not particularly pronounced. The final part of the signals exhibits a damped harmonic oscillation at the dominant frequency of the system, which is much lower than the dominant frequency of the initial parts of the signals. Such oscillation is mainly transmitted from the loaded to the receiver piles by low frequency P-, S- and surface waves. Fig. 9 refers to the Hx–y and Hy–x tests; despite accelerations are measured in the direction orthogonal to that of the impact load, amplitudes are only slightly reduced with respect to those recorded during tests Hx–x and Hy–y. This may be motivated by several factors: energy radiates in all the directions due to the circular cross section of the pile; the third pile might reflect energy from the source to the receiver pile; the impact could have a small component along the orthogonal direction; and the stiffeners at the pile head together with the steel profiles welded along the pile make the loaded pile not perfectly symmetric with respect to x- and y-directions. The concomitance of some of these factors can produce vibrating modes, especially cross-sectional modes, not symmetric with respect to x-

and y-directions and induce the motion of the receiver piles also in the direction orthogonal to the input. Analogous considerations, expressed above for the tests in Figs. 8 and 9, hold for tests Hxy–x and Hxy–y (in Fig. 10) since the impact load in diagonal direction can be considered as the resultant of two components in x- and y-directions.

3.2. Frequency domain response In this section the dynamic response of the system of near-shore piles is analyzed in the frequency domain to identify the fundamental frequencies of the system and to investigate the contribution of different wave types to pile motion varying the test configuration (i.e. spacing between loaded and receiver pile and impact direction). To this purpose, Frequency Response Functions, obtained dividing the acceleration at the head of the receiver pile Ar (output) by the impact force Fl (input) FRFðoÞ ¼

Ar ðoÞ , F l ð oÞ

ð1Þ

are evaluated. A peak in the FRF indicates a resonance frequency of the whole system, which is composed by the loaded pile, soil, water, and receiver piles. In the sequel the FRFs, averaged on the ten impacts for each test configuration, are shown and considerations on the variation in time of the system response are also made. Fig. 11 shows the averaged FRFs obtained from the accelerations measured at the head of the receiver piles for all test configurations. Black lines refer to FRFs of the first series of tests and light blue lines to the second series. All FRFs relative to pile P2 (left graphs) present a clear peak that identifies the first resonance frequencies of the system, between 6.5 Hz and 7.0 Hz for the first series. FRFs relative to pile P3 (right graphs) present two close peaks, in a range between 5.5 Hz and 7.0 Hz (first series). It can be also observed that the resonance frequency for impacts in x-direction is generally a little bit higher than in y-direction. This is likely due to the imperfect radial symmetry of pile P1 (determining different pile flexural stiffness in different directions) that is caused by UPN profiles welded along the pipe to protect strain gauges and cables as reported in [28]. By analyzing the values of FRF peaks, some considerations can be made on the quantitative contributions given by different types of waves to the receiver pile motion and on their attenuation with distance. Fig. 12 reports the mean value of the FRF peaks and the standard deviation calculated on the ten impacts for all test configurations of the first (black lines) and the second (blue lines) series. In all cases the standard deviation can be considered quite small and surely acceptable for the type of test considered. In Fig. 12, the upper graph on the left refers to the acceleration recorded on the piles P2 and P3 during the tests Hx–x and Hy–y respectively and the contributions mainly due to P- and surface waves are evaluated for two distances. Whereas, the upper graph on the right refers to the acceleration recorded on the piles P2 and P3 during the tests Hy–x and Hx–y, respectively and the contribution mainly due to S-waves is illustrated. Comparing these graphs, it can be observed that: (i) P- and surface waves induce higher amplitude (major contribution) than S-waves; and (ii) the contribution of P- and surface waves decays with distance more rapidly than that of S-waves. Furthermore, looking at the three graphs reported on each column of Fig. 12, it can be noticed how the peak amplitude of the mean FRF varies with the direction of the impact load (0, 45, and 90 degrees with respect to the measured acceleration). As general trend, it can be noted that the amplitudes decrease as the angle increses and that it remains quite important also for impact direction orthogonal to the measuring direction.

F. Dezi et al. / Soil Dynamics and Earthquake Engineering 48 (2013) 282–293

6.5 Hz

7.0 Hz

1

A2x

A3x 7.0 Hz

1st series 2nd series

0 2

Hx-x

2

289

6.5 Hz

A2y

A3y

1

Hy-y

7.5 Hz 7.0 Hz 7.0 Hz

A2x

A3x

7.5 Hz

Hy-x

7.0 Hz

1 7.0 Hz

0 2

7.5 Hz

A2y

A3y

Hx-y

FRF Amplitude [ms-2/kN]

0 2

7.5 Hz

1 7.0 Hz

6.0 Hz

6.5 Hz

0 2 7.0 Hz

6.5 Hz

A2x

A3x

Hxy-x

6.5 Hz

1 6.5 Hz

0 2

7.0 Hz

A2y

7.0 Hz

Hxy-y

1

A3y

7.5 Hz 7.0 Hz

7.0 Hz

0 0

10

20

30

10

40 0

f [Hz]

20

30

40

f [Hz]

1

A3y P-waves

A3x S-waves

0 3 2

A2y

A2x A2y

1

A3x

A3y

0 3 2

A2x

1 0

d12

pile spacing

A3y

A2y

d13

d12

A3x

Hxy-x & Hxy-y

FRF Peak Amplitude [ms-2/kN]

A2x

S-waves

2

P-waves

1st series 2nd series

Hx-y & Hy-x

3

Hx-x & Hy-y

Fig. 11. Frequency Response Functions of the pile–soil–pile system. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

d13

pile spacing

Fig. 12. Mean values and standard deviation of peak values of FRFs for different pile spacing and input direction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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As regards the comparison between the results of tests performed at 1 and 10 weeks after pile installation, it is worth noting that the first resonance frequency increases by about 0.4 Hz (mean value) with respect to the first campaign and the relative amplitudes are generally higher, with a mean increment of 0.17 ms  2/kN. These increments may be attributed to an increase in the soil stiffness with consequent reduction of the damping, and may be due to the re-consolidation of the soil close to the piles after pile vibro-driving (or pile ‘‘set-up’’ as it is often termed). This confirms the result obtained in [28] regarding tests on the single pile. Such phenomenon can be explained by the fact that excess pore water pressures develop in the soil during pile driving. As the pore pressures dissipate, the soil recovers its strength and the frequency of the system increase. In [30], on the basis of a number of well-documented cases of short-term pile set-up, it is shown that the increase in soil strength can be linked by a log relationship with time. In [31] it is explained that the rate of dissipation of excess pore pressures around openended piles is controlled by the volume of steel forced into the soil and that the ‘‘cylindrical cavity expansion’’ theory generally appears to offer a reasonable approach for estimating stress changes during installation and subsequent consolidation. The associated increase in lateral effective stress with increasing time is an important issue in the design of off-shore structure (e.g. when checking that the foundation can survive an appropriate design storm during the first months of operation).

Acc. [ms-2]

0.6

-0.6 0

0.2

0.4

0.6

t [s]

f [Hz]

0

1000

Amplitude

f [Hz]

0

3.3. Time–frequency analysis

1000 0.2

0.4

0.6

In this section the methodology and the main results of a time–frequency analysis, carried out by computing the Fourier spectra using a sliding temporal window (Short Time Fourier Transform STFT), are presented. This analysis allows describing how the spectral content of the signal changes with time.

t [s] Fig. 13. Schematic procedure for spectrogram construction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Acc. [ms-2]

0.6

A2x

0 Raw signal Filtered signal

-0.6 0

f [Hz]

A3x

Hx-x

0

A3x

500 A2x 1000 A2y

A3y

0

Hy-y

Acc. [ms-2]

0.6

-0.6 0

f [Hz]

A3y 500

A2y

1000 00.01

0.2

0.4

t [s]

0.6 00.01

0.2

0.4

t [s]

Fig. 14. Time histories and spectrograms of accelerations: Tests Hx–x and Hy–y.

0.6

F. Dezi et al. / Soil Dynamics and Earthquake Engineering 48 (2013) 282–293

A2x

0

f [Hz]

Hxy-x

Raw signal Filtered signal

-0.6 0

A3x

500 A2x

1000 0.6

Acc. [ms-2]

A3x

A2y

A3y

0

Hxy-y

Acc. [ms-2]

0.6

291

-0.6 0

f [Hz]

A3y

500

1000

A2y

0 0.01

0.2

0.4

t [s]

0.6 0 0.01

0.2

0.4

0.6

t [s]

Fig. 15. Time histories and spectrograms of accelerations: Tests Hxy–x and Hxy–y.

The results are presented in two-dimensional plots (Figs. 13–15) with time in the horizontal axis and frequency in the vertical one; a third dimension indicating the amplitude of a particular frequency at a particular time is represented by the colour of each point in the image. The dominant frequencies of the system are individuated, time by time, by the higher amplitude values in the spectrogram. The STFT is calculated according to following formula (valid for continue functions): Z þ1 n STFTðt, oÞ ¼ xðtÞh ðttÞeiot dt ð2Þ 1

by means of the Matlab function ‘‘spectrogram’’ [32], that uses the n Hamming window h ðttÞ and computes the FFT (for discrete records) for each time window. In this case, a 500 sampling window with an overlap of 499 is considered to obtain a time resolution equal to that of the original signal (104 s) and a frequency resolution of 20 Hz. Furthermore, to obtain the spectrogram also for the initial instants (first 250) artificial zeros are appended to the beginning of the signal (zero padding). Fig. 13 shows schematically the procedure applied: (a) zero padding and windowing of the original signal (in this figure three windows are considered: 0.025–0.075 s with blue line, 0.105–0.155 s with green line and 0.255–0.305 s with red line); (b) computation of the FFTs relevant to the windowed signals; and, finally, (c) construction of the spectrogram. It is worth noting that in this case the analysis is performed for frequencies up to 1000 Hz which is the superior limit of a typical impact spectrum (Fig. 5). However, as the impact spectrum is characterized by a constant force level up to about 100 Hz and decreases for higher frequencies, spectrograms give only qualitative information in the 100– 1000 Hz range. Fig. 14 shows spectrograms obtained for the tests Hx–x and Hy–y where the accelerations are measured along the impact direction (note that signals reported in this figure and in Fig. 8 correspond to different impacts). Regarding piles disposed along the impact direction, spectrograms relative to signals A2x and

A3y clearly show that the first arriving waves, P-waves, are characterized by high frequency content (400–600 Hz in A2x and 800 Hz in A3y). Successively, the second part of the signals is characterized by both high and low frequency content. The high frequency vibrations may be attributed to the pile cross-sectional vibration modes that are particularly susceptible to the variability of the hammer impact point with respect to the stiffeners location at the pile head. Low frequency vibrations are more likely generated by surface waves. Spectrograms relative to signals A3x and A2y, recorded on piles disposed orthogonally to the impact direction, show that the main contribution to the pile motion is given by the second arriving waves, S-waves, with lower frequency content (below 100 Hz). The final part of the signals is only due to the first mode of vibration of the pile (about 7 Hz) that gets damped out more slowly. The spectrograms relevant to tests Hxy–x and Hxy–y are reported in Fig. 15. In these configurations the input excites in both directions the receiver piles. Peaks of the spectrograms relevant to signals A2x and A2y, demonstrate that the motion of pile P2 is mainly due to P-waves in x-direction and to S-waves in y-direction, respectively. Vice-versa for pile P3. This results is likely to be obvious when considering the impact force as the sum of two components along x and y directions.

4. Evaluation of low strain shear wave velocity of the soil In this section an unconventional simple procedure for the evaluation of S-wave and surface wave velocity of superficial deposits is presented. This procedure is fully described and then applied to estimate the wave velocities in the actual case. The L-shape layout with different pile spacing enables the estimation of the wave propagation velocity through the superficial soil starting from the evaluation of time delays of the recorded acceleration signals. Waves induced by the impact load at the head of the pile P1 propagate firstly down the pile, through

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direction and at different spacing from the pile P1, an average S-wave velocity of the soil among piles may be estimated. In the upper part of Fig. 16, the test configurations considered are shown. The middle part of Fig. 16, illustrates the time histories recorded on the loaded pile P1, and on the receiver piles: P3 for test Hx–x and P2 for test Hy–y, respectively. A low-pass filter is applied to the signals in order to eliminate the high frequency content mainly due to P-waves. The lower part of Fig. 16 shows the crosscorrelations functions (CCF) of the signals and the time delays relevant to these tests. Assuming the travelling time of waves along the piles to remain constant, the difference in time delay is namely due to the different pile spacing, d13 and d12, and consists in the shear wave travel time through the portion of soil of length d13–d12. The difference in time delay divided by the distance d13–d12 gives an average shear wave velocity of the upper soil of about 55 m/s. The same method can be applied to estimate the surface wave velocity. In this case, an important step of the processing is the use of the low-pass filter to eliminate the high frequency content mainly due P-waves. To this scope, the difference between the time delays (obtained by means of CCF of the filtered signals) relative to the receiver piles, P2 for test Hx–x and P3 for test Hy–y, placed along the direction of the impact are considered as shown in Fig. 17. Dividing this difference by d13–d12 a mean value of 49 m/s is obtained. It is worth noting that this value is slightly less than that obtained for S-waves and this is consistent with theory. The method does not furnish reliable P-wave velocity values due to the fact that for near-shore piles the contributions given by P-waves travelling through soil and water are mixed together and cannot be separated by means of simple signal filtering process.

the water and then also through the soil, exciting the neighbouring piles, and finally propagating to up the receiver piles P2 and P3 exciting the accelerometers at their heads. Therefore, the travelling time of the waves from the loaded to the receiver pile is the time delay of the acceleration signal recorded at the receiver pile with respect to the acceleration signal recorded at the loaded pile. In general, time delay between signals x(t) and y(t) of two receiver transducers located at different position respect the wave source can be accurately evaluated by means of cross-correlation function (CCF) [32] between the two signals. In case of two signals xðtÞ ¼ ½xðt 0 Þ,xðt 1 Þ,:::,xðt i Þ,. . .,xN1 

ð3Þ

yðtÞ ¼ ½yðt 0 Þ,yðt 1 Þ,:::,yðt i Þ,. . .,yN1 

ð4Þ

with constant sampling rate Dt ¼ti  ti  1, a CCF can be given by Rxy ðjÞ ¼

N1j X

xðt i Þ  yðt i þjDtÞ

for j ¼ 1,. . .,N1

ð5Þ

i¼0

In this paper, for the calculation of the time delay between two accelerometer signals, the following formula is used: 8 N1j X > > < 1 xðt i Þ  yðt i þ jDtÞ j Z0 ð6Þ Rxy ðjÞ ¼ N9j9 i ¼ 0 > > : R ðjÞ j o0 yx

where the time delay is t ¼jDt in correspondence of the maximum value of the CCF. In particular, by computing time delays for test configurations in which the receiver piles are placed orthogonally to the impact

Hy-y

Hx-x

d13

A3x

d12 A1x S-w

ave

S-wave

Acc. [ms-2]

50

0.6

0

0

A1x A3x

CCF

-50 0.1

A1y

A2y

-0.6

A1x-A3x

24

0.6

0

0

A1y A2y

-24 0.06

-0.6

A1y-A2y

0

0 Time delay 0.095 s

-0.1 0 0.01

Time delay 0.063 s

-0.06

0.2

0.4

0.6

0 0.01

0.2

t [s]

0.4

0.6

t [s]

Fig. 16. Estimation of shear wave velocity: test configurations and wave propagation; time histories of acceleration on loaded and receiver piles; and Cross-Correlation Functions.

Hy-y

Hx-x

d13

A3y d 12

A2x

A1y

A1x Surface wave

Fig. 17. Estimation of surface wave velocity: test configurations and wave propagation.

ce rfa Su ave w

F. Dezi et al. / Soil Dynamics and Earthquake Engineering 48 (2013) 282–293

However, when applied in superficial soil deposits, it seems to be an interesting test promising for practical purposes.

5. Conclusions The results of full-scale impact load tests on a system of three steel pipe piles vibro-driven into soft clay in a near-shore marine environment, has been presented. Piles are arranged in an ‘‘L’’ shaped horizontal layout with different spacing and are instrumented with accelerometers at their free heads. The results are analyzed in both time and frequency domains to identify the fundamental frequencies of the system and the contribution of different wave types to pile motion varying the test configuration (i.e. spacing between loaded and receiver pile and impact direction). Time–frequency analyses are performed to describe how the spectral content of the signals changes with time. An unconventional procedure for the evaluation of the wave velocity of superficial deposits is also presented. The following conclusions can be drawn.

 Pile-to-pile interaction is a complex phenomenon involving







different types of waves (P-, S- and surface waves) radiating from the source pile and propagating through soil and water up to excit the neighbouring piles. In the case of piles disposed along the impact direction, the main contribution to the pile motion is given by the first arriving waves, P-waves, with high frequency content; while, in the case of piles disposed orthogonally to the impact direction the main contribution is given by the second arriving waves, S-waves, with lower frequency. The contribution of different wave types to the pile motion is also affected by the distance between loaded and receiver piles; actually, P-waves, travelling from pile to pile, attenuate much more rapidly with distance than S-waves. The comparison between results of two campaigns, carried out at a time distance of 9 weeks, permitted to evidence an increase of the dominant frequency of the pile–soil–pile system in the second test series that can be attributed to the effects of soil re-consolidation after pile vibro-driving. the presented test for the evaluation of the wave velocity of superficial deposits, requiring standard measurement instrumentation and the basic understanding of signal processing, can be considered a promising technique for practical purposes.

Acknowledgements The in-kind and financial support of Piacentini Costruzioni S.p.A., based in Modena, is greatly appreciated. The contributions of Luca Piacentini and Fabio Dall’Aglio (Piacentini Ingegneri S.r.l.) in supplying technical support are highly appreciated. References [1] Brown DA, Shie CF. Three dimensional finite element model of laterally loaded piles. Computers and Geotechnics 1990;10:59–79. [2] Muqtadir A, Desai CS. Three dimensional analysis of a pile-group foundation. International Journal of Numerical and Analysis Methods in Geomechanics 1986;10:41–58. [3] Pressley JS, Poulos HG. Finite element analysis of mechanisms of pile group behavior. International Journal for Numerical and Analytical Methods in Geomechanics 1986;10:213–21. [4] Trochanis AM, Bielak J, Christiano P. Three-dimensional nonlinear study of piles. Journal of Geotechnical Engineering 1991;117(3):429–47.

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