Seismic response of clay-pile-raft-superstructure systems subjected to far-field ground motions

Soil Dynamics and Earthquake Engineering 101 (2017) 209–224

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Seismic response of clay-pile-raft-superstructure systems subjected to farfield ground motions Lei Zhang, Huabei Liu

MARK

⁎

School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China

A R T I C L E I N F O

A B S T R A C T

Keywords: Earthquake Clay Pile bending moment Acceleration Finite element analysis Superstructure

A series of three-dimensional (3D) finite element analyses incorporated with a hyperbolic-hysteretic soil model were performed to investigate the seismic response of pile-raft-superstructure systems constructed on soft clay stratum, focusing on the seismic pile bending moment and superstructural responses. The seismic pile bending moment results suggested that using a lumped mass to represent the superstructure, which has been widely used in many other studies, could only perform well for a relatively low-rise superstructure; on the other hand, the seismic response of superstructure was found to be significantly affected by the soil-structure interaction, and both the detrimental and beneficial effects of dynamic soil-structure interaction were observed. Hence, coupled soil-foundation-superstructure analyses were primarily performed in this study. The influences of peak base acceleration, pile flexural rigidity and the configuration of superstructure on both the pile bending moment and superstructural responses were studied. Furthermore, some correlations were derived to relate the maximum pile bending moment to the influencing factors, which can be used as useful tools for obtaining preliminary and firstorder estimates of the maximum pile bending moment for pile-raft-superstructure systems constructed on soft clay deposits.

1. Introduction It is a common practice to assume that the structure is fixed at the base and to apply the free-field ground motion at the base (e.g. [40]) when investigating the seismic response of a structure. In so doing, the influence of dynamic soil-structure interaction (SSI) is neglected, which may induce large prediction errors as the seismically-induced motion at ground surface is not likely to be the same as that at building foundation level [43,45,46]. The seismic SSI tends to increase the fundamental resonance period and damping of the system in comparison with the fixed-base assumption; as a result, the effect of seismic SSI is conventionally considered beneficial and hence neglected as recommended in many seismic codes such as ATC-3-06 [3] and NEHRP [16]. However, the detrimental effect of dynamic SSI was also reported in many published studies (e.g. [41,27]); the effect of seismic SSI can have either beneficial or detrimental effects on the seismic response of a structure, depending on the factors of earthquake type, soil type, foundation configuration and dynamic characteristics of the structure (e.g. [28,36]). In fact, the seismic SSI has been recognized as being important and the coupled soil-foundation-superstructure analysis has been recommended by many researchers [21,28,36,38]. Pile foundations have been widely used for buildings built on thick

⁎

Corresponding author. E-mail addresses: [email protected] (L. Zhang), [email protected] (H. Liu).

http://dx.doi.org/10.1016/j.soildyn.2017.08.004 Received 21 March 2017; Received in revised form 16 May 2017; Accepted 6 August 2017 0267-7261/ © 2017 Elsevier Ltd. All rights reserved.

layers of soft clays. The performance of the pile-superstructure system against seismic shaking is an important area of study, which involves complex dynamic soil-pile-superstructure interaction (SPSI) mechanisms. During an earthquake, piles are subjected to kinematic and inertial forces respectively imposed by the surrounding soils and the superstructure that they support, which may result in the piles being subjected to structural distress leading to cracking or the formation of plastic hinges as observed in many postearthquake investigations (e.g. [9,17,26]). Besides, a major concern in seismic SSI is the amplification of ground motion induced by the soft soil layer [8,34,39,47], which may result in the piles and the superstructure being subjected to amplified loading even under small to moderate earthquakes. Furthermore, the performance of pile-superstructure system constructed on soft clay stratum against earthquake is also an important consideration under many national design codes, e.g. NEHRP [16], GB50011-2010 [37] and Eurocode 8 [14]. Significant works have been done in the area of seismic soil-pilestructure interaction over the past decades. Most of the laboratory experiments including centrifuge tests (e.g. [1,10,11,19,22,50]) and 1-g shaking table tests (e.g. [4,18,23,24,25,30,48]) were focused on the seismic response of soil-pile-superstructure installed in predominantly sandy (liquefiable or dry) soil, while the relevant studies involving soft

Soil Dynamics and Earthquake Engineering 101 (2017) 209–224

L. Zhang, H. Liu

superstructure were presented. Given the fact that the relevant studies involving soft clays are still relatively few, the findings obtained from the present study can provide a useful reference for practical seismic design of pile-raft-superstructure systems constructed on soft clays subjected to far-field ground motions.

PBA = 0.01 g, 0.03 g and 0.06 g, respectively

0

PBA 0

5

10 15 Time (s)

20

25

2. Numerical modelling procedure 2.1. General information Fig. 2 shows the configuration of the clay-pile-raft-superstructure systems adopted in the present numerical study, which contains a superstructure with storey number ranging from 0 to 20 and supported by a 5×5 pile-raft system installed in a soft clay bed, the properties of which are shown in Table 1. The piles were embedded in a pure clay bed, with the toes sitting atop a 0.5 m-tick sand layer. The properties of the sand were adopted following Banerjee [7], which are listed in Table 2. As can be seen, these clay-pile-raft-superstructure systems are self-symmetrical with respect to the ground motion orientation, hence only a half 3D finite model of each system was set up using ABAQUS/ Explicit 6.13. Fig. 3 shows the 3D finite element model of the 20-storey building supported by a clay-pile-raft system, which contains 19200 linear hexahedral elements, 5760 linear quadrilateral elements, and 3225 linear beam elements. 2.2. Soil model The behaviour of the soft clay was simulated using a hyperbolichysteretic soil model as shown in Fig. 4, which was proposed by Banerjee [7] and calibrated using laboratory test data from cyclic triaxial and resonant column tests on kaolin clay. The basic shear stressstrain relationship for this hyperbolic-hysteresis model is shown in Eq. (1). 1 3G max ⎧q − ⎡ ⎤ Initial loading (backbone) path 3G max / qf 1 + 3G max εs / qf ⎪ f ⎣ ⎦ ⎪ ⎪ 2 3G max q = − 2qf + 3G / q ⎡ 1 + 3G (ε − ε ) / 2q ⎤ + qr1 Unloading path s max f max r 1 f⎦ ⎨ ⎣ ⎪ 2 3G max ⎪ 2qf − ⎡ ⎤ − qr 2 Reloading path ⎪ 3G max / qf 1 + 3G max (εs − εr 2) / 2qf ⎣ ⎦ ⎩

(1)

where q and εs are the current deviator stress and generalized shear strain, respectively; qr1 and qr2 are the respective deviator stresses at the reversal points; εr1 and εr2 are the respective generalized shear strains at the reversal points; Gmax is the small-strain shear modulus; qf is the deviator stress at failure. For normally consolidated kaolin clay, the small-strain shear Fig. 1. Input base motions adopted in this study: (a) time history, (b) response spectrum for the base motion with peak base acceleration (PBA) of 0.06 g (5% damping).

0.2 Spectral acceleration (g)

Acceleration (g)

clays are still relatively limited. One significant work in this area was carried out by Meymand [35], who conducted a series of large scale 1-g shaking table tests to study the seismic interaction of soft clay-pile-superstructure; Hokmabadi et al. [27] also performed a series of 1-g shaking table tests to investigate the seismic response of superstructure supported by a 4×4 pile group installed in a synthetic clay bed. Banerjee [7] and Banerjee et al. [8] performed a series of centrifuge tests to study the dynamic response of pile-raft system embedded in soft kaolin clay subjected to short-duration far-field earthquakes. In their work, the pile spacing along the shaking direction was 10 times the pile diameter or more, and their test results were largely representative of the seismic response of single piles embedded in soft clay. Zhang [51], Zhang et al. [52,53] also performed a series of centrifuge tests to investigate the influence of pile group configuration on the seismic response of clay-pile-raft systems subjected to both long- and shortduration far-field ground motions. With the exception of the studies by Ayothiraman et al. [4] and Hokmabadi et al. [27], most of the aforementioned experimental studies treated the superstructure as either a lumped mass or a simplified single degree of freedom oscillator and hence the effect of higher modes of the superstructure was not accounted for in these studies. On the other hand, in order to fully account for the nonlinear behaviour of the soil under seismic loadings, numerical simulations such as finite element analysis (e.g. [8,21,33]) and finite difference analysis (e.g. [27,29]) are commonly performed in time domain to investigate the seismic SPSI. In addition, beam-on-dynamicWinkler-foundation model or dynamic p-y method is also a popular approach to account for the dynamic SPSI (e.g. [12,38]), for which the parameters assigned to the springs and dashpots used for the p-y curve are usually back-calculated from the measured pile response. In this study, a total of 90 three-dimensional (3D) finite element analyses were performed using ABAQUS/Explicit to investigate the seismic response of different pile-raft-superstructure systems constructed on soft clay subjected to far-field ground motions. A newly developed VUMAT subroutine was incorporated to account for the hyperbolic-hysteretic soil behaviour that was proposed by Banerjee [7] on the basis of a series of resonant column and cyclic triaxial tests for soft clay. Two approaches, namely lumped mass and detailed modelling of the superstructure, which are respectively termed "added mass" and "detailed model", were used to account for the inertial effect imposed by a superstructure during the seismic shaking event. As Fig. 1 shows, the reference ground motion (PBA = 0.06 g) adopted in the present study is similar to that used by Banerjee et al. [8], which represents the type of shaking that may be experienced in Singapore due to a typical farfield earthquake arising from the strike-slip Great Sumatran Fault. In order to study the effect of different earthquake intensity, the reference ground motion was scaled down to two other different peak ground accelerations about 0.01 g and 0.03 g. In addition, some other influencing factors such as pile flexural rigidity, mass of the raft and storey number of the superstructure were varied in the numerical simulations. The computed results of pile bending moment, deflection of the superstructure, inter-storey drift ratio and shear force of the column of

0.15 0.1

0.05 0

0

2

4 6 Period (s)

(a)

(b) 210

8

10

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Fig. 2. Elevation and plan views of the soil-pile-raft-superstructure systems adopted in the three-dimensional (3D) finite element analyses (n =0, 4, 10, 15 and 20).

6m Storey n

3m

Storey (n-1)

0.1-m thick slab Storey 3 Storey 2

Column 1.2 m

Storey 1 Raft

Pile 21.7 m

20 m 1m

Pure clay

Elevation View 65 m

Raft

7.5 m

4.5 m Pure clay

4.5 m Pile 15 m

30 m

25 m

Section: 0.6 m (height) × 0.3 m (width)

3m 15 m

3m Plan View

Shaking direction

Table 1 Properties of clay adopted in the numerical simulations.

Table 2 Properties of the other materials adopted in the numerical simulations.

Property

Values/Range

Property

Values/Range

Poisson's ratio Density (kg/m3) Frictional angle of clay Small-strain modulus (kPa)

0.3 1600 25° 2060(p0’)0.653

Pile Young's modulus (GPa) Young's moduli of raft, slab, column and girder (GPa) Young's modulus of sand (MPa) Pile flexural rigidity (kNm2)

30; 70; 210 30

Note: p0’is the initial mean effective normal stress, with the unit of kPa. Poisson's ratio of pile, raft, slab, column and girder Poisson's ratio of sand Density of pile, slab, column and girder (kg/ m3) Density of raft for "detailed model" model (kg/m3) Density of raft for "added mass" model (kg/ m3) Density of sand (kg/m3) Frictional angle of sand

modulus can be expressed by the following equation [7], modified from Viggiani and Atkinson [49]:

Gmax = 2060(p0′ )0.653

(2)

where p'0 is the initial mean effective normal stress, and the units for both Gmax and p'0 are kPa. Besides, the degradation of the backbone curve under repeated loading was also taken into account in this soil model. The interested readers may refer to Banerjee [7] for more detailed information on this hyperbolic-hysteretic soil model. In this study, the hyperbolic-hysteresis model was recoded into a VUMAT subroutine for the 3D finite element analyses using the explicit time integration scheme, which yields significant savings of the computational time [51,52].

100 1472,622; 3436,117; 10,308,351 0.2 0.49 2500 2500 2500–9960 1600 35°

2.3. Modelling of pile-raft system The piles and raft were modelled as linear elastic materials, the properties of which are listed in Table 2. The piles were extended through the overlying raft, with the same nodes shared at the interface between the piles and raft. Three different piles with flexural rigidities ranging from 1,472,622 to 10,308,351 kNm2 were used; according to Singapore Standard CP4 [44], the bearing capacity of the 5×5 pile-raft 211

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system is more than 31,000 kN based on the undrained shear strength profile of the clay measured by T-bar testing during the centrifuge test [53], which can sufficiently support the superstructures considered in this study. Rayleigh damping coefficients are applied to the pile and raft materials to yield a damping ratio of 5% to the two characteristic frequencies corresponding to the two peaks in the acceleration response spectrum plot of the input ground motion shown in Fig. 1(b). Following the study of Banerjee et al. [8], this study assumed a perfect bonding between the pile and soil under the seismic shaking events. Hence the pile and soil elements were modelled as sharing the same nodes at the interface between the pile circumference and the soil. This method has also been successfully applied in many previous numerical pile-soil interaction analyses, such as those reported by Alsaleh and Shahrour [2], Rovithis et al. [42] and Dai and Roesset [20]. In this study, to combine the merits of both solid and beam elements, a "hybrid" modelling method (e.g. [8]) in which the relatively flexible beam elements are embedded in the surrounding solid pile elements to jointly model the pile; the surrounding solid pile elements share 90% of the flexural rigidity and mass of the pile, and the left 10% of the flexural rigidity and mass of the pile is assigned to the embedded beam elements. The final pile bending moments are 10 times the computed bending moments obtained from the embedded beam elements. This approach of modelling piles have been favourably examined by a series of centrifuge tests on different pile-raft systems embedded in kaolin clay bed [51,52]. 2.4. Modelling of superstructure

C Two approaches, namely "added mass" and "detailed model", were used to account for the inertial effect imposed by a superstructure during the seismic shaking event in the present numerical study. The term "added mass" originally referred to affixing masses on the top of a raft to model the weight of a superstructure in centrifuge tests (e.g. [8,51,52,53]), and then was extended to numerical simulations in which the superstructure weight was accounted for by increasing the density of raft (e.g. [8,51,52]). However, this approach may only perform well for comparatively stiff buildings where the response due to higher modes is less significant. On the other hand, to more realistically represent a superstructure, "detailed model" which implies the detailed modelling of the superstructure (e.g. [27]) was primarily adopted in the present study. In this paper, the focus is placed on the seismic response of pile-raft-superstructure system built on soft clay stratum under small to moderate levels of seismic shaking, and the superstructures were assumed to respond within the linear elastic range; thereby the slabs, columns and girders were modelled as linear elastic materials, the properties of which are listed in Table 2. General geometrical properties of the superstructure are provided in Fig. 2, and the section dimensions of the columns for different superstructures are shown in Table 3. The dimensions and elastic properties of the structural components were adopted in accordance with Eurocodes 1 [13] and 2 [15], with the consideration of both the permeant and imposed loads associated with the superstructure; they are also consistent with the design practice in Singapore as reported by Balendra et al. [5], Balendra et al. [6], and Shao and Tiong [54]. Rayleigh damping coefficients are applied to the superstructures to yield a damping ratio of 5% to the respective firstand second-mode frequencies of the superstructure as listed in Table 4, which were obtained from the modal analyses of the superstructures under fixed-base condition.

B

Fig. 3. 3D finite element model of 20-storey superstructure supported by a 5 × 5 pile-raft system (19200 linear hexahedral elements of type C3D8R, 5760 linear quadrilateral elements of type S4R, and 3225 linear line elements of type B31).

2.5. Lateral boundary condition In the numerical simulation of soil-structure systems subjected to seismic base shaking, the lateral boundaries perpendicular to the shaking direction should be treated in a manner so that the influence of wave reflection from the lateral boundaries can be minimized and also the analysis is computationally efficient. In this study, the boundary condition in a laminar container commonly used in seismic shaking

Fig. 4. The shear stress-strain relationship for the hyperbolic-hysteretic soil constitutive model (q and εs are the current deviator stress and generalized shear strain, respectively; Gmax is the small-strain shear modulus; qf is the deviator stress at failure; R= Gmax/ qf.).

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Table 3 Section dimensions of the columns in the four superstructures. Storey level

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Column section: depth (mm) × width (mm) 4 storeys

10 storeys

15 storeys

20 storeys

400 400 400 400 – – – – – – – – – – – – – – – –

640 640 600 600 550 550 500 500 450 450 – – – – – – – – – –

800 800 750 750 700 700 650 650 600 600 550 550 500 500 450 – – – – –

910 910 850 850 800 800 750 750 700 700 650 650 600 600 550 550 500 500 450 450

× × × ×

400 400 400 400

× × × × × × × × × ×

640 640 600 600 550 550 500 500 450 450

× × × × × × × × × × × × × × ×

800 800 750 750 700 700 650 650 600 600 550 550 500 500 450

× × × × × × × × × × × × × × × × × × × ×

910 910 850 850 800 800 750 750 700 700 650 650 600 600 550 550 500 500 450 450

Table 4 First- and second-mode frequencies of the fixed-base superstructures. Superstructure

First mode frequency (Hz)

Second mode frequency (Hz)

4 storeys 10 storeys 15 storeys 20 storeys

2.28 1.17 0.80 0.60

7.02 3.42 2.32 1.70

Fig. 6. 3D finite element model of the centrifuge test sample with 4 × 3 pile-raft system (7200 linear hexahedral elements of type C3D8R, 328 linear line elements of type B31.).

comparable with that at the top of the lateral boundary for the pilefoundation model with 20-storey superstructure; hence, a consistent free-field acceleration response can be ensured with the lateral boundaries connected using rigid tie-rods as adopted in this study. Besides, several 3D finite element models with different dimensions of the lateral boundary were used to investigation the influence of dimension of the lateral boundary on the raft acceleration and pile bending moment responses [51], which indicate that the lateral boundary with a dimension of 65 m is long enough to minimise the effect of wave reflection induced by the truncated boundaries in numerical modelling.

table tests was replicated in the numerical simulations; the vertically collocated nodes on the two lateral boundaries perpendicular to the shaking direction were connected using rigid tie-rods so that the corresponding nodes on these two faces are constrained to undergo the same motion in the direction of shaking. This approach was adopted in many previous studies (e.g. [8,31,32]) to replicate the free-field ground motion. Fig. 5 shows the acceleration response at the top of the lateral boundary for the pile-foundation model with 20 storeys subjected to the 0.06-g PBA ground motion, along with the corresponding free-field ground acceleration responses; the locations of Points B and C are indicated in Fig. 3, which represent ground surface nodes respectively located at and far away from the lateral boundary. The free-field acceleration response was computed at the clay surface from a pure clay stratum model without embedded pile-raft-superstructure system. As can be seen from Fig. 5, the free-field acceleration responses computed from Points B and C are almost the same, which are also very

3. Numerical validation analysis The test results from a series of centrifuge tests on both single piles [8] and pile groups [51,53] embedded in soft clay stratum can be used to examine the numerical modelling procedure adopted in this study. Fig. 6 shows the 3D finite element half-model of a 4 × 3 aluminum pileraft system installed in soft kaolin bed, which follows the same Fig. 5. Comparison of the acceleration response at the top of lateral boundary for the pile-foundation model with 20 storeys against the free-field ground surface accelerations (EpIp = 1,472,622 kNm2 for the pile-foundation model with 20 storeys, PBA = 0.06 g, locations of Points B and C are shown in Fig. 3.): (a) acceleration time histories, (b) response spectra.

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Fig. 7. Computed and measured acceleration responses at raft top for 4×3 pile group (structural mass, mstr = 597 t; pile flexural rigidity, EpIp = 3,436,117 kNm2), subjected to the 0.06-g PBA ground motion: (a) acceleration time histories, (b) acceleration response spectra.

Fig. 8. Computed and measured maximum pile bending moment profiles for 4×3 pile group (mstr = 597 t, EpIp = 3,436,117 kNm2), subjected to the 0.06-g PBA ground motion: (a) outer pile, (b) inner pile.

4. Seismic response of pile bending moment

numerical modelling procedure adopted in this study. Fig. 7 shows the measured and computed raft acceleration responses for the 4 × 3 aluminum pile-raft model with a structural mass of 597 t, subjected to the 0.06-g PBA ground motion. As can be seen, the computed and measured acceleration data compare well, with favourable agreement observed in the peak values and the overall trend. Furthermore, Fig. 8 shows the generally favourable agreement between the computed and measured maximum pile bending moment profiles for both the outer and inner piles, in which the maximum pile bending moment profiles are obtained by selecting the instantaneous bending moments along the pile shaft corresponding to the instant when the uppermost strain gauge reading attains its maximum value. It is noted that, due to the pile group effect, the inertial forces transferred from the raft to the supporting piles are uneven, which results in the discrepancy in the bending moment response between the outer and inner piles. Although not shown here, some more similarly favourable comparisons of the ground acceleration and pile bending moment response between the centrifuge tests and numerical simulations can be found in other studies [8,51,52]. In the subsequent sections, the same numerical procedure is used to perform a total of 90 3D finite element analyses, with the consideration of some varying factors including peak base acceleration, pile flexural rigidity, and storey mass and number. The results of the pile bending moment, superstructural deflection, interstorey drift ratio and column shear force are presented in the following sections.

As indicated in Fig. 3, the outer pile termed "reference pile" was selected to present the results of pile bending moment during the seismic shaking events. However, as also mentioned in the previous section, due to the pile group effect, the pile bending moment response near pile head can be influenced by the pile location; more detailed discussions on the difference in the pile bending moment response due to the influence of pile location can be found in [51]. Fig. 9 shows the bending moment time history computed at the pile head (EpIp = 3,436,117 kNm2) for pure raft model along with the corresponding input base acceleration time history. As can be seen, there is a time lag between the peak base acceleration and peak bending moment, which is attributed to the seismic wave propagation through the embedded piles and clay stratum. In the following subsections, the results of the pile bending moment will be presented in the form of envelop of pile bending moment along the pile shaft and the maximum bending moment experienced at pile head. In addition, some comparisons of the computed maximum shear force distribution along pile shaft between the “added mass” and “detailed model” models are also provided in Subsection 4.1. 4.1. Typical computed envelopes of the pile bending moment and shear force Fig. 10 shows some of the computed envelopes of the pile bending moment, which were obtained by selecting the maximum bending moments experienced at each of the points (nodes) along the pile shaft 214

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bending moment response refers to that associated with the superstructure with detailed modelling unless otherwise stated. The normalized maximum pile bending moment can be employed to more conveniently investigate the influence of storey number, which is defined as shown below.

MN1 =

Mmax Mmax , 0

(3)

where Mmax and Mmax, 0 are the maximum pile bending moments for pile foundation supporting an n-storey (n = 0, 4, 10, 15 and 20) superstructure and a pure raft, respectively. As Fig. 13 shows, from a total of 45 analyses associated with the detailed superstructures, the normalized maximum pile bending moment and the storey number can be approximately represented by the following expression.

Mmax = e 0.032n Mmax , 0

Fig. 9. Bending moment time history computed at the pile head (EpIp = 3,436,117 kNm2) for the numerical model with a pure raft versus the input base acceleration time history.

(4)

where n is the storey number of a superstructure. Despite the scatter shown in Fig. 13, Eq. (4) can be employed to estimate the influence of the storey number on the maximum pile bending moment response with a maximum prediction error less than 25%, which is still acceptable from a practical engineering standpoint.

during the respective seismic shaking events. As can be seen, the piles experience the largest bending moments at pile head while the smallest bending moments at pile tip, which is due to the fact that the piles are effectively fixed at the heads by the overlying raft and nearly pinconnected at the tips with the underneath soils. Besides, the use of "added mass" to model the superstructure tends to underestimate the pile bending moment response compared with the approach using "detailed model"; as Fig. 10(b) and (d) show, the underestimation ratios of the maximum pile head bending moment involving "added mass" approach are about 15% and 51% respectively for the 10- and 20-stroey buildings, albeit Fig. 10(a) also suggests that these two approaches lead to very similar pile bending moment response for the superstructure with 4 storeys. Similarly, as shown in Fig. 11 of the computed envelopes of the shear force along pile shaft, while these two approaches lead to quite comparable maximum shear force distributions for the 4-storey building, the use of "added mass" to model the superstructure generally tends to underestimate the shear force response especially at the pile head. In addition, as shown in Fig. 11, the maximum shear force is not necessarily experienced at the pile head, but can also be experienced at a depth between 5 and 8 m 5–8 times pile diameter). This trait is different from that of the pile bending moment response plot shown in Fig. 10 and indicates the importance of considering the kinematic effect arising from the surrounding soils.

4.3. Influence of peak base acceleration As Fig. 14 shows, the maximum pile bending moment can be significantly influenced by the peak base acceleration following a clear increasing trend. Similarly, the maximum pile bending moments are normalized to study the effect of PBA, following the expression shown below.

MN 2 =

Mmax ,

Mmax 0.032n 0.01 × e

(5)

where Mmax, 0.01 is the maximum pile bending moment corresponding to the PBA of 0.01 g. As Fig. 15 shows, the normalized maximum pile bending moment can be well correlated with the PBA following a linear line, which is expressed as:

Mmax ,

Mmax = 77.641 × PBA 0.032n 0.01 × e

(6)

As can be inferred from Fig. 15, Eq. (6) can be used to estimate the effect of PBA on the maximum pile bending moment response, with a prediction error ranging from −23% to 20%.

4.2. Influence of storey number Fig. 12 shows the influence of storey number of superstructure on the maximum bending moment computed at pile head, in which storey number "0" denotes a pure raft without overlying superstructure. As can be seen, the maximum bending moment computed at pile head can be significantly influenced by the storey number and peak base acceleration with an overall increasing trend, regardless of approaches used to model the superstructure. However, it is also noted that the increasing trend becomes much less evident when comparing the maximum pile bending moments between the 15- and 20-storey superstructures modelled using “detailed model”. Besides, similar to that observed in Fig. 10, using "added mass" to model a superstructure tends to underestimate the maximum pile bending moment response in comparison with the approach using "detailed model". However, these two methods lead to very similar pile bending moment response for the superstructure with storey number of 4. This finding suggests that the use of "added mass” to account for the inertial effect of superstructure may be only valid for relatively stiff or low-rise superstructures for which the effect of higher modes of the superstructure is comparatively less significant; to more realistically account for the inertial effect imposed by a high-rise superstructure, a detailed model of the superstructure should be used in the numerical simulations. Hereafter, seismic pile

4.4. Influence of pile flexural rigidity Fig. 16 plots the maximum pile bending moment against the pile flexural rigidity for models with different superstructures subjected to the 0.06-g PBA base motion, which suggests an overall increasing trend, regardless of the storey number. Using the same data shown in Fig. 16, Fig. 17 plots the maximum pile curvature against the stiffness-to-mass ratio, which can be reasonably fitted using a power law shown below. −0.706

ΣEp Ip ⎤ Mmax = 0.0012 ⎡ ⎢ m l3 ⎥ Ep Ip ⎣ str p ⎦

(7)

where EpIp is the pile flexural rigidity, with unit kPa; mstr is the mass of the raft and the superstructure, with unit tonne; lp is the pile length, with unit m; Mmax/(EpIp) is the maximum pile curvature, with unit m−1; ∑EpIp/(mstrlp3) is the stiffness-to-mass ratio, with unit s−2. The maximum curvature of pile decreases sharply for small stiffness215

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Fig. 10. Computed envelopes of pile bending moment for numerical models using "added mass" and "detailed model" to simulate the inertial effect of superstructure (EpIp = 1,472,622 kNm2, PBA = 0.06 g): (a) 4 storeys, (b) 10 storeys, (c) 15 storeys, (d) 20 storeys.

consistent with the findings of many previous studies performed on soft clays [8,34,39,47]; the response spectra of the raft accelerations underlying different superstructures may have different magnitudes, but they have almost the same two characteristic frequencies of about 0.68 Hz and 1.1 Hz and mainly depend on the input ground motion as well as the dynamic characteristics of clay deposit. As a result, the superstructures supported by pile-raft systems installed in soft clay deposit likely also experience amplified deformation and load during the seismic shaking events. In the following subsections, some results of the maximum lateral deflection, maximum inter-storey drift ratio and maximum column shear force of the superstructure are to be presented, which were

to-mass ratios up to about 5 and remains relatively unchanged for large stiffness-to-mass ratios greater than about 20, which is consistent with the findings observed from the centrifuge tests performed on different pile-raft systems installed in soft kaolin clay bed [53].

5. Seismic response of the superstructure Fig. 18 shows the typical comparisons of time history and response spectrum between raft acceleration and the corresponding input base acceleration. As can be seen, the raft accelerations are generally different from the free-field accelerations plotted in Fig. 5, and they are significantly amplified due to the presence of soft clay deposit, which is 216

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Fig. 11. Computed envelopes of pile shear force for numerical models using "added mass" and "detailed model" to simulate the inertial effect of superstructure (EpIp = 1,472,622 kNm2, PBA = 0.06 g): (a) 4 storeys, (b) 10 storeys, (c) 15 storeys, (d) 20 storeys.

h is the height of the storey.

calculated based on the numerical models with detailed modelling of the superstructure. The maximum lateral deflection of the superstructure and maximum inter-storey drift ratio are respectively defined by the following two expressions.

Defi = max Ui (t ) − U0 (t )

(8)

Dri i = max Ui (t ) − Ui − 1 (t ) / h

(9)

Similar to the pile bending moment response, the columns at the same storey level usually do not evenly share the inertial force arising from the above storeys; the inner columns C2 and C5 shown in Fig. 3 tend to experience comparatively larger shear force responses than the outer columns C1, C3, C4 and C6 shown in the same figure. In this study, the averaged column shear force of columns C1 to C6 is presented rather than that of any individual column, which can better reflect the overall trend of shear force demand for the superstructures.

wherein Defi, Drii are the maximum lateral deflection and maximum inter-storey drift ratio at the ith level, respectively; i is the storey level, ranging from 1 to 20; t is time, ranging from 0 to 25 s; Ui(t) and U0(t) are the lateral displacements of the ith floor and raft (building base) at time t, respectively;

5.1. Influence of soil-structure interaction To investigate the influence of soil-structure interaction (SSI) on the seismic response of superstructure, two numerical models namely 217

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Fig. 15. Normalized maximum pile bending moment at the pile head versus PBA (totally 45 analyses). Fig. 12. Influence of storey number of superstructure on the maximum bending moments computed at the pile head for analyses involving both "added mass" and "detailed model" (EpIp = 1,472,622 kNm2).

Fig. 16. Influence of pile flexural rigidity on the maximum bending moment at pile head (PBA = 0.06 g).

Fig. 13. Normalized maximum bending moment at the pile head against the storey number of superstructure for analyses involving "detailed model" (totally 45 analyses).

Fig. 17. Maximum pile curvature plotted against stiffness-to-mass ratio of the pile-raftsuperstructure system, for different pile types (PBA = 0.06 g).

both the fixed-base and pile-foundation models. As can be seen, for fixed-base models, the time domain and modal response spectrum analyses generally leads to more comparable results of the superstructure response, which significantly differ from those computed from the pile-foundation models. For the 4-storey superstructure, the SSI is detrimental as the time domain analysis performed on the fixed-base model tend to underestimate the response of superstructural deflection and column shear force, with the maximum underestimation ratios respectively being about 51% and 31%. On the other hand, without consideration of SSI, the fixed-base model leads to too conservative results for the 20-storey superstructure, the time domain analysis performed on which overpredicts the maximum superstructural deflection and maximum column shear force by up to 65% and 126%, respectively. Besides, as Fig. 19(a)–(d) show, the fixed-base models also tend to underestimate the maximum superstructural deflection and maximum inter-storey drift ratio at the first storey, regardless of the storey number, which is likely due to that base rotation of the superstructure is fully constrained for the fixed-base models. The difference in the effect

Fig. 14. Influence of PBA on the maximum bending moment computed at the pile head (EpIp = 1,472,622 kNm2).

"fixed-base" and "pile-foundation" models which respectively represent the superstructure model with fixed base and full model of the clay-pileraft-superstructure system were used. Time domain analyses were performed for the pile-foundation models, with input base acceleration time history shown in Fig. 1; both time domain and modal response spectrum analyses (recommended in most seismic design codes for building such as Eurocode 8) were performed for the fixed-base models, with the free-filed ground acceleration time history and response spectrum (shown in Fig. 5) applied at the tips of the first-level columns of the superstructure. Fig. 19 shows the distributions of maximum lateral deflection, maximum inter-storey drift ratio and maximum column shear force for the 4- and 20-storey superstructures computed from 218

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Fig. 18. Typical comparison of the raft accelerations with the input base acceleration (EpIp = 1,472,622 kNm2, PBA = 0.06 g): (a) acceleration time histories, (b) acceleration response spectra.

Fig. 19. Seismic response of superstructure with and without consideration of soil-structure interaction (SSI) (EpIp = 1,472,622 kNm2, PBA = 0.06 g, TD: time domain analysis, MRS: modal response spectrum analysis): (a) maximum lateral deflection (MLD) for 4 storeys, (b) MLD for 20 storeys, (c) maximum inter-storey drift ratio (MISDR) for 4 storeys, (d) MISDR for 20 storeys, (e) maximum column shear force (MCSF) for 4 storeys, (f) MCSF for 20 storeys.

fundamental frequencies of the 4- and 20-storey superstructures being respectively close to and departing from the dominant frequency of the raft motion. In general, decreasing difference between the first-mode frequency of a superstructure and the dominant frequency of the base motion leads to more intense seismic response, and vice versa. The foregoing discussions and comparisons suggest that SSI has a

of SSI between the 4- and 20-storey superstructures can be partly explained by comparing the first-mode frequencies of these two superstructures (respectively 2.28 Hz and 0.60 Hz as listed in Table 4) with the dominant frequency of the raft/free-field motion of about 0.66–0.68 Hz as shown in Figs. 5 and 18; the SSI tends to reduce the fundamental frequency of the superstructure, which results in the 219

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Fig. 20. Influence of PBA on the seismic response of superstructure (EpIp = 1,472,622 kNm2): (a) MLD for 4 storeys, (b) MLD for 15 storeys, (c) MISDR for 4 storeys, (d) MISDR for 15 storeys, (e) MCSF for 4 storeys, (f) MCSF for 15 storeys.

significant influence on the seismic response of superstructure, regardless of the detrimental or beneficial effects. Hence, SSI should be taken into consideration when studying the seismic response of a superstructure, which was also proposed by many other researchers (e.g. [21,26,28,36,38]). Hereafter, the seismic response of a superstructure refers to that with the consideration of SSI unless otherwise stated.

n

Fi (t ) =

⎛ ⎞ 1 abs ∑ [m i × Ai (t )] ⎜ ⎟ N ⎝ j=i ⎠

(10)

where i is the storey level; t is time, ranging from 0 s to 25 s in this study; Fi(t) is the averaged shear force for columns below the ith storey at time t; N is the total number of columns below the ith storey ( N = 9 in this study); n is the total number of floors (n = 4, 10, 15 and 20 in this study); mi is the mass of the ith floor; Ai(t) is acceleration of the ith floor at time t.

5.2. Influence of peak base acceleration As Fig. 20 shows, the distribution profiles of the maximum lateral deflection, maximum inter-storey drift ratio and maximum column shear force for the 4- and 15-storey superstructures increase significantly with the increasing peak base acceleration. Besides, Fig. 20(f) suggests that the maximum shear force of the 15-storey superstructure may not necessarily occur at the first-level columns as that for the 4storey superstructure as shown in Fig. 20(e), but can also be experienced by the second-level columns, depending on the levels of PBA of the motions applied. The column shear forces mainly arise from the inertial forces exerted by the floors during the seismic shaking events, the averaged value of which can be expressed by the following equation:

Fig. 21 shows the acceleration distribution profiles of the 15-storey superstructure when the first-storey columns experience the maximum averaged shear force for the superstructure subjected to different PBA ground motions. As can be seen, the first floor experiences the acceleration towards the opposite direction in comparison with the upper floors associated with the PBA of 0.01 g and 0.03 g, while all the 15 floors experience the accelerations in the same direction for the PBA of 0.06 g. Hence, by use of Eq. (10), the discrepancy in the maximum 220

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profiles of the 4- and 20-storey superstructures supported by pile foundations with varying pile flexural rigidities, which suggest a consistent decreasing trend of the maximum superstructural deflection with the pile flexural rigidity for storey levels up to four; however, as Fig. 22(b) shows, for the storey levels ranging from 5 to 20, the maximum lateral deflection of the 20-storey superstructure seems to be relatively insensitive to the variation in pile flexural rigidity. Similar findings are also found in the corresponding maximum inter-storey drift ratio profiles shown in Fig. 22(c) and (d). Besides, as Fig. 22(d) shows, for storey levels ranging from 5 to 15 of the 20-storey superstructure, the maximum inter-storey drift ratio tends to increase with the increasing pile flexural rigidity. Fig. 22(e) and (f) show the plots of the maximum column shear force against pile flexural rigidity, which suggest the opposite trends of the maximum column shear force response with the increasing pile flexural rigidity between the 4- and 20storey superstructures. The discrepancy in the seismic response of superstructure against the pile flexural rigidity is largely dependent on its fundamental frequency and the dominant frequency of the building base motion. As can be seen from Table 4, the first-mode frequencies of the 4- and 20-storey superstructures under fixed-base condition are 2.28 Hz and 0.6 Hz, respectively. The actual fundamental frequencies of the 4- and 20-storey superstructures overlying pile foundation likely are respectively larger and smaller than the dominant frequency of the

Fig. 21. Computed accelerations at different floors and raft for the 15-storey superstructure subjected to different base motions (EpIp = 1,472,622 kNm2, time ≈ 6.5 s).

column shear force distribution as shown in Fig. 20(f) among analyses involving different PBA ground motions can be reasonably explained.

5.3. Influence of pile flexural rigidity Fig. 22(a) and (b) show the maximum superstructural deflection

Fig. 22. Influence of pile flexural rigidity on the seismic response of superstructure (PBA = 0.06 g): (a) MLD for 4 storeys, (b) MLD for 20 storeys, (c) MISDR for 4 storeys, (d) MISDR for 20 storeys, (e) MCSF for 4 storeys, (f) MCSF for 20 storeys.

221

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Fig. 23. Influence of storey number of superstructure on the seismic response of superstructure (EpIp = 1,472,622 kN m2, PBA = 0.06 g): (a) MLD, (b) MISDR, (c) MCSF.

with a fundamental frequency of 0.8 Hz under the fixed-base condition. It is largely due to SSI effect which can effectively reduce the fundamental frequency of the superstructure; as a result, the 15-storey superstructure likely has an actual fundamental frequency comparatively closer to the dominant frequency of the building base motion. Hence, the influence of storey number on the seismic response of superstructure is also frequency-dependent, which depends on the dynamic characteristics of the input ground motion as well as the soilfoundation-superstructure system.

building base motion of about 0.68 Hz as shown in Fig. 18. As the pile flexural rigidity increases, the fundamental frequency increases; as a result, the fundamental frequencies of the 4- and 20-storey superstructures supported by pile foundation approach and depart from the dominant frequency of the building base motion, respectively. From the above discussions, the pile flexural rigidity can effectively influence the seismic response of a superstructure. However, its influence on the seismic response of a superstructure is less significant as compared to that on the pile bending moment response. 5.4. Influence of storey number

6. Discussions

As Fig. 23 shows, the maximum lateral deflection, maximum interstorey drift ratio and maximum column shear force of the superstructure can be significantly influenced by the storey number of superstructure. As Fig. 23(a) shows, at the same storey level, the maximum lateral superstructural deflection tends to increase as the storey number increases up to 15, and then becomes much smaller when the storey number changes from 15 to 20. As Fig. 23(b) shows, the 15storey superstructure experiences the largest maximum inter-storey drift ratio for storey levels below 12; for storey levels above 12, the 20storey superstructure experiences the largest maximum inter-storey drift ratio. Similar findings are also observed in Fig. 23(c) of the maximum column shear force profile, except that the transition is at the 10th floor. Similarly, the discrepancy in the seismic response of the superstructure among these four superstructures can be partly explained by comparing the fundamental frequencies of the superstructures with the dominant frequency of the base motion of the superstructure. As Table 4 shows, under the fixed-base condition, the fundamental frequencies of the 4-, 10- and 15-storey superstructure change from 2.28 to 0.8 Hz, which gradually become closer to the dominant frequency (0.68 Hz as shown in Fig. 18) of the building base motion. Furthermore, the 20-storey superstructure under fixed-base condition has a fundamental frequency of 0.6 Hz which is the nearest to the dominant frequency of the building base motion; however, it generally has less intense seismic responses than 15-storey superstructure

Section 4 presents the computed results of pile bending moment for different pile-raft-superstructure systems constructed on soft clay subjected to far-field ground motions. The pile bending moment response was found to be significantly influenced by peak base acceleration, pile flexural rigidity, and the inertial effect imposed by a superstructure, with a general increasing trend. The approach using "added mass” to account for the inertial effect imposed by a superstructure may be only valid for low-rise superstructures; to more realistically account for the inertial effect imposed by a relatively high-rise superstructure, detailed modelling of the superstructure should be adopted. Furthermore, Eqs. (4), (6) and (7) were derived to favourably respectively represent the effects of the three factors on the maximum pile bending moment response experienced at the pile head. It should be noted that, however, upon the derivation of Eqs. (4), (6) and (7), variations in some other factors such as pile length and clay thickness were not taken into consideration. In the previous study [51], based on a series of centrifuge tests and numerical parametric studies, a semi-empirical equation was derived to predict the maximum pile bending moment at the pile head for pile foundations installed in soft clay deposits, which can be expressed as:

222

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Mmax ,

0

influenced by the former two factors, while affected to a lesser extent by the pile flexural rigidity. Besides, the coupled soil-foundation-superstructure analysis with a detailed modelling of the superstructure is highly recommended as the SSI and the configuration of a superstructure can significantly influence the seismic responses of both the foundation and superstructure. This study provides a useful reference for the practical seismic design of pile-raft-superstructure systems constructed on soft clay deposits. The findings drawn from the present study may be only valid for pile-raft-superstructure systems subjected to small to moderate far-field ground motions, where the pile-raft-superstructure systems can still be modelled by linear elastic materials. Future studies can be performed to further examine the seismic response of the pile-raft-superstructure systems when strong ground motions, more sophisticated superstructure and plastic deformation of the pile-raft-superstructure systems are taken into consideration.

2 l p −0.595 ⎛ (∑ EP IP ) ρsoil Hsoil E I ⎞ = 6.68 × 10−3 ⎛ P P ⎞ ⎛ ⎞ ⎜ ⎟ 3 r r G m l ⎝ ⎠⎝ ⎠ soil str p ⎠ ⎝ ⎜

⎟

−0.3

mstr ⎞ × PBA1.092 ⎛⎜ ⎟ ⎝ ρsoil l p Araft ⎠ ρpile ⎞0.29 ⎛ Hsoil ⎞0.893 × M−0.032 ⎛⎜ ⎟ ⎜ ⎟ ⎝ ρsoil ⎠ ⎝ l p ⎠

(11)

wherein Mmax, 0 is the predicted maximum pile bending moment for pile foundation supporting a pure raft, same as that defined in Eqs. (3) and (4); Araft is the area of raft footprint; Hsoil is the thickness of soil; M is the slope of critical state line, which can be expressed as M = 6sinϕ/(3-sinϕ) (ϕ is the effective internal friction angle of soil); ρpile and ρsoil are the densities of the pile and soil, respectively; Gsoil is the average maximum soil shear modulus which can be represented by the following equation:

Gsoil =

∫0

Hsoil

Acknowledgements The first author is grateful to Associate Professor Siang Huat Goh, Professor Fook Hou Lee and Assistant Professor Subhadeep Banerjee for their invaluable guidance and help in centrifuge and numerical modelling of soil-structure systems subjected to seismic base shakings. The centrifuge tests were carried out with the support and assistance of the technical staff at the Centre for Soft Ground Engineering, NUS.

Gmax dz

Hsoil

(12)

where Gmax is the depth-dependent maximum or small-strain shear modulus of the soil, which can be obtained from Eq. (2). Apart from the three factors as those considered in this study, five more factors namely pile length, soil stiffness, soil frictional angle, soil thickness and pile density were considered in Eq. (11). The seismic maximum pile bending moment for pile-raft-superstructure systems constructed on soft clay can be approximately estimated following the procedure proposed herein. Firstly, a maximum pile bending moment for pile foundation supporting a pure raft can be estimated using Eq. (11); secondly, the maximum pile bending moment for the same pile foundation supporting a superstructure can be approximately estimated using Eq. (4); thirdly, Eqs. (6) and (7) can be employed to make further adjustments to the predicted maximum pile bending moment to account for more complex situations. The procedure proposed herein could provide a quick and first-order prediction of the seismic maximum pile bending moment prior to performing more detailed and rigorous analyses, which likely can serve as a useful tool for practical design of pile foundation against seismic shaking. On the other hand, as Section 5 presents, the seismic response of a superstructure is not so straightforward; similar correlations as those derived for the seismic pile bending moment response were not obtained at this time. The seismic response of a superstructure is highly frequency-dependent, and the effect of seismic SSI is significant and can be either beneficial or detrimental to the seismic response of a superstructure; hence, SSI should be taken into consideration when studying the seismic response of a structure supported by pile foundation. Furthermore, the superstructures considered in this study are rather simple, and the applicability of the findings drawn in this study may need to be further examined when more complex superstructures with significantly different dynamic characteristics are encountered.

References [1] Abdoun T, Dobry R, O'Rourke TD, Goh SH. Pile response to lateral spreads: centrifuge modeling. ASCE J Geotech Geoenviron Eng 2003;129(10):869–78. [2] Alsaleh H, Shahrour I. Influence of plasticity on the seismic soil-micropiles-structure interaction. Soil Dyn Earthq Eng 2009;29(3):574–8. [3] ATC. Amended tentative provisions for the development of seismic regulations for buildings. ATC Publication ATC 3-06, NBS Special Publication 510, NSF Publication 78-78, Washington, DC; 1978. [4] Ayothiraman R, Matsagar VA, Kanaujia VK. Influence of superstructure flexibility on seismic response pile foundation in sand. In: Proceedings of the 15th world conference on earthquake engineering, 24–28 September 2012, Lisbon; 2012. [5] Balendra T, Lam NTK, Perry MJ, Lumantarna E, Wilson JL. Simplified displacement demand prediction of tall asymmetric buildings subjected to long-distance earthquakes. Eng Struct 2005;27(3):335–48. [6] Balendra T, Suyanthi S, Tan KH, Ahmed A. Seismic capacity of typical high-rise buildings in Singapore. Struct Des Tall Spec Build 2013;22(18):1404–21. [7] Banerjee S. Centrifuge and numerical modeling of soft clay-pile-raft foundations subjected to seismic shaking Ph.D. Thesis Singapore: National University of Singapore; 2009. [8] Banerjee S, Goh SH, Lee FH. Earthquake-induced bending moment in fixed-head piles in soft clay. Géotechnique 2014;64(6):431–46. [9] Bhattacharya S, Adhikari S, Alexander NA. A simplified method for unified buckling and free vibration analysis of pile-supported structures in seismically liquefiable soils. Soil Dyn Earthq Eng 2009;29(8):1220–35. [10] Boulanger RW, Curras CJ, Kutter BL, Wilson DW, Abghari A. Seismic soil-pilestructure interaction experiments and analyses. ASCE J Geotech Geoenviron Eng 1999;125(9):750–9. [11] Brandenberg SJ, Boulanger RW, Kutter BL, Chang D. Behavior of pile foundations in laterally spreading ground during centrifuge tests. ASCE J Geotech Geoenviron Eng 2005;131(11):1378–91. [12] Brandenberg SJ, Zhao M, Boulanger RW, Wilson DW. p-y plasticity model for nonlinear dynamic analysis of piles in liquefiable soil. ASCE J Geotech Geoenviron Eng 2013;139(8):1262–74. [13] BSI. Eurocode 1: actions on structures – Part 1-1: general actions – densities, selfweight, imposed loads for buildings. London, UK: BSI; 2002. [14] BSI. Eurocode 8: design of structures for earthquake resistance – Part 5: foundations, retaining structures and geotechnical aspects. London, UK: BSI; 2004. [15] BSI. Eurocode 2: design of concrete structures – Part 1-1: general rules and rules for buildings. London, UK: BSI; 2004. [16] BSSC. Recommended provisions for the development of seismic regulations for new buildings and other structures. Washington, DC: Building Seismic Safety Council; 2000. [17] Castelli F, Maugeri M. Postearthquake analysis of a piled foundation. ASCE J Geotech Geoenviron Eng 2013;139(10):1822–7. [18] Chau KT, Shen CY, Guo X. Nonlinear seismic soil-pile-structure interactions: shaking table tests and FEM analyses. Soil Dyn Earthq Eng 2009;29(2):300–10. [19] Curras CJ, Boulanger RW, Kutter BL, Wilson DW. Dynamic experiments and analyses of a pile-group-supported structure. ASCE J Geotech Geoenviron Eng 2001;127(7):585–96. [20] Dai W, Roesset JM. Horizontal dynamic stiffness of pile groups: approximate

7. Conclusions As an extension to a previous study [51] in which the superstructure was modelled by added mass and increasing the raft density respectively in the centrifuge tests and numerical parametric studies, a series of 3D finite element analyses incorporated with a hyperbolic-hysteretic soil model were performed to investigate the seismic response of pileraft-superstructure systems constructed on soft clay stratum. Three factors, namely peak base acceleration, configuration of superstructure, and flexural rigidity of pile, were accounted for. It is observed that all the three factors have significant influences on the pile bending moment response; the superstructural response can also be significantly 223

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[38] Nikolaou S, Mylonakis G, Gazetas G, Tazoh T. Kinematic pile bending during earthquakes: analysis and field measurements. Géotechnique 2001;51(5):425–40. [39] Pan TC. Site-dependent building response in Singapore to long-distance Sumatra earthquakes. Earthq Spectra 1997;13(3):475–88. [40] Pan TC, Megawati K, Goh KS. Response of high-rise buildings in Singapore due to a potential giant earthquake in the sumatran megathrust. J Earthq Eng 2011;15(Suppl 1):90–106. [41] Renzi S, Madiai C, Vannucchi G. A simplified empirical method for assessing seismic soil-structure interaction effects on ordinary shear-type buildings. Soil Dyn Earthq Eng 2013;55:100–7. [42] Rovithis EN, Pitilakis KD, Mylonakis GE. Seismic analysis of coupled soil-pilestructure systems leading to the definition of a pseudo-natural SSI frequency. Soil Dyn Earthq Eng 2009;29(6):1005–15. [43] Sarma SK, Srbulov M. A simplified method for prediction of kinematic soil-foundation interaction effects on peak horizontal acceleration of a rigid foundation. Earthq Eng Struct Dyn 1996;25(8):815–36. [44] SSC. CP4: code of practice for foundations. Singapore: Singapore Standards Council; 2003. [45] Stewart JP. Variations between foundation-level and free-field earthquake ground motions. Earthq Spectra 2000;16(2):511–32. [46] Tabatabaiefar HR, Fatahi B, Samali B. Seismic behavior of building frames considering dynamic soil-structure interaction. ASCE Int J Geomech 2013;13(4):409–20. [47] Tinawi R, Sarrazin M, Filiatrault A. Influence of soft clays on the response spectra for structures in eastern Canada. Soil Dyn Earthq Eng 1993;12(8):469–77. [48] Tokimatsu K, Suzuki H, Sato M. Effects of inertial and kinematic interaction on seismic behavior of pile with embedded foundation. Soil Dyn Earthq Eng 2005;25(7–10):753–62. [49] Viggiani G, Atkinson JH. Stiffness of fine-grained soil at very small strains. Géotechnique 1995;45(2):249–65. [50] Wilson DW, Boulanger RW, Kutter BL. Observed seismic lateral resistance of liquefying sand. ASCE J Geotech Geoenviron Eng 2000;126(10):898–906. [51] Zhang L. Centrifuge and numerical modelling of the seismic response of pile groups in soft clays Ph.D. Thesis Singapore: National University of Singapore; 2014. [52] Zhang L, Goh SH, Liu H. Seismic response of pile-raft-clay system subjected to a long-duration earthquake: centrifuge test and finite element analysis. Soil Dyn Earthq Eng 2017;92:488–502. [53] Zhang L, Goh SH, Yi J. A centrifuge study of the seismic response of pile–raft systems embedded in soft clay. Géotechnique 2017;67(6):479–90. [54] Shao Z, Tiong RLK. Estimating potential economic loss from damage to RC buildings in singapore due to far-field seismic risk. J Earthq Eng 2015;19(5):770–83.

expressions. Soil Dyn Earthq Eng 2010;30(9):844–50. [21] De Sanctis L, Maiorano RMS, Aversa S. A method for assessing kinematic bending moments at the pile head. Earthq Eng Struct Dyn 2010;39(10):1133–54. [22] Dobry R, Abdoun T, O'Rourke TD, Goh SH. Single piles in lateral spreads: field bending moment evaluation. ASCE J Geotech Geoenviron Eng 2003;129(10):879–89. [23] Dungca JR, Kuwano J, Takahashi A, Saruwatari T, Izawa J, Suzuki H, Tokimatsu K. Shaking table tests on the lateral response of a pile buried in liquefied sand. Soil Dyn Earthq Eng 2006;26(2–4):287–95. [24] Durante MG, Di Sarno L, Mylonakis G, Taylor CA, Simonelli AL. Soil-pile-structure interaction: experimental outcomes from shaking table tests. Earthq Eng Struct Dyn 2015;45(7):1041–61. [25] Gohl WB. Response of pile foundations to simulated earthquake loading: experimental and analytical results Ph.D. Thesis University of British Columbia; 1991. [26] Hamada M, Towhata I, Yasuda S, Isoyama R. Study on permanent ground displacement induced by seismic liquefaction. Comput Geotech 1987;4(4):97–220. [27] Hokmabadi AS, Fatahi B, Samali B. Assessment of soil-pile-structure interaction influencing seismic response of mid-rise buildings sitting on floating pile foundations. Comput Geotech 2014;55:172–86. [28] Jeremić B, Jie G, Preisig M, Tafazzoli N. Time domain simulation of soil-foundationstructure interaction in non-uniform soils. Earthq Eng Struct Dyn 2009;38(5):699–718. [29] Klar A, Baker R, Frydman S. Seismic soil-pile interaction in liquefiable soil. Soil Dyn Earthq Eng 2004;24(8):551–64. [30] Lombardi D, Bhattacharya S. Modal analysis of pile-supported structures during seismic liquefaction. Earthq Eng Struct Dyn 2014;43:119–38. [31] Lu JC. Parallel finite element modeling of earthquake ground response and liquefaction Ph.D. Thesis San Diego: University of California; 2006. [32] Ma K, Banerjee S, Lee FH, Xie HP. Dynamic soil-pile-raft interaction in normally consolidated soft clay during earthquakes. J Earthq Tsunami 2012;06(03). 1250031_1-1250031_12. [33] Maheshwari BK, Truman KZ, El Naggar MH, Gould PL. Three-dimensional nonlinear analysis for seismic soil-pile-structure interaction. Soil Dyn Earthq Eng 2004;24(4):343–56. [34] Mayoral JM, Alberto Y, Mendoza MJ, Romo MP. Seismic response of an urban bridge-support system in soft clay. Soil Dyn Earthq Eng 2009;29(5):925–38. [35] Meymand PJ. Shaking table scale model test of nonlinear soil-pile-superstructure interaction in soft clay Ph.D. Thesis Berkeley: University of California; 1998. [36] Mylonakis G, Gazetas G. Seismic soil-structure interaction: beneficial or detrimental? J Earthq Eng 2000;4(3):277–301. [37] NSPRC. GB50011-2010: code for seismic design of buildings. Beijing, China: National standard of the People's Republic of China; 2010.

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