Nonlinear seismic soil–pile–structure interactions: Shaking table tests and FEM analyses

ARTICLE IN PRESS Soil Dynamics and Earthquake Engineering 29 (2009) 300–310

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Nonlinear seismic soil–pile–structure interactions: Shaking table tests and FEM analyses K.T. Chau a,, C.Y. Shen b, X. Guo c a b c

Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, China Earthquake Engineering Research Test Center, Guangzhou University, Guangzhou, China Institute of Engineering Mechanics, Harbin, China

a r t i c l e in f o

a b s t r a c t

Article history: Received 7 November 2007 Received in revised form 15 February 2008 Accepted 26 February 2008

In this paper, a soil–pile–structure model is tested on a shaking table subject to both a sinusoidal wave and the acceleration time history of the scaled 1940 El Centro earthquake. A medium-size river sand is compacted into a 1.7-m-high laminar rectangular tank to form a loose fill with a relative density of 15%. A single-storey steel structure of 2.54 ton is placed on a concrete pile cap, which is connected to the four end-bearing piles. A very distinct pounding phenomenon between soil and pile is observed; and, the acceleration response of the pile cap can be three times larger than that of the structural response. The pounding is due to the development of a gap separation between soil and pile, and the extraordinary large inertia force suffered at the top of the pile also induces cracking in the pile. To explain this observed phenomenon, nonlinear finite element method (FEM) analyses with a nonlinear gap element have been carried out. The spikes in the acceleration response of the pile cap caused by pounding can be modeled adequately by the FEM analyses. The present results suggest that one of the probable causes of pile damages is due to seismic pounding between the laterally compressed soil and the pile near the pile cap level. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Soil–pile–structure interaction Shake table Finite element analyses

1. Introduction Many big cities in the world are built on flat lands containing a thick layer of sediment, such as basins, river deltas, or valleys. Tall buildings or important structures in these cities have to be founded on piles to avoid excessive ground settlements. In addition to static load transferred from the dead load of the structures, piles are also subject to dynamic loads. The most commonly encountered dynamic loads on a pile–soil–structure system are those due to earthquakes. Past earthquake events demonstrate that damages in piles are commonly induced during moderate to strong earthquakes. Mizuno [1] compiled the earthquake-induced damages of piles reported in Japan from 1923 to 1983, including those of the great Kanto earthquake. Damages in pile have been observed during the 1964 Niigata earthquake, the 1964 Alaska earthquake, the 1985 Mexico City earthquake, and the 1989 Loma Prieta earthquake [2]. More recently, severe damages in piles were also reported during the 1995 Kobe earthquake [3–6]. The remedial works needed for damaged piles can be very costly. Thus, pile–soil–structure interaction and mechanism for

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E-mail address: [email protected] (K.T. Chau). 0267-7261/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2008.02.004

pile damages need to be further examined. For comprehensive reviews on theoretical soil–pile–structure interaction (SPSI), we refer to Meymand [2] and Novak [7]. The SPSI problem has also been investigated by using the shaking table test [2,8] and the centrifuge test [9,10]. The present study continues the line of works on shaking table tests on the soil–pile–structure system. The main focus of the present study is to report a newly observed phenomenon in our shaking table tests—pounding between soil and pile when a soil–pile–structure model is subject to seismic excitations. When the soil–pile–structure model is subject to seismic excitations, the soil surrounding the pile may be compressed laterally such that a soil–pile gap separation may develop. Consequently, pounding may appear between soils and piles due to the different dynamic responses of the pile–structure system and the soil. We will show that this pounding may lead to a very large inertia force at the pile cap level, which may lead to cracking in the foundation piles. Finite element analysis is used to explain the unusual large acceleration suffered at the pile cap level. Although soil–pile gaps have been observed in the field after earthquakes and in shaking table tests after soil–pile–structure models are subject to seismic excitations, the pounding between soil and pile has not been recognized and examined. Photographs in Fig. 1 show soil–pile gap separations observed in the field and in the laboratory. For soil–pile gaps observed in the field, Figs. 1(a)

ARTICLE IN PRESS K.T. Chau et al. / Soil Dynamics and Earthquake Engineering 29 (2009) 300–310

and (b) show two photographs of soil–pile gaps observed on the reclaimed Port Island after the 1995 Kobe earthquake, while Figs. 1(c) and (d) show two photographs of soil–pile gaps developed along the Struve Slough Crossing during the 1989 Loma Prieta earthquake. For soil–pile gaps observed in shaking table tests, Figs. 1(e) and (f) are reproduced from Fig. 8 of Wei et al. [11] and Fig. 8.31 of Meymand [2], respectively. There has been no previous attempt to investigate the possibility of pounding between soil and pile induced by these gaps. Therefore, shaking table tests demonstrating the pounding between soil and pile will be presented here. To simulate the free field response of soil, various soil tank designs have been proposed to minimize the boundary effect of the finite soil tank. They include rigid tank with sufficiently large size [12,13], rigid tank packed with foam at the sides of the tank [14–17], laminated soil tank [18–27], soil tank with walls having a hinged-base [28], and flexible circular container [2,29,30]. There is no conclusion on which particular soil tank system is better than others. For this study, a rectangular laminated tank system was selected. The results of the present study provide a new potential

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cause of pile damages observed in the field especially when no liquefaction is observed around the damaged piles [6].

2. Experimental set-up Experiments on a model of a soil–pile–structure system were performed on an MTS uniaxial seismic shaking table of size 3 m  3 m. Fig. 2(a) shows a photograph of the experimental setup, while schematic diagrams of the laminated soil tank and the cross-sections of the members used in constructing the pile, the columns of the structure, and the soil tank are shown in Figs. 2(b) and (c), respectively. A maximum horizontal acceleration of 1g can be applied at the full load of 10 ton. The working frequency of the table ranges from 1 to 50 Hz. The shaking table can simulate motions with displacement, velocity or acceleration control. The displacement control is primarily for low frequency range, velocity control for middle frequency range, and acceleration control for high frequency range. The maximum overturning moment that can be restrained by the bearing of the table is

Fig. 1. Photographs of soil–pile gap observed in the field and laboratory: (a,b) piles in the reclaimed island of Kobe during the 1995 Kobe earthquake (after Refs. [2,5]); (c,d) piles for the Struve Slough Crossing during the 1989 Loma Prieta earthquake ((c) after [2] and (d) photographed by H. G. Wilshire); (e) gap observed in shaking table test (after [11]); and (f) gap observed in shaking table test (after [2]).

100

1260

1200 Pile 90 Column

90

H=1700

Laminated soil tank

50

50 Soil tank Unit: mm 1500

Unit: mm

Fig. 2. (a) A photograph of the soil–pile–structure system used; (b) an elevated side view of the system showing the sizes and the laminated soil tank; and (c) cross-sections used for piles and columns, and for constructing the laminar frame of the tank.

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two 1-mm-thick layers of Teflon (or polytetrafluoroethylene) are glued to the top and bottom of each steel frame section. The frictional coefficient between two Teflon surfaces is found equal to 0.126. The height of the soil tank is about 1.7 m. To ensure the overall sliding stability, the bottom frame section is welded to a bottom steel plate of 12 mm thickness, on which another threedimensional (3-D) steel box frame with cross bracing is constructed to limit the maximum translation of the laminated soil

10 ton-m. In our experiment, the total weight of our soil–pile– structure system is close to the limit of 10 ton. To simulate the shaking of soil in the free field, a rectangular laminated soil tank is constructed by stacking up 32 laminar rectangular steel frames made by welding four rectangular hollow sections of 50 mm  50 mm  2.8 mm together (see Fig. 2(c)). The laminar rectangular frame has an internal size of 1.4 m  0.9 m. To reduce the friction and allow sliding between adjacent frames,

M

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as structure ap

213

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1700

1700

800

a1

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φ 100

board

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367

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Shaking table Laminated tank Ground

100

Shaking table

C6 S6

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C2 S2

C3 S3

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Pile 2# C4 S4

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C5 S5

Pile cap

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800 1500

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: displacement transducer

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: accelerometer

: sand

: strain gauge Fig. 3. A vertical cross-section showing the piles and soil within the laminated tank with a horizontal cross-section cut at the bottom level of the pile cap. Locations of the strain gauges for steel bars (S1–S8) and for concrete surfaces (C1–C8), the nine displacement transducers, and the five accelerometers are also showed.

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tank, as shown in Fig. 2(a). This box frame also provides a reference for measuring the horizontal distance of the soil tank at various levels (see Fig. 3). Four concrete piles are cast independently using a template of PVC pipe of 100 mm in diameter. The piles are 1.7 m long, which gives a slenderness ratio of the piles as 17. The Young’s modulus, Poisson ratio and the 28-day cube strength of the concrete are 21.8 GPa, 0.18, and 19.55 MPa, respectively. The reinforcement in the pile consists of eight vertical mild steel bars of diameter 6 mm (or a steel ratio of 2.8%). Circular stirrups made of 9 mm mild steel with a spacing of 20 mm are fixed to the vertical bars. Eight strain gauges were attached to the vertical steel bars near the top of the piles, shown as S1–S8 in Fig. 3, with a pair of strain gauges is installed on the surfaces of each pile along the shaking direction. After the concrete is cast, eight more strain gauges were installed to the surface of the concrete piles, again on the surface of each pile along the shaking direction (shown as C1–C8 in Fig. 3). The spacing of the piles along the shaking direction is 800 mm while the spacing along the transverse direction is 500 mm. Therefore, since the spacing for in-line shaking piles is larger than six diameters of the pile, the pile–pile interaction can be neglected [16]. The piles are fixed to the bottom steel plate by a wooden template of 10 mm thickness when soil is put into the laminated soil tank. Thus, the piles can be considered as hinged end-bearing piles.

Table 1 Test program of the shaking table tests, where Amax is the peak acceleration. Experiment number

Test type

Wave form

Amax (g)

Frequency (Hz)

E1 E2 E3 (61) E4 E5 E6 (29) E7 E8 (27) E9 E10 E11 E12 E13 E14 E15 E16 E17 E18 E19

Sweep Random Spectrum Small EQ Random Spectrum Small EQ Spectrum Small EQ Random Moderate EQ Random Moderate EQ Random Random Moderate EQ Random Large EQ Random

Sinusoidal Random Sinusoidal Sinusoidal Random Sinusoidal Sinusoidal Sinusoidal Sinusoidal Random Sinusoidal Random El Centro Random Random Sinusoidal Random Sinusoidal Random

0.02 0.02 0.02 0.04 0.02 0.02 0.05 0.02 0.06 0.02 0.116 0.02 0.135 0.02 0.02 0.134 0.02 0.2 0.02

1–10 1–10 1–10 4.7 1–10 1–10 4.4 1–10 4.3 1–10 4.3 1–10

Acceleration ratio

10

1–10 1–15 3.2 1–15 3.2 1–15

The soil used is poorly graded river sand imported from the Mainland China. The D10, D30, D50, and D60 of the sand are about 0.22, 0.34, 0.41, and 0.42 mm, respectively, with all particles smaller than 1 mm. The specific gravity of the sand is 2.662. The fine content (i.e. particles smaller than 0.063 mm) is less than 0.1%. Therefore, it can be considered as pure sand, 35% coarse (0.6–2 mm), 61% medium (0.2–0.6 mm) and 4% fine sand (0.06–0.2 mm). From the results of seven triaxial tests, the Young’s modulus of the soil is estimated to range from 0.375 to about 5 MPa depending on the confining stress and the strain level. Before the sand is packed into the laminated soil tank, an expansible water-resistant nylon bag is custom made to fit the size of the soil tank to prevent the loss of soil particles through the joints of the laminated tank. A total of 3622 kg of sand is used to fill the laminated tank in 11 layers. When each sub-layer is filled, an electric hammer of 9.55 kg is used to compact the soil to a specific thickness of about 154 mm. The hammer is the Kango Type 628 Light Demolition Hammer, and the base of the hammer is a flat disk of 145 mm diameter. The overall density of the soil is 1.459 Mg/m3. The fill is relatively loose and should resemble the condition of loose hydraulic fill found in the reclaimed areas of Hong Kong. The water content of the sand in the laminated shear tank is about 4%, therefore, it can be basically considered dry. Thus, no capillary stress needs to be considered, and the sandy soil can be considered as cohesionless. After the soil is filled, a concrete pile cap for all four piles is cast. The size of the pile cap is 1200 mm (length)  800 mm (width)  200 mm (thickness). Mild steel bars of 4 mm diameter are placed at 20 mm spacing along both the shaking direction and its orthogonal direction, and at both the top and bottom of the cap. The pile cap can, therefore, be considered as rigid. A single-storey structure made of steel frame is then attached to the pile cap by four tie-down bolts. Two steel plates of 1200 mm (length)  800 mm (width)  20 mm (thickness) are used as the base and top of the frame structure. Four columns of hollow square section of 90 mm  90 mm  5.5 mm are welded to both the upper and lower plates (see Fig. 2(c)). The Young’s modulus, Poisson ratio and yield strength of the mild steel are 206 GPa, 0.28, and 215 MPa, respectively. Additional mass of 2 ton is added to the top plate of the structures (see Fig. 2(a)) and the total mass of the structure is 2358 kg. Five accelerometers are installed at various locations of the soil–pile–structure systems, shown as triangles in Fig. 3. The accelerometers a0, a1, a2, ap and as are installed at the surface of the shaking table, at the soil tank at an elevation of 804 mm above the table, at the top level of the soil tank, on the pile cap, and at the top steel plate of the structure. Another nine displacement transducers are installed at various levels, as shown in Fig. 3.

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303

3 4 5 6 7 Frequency (Hz)

8

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3 4 5 6 7 Frequency (Hz)

Fig. 4. The acceleration response spectra at the pile cap and structure at various test stages: tests (a) E3, (b) E6, and (c) E8.

8

9 10

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Therefore, a grand total of 133 shaking table experiments was conducted on the soil–pile–structure system. For checking purposes, additional tests have also been carried out for the structures, the soil in the laminated tank and the pile–soil systems.

3. Shaking table test program Table 1 lists a total of 19 sets of shaking table tests carried out on the soil–pile–structure system (i.e. E1–E19). The test type, the waveform of the acceleration, the peak acceleration of the input, and the frequency range of these tests are given in Table 1. Both the frequency sweep and random vibrations are for the determination of the fundamental frequency of the soil–pile–structure system. The spectrum test is to find the acceleration response spectrum of the system. The acceleration time history of the 1940 El Centro earthquake is also used as input (E13 in Table 1), but the peak acceleration has been scaled to 0.135g to avoid excessive overturning moment. Sinusoidal waves have been used for the frequency sweep (E1), all spectrum tests (E3, E6, and E8) and all earthquake tests with peak ground acceleration larger than 0.02g (E4, E7, E9, E11, E13, E16, and E18). For the spectrum tests, the numbers in the brackets behind E3, E6, and E8 in Table 1 are the actual number of tests used in obtaining the spectrum. For the earthquake tests, the magnitudes of the applied sinusoidal waves increase gradually from 0.02 to 0.2g, and the applied frequency is the current fundamental frequency of the system. The natural frequency of the soil–pile–structure system is checked after each earthquake test. The durations for all sine wave inputs are 20 s and those for random tests are 90 s.

4. General observations of the shaking table tests 4.1. Cracking in the concrete piles In general, strain gauge data at the surface of the concrete piles indicate that cracking occurs at the top of the pile when Amax is increased to 0.116g in test E11 (with a tensile strain of 0.06%). When Amax ¼ 0.134 (i.e. E16), the tensile strain on the concrete surface is up to 0.15%. And, when Amax ¼ 0.2, the tensile strain in concrete is about 0.35%. 4.2. Deflections of the laminated soil tank The maximum deflections at the top of the soil tank are 1, 2, 2.5, and 4 mm when the acceleration a2 is 0.035, 0.064, 0.087, and 0.116g, respectively. The deflection profile of the laminated tank

2 acce. (m/s2)

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11 ap as

Fig. 5. The acceleration response spectra at the pile cap (dotted lines) and structure (solid lines) at various levels of ground input (Amax): (a) E3 sinusoidal wave input, f ¼ 4.8 Hz, Amax ¼ 0.02g; (b) E7 sinusoidal wave input, f ¼ 4.4 Hz, Amax ¼ 0.05g; (c) E11 sinusoidal wave input, f ¼ 4.3 Hz, Amax ¼ 0.116g; and (d) E18 sinusoidal wave input, f ¼ 3.2 Hz, Amax ¼ 0.2g. The chosen frequencies at various stages correspond to the updated natural frequency of the soil–pile–structure system, which changes with time. The enlargement is plotted to illustrate the differences in the acceleration response of the pile cap and the structure.

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recorded from the displacement transducers verifies that only mode one shaking is induced in the soil.

laminated tank, displacement, velocity, and acceleration transducers are installed along the various levels of the tank such that the natural period can be measured by inputting a random wave with a peak acceleration of less than 0.02g. More specifically, it can be identified by noting the frequency at the peak of the Fourier spectra plot. The equivalent shear wave speed and dynamic shear modulus of the sand are 78 m/s and 8.865 MPa, respectively. This equivalent shear modulus appears to be larger than the static elastic modulus measured in triaxial tests reported in Section 2. This increase can be attributed to the fact that dynamic modulus is normally larger than the static one, and that the friction between the laminates of

4.3. Dynamic characteristics of different components

acceleration (m/s2)

acceleration (m/s2)

Different components of the system are also tested independently using the shaking table. In particular, the fundamental frequencies of the structure with the additional mass, and the soil with laminated tank are, respectively, 7.6 and 11.5 Hz (or with natural periods of 0.13 and 0.087 s). For the case of only soil in

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acce. (m/s2)

Fig. 6. The phase diagrams of acceleration versus displacement at the pile cap for those enlargements shown in Fig. 5.

1940 El Centro earthquake

2 0

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10

15

20

-1 0

5

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20

-2 5

acce. (m/s2)

3 1

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ap time (s)

as

Fig. 7. (a) The acceleration time history of the 1940 El Centro earthquake, and (b) acceleration responses of the system at pile cap and at structure level (test E13 in Table 1). The peak ground acceleration of the El Centro wave has been scaled down to 1.35 m/s2.

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Figs. 4(a) to (c) plot the acceleration ratios at the pile cap and at the structure (i.e. ap/a0 and as/a0) versus the excitation frequency of a sinusoidal wave of 0.02g in magnitude. Fig. 4(a) shows that the initial natural frequency of the system is about 4.9 Hz (from E3). As expected, the acceleration response of the structure is larger than that of the pile cap. After a sinusoidal wave of magnitude 0.04g (E4) is applied to the system, Fig. 4(b) shows that the natural frequency drops to about 4.5 Hz. More importantly, the acceleration response at pile cap is larger than that of the structure, which is somewhat unexpected. After a sinusoidal wave of magnitude 0.05g (E7) was applied to the system, Fig. 4(c) shows that the natural frequency further drops to 4.3 Hz. Again, the acceleration response at pile cap is larger than that of the structure. To further examine this phenomenon, Figs. 5(a) to (d) plot the acceleration at the pile cap ap (dotted lines) and at the structure as (solid lines) versus time. To make a better comparison, enlargements of each of the acceleration responses are also given in Figs. 5(a) to (d). For experiment E3 (or Amax ¼ 0.02g), the response of the pile cap is clearly less than that of the structure. In addition, the response of the structure resembles the input sinusoidal wave more closely than that of the pile cap. For experiment E7 (or Amax ¼ 0.05g), Fig. 5(b) shows clearly that a number of spikes is observed in the acceleration response of the pile cap, comparing to the roughly sinusoidal response of the structure. The maximum acceleration at ap is about the double of that of as. For experiment E11 (or Amax ¼ 0.116g), Fig. 5(c) shows that the acceleration at the pile cap is about three times of that of the structure. From E7 to E11, although the input acceleration is more than double, the structural response remains roughly constant at about 3 m/s2. For the largest earthquake wave input used in E18 (or Amax ¼ 0.2g), the conclusion is again similar to those obtained in Figs. 5(b) and (c), except that the difference between the acceleration of the pile cap and the structure increase further. The spikes observed in the acceleration responses of the pile cap suggest that impact or pounding may occur between the pile and the soil. To further verify this, Figs. 6(a) to (d) plot the phase diagram of acceleration versus displacement for those ‘‘onesecond responses’’ of pile cap shown in Figs. 5(a) to (d). It is clear that there is a jump of the acceleration of the pile cap at a fixed displacement; and this is a unique feature of pounding or impact. Our speculation is that after strong ground motions are input, repeated dynamic contacts between the soil and the piles lead to a lateral compression of the soil. Thus, a gap between the soil and the pile is developed. As remarked in the Introduction, gap between soil and pile has been observed in other shaking table tests and in the field after some major earthquakes (see Fig. 1). To further examine this phenomenon, detailed analyses of the Fourier spectra at the top of the structure, pile cap, and the soil tank were conducted. We found that when the system is subject to shaking of acceleration less than 0.02g, all displacements (i.e. a2, ap as, and shown in Fig. 3) are in phase; when the system is

5.2. Model subject to the acceleration time history of the 1940 El Centro earthquake All previous experiments are carried out for the soil–pile– structure system subject to sinusoidal waves. Fig. 7 shows plots of the acceleration time histories of the 1940 El Centro earthquake and the acceleration responses of the pile cap and structure. Note that the peak acceleration of the 1940 El Centro earthquake has been scaled down to 0.135g to avoid excess overturning moment exerted on the table. Fig. 7 clearly shows that the pile cap response is again larger than the response at the structure.

6. Finite element analyses In order to demonstrate what has happened in the system that leads to a larger acceleration response at the pile cap than at the structure, the finite element method (FEM) has been applied to

δ k Gap Element

Structure

Pile cap

L

5.1. Response spectra of the system at various stages

Sand h1

5. Experimental results and discussion

subject to shaking of acceleration larger than 0.04g, out-of-phase motions are observed between the structure and the soil tanks. More importantly, the fundamental frequency recorded at the top of the soil tank increases from 4.6 to 11.6 Hz, which agrees with the fundamental frequency of the soil and the laminated tank alone (without pile and structure) reported earlier. Therefore, it is clear that the soil and laminated tank vibrate independently from the pile–structure system. This again supports our earlier speculation that the soil has compressed laterally and a gap is developed between soil and pile.

h2

the soil tank inevitably exists. Note that the predominant frequency of the structure (7.6 Hz) is lower than that of the soil (11.5 Hz), and thus, radiation damping of the piles of the system is negligible [31]. In addition, accelerometers have also been attached to the edge of the structure along the direction perpendicular to the shaking direction, and the shaking table responses are again recorded. The acceleration records for these two channels are essentially the same, and this shows that no torsional or rotational motion has been triggered in our shaking table tests.

H

306

Fig. 8. The two-dimensional finite element model used in SAP 2000 Nonlinear. The soil and the additional masses on the top of the structure are modeled by fournode plane strain elements, while all piles, pile cap, and structures are modeled by frame elements. The gap element used between pile and soil from the top of the soil to L meter below the soil surface is enlarged. The gap element is characterized by a stiffness k and a gap distance d. Although it is not shown explicitly in the diagram, gap elements are installed on both sides of the two piles.

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divided into 15 layers. In order to model the depth of the gap L more accurately, the top 12 layers are of smaller thickness h1 while the bottom three layers are of larger thickness h2. In our actual input, we have set h1 ¼ 0.08 m and h2 ¼ 0.24 m. Although it is not shown explicitly in Fig. 8, the gap elements have been installed on both sides of each of the two piles. Fig. 9 plots the acceleration time histories at the pile cap and the structure versus time for test E9, together with three FEM simulations. The input frequency in the FEM analyses is 5 Hz which is about the same as that applied in test E9 (i.e. 4.3 Hz). The actual stiffness of contact between the soil and the pile (the so-called dynamic sub-grade reaction) has not been measured in the present study. The shaking table tests by Yahata et al. [18] suggest that the sub-grade reaction can be very complicated, in contrast to an increasing trend assumed in static case [33]. Therefore, the triangle, rectangle, and inverse triangle shown in Figs. 9(b), (c) and (d) respectively, indicate that a linear increasing, a constant, or a linear decreasing trend of the contact stiffness k has been assumed in the FEM analysis. The maximum stiffnesses k used in Figs. 9(b), (c) and (d) are 0.1, 0.05, and 0.08 GN/m, respectively. In these analyses, the depth of the gap is assumed as L/H ¼ 6/21, where H is the total thickness of the soil shown in Fig. 8. This assumed value, however, cannot be verified since no pressure transducers have been installed along the piles. In the calculations of Fig. 9, the gap separation has been assumed to vary from 0.2 mm from the top of

simulate the responses of the system and the results are compared to the experimental observation. Initially, the program FLUSH was used, but the results were not satisfactory even when a gap was artificially inserted between the soil and the pile. Apparently, the pounding between the soil and the pile has not been modeled appropriately. Subsequently, ‘‘SAP 2000 Nonlinear’’ is used to model the gap development [32]. In particular, the ‘‘Gap element’’ in the NLLink properties is selected to model the pounding between the soil and the pile. The nonlinear force– deformation relation for the Gap element is given by

otherwise;

(1)

acce. (m/s2)

where k is the spring constant (or contact stiffness), d denotes deflection of the Gap element, and d is the initial gap separation (dX0). Note that d40 for opening mode and do0 for closing mode of the gap. A sketch for the FEM modeling is shown in Fig. 8. An equivalent 2-D model is proposed. The structure and pile foundation are modeled by beam elements, while the additional mass on the structure as well as the soil is modeled by four-node plane strain solid elements. As shown in the enlargement, the characteristics of the Gap element are controlled by two input parameters: the contact stiffness k and the gap separation d. The 1.7 m soil is

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0 12.1 -6 -12

13.1 pilecap

time (s)

structure

FEM:

0 12.1 -6

12

structure

FEM:

12.6

13.1 pilecap

-12

structure

0

time (s)

0 12.1 -6

12

13.1 pilecap

-12

structure

0

12.6

-12

structure

0

Experiment E9

0 12.1 -6

12

-12

acce. (m/s2)

15 pilecap

-12

acce. (m/s2)

10

acce. (m/s2)

if d þ do0;

acce. (m/s2)

kðd þ dÞ 0

acce. (m/s2)

f ¼

acce. (m/s2)

(

307

time (s)

structure

FEM:

12.6

13.1 pilecap

time (s)

structure

Fig. 9. (a) The experimentally observed acceleration time histories at ap and as for test E9 in Table 1 (f ¼ 4.3 Hz, Amax ¼ 0.06g); (b) FEM results by assuming a linear variation of the stiffness k with depth; (c) FEM results by assuming a constant stiffness k with depth; and (d) FEM results by assuming a linear decreasing stiffness k with depth. For all FEM results, we have assumed L/H ¼ 6/21, and that the gap distance varies linearly from 0.2 mm at the top to zero at the base of the gap. The maximum stiffnesses kmax for (b), (c), and (d) are 0.1, 0.05, and 0.0857 GN/m, respectively.

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for Figs. 10(b), (c), (d), (e), (f) and (g). In particular, the maximum gap separations at the top dmax used are 0.08, 0.2 and 0.35 mm for cases of L/H ¼ 4/21, 6/21 and 9/21, respectively. For cases of increasing k, the maximum stiffnesses k used in Figs. 10(b), (c) and (d) are 4, 0.0857 and 0.06 GN/m respectively; whereas, for cases of decreasing k, the maximum stiffnesses k used in Figs. 10(e), (f) and (g) are 3, 0.1 and 0.08 GN/m, respectively. Fig. 10 shows that the number of impacts between the soil and the pile per each cycle of the structural response increases with the depth L for both cases of decreasing and increasing contact stiffnesses. Among these figures, Fig. 10(c) appears to model the experiment better. In short, although there is uncertainty regarding the assumed dynamic sub-grade reaction, our results of the FEM analyses are not sensitive to the actual distribution of the stiffness k. Therefore, our analyses should reliably reflect what has happened in the shaking table tests.

the gap to 0 at the bottom of the gap (i.e. L below the soil surface as shown in Fig. 8). The acceleration time histories of the pile cap shown in Figs. 9(b) and (d) agree well with the experimental results given in Fig. 9(a). More importantly, the FEM results are capable of capturing the essential feature that the pile cap acceleration response is larger than the structural response. In conclusion, the abnormally large pile cap response is caused by pounding, which is simulated by installing gap elements between soil and the pile in our FEM analyses. Thus, this verifies our speculation of pounding between the soil and pile. Although uncertainties exist in assigning the values of sub-grade reaction and the depth of the gap, the results given in Fig. 9 clearly demonstrate that the spikes in acceleration are the results of pounding between the soil and the pile. Since the depth of the gap has not been observed, Fig. 10 shows the acceleration response at the pile cap and at the structure versus time for various depths of gap L (L/H ¼ 4/21, 6/21 and 9/21). In Figs. 10(b), (c) and (d), a linear decreasing k with depth was assumed, whereas, in Figs. 10(e), (f) and (g) a linear increasing k with depth was assumed. Note that Figs. 10(c) and (f) are identical to Figs. 9(d) and (b), respectively. Again, a linear gap separation has been assumed, but because of the changing depth of the gap, different maximum gap separation has been assigned

2 acce. (m/s )

12

0 12.112.613.1 12.1 -6

12

13.1 pilecap

time (s)

-12

13.1 pilecap

time (s)

20 4 -412.112.613.1

-20

pilecap

time (s)

structure

13.1 pilecap structure

L/H = 6/21

6 0 12.1 -6

12.6

13.1 pilecap

time (s)

12

12

12.6 time (s)

-12

structure

L/H = 9/21

-12

0 12.1 -6

12

6 12.6

L/H = 4/21

6

-12

structure

L/H = 6/21

0 12.1 -6

2 acce. (m/s )

12.6

acce. (m/s2)

0 12.1 -6

13.1 pilecap pilecap structure structure

time(s) time (s)

acce. (m/s2)

2

acce. (m/s )

acce. (m/s2)

12.6

6

12

2

Experimental result (E9) (b) L/H=4/21

L/H = 4/21

-12

acce. (m/s )

In this paper, a soil–pile–structure model is tested on a shaking table subject both sinusoidal wave of various magnitudes and

6

-12 12

7. Conclusion

structure

L/H = 9/21

6 0 -6 -12

12.1

12.6

13.1 pilecap

time (s)

structure

Fig. 10. FEM results by assuming the stiffness of the gap elements increases or decreases linearly with depth. (a) The experimentally observed acceleration time histories at ap and as for test E9 in Table 1; (b) FEM results by assuming L/H ¼ 4/21, dmax ¼ 0.08 mm, and kmax ¼ 4 GN/m; (c) FEM results by assuming L/H ¼ 6/21, dmax ¼ 0.2 mm, and kmax ¼ 0.0857 GN/m; (d) FEM results by assuming L/H ¼ 9/21, dmax ¼ 0.35 mm, and kmax ¼ 0.06 GN/m; (e) FEM results by assuming L/H ¼ 4/21, dmax ¼ 0.08 mm, and kmax ¼ 3 GN/m; (f) FEM results by assuming L/H ¼ 6/21, dmax ¼ 0.2 mm, and kmax ¼ 0.1 GN/m; and (g) FEM results by assuming L/H ¼ 9/21, dmax ¼ 0.35 mm, and kmax ¼ 0.08 GN/m. Linear decreasing and linear increasing are denoted by inverted triangle and triangle, respectively. The gap distance d is linearly decreasing with depth, with zero value at the base of the gap.

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frequencies and the acceleration time history of the 1940 El Centro earthquake. The soil is medium-graded river sand and is embedded into a 1.7 m laminated tank made of steel sections covered with Teflon to reduce the sliding friction. A single-storey steel structure is placed on a concrete pile cap, which is supported by four end-bearing concrete piles. A very distinct but unexpected phenomenon is observed. After the system has been subjected to a number of sinusoidal waves of moderate magnitude (say peak acceleration larger than 0.05g), the acceleration response at the pile cap level may increase to three times of that of the structural response (e.g. see Fig. 5). In addition, the acceleration response of the pile cap shows spikes of large acceleration response, which resemble that of nonlinear pounding between two systems. This observation seems to contradict the prediction by structural dynamics. However, a closer look of the model after the test reveals that gaps develop between soil and piles, probably due to the lateral soil compression induced by the prolonged shaking of moderate earthquake waves input to the system. Finite element analyses were carried out using ‘‘SAP 2000 Nonlinear’’ incorporating a nonlinear gap element installed along the top one-third of the soil–pile interface. Various contact stiffness and gap separations have been assumed and it turns out that as long as appropriate magnitudes of the stiffness, depth of the gap, and initial gap separation are assumed, the spikes in the acceleration response of the pile cap can be modeled quite adequately. The results appear to be insensitive to the depth variation of stiffness of the gap element. In addition, when the magnitude of the input acceleration is 0.116g or above, strain gauge data show that cracking can occur at the pile near the pile cap level. This cracking is clearly induced by the large inertia force experienced by the pile cap due to the pounding between soil and pile. However, it remains to be seen whether such a pounding between soil and pile did occur in the field during strong earthquakes. If it does happen, those pile damages reported in the field may be caused by soil–pile pounding, instead of liquefaction. The shaking table tests by Lui and Chen [34] showed that the maximum response of the pile foundation may appear before the onset of liquefaction. In addition, Luo and Murono [6] showed that severe pile damages did occur when no liquefaction was observed. Since the pounding phenomenon between soil and pile was observed in a scaled model, direct application to field situations may not be straightforward. Therefore, a brief discussion of the scaling model that we have adopted is given here. When we designed the shaking table model, we have assumed a 1:7 scale model. This scaling is based upon the scale laws discussed for shaking table test for structures by Harris and Sabnis [35] and for soil–structure models by Iai [36]. More specifically, our soil– pile–structure system roughly corresponds to a three-storey building with a natural period of 0.4 s resting on end-bearing piles of 0.7 m diameter and 12 m length. Therefore, we also expect that the same pounding phenomenon between soil and pile will occur in the field for a prototype of such scale. We should, however, emphasize that this is only an approximation since a complete set of scaling for soil–pile–structure model is still not available in the literature. Nevertheless, the present study provides a new explanation for the observed damages in piles during strong earthquakes. In particular, we speculate that one of the causes of damaging the piles may be due to pounding between the laterally compressed soil and the pile near the pile cap level. However, much work remains to be done on this seismic pounding phenomenon between soil and pile, before conclusive statements can be made.

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Acknowledgments This research was by a grant from the Research Grants Council of Hong Kong Special Administrative Region, China (Project no. PolyU5035/02E) and fully supported by the Hong Kong Polytechnic University through the ASD project of ‘‘Seismic and Landslide Hazards in Dense Urban Areas’’ (A226). The shaking tests were inspired by the discussions with Professors John Berrill and Rob Davis when K.T. Chau visited the shaking table facility at University of Canterbury, New Zealand in 1996. Technical support from Mr. T.T. Wai and Mr. C.F. Cheung is acknowledged. References [1] Mizuno H. Pile damage during earthquake in Japan (1923–1983). In: Nogami T, editor. Dynamic responses of pile foundations—experiment, analysis and observation. Geotechnical Special Publication no. 11. ASCE; 1987. p. 53–78. [2] Meymand PJ. Shaking table scale model test of nonlinear soil–pile–superstructure interaction in soft clay. PhD dissertation, University of California, Berkeley, 1998. [3] Matsui T, Oda K. Foundation damage of structures. Spec Issue Soils Found 1996:189–200. [4] Tokimatsu K, Mizuno H, Kakurai M. Building damage associated with geotechnical problems. Spec Issue Soils Found 1996:219–34. [5] Horikoshi K, Tateishi A, Ohtsu H. Detailed investigation of piles damaged by Hyogoken Nambu earthquake. In: Proceedings of the 12th world congress on earthquake engineering 2000, Paper no. 2477 (in CD-ROM). [6] Luo X, Murono Y. Seismic analysis of pile foundations damaged in the January 17, 1995 South-Hyogo earthquake by using the seismic deformation method. In: Proceedings of the fourth international conference on recent advances in geotechnical earthquake engineering and soil dynamics. 2001, Paper no. 6.18. [7] Novak M. Piles under dynamic loads. In: State of the art paper. Second international conference on recent advances in geotechnical earthquake engineering and soil dynamics, vol. III. Missouri: University of Missouri-Rolla; 1991. p.250–73. [8] Normand P. Shaking table tests on model piles: a literature survey. Research Report 95–3. Department of Civil Engineering, University of Canterbury, New Zealand, 1995. [9] Hushmand B, Scott RF, Crouse CB. Centrifuge liquefaction tests in a laminar box. Geotechnique 1988;38:253–62. [10] Dorby R, Abdoun T. Recent studies on seismic centrifuge modelling of liquefaction and its effect on deep foundations. In: Proceedings of the fourth international conference on recent advances in geotechnical earthquake engineering and soil dynamics, 2001, Paper no. SOAP-3. [11] Wei X, Fan L, Wu X. Shaking table tests of seismic pile–soil–pier–structure interaction. In: Proceedings of the fourth international conference on recent advances in geotechnical earthquake engineering and soil dynamics, 2001, Paper no. 9.18. [12] Sato H, Kouda M, Yamashita T. Study on nonlinear dynamic analysis method of pile subjected to ground motion, Part 2: comparison between theory and experiment. In: Proceedings of the 11th world conference on earthquake engineering, 1996, Paper no. 1289. [13] Iiba M, Tamori S, Kitagawa Y. Shaking table test on effects of combination of soil and building properties on seismic response of building. In: Proceedings of the fourth international conference on recent advances in geotechnical earthquake engineering and soil dynamics, 2001, Paper no. 9.23. [14] Mizuno H, Sugimoto M, Mori T, Iiba M, Hirade T. Dynamic behavior of pile foundation in liquefaction process-shaking table tests utilizing big shear box. In: Proceedings of the 12th world congress on earthquake engineering, 2000; Paper no. 1883 (in CD-ROM). [15] Mizuno H, Iiba M, Kitagawa Y. Shaking table testing of seismic building– pile–two-layered–soil interaction. In: Eighth world conference on earthquake engineering, San Francisco, vol. 3, 1984, p. 649–56. [16] Finn WDL, Gohl WB. Response of model pile groups to strong shaking. In: Prakash S, editor. Piles under dynamic loads. Geotechmical Special Publication No. 34. ASCE; 1992. p. 27–55. [17] Nomura S, Tokimatsu K, Shamoto Y. Soil–pile–structure interaction during liquefaction. In: Proceedings of the second international conference on recent advances in geotechnical engineering and soil dynamics, 1991, Paper no. 5.16, p. 743–50. [18] Yahata K, Suzuki Y, Funahara H, Yoshizawa M, Tamura S, Tokimatsu K. Pile response characteristics of liquefied soil layers in shaking table tests of a large scale laminar shear box. In: Proceedings of the fourth international conference on recent advances in geotechnical earthquake engineering and soil dynamics, 2001; Paper no. 6.34. [19] Adachi N, Suzuki Y, Tsugawa T. Experimental study on pile stress in liquefied and laterally spreading soils. In: Proceedings of the 12th world congress on earthquake engineering, 2000, Paper no. 0799 (in CD-ROM). [20] Tokimatsu K, Suzuki H, Suzuki Y. Back-calculated p–y relation of liquefied soils from large shaking table tests. In: Proceedings of the fourth international

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