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Using peak ground velocity to characterize the response of soil-pile system in liquefying ground
Accepted Manuscript Using peak ground velocity to characterize the response of soilpile system in liquefying ground
Xiaoyu Zhang, Liang Tang, Xianzhang Ling, Andrew Hin Cheong Chan, Lu Jinchi PII: DOI: Reference:
S0013-7952(17)30539-2 doi:10.1016/j.enggeo.2018.04.011 ENGEO 4822
To appear in:
Engineering Geology
Received date: Revised date: Accepted date:
3 April 2017 7 April 2018 15 April 2018
Please cite this article as: Xiaoyu Zhang, Liang Tang, Xianzhang Ling, Andrew Hin Cheong Chan, Lu Jinchi , Using peak ground velocity to characterize the response of soilpile system in liquefying ground. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Engeo(2017), doi:10.1016/ j.enggeo.2018.04.011
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ACCEPTED MANUSCRIPT Using Peak Ground Velocity to Characterize the Response of Soil-Pile System in Liquefying Ground
Xiaoyu ZHANG a, Liang TANG
, Xianzhang LING c, Andrew Hin Cheong CHAN d , and Jinchi LU e
Ph. D Candidate, School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090,
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a.
b*
China, [email protected] b.
Professor, School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China,
c.
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[email protected], [email protected]
Professor, School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China,
d.
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[email protected]
Professor, School of Engineering and ICT, University of Tasmania, Hobart, Tasmania 7001, Australia, [email protected]
Associ at e Project Scientist , Depart m ent of Structural Engineeri ng, Univers it y of Californi a, San Diego, La Jolla,
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e.
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CA 92093-0085, USA, [email protected]
Corresponding Author: Liang Tang
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Address: School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China Tel: +86-13796627061
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Email: [email protected]
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Fax: 86-451-86282704
ACCEPTED MANUSCRIPT Abstract Performance of a soil-pile system can be significantly influenced by many characteristics of an earthquake ground motion, and it is vitally important to identify the ground motion parameters that have the most significant effects on the response when predicting the level of movement or damage in the pile. In this paper, three-dimensional finite element (FE) analysis was conducted to simulate a centrifuge experiment on the nonlinear behavior of a pile founded in liquefiable soil subjected to strong
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earthquake motions. The result of the FE analysis was foun d to be in reasonable agreement with the experimental data. As such, the calibrated FE model was used to investigate the influence of ground
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motion parameters on the pile-soil response in both liquefied and non-liquefied soils. It was found that
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peak ground velocity (PGV) is an appropriate ground motion parameter to characterize the response of the soil-pile system in liquefying ground. The maximu m pile bending moment, pile lateral
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displacement, and soil lateral displacement increased with increasing PGV. Moreover, near-fault ground motions could result in more severe damage to the pile compared to far-fault grounds motions.
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This study provided a new insight on the influence of ground motion parameters, in particular PGV, on the dynamic performance of a pile foundation.
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Keywords: Liquefaction; Pile foundation; Peak ground velocity; Ground motion parameters; Finite
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element analysis; Centrifuge test
ACCEPTED MANUSCRIPT 1. Introduction Seismically-induced liquefaction, one of the most devastating geotechnical phenomena from earthquakes, has received wide attention from the engineering geology and geotechnical engineering communities in recent decades (Chen et al. 2016; Gong et al. 2016; Pokhrel et al. 2013). Earthquakeinduced liquefaction has caused significant damage to pile-supported structures in past earthquakes, such as, the failure of Showa Bridge during the 1964 Niigata earthquake, and the damage to the
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battered piles that supported a wharf at the Port of Oakland in the 1989 Loma Prieta Earthquake (Brandenberg 2005; Ishihara 1993; Valverde-Palacios et al. 2012). As such, the observed damage
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induced liquefaction affecting embedded pile foundation systems.
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patterns have been a catalyst in driving research to elucidate the basic mechanisms of seismically-
Many attempts have been made in recent decades to study the dynamic behavior of a pile
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foundation in liquefied soil, using various experimental techniques including dynamic centrifuge experiments, shaking table tests and full-scale field tests as well as various numerical modeling
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methods (Liu et al. 2016; Rahmani and Pak 2012; Tang et al. 2014). It can be clearly observed that the seismic performance of a soil-pile system is strongly influenced by the characteristics of earthquake
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ground motions. For instance, Haldar and Babu (2010) stated that the increase in the peak ground acceleration (PGA) increases the maximu m shear strain in the soil. Tang and Ling (2014) concluded
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that increase of the acceleration amplitude and decrease of the frequency of earthquake excitation may increase the pile bending moment as well as the rate of the free-field excess pore pressure build-up. Chatterjee et al. (2015) observed that as the input motion changes from Bhuj (PGA=0.106g) to Kobe
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(PGA=0.834g), the normalized pile bending moment rises by 40%. Many ground motion parameters have been proposed to describe the important characteristics of an earthquake ground motion in a compact and quantitative form, such as PGA, peak ground velocity (PGV), Bracketed duration (DB ), and so on. In practice, these parameters are usually employed in the selection of a suite of design ground motions for a given site. Thus, it is important to explore the relationship between ground motion parameters and pile response, which would be useful for selecting ground motions in designing a pile foundation in liquefiable soil. In this regard, knowledge of the most effective ground motion parameters for predicting a given response (or demand measure) in liquefied soil or pile is critically needed. Nevertheless, a few studies have been carried out to discuss the effect of ground motion parameters on pile response in liquefied sand, and some researchers found that the PGA,
ACCEPTED MANUSCRIPT predominant frequency and the Arias intensity have a significant influence on t he pile lateral displacement and bending moment (Choobbasti et al. 2012; Liyanapathirana and Poulos 2005; Rahmani and Pak 2012). Moreover, in these studies, only a few widely-used parameters such as PGA and Arias intensity have been explored, while, to-date, PGV has received little attention. In this paper, a finite element (FE) study is used to perform parametric studies to determine the most appropriate characterizing parameter by comparing 23 ground motion parameters (including PGV) of an
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earthquake input motion.
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In the following sections, the numerical modeling techniques employed to simulate a centrifuge experiment are first described. Then, the relationship between ground motion parameters and the
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response of a soil-pile system is investigated using a number of selected near-fault and far-fault ground motions. Twenty-three ground motion parameters (see Appendix A) are compared before PGV is
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identified as the best parameter in characterizing the behavior of the soil-pile system in liquefying ground, and possible reasons why PGV is a suitable parameter are discussed. Finally, conclusions are
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drawn.
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2. Numerical modeling
It is difficult to explore the effect of ground motion characteristics on the seismic response of a pile
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by means of a large number of earthquake ground motions using experimental techniques, because it is costly and time consuming. Meanwhile in recent years numerical modeling has increasingly emerged as a versatile tool to study this issue (Elgamal et al. 2008; Liyanapathirana and Poulos 2005). In this
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section, a three-dimensional FE nonlinear analysis was carried out to simulate a centrifuge experiment on the dynamic behavior of a pile foundation in liquefied ground. 2.1. Centrifuge test
A centrifuge test (event F in test Csp2) was performed by Wilson (1998) to study the dynamic response of a pile foundation in liquefying sand (Fig. 1). All values described below are presented in prototype scale, which is based on the theory of centrifuge test described in detail by Taylor (2003). The soil model consisted of two layers of saturated Nevada sand (fine, and uniformly graded; see Fig. 1). A pipe pile with a diameter of 670 mm and a wall thickness of 19 mm was partially embedded in the soil (Fig. 1). The embedded length of the pile was 16.8 m. The pile top, which was 3.8 m above the ground surface, was applied with a superstructure load of 500 kN.
ACCEPTED MANUSCRIPT 2.2. Finite element modeling All FE simulations were performed using OpenSees, a software framework for simulating the seismic response of structural and geotechnical systems (http://opensees.berkeley.edu, Mazzoni et al. 2006). The FE mesh depicted in Fig. 2(a) was used to model the centrifuge experiment. Only half of the model has been meshed along the center-line of the pile (parallel to the shaking direction) for numerical
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analysis due to symmetry. The two-phase material response of saturated sand was formulated based on
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a u-p formulation (Chan 1988), and the Newmark implicit method was used for time integration. Loose and dense sand were simulated with a multi-yield-surface plasticity constitutive model (Yang et al.
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2003). The soil constitutive model was developed based on the multi-surface plasticity theory for frictional cohesionless soils proposed by Prevost (1985). This model was developed with emphasis on
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simulating the volumetric strain accumulation mechanism in clean cohesionless soils due to cyclic shear strain (Yang et al. 2003). A bilinear material “Steel01” with kinematic hardening illustrated in
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Fig. 2(b) was selected to describe the nonlinear response of the pile (Mazzoni et al. 2006). The pile was simulated using nonlinear beam-column elements, which had six degrees of freedom
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(DOFs) at each node: three for translational displacements and three for rotations (Mazzoni et al. 2006). The soil domain was discretised into 8-node, effective-stress solid-fluid fully coupled brick
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elements (Biot 1955; Lu et al. 2011), which was based on the solid-fluid formulation for saturated soil (Biot 1955; Chan 1988). Each node of this type of brick element had four DOFs: three for translational displacements of soil skeleton and one for pore water pressure. The superstructure was represented as a
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lumped mass at the pile head.
In order to represent the geometric space occupied by the pile [Fig. 2(c)], rigid beam-column links were used in the direction normal to the pile vertical axis (Elgamal et al. 2008). These rigid links acted together as a rigid body (at each horizontal plane where links are located). The soil domain 3D brick elements are connected to the pile geometric configuration at the outer nodes of these rigid links. The soil-pile interface was simulated by the zero-length interface element (i.e., Zerolength element in OpenSees), which could describe the slippage between the pile and soil. More specifically, the zerolength interface element was defined by two nodes (Rigid link node and Soil node) at the same location where the rigid beam-column link was connected to the surrounding soil [Fig. 2(c)]. Moreover, due to the difference between the DOFs at the rigid link node and soil node, an additional node (at the same
ACCEPTED MANUSCRIPT location with soil node) was added to connect the zero-length interface element [Fig. 2(c)]. An elasticperfectly plastic material model was utilized for the interface elements. Young’s modulus and yielding strain of this material were selected to be 2 MPa and 0.04 respectively (Rahmani and Pak 2012). The boundary conditions imposed on the FE model were given below: (1) at any given depth, displacement degrees of freedom of the both side boundary planes (perpendicular to the excitation direction) are tied together (in the horizontal and vertical directions) to
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reproduce laminar box boundary effects (Parra 1996) using the OpenSees equalDOF command; (2) at the side planes parallel to the shaking direction, nodes are restrained from movement in the
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traverse y direction;
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(3) the base and lateral boundaries were impervious (due to symmetry);
(4) the soil surface was stress free, with zero prescribed pore pressure; and
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(5) the vertical deformations at the base was restrained and the recorded base acceleration (Fig. 3) in
2.3. Validation of the numerical model
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the test was applied to the base of the FE model as a uniform accelerat ion boundary condition.
Soil properties employed in the FE simulations are listed in Table 1 (Lu et al. 2006), which are
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obtained based on an earlier calibration process by Elgamal et al. (2002). The permeability of the sand is from the measured values for Nevada sand (Popescu and Prevost 1993). Properties of the pile are
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given in Table 2 (Wilson 1998). The strain hardening ratio b is 0.1 (Bhattacharya 2003). The excess pore pressure (u e) and acceleration time histories (computed and experimental) in the free field are presented in Figs. 4 and 5. It is noted that the onset of liquefaction condition is attained when the
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excess pore pressure ratio ru , defined as the ratio of u e to overburden effective stress, reaches a value close to unity (Wilson 1998). For the loose sand, after an initial rise, a peak is achieved and then the liquefaction-level of the u e is maintained until the end of the shaking process, while the dense sand does not liquefy. The superstructure acceleration (Fig. 6) and pile bending moment resposne (Fig. 7) obtained from the numerical model agree reasonably well with the experimental measurements. Overall, the results obtained from the numerical model agree reasonably well with the experimental data.
3. Ground motion database Earthquake ground motion is an intricate phenomenon which resulted from the sudden energy
ACCEPTED MANUSCRIPT release caused by fault rupture, and the ground motion recorded at stations located within the near-fault region of an earthquake is significantly different from the usual far-fault ground motion observed at a large distance (Davoodi et al. 2013; Zhang et al. 2013). Near-fault ground motion is characterized by a pulse-type wave shape, long pulse period, abundant long-period components, a high ratio of peak ground velocity to peak ground acceleration (PGV/PGA ) and possible significant permanent ground displacement (Davoodi et al. 2013). Therefore, the ground motion database compiled for nonlinear
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analyses constitutes a representative number of near-fault and far-fault ground motions.
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From these databases (Consortium of Organizations for Strong-Motion Observation Systems http://cosmos-eq.org/ and the Pacific Earthquake Engineering Research Center
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http://peer.berkeley.edu/), a total of 16 ground motions were selected to cover a range of frequency content, duration and amplitude (Table 3). All the selected recordings were obtained from Northridge
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(1994), Imperial Valley (1979), Loma Prieta (1989), and Chi-Chi (1999) earthquakes and are related to large ground failures and extensive liquefaction phenomena (Zhang and Wang 2013). Eight ground
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motions, recorded at closest fault distance in range of 0.0-10 km, are selected to represent the features of near-fault ground motions. For all the near-fault ground motions, the velocity pulse duration is larger
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than 1.0 sec, and the PGV/PGA is over 0.1 sec (Table 3). On the other hand, another set of ground motions, recorded from the same earthquake events with site far away from the epicenter (in range of
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15-40 km), is used to represent the far-fault ground motions. All the earthquake records, as shown in Fig. 8(a), are scaled to a PGA of 0.2 g for initial comparison (the influence of PGA will be discussed in Section 4.3). The acceleration response spectrum with a damping ratio of 5% for all selected ground
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motion records are shown in Fig. 8(b). The elastic acceleration response spectra is computed by means of time-integration of the equation of motion of a series of single-degree-of-freedom systems, from which the acceleration response quantities are then obtained and plotted in period vs. amplitude graphs [Fig. 8(b)], using the computer program SeismoSignal (2016). It is observed that the long period response of a near-fault ground motion is more substantial than a far-fault ground motion. Note that all the ground motion parameters used in this study are calculated according to the method described in Appendix A (Kramer 1996), using SeismoSignal (2016). Moreover, the motion at ground surface is
used as the input motion in this study. It is a common practice to use ground surface motion as the input motion in soil liquefaction FE modelling (Asgari et al. 2013; Haldar and Babu 2010; Liyanapathirana and Poulos 2005) since it is difficult to obtain the input motion as the site
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4. Results and discussions In order to find the influence of near-fault ground motions on the soil-pile system, the performance of soil-pile system subjected to both selected NF-P and NF-NP ground motions is examined using the calibrated FE model.
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4.1. Free-field soil response
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Liquefaction is a phenomenon that is associated with a buildup of u e. Free-field u e time histories of loose sand at the depth of 4.55 m for the near-fault and far-fault ground motions are presented in Fig. 9.
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It is observed that soil liquefied in all the cases studied. The peak u e is reached after an initial rise and then the liquefaction-level u e is maintained until the end of shaking. Moreover, the u e distribution under
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the near-fault ground motions shows sharp pore pressure decrease (dilation spikes) which is due to soil dilation, and it leads to an increase in the shear strength of the soil due to the increase in mean effective
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stress. Nevertheless, only slight fluctuations in the u e is observed in the far-fault ground motion cases. In order to provide better insights into the influences of acceleration, velocity, displacement and
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energy of ground motion on soil response, the time histories of free-field u e and lateral displacement at 4.55 m depth when the model is subjected to Nos. 15 and 16 ground motions are showed in Fig. 10.
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Ground motion energy is defined based on the Arias intensity (Ia ). It is noted that the peak soil lateral displacement and dilation spikes could be caused by ground motions with less input energy and acceleration. On the other hand, the peak soil lateral displacement and dilation spikes occur almost at
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the same time with PGV. As similar results were obtained for all the earthquake ground motions used, only the results of Nos. 15 and 16 ground motions are presented here. It can be inferred that PGV has a significant influence on the response of liquefied soil. 4.2. Pile response
The loss of soil strength and stiffness caused by liquefaction under strong shaking will lead to substantial deformation in pile foundation. In this section, the seismic behavior of pile in liquefying ground is evaluated by considering two different criteria: (a) strength criterion expressed in terms of bending moment envelopes along the pile; and (b) damage criterion expressed in terms of maximu m lateral displacement.
ACCEPTED MANUSCRIPT Figs. 11 and 12 show maximu m pile bending moment and maximu m pile lateral displacement envelopes, respectively. It is clear from Fig. 11 that the maximu m bending moment invariably develops at the depth corresponding to the interface between liquefiable (loose sand) and non-liquefiable (dense sand) layers (i.e., 9.1 m depth), and the maximu m lateral displacement is attained at the pile head (Fig. 12). The values of maximu m pile bending moment and lateral displacement when the model is subjected to near-fault ground motions are generally greater than those under far-fault ground motions
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although the PGA of all ground motions used are the same. This demonstrates that pile in liquefying
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ground is more susceptible to damage when subjected to near-fault ground motions.
The effects of acceleration, velocity, displacement and Arias intensity of a ground motion on the
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bending moment and lateral displacement when the model is subjected to Nos. 5 and 6 ground motions are shown in Fig. 13. Similar to soil response, the maximu m pile bending moment and lateral
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displacement also occur at the time of PGV but not at peak acceleration amplitude, peak displacement amplitude or maximu m accumulated input energy. Similar observations can be found for other ground
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motions used.
4.3. Effect of PGV on the response of soil-pile system
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Based on the findings above (Figs. 10 and 13), it can be concluded that peak response of soil and pile occur at the time of PGV. To further investigate of the effect of PGV on the response of soil-pile
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system, each earthquake time acceleration data are scaled to 0.1-, 0.2-, 0.3-, 0.4- and 0.5-g peak acceleration values, respectively.
The influences of PGV on maximu m pile bending moment, pile lateral displacement, and soil lateral
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displacement under various PGA are presented in Fig. 14. A linear relationship is found between PGV and these maximum pile and soil response with good correlation where the linear correlation coefficients (R2 ) obtained are 0.89, 0.89, and 0.87 for maximu m pile bending moment, pile lateral displacement, and soil lateral displacement, respectively. The interesting finding of the relationship between PGV and maximu m soil lateral displacement may explain the differences of dilation phenomena between near-fault and far-fault ground motions. As reported by Asgari et al. (2013), the dilation response could be strongly influenced by the soil lateral displacement. This is also observed in Fig. 10, the dilation spikes occur almost at the same time as the peak soil lateral displacement reaches. Meanwhile, a linear relationship was found between PGV and
ACCEPTED MANUSCRIPT maximu m soil lateral displacement [Fig. 14(c)], and the near-fault ground motions have a much larger PGV than the far-fault ground motions (Table 3). Therefore, it would be logical to conclude that the dilation phenomena were observed more prevalently in the cases of near-fault ground motions. Based on the findings of the relationship between PGV and pile response, the relationship between PGV and the normalized maximu m moment could be expressed as:
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M max / M y k1 PGV (1)
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where PGV is expressed in units of m/sec, Mmax is the maximu m pile moment, My is the yield moment of pile, k 1 is the slope of the line, the mean of k 1 is 0.76 and the standard deviation of k 1 is 0.23.
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Similarly, the relationship between PGV and the normalized maximu m displacement can also be expressed by Equation (2):
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ymax / D k2 PGV
(2)
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where PGV is expressed in units of m/sec, ymax is the maximu m pile displacement, D is pile diameter, k 2 is the slope of the line. The mean of k 2 is 0.82 and the standard deviation of k 2 is 0.29. The results from seven centrifuge tests which were performed by Wilson (1998) as shown in Table 4, were used to
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verify these relationships. As shown in Fig. 15, the test results agree well with the mean line. Therefore, these relationships can be used to estimate the maximu m moment and displacement of pile which is
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located in the similar site conditions as this study. 4.4. PGV versus other ground motion parameters To identify an appropriate ground motion parameter to characterize the behavior of the soil-pile
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system, the effect of a total of 23 ground motion parameters (Appendix A) were compared in this study. The coefficient of correlation between the ground motion parameters and the response of the soil-pile system is listed in Table 5. The top three parameters PGV, vRMS , and SMV are closely related to each other (R2 : 0.80-0.89) and these parameters are all velocity-related parameters. This implies that velocity is a reliable parameter to deduce the level of strain produced due to the ground motion. While PGV has the best correlation on both dynamic behavior of soil and pile, it is suggested that PGV is the best ground motion parameter to characterize the response of a soil-pile system in liquefying ground. One possible reason for the good performance of velocity related parameters is that the effect on the dynamic behavior of soil and pile is closely related to the strain level of the soil. Although the strain is
ACCEPTED MANUSCRIPT related to displacement gradient, it is the accumulation of velocity gradient. In this relatively simple case, the displacement distribution is almost linear along the pile (e.g., Fig. 12), therefore the strain experienced by the soil and pile is directly related to the displacement. From Figs. 10 and 13, it can be seen that, despite the many peaks for the acceleration trace, there is only one distinct peak pile displacement and one PGV. It would be logical to infer that the higher the PGV, the higher the peak pile displacement which leads to the higher bending moment in the pile. Therefore, PGV turns out to be a
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better indicator for peak pile displacement and maximu m bending moment in the pile and PGV has a
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very good correlation with all these quantities for a wide range of earthquake input motions. To investigate whether PGV is also a suitable parameter to characterize the response of pile in the
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non-liquefied soils, the DOFs for pore water pressure in each soil node were fixed in the numerical model. The coefficients of linear correlation between ground motion parameters and the response of the
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soil-pile system are listed in Table 5. It is found that the parameter with the best correlation for nonliquefied soil is HI which can capture important aspects of the amplitude and frequency content of a
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ground motion and it relates to some form of displacement, while for liquefied soil it is PGV which is an amplitude parameter of ground motion. Therefore, PGV is a better parameter to characterize the
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response of the soil-pile system in liquefying soil than in the non-liquefied soil though PGV is still performing reasonably well for non-liquefying soil. Moreover, it should be noted that the top three
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parameters for the non-liquefied soils (i.e., VSI, HI, and PGV) are also velocity-related parameters. Therefore, it can be concluded that the velocity-related parameters have a better correlation with the soil-pile system in both liquefied and non-liquefied ground.
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Site effect is a major issue in the field of earthquake engineering since the seismic motion could be strongly modified in some specific sites, and it is mainly affected by the site conditions (De Ferrari et al. 2017). Therefore, it is necessary to investigate the influence of the s ite effects on the findings of the relationship between PGV and the response of pile-soil system. In this study, the selected motions are recorded from different stations with different site conditions , and each earthquake time acceleration data are scaled to 0.1-, 0.2-, 0.3-, 0.4- and 0.5-g peak acceleration values, respectively. As shown in Fig. 14, the linear relationship is found between PGV and the maximu m pile and soil response for each case with different PGA. And it is also found the PGV has a better correlation with the soil-pile system in both liquefied and non-liquefied soils (Table 5). So the site effects may not alter the relationship between PGV and the response of pile-soil system. To further investigate the influence of site effect on
ACCEPTED MANUSCRIPT the findings in this study, the material parameters for the loose sand in the numerical model has been changed to medium sand and medium-dense sand. These parameters, as listed in Table 1, are suggested by Lu et al. (2006). The correlation between PGV and maximu m pile displacement for the case of PGA=0.2 g are shown in Fig. 16. It can be clearly observed that PGV is still good for different soil conditions. Therefore, it could be concluded that the site effect s will not alter the findings of the relationship between PGV and the response of pile-soil system.
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For any correlation index method, there will be an uncertainty band as it does not consider a lot of finer details. Therefore, additional experimental data, along with related numerical analyses, should be
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examined to verify if this correlation between PGV and the response of soil-pile system in liquefied
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limited information from this one physical configuration.
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soil applies to other physical settings , and also to derive a better physical explanations as we have
5. Conclusions
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This study provides a better insight into the seismic performance of a pile foundation in liquefied soil. In this regard, three-dimensional FE method was employed to simulate a centrifuge test. Based on the calibrated FE model, effect of PGV on the dynamic behavior of a pile foundation in liquefied soil
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conclusions are as follows:
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was invsetigated by carrying out eighty nonlinear time history analyses at five intensity levels. Main
(1) The numerical model is effective in simulating the nonlinear response of the soil-pile system in liquefying ground.
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(2) PGV is the most reliable ground motion parameter for predicting the dynamic performance of the soil-pile system in liquefying ground. Increase of PGV will cause larger soil lateral displacement, pile bending moment and pile lateral displacement. It is likely because, despite there are many peaks in the acceleration traces that are the same in magnitude of PGA, there is only one distinct peak in velocity time history and the same can be concluded for soil lateral displacement, pile bending moment and pile lateral displacement. Furthermore, these peak values occurred at the same time approximately. Therefore, it can be inferred that these peak values are correlated well with each other. (3) Velocity-related parameters have a better correlation with the soil-pile system in both liquefied and non-liquefied soils. PGV is the best parameter for the liquefying ground cases, and Housner Intensity is the best parameter for the non-liquefied soil cases.
ACCEPTED MANUSCRIPT (4) Relative to far-fault ground motions, sharp excess pore pressure spikes caused by soil dilation, easy to occur in near-fault ground motion cases. Moreover, near-fault ground motions can create larger pile bending moment and lateral displacement than those under far-fault ground motions although PGA used for the records are the same.
Acknowledgments
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The presented research work was funded by the National Key R&D Program of China (Grant No. 2016YFE0205100), the National Natural Science Foundation of China (Grant No. 51578195), the
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Open Research Fund of State Key Laboratory of Geo mechanics and Geotechnical Engineering,
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Institute of Rock and So il Mechanics, Chinese Academy of Sciences (Grant No. Z016007), the Special Project Fund of Taishan Scholars of Shandong Province, Ch ina (Grant No. 2015 -212), the Natural
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Science Foundation of Heilongjiang Province of China (Grant No. E2015017), and the Opening Fund
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for Innovation Platform of China (Grant No. 2016YJ004).
Appendi x A. Description of ground motion parameters Detailed description for all the ground motion parameters used in this study can be found in
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Kramer (1996). Only a brief description of these parameters is provided below due to space limitations. PGA: Peak ground acceleration
2.
PGV: Peak ground velocity
3.
PGD: Peak ground displacement
4.
PGV/PGA : The ratio of peak ground velocity to peak ground acceleration
5.
a RMS : Acceleration RMS aRMS
7.
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6.
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1.
1 Td
vRMS : Velocity RMS vRMS
Ia : Arias Intensity I a
2g
1 Td
Td
[a(t )] dt where Td is the duration of the strong motion 2
0
Td
[v(t )] dt 2
0
Td
[a(t )] dt 2
0
3
8.
Ic: Characteristic Intensity I c (aRMS ) 2 Td
9.
SED: Specific Energy Density SED [v(t )]2 dt
Td
0
ACCEPTED MANUSCRIPT 10. CAV: Cumulative Absolute Velocity CAV
Td
a(t ) dt 0
11. ASI: Acceleration Spectrum Intensity. The area under the acceleration response spectrum between periods of 0.1 sec and 0.5 sec 12. VSI: Velocity Spectrum Intensity. The area under the velocity response spectrum between periods of 0.1 sec and 0.5 sec
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13. HI: Housner Intensity. The area under the pseudo-velocity response spectrum between periods of 0.1 sec and 2.5 sec
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14. SMA: Sustained Maximum Acceleration. This parameter gives the sustained maximum
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acceleration during three cycles, and is defined as the third highest absolute value of acceleration in the time-history (note: in order for an absolute value to be considered as a
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"maximu m", it must be larger than values 20 steps before and 20 steps after). 15. SMV: Sustained Maximum Velocity. This parameter gives the sustained maximum velocity
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during three cycles, and is defined as the third highest absolute value of velocity in the timehistory.
16. EDA: Effective Design Acceleration. This parameter corresponds to the peak acceleration
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value found after lowpass filtering the input time history with a cut -off frequency of 9 Hz. 17. A95 : The acceleration level below which 95% of the total Arias intensity is contained.
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18. Tp : Predominant Period. This is the period at which the maximu m spectral acceleration occurs in an acceleration response spectrum calculated at 5% damping.
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Ci 2 f i 19. Tm : Mean Period Tm Ci 2
20. Du : Uniform Duration. The total time during which the acceleration is larger than a given threshold value (5% of PGA). 21. DB : Bracketed Duration. The total time elapsed between the first and the last excursions of a specified level of acceleration (5% of PGA). 22. DS : Significant Duration. The interval of time over which a proportion (percentage) of the total Arias Intensity is accumulated (the interval between the 5% and 95% thresholds). 23. DE : Effective Duration. It is based on the significant duration concept but both the start and end of the strong shaking phase are identified by absolute criteria.
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http://dx.doi.org/10.1016/j.enggeo.2013.08.002.
216 -236, doi:
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Table 1 Parameters for the soil model (after Lu et al., 2006; Popescu and Prevost, 1993)
3
2100 kg/m3
Medium sand
Mass density
1700 kg/m3
1900 kg/m
Low-strain shear modulus, Gr
55.5 MPa
75 MPa
100 MPa
130.0 MPa
Reference confining pressure, Pr
80 kPa
80 kPa
80 kPa
80 kPa
Friction angle,
29°
33°
37°
40°
Liquefaction yield strain, y
1%
1%
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Dense sand
Loose sand
1%
0
Contraction parameter, c1
0.21
0.07
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Mediumdense sand
Parameters
0.05
0.03
Phase transformation angle, PT
29°
27°
27°
27°
Dilation parameter, d 1
0
0.4
3.0
0.8
Dilation parameter, d 2
0
5.0
5.0
Permeability, k
6.6×10-5 m/s
2000 kg/m
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-5
6.6×10 m/s
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3
-5
6.05×10 m/s
3.7×10-5 m/s
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Table 2 Pile properties (Wilson, 1998) Value
Young’s modulus
7.0×104 MPa
Yield stress
290 MPa
Moment of inertia
6.1×10-3 m4
Yield moment
5.3×103 kN-m
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Parameters
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Table 3 Shaking events employed in this study (after Zhang and Wang, 2013) No.
Motion type
Earthquake
Fault distance (km)
Station
Magnitude
PGA (g)
PGV (m/sec)
1
Near-fault
Northridge 1994
8.6
Los Angeles Reservoir
6.7
0.32
0.44
2
Far-fault
Northridge 1994
18.4
Los Angeles, CA - Fire Station 108
6.7
0.59
3
Near-fault
Northridge 1994
7.1
Newhall, CA - Los Angeles County Fire
6.7
0.59
4
Far-fault
Northridge 1994
29.4
Warm Springs
6.7
5
Near-fault
Imperial Valley 1979
5.2
El Centro, CA - Array Sta 5
6.5
6
Far-fault
Imperial Valley 1979
29.5
Plaster City, CA
7
Near-fault
Imperial Valley 1979
8.8
Holtville, CA - Post Office
8
Far-fault
Imperial Valley 1979
21.8
Superstition Mtn, CA - Camera Site
9
Near-fault
Loma Prieta 1989
6.3
Gilroy Array Sta 3
10
Far-fault
Loma Prieta 1989
22.7
11
Near-fault
Loma Prieta 1989
7.9
12
Far-fault
Loma Prieta 1989
16.9
13
Near-fault
Chi-Chi 1999
8.9
14
Far-fault
Chi-Chi 1999
32.0
15
Near-fault
Chi-Chi 1999
16
Far-fault
Chi-Chi 1999
37.2
Ia (m/sec)
Tm (sec)
DB (sec)
0.39
0.14
1.37
0.80
24.64
0.05
2.85
0.33
22.30
0.42
0.17
5.61
0.70
59.29
0.23
I R
1.20
0.14
0.07
0.06
0.22
0.26
19.81
0.37
0.98
0.77
0.27
1.63
1.28
36.45
0.04
0.03
0.01
0.08
0.03
0.36
17.62
6.5
0.25
0.52
0.75
0.21
0.85
0.64
28.90
6.5
0.19
0.08
0.07
0.05
0.19
0.25
21.00
6.9
0.37
0.44
0.16
0.12
1.29
0.65
31.56
Gilroy Array Sta 7
6.9
0.32
0.16
0.05
0.05
0.82
0.39
26.87
Gilroy Array Sta 4
6.9
0.22
0.39
0.10
0.18
0.97
0.78
36.51
Coyote Lake Dam, CA
6.9
0.48
0.38
0.14
0.08
1.48
0.61
18.75
Taichung, Taiwan
7.6
0.15
0.34
0.50
0.24
0.84
0.76
108.06
Ilan, Taiwan
7.6
0.20
0.12
0.09
0.06
0.60
0.41
42.42
Taichung, Taiwan
7.6
0.34
0.61
0.41
0.18
3.53
0.50
111.40
Chiayi, Taiwan
7.6
0.26
0.23
0.06
0.09
1.69
0.55
54.81
D E
C S
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A M
T P
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C A 3.2
PGV/PGA (sec)
6.5
0.30 0.96
PGD (m)
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PGA (g)
PGV (m/sec)
D
Kobe
0.04
0.05
E
Santa Cruz
0.49
0.33
F
Kobe
0.22
0.25
G
Santa Cruz
0.1
0.07
H
Kobe
0.1
0.11
J
Santa Cruz*
0.45
0.27
K
Santa Cruz*
0.12
0.07
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Event
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Table 5 Linear correlation coefficients (R2 ) between ground motion parameters and response of soilpile system Maximum pile displacement
Maximum pile moment
Maximum soil displacement
Liquefied
Non-liquefied
Liquefied
Non-liquefied
Liquefied
Non-liquefied
PGA
0.24
0.45
0.22
0.37
0.22
0.57
PGV
0.89
0.75
0.89
0.78
0.87
PGD
0.71
0.38
0.74
0.38
0.76
0.19
PGV/PGA
0.58
0.28
0.58
0.33
a RMS
0.28
0.47
0.27
0.42
vRMS
0.87
0.65
0.87
Ia
0.33
0.43
0.33
Ic
0.38
0.58
SED
0.47
0.29
CAV
0.28
0.30
ASI
0.36
0.57
VSI
0.54
HI
0.67
SMA
0.28
SMV EDA
0.53
0.58
0.08
0.24
0.53
0.65
0.86
0.41
0.42
0.34
0.53
0.38
0.55
0.37
0.68
0.50
0.29
0.52
0.19
0.28
0.29
0.30
0.37
0.36
0.49
0.34
0.65
0.92
0.55
0.88
0.52
0.73
0.92
0.68
0.90
0.64
0.67
0.59
0.27
0.51
0.26
0.67
0.87
0.66
0.85
0.68
0.86
0.46
0.25
0.46
0.23
0.38
0.23
0.59
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Ground motion parameters
A95
0.23
0.44
0.22
0.36
0.21
0.57
Tp
0.05
0.17
0.05
0.15
0.05
0.09
0.40
0.29
0.40
0.28
0.38
0.07
DU
0.06
0.02
0.06
0.02
0.08
0.02
DB
0.11
0.05
0.13
0.06
0.14
0.02
DS
0.02
0.00
0.02
0.00
0.03
0.00
DE
0.03
0.00
0.03
0.00
0.04
0.01
Tm
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3.8 m
Ground surface 9.1 m loose sand (Dr =35%)
16.8 m
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11.4 m dense sand (Dr =80%)
Pore pressure
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Acceleration
Strain
Displacement
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Fig. 1. Centrifuge test setup (after Wilson, 1998)
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Z Z
Y Y
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20.5 m
XX
SC NU
Stress or force
(a) Finite element mesh
b×E 0
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Fy
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E0 Strain or deformation
-F y
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b×E 0
(b) Stress-strain relationship of Steel01 in OpenSees (Mazzoni et al. 2006)
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Soil elements
Pile element
Rigid link node
Zerolength element
Pile node Rigid beam-column link
Rigid beam-column links Pile elements
Interface elements
(c) Connection between pile and soil elements Fig. 2. Finite element modeling
Additional node node Soil node EqualDOF
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Fig. 3. Base input motion (Wilson, 1998)
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Fig. 4. Computed and experimental free-field excess pore pressure time histories
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Fig. 5. Computed and experimental free-field acceleration time histories
PT
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Fig. 6. Computed and experimental acceleration time histories at the pile head
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Fig. 7. Computed and experimental pile bending moment time histories
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(a)
0.2
No. 1
No. 5
No. 9
No. 13
No. 2
No. 6
No. 10
No. 14
No. 3
No. 7
No. 11
No. 15
No. 4
No. 8
No. 12
No. 16
0.0 -0.2
Acceleration (g)
0.2 0.0 -0.2 0.2 0.0
0.2 0.0 -0.2 6
12
18
24 0
7
14
21
28 0
10
1.2
No. 1 No. 3 No. 5 No. 7 No. 9 No. 11 No. 13 No. 15
0.6
0.3
0.0
40 0
20
40
60
0.9
80 100
No. 2 No. 4 No. 6 No. 8 No. 10 No. 12 No. 14 No. 16
Far-fault
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0.9
1.2
0.6
0.3
0.1
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Spectral acceleration (g)
Near-fault
30
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Time (sec)
(b)
20
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0
PT
-0.2
1
ED
Period (sec)
0.0
0.1
1 Period (sec)
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Fig. 8. The ground motions used in this study (scaled to a PGA of 0.2 g): (a) acceleration time histories; and (b) acceleration response spectra (5% damping ratio)
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Fig. 9. Free-field excess pore pressure time histories at 4.55-m depth for the shaking events of (a) Northridge; (b) Imperial Valley; (c) Loma Prieta; and (d) Chi-Chi earthquakes
Acceleration (g)
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Base input motion (x-direction) Time of PGV (No. 16)
Velocity (m/sec)
Time of PGV (No. 5)
PT
Displacement (m)
Base input motion (x-direction)
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Excess pore pressure, ue Displacement Arias Intensity (m) (%) (kPa)
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Base input motion (x-direction)
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Base input motion
4.55 m depth (x-direction)
4.55 m depth
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Fig. 10. Free-field excess pore pressure and displacement time histories along with the acceleration, velocity, displacement and Arias intensity time histories of Nos. 15 and 16 base input motions for comparison
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Fig. 11. Maximum pile bending moment profiles for: (a) near-fault ground motions; and (b) far-fault ground motions
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Fig. 12. Maximum pile lateral displacement profiles for: (a) near-fault ground motions; and (b) far-fault ground motions
Acceleration (g)
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Base input motion (x-direction)
Velocity (m/sec)
Time of PGV (No. 5)
Time of PGV (No. 6)
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Displacement (m)
Base input motion (x-direction)
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Arias Intensity (%)
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Base input motion (x-direction)
EP T
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Displacement (m)
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Moment (×103 kN-m)
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9.1 m depth (x-direction)
Pile head (x-direction)
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Fig. 13. Pile bending moment and lateral displacement time histories along with the acceleration, velocity, displacement, and Arias intensity time histories of Nos. 5 and 6 base input motions for comparison
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Fig. 14. Effect of PGV on: (a) maximu m pile bending moment; (b) maximu m pile lateral displacement; and (c) maximu m soil lateral displacement
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Fig. 15. Comparison of the mean line with the centrifuge tests: (a) normalized maximu m moment;
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Fig. 16. Effect of PGV on maximum pile lateral displacement: (a) medium sand; and (b) medium-
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ACCEPTED MANUSCRIPT Highlights
A 3D FEM was employed to simulate a seismic soil-pile interaction centrifuge test Influence of ground motion parameters on soil-pile system is investigated
PGV is a reliant parameter to characterize the response of soil-pile system
Near-fault ground motions could result in more severe damage to the pile
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Xiaoyu Zhang, Liang Tang, Xianzhang Ling, Andrew Hin Cheong Chan, Lu Jinchi PII: DOI: Reference:
S0013-7952(17)30539-2 doi:10.1016/j.enggeo.2018.04.011 ENGEO 4822
To appear in:
Engineering Geology
Received date: Revised date: Accepted date:
3 April 2017 7 April 2018 15 April 2018
Please cite this article as: Xiaoyu Zhang, Liang Tang, Xianzhang Ling, Andrew Hin Cheong Chan, Lu Jinchi , Using peak ground velocity to characterize the response of soilpile system in liquefying ground. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Engeo(2017), doi:10.1016/ j.enggeo.2018.04.011
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ACCEPTED MANUSCRIPT Using Peak Ground Velocity to Characterize the Response of Soil-Pile System in Liquefying Ground
Xiaoyu ZHANG a, Liang TANG
, Xianzhang LING c, Andrew Hin Cheong CHAN d , and Jinchi LU e
Ph. D Candidate, School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090,
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a.
b*
China, [email protected] b.
Professor, School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China,
c.
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[email protected], [email protected]
Professor, School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China,
d.
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[email protected]
Professor, School of Engineering and ICT, University of Tasmania, Hobart, Tasmania 7001, Australia, [email protected]
Associ at e Project Scientist , Depart m ent of Structural Engineeri ng, Univers it y of Californi a, San Diego, La Jolla,
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e.
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CA 92093-0085, USA, [email protected]
Corresponding Author: Liang Tang
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Address: School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China Tel: +86-13796627061
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Email: [email protected]
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Fax: 86-451-86282704
ACCEPTED MANUSCRIPT Abstract Performance of a soil-pile system can be significantly influenced by many characteristics of an earthquake ground motion, and it is vitally important to identify the ground motion parameters that have the most significant effects on the response when predicting the level of movement or damage in the pile. In this paper, three-dimensional finite element (FE) analysis was conducted to simulate a centrifuge experiment on the nonlinear behavior of a pile founded in liquefiable soil subjected to strong
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earthquake motions. The result of the FE analysis was foun d to be in reasonable agreement with the experimental data. As such, the calibrated FE model was used to investigate the influence of ground
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motion parameters on the pile-soil response in both liquefied and non-liquefied soils. It was found that
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peak ground velocity (PGV) is an appropriate ground motion parameter to characterize the response of the soil-pile system in liquefying ground. The maximu m pile bending moment, pile lateral
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displacement, and soil lateral displacement increased with increasing PGV. Moreover, near-fault ground motions could result in more severe damage to the pile compared to far-fault grounds motions.
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This study provided a new insight on the influence of ground motion parameters, in particular PGV, on the dynamic performance of a pile foundation.
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Keywords: Liquefaction; Pile foundation; Peak ground velocity; Ground motion parameters; Finite
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element analysis; Centrifuge test
ACCEPTED MANUSCRIPT 1. Introduction Seismically-induced liquefaction, one of the most devastating geotechnical phenomena from earthquakes, has received wide attention from the engineering geology and geotechnical engineering communities in recent decades (Chen et al. 2016; Gong et al. 2016; Pokhrel et al. 2013). Earthquakeinduced liquefaction has caused significant damage to pile-supported structures in past earthquakes, such as, the failure of Showa Bridge during the 1964 Niigata earthquake, and the damage to the
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battered piles that supported a wharf at the Port of Oakland in the 1989 Loma Prieta Earthquake (Brandenberg 2005; Ishihara 1993; Valverde-Palacios et al. 2012). As such, the observed damage
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induced liquefaction affecting embedded pile foundation systems.
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patterns have been a catalyst in driving research to elucidate the basic mechanisms of seismically-
Many attempts have been made in recent decades to study the dynamic behavior of a pile
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foundation in liquefied soil, using various experimental techniques including dynamic centrifuge experiments, shaking table tests and full-scale field tests as well as various numerical modeling
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methods (Liu et al. 2016; Rahmani and Pak 2012; Tang et al. 2014). It can be clearly observed that the seismic performance of a soil-pile system is strongly influenced by the characteristics of earthquake
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ground motions. For instance, Haldar and Babu (2010) stated that the increase in the peak ground acceleration (PGA) increases the maximu m shear strain in the soil. Tang and Ling (2014) concluded
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that increase of the acceleration amplitude and decrease of the frequency of earthquake excitation may increase the pile bending moment as well as the rate of the free-field excess pore pressure build-up. Chatterjee et al. (2015) observed that as the input motion changes from Bhuj (PGA=0.106g) to Kobe
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(PGA=0.834g), the normalized pile bending moment rises by 40%. Many ground motion parameters have been proposed to describe the important characteristics of an earthquake ground motion in a compact and quantitative form, such as PGA, peak ground velocity (PGV), Bracketed duration (DB ), and so on. In practice, these parameters are usually employed in the selection of a suite of design ground motions for a given site. Thus, it is important to explore the relationship between ground motion parameters and pile response, which would be useful for selecting ground motions in designing a pile foundation in liquefiable soil. In this regard, knowledge of the most effective ground motion parameters for predicting a given response (or demand measure) in liquefied soil or pile is critically needed. Nevertheless, a few studies have been carried out to discuss the effect of ground motion parameters on pile response in liquefied sand, and some researchers found that the PGA,
ACCEPTED MANUSCRIPT predominant frequency and the Arias intensity have a significant influence on t he pile lateral displacement and bending moment (Choobbasti et al. 2012; Liyanapathirana and Poulos 2005; Rahmani and Pak 2012). Moreover, in these studies, only a few widely-used parameters such as PGA and Arias intensity have been explored, while, to-date, PGV has received little attention. In this paper, a finite element (FE) study is used to perform parametric studies to determine the most appropriate characterizing parameter by comparing 23 ground motion parameters (including PGV) of an
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earthquake input motion.
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In the following sections, the numerical modeling techniques employed to simulate a centrifuge experiment are first described. Then, the relationship between ground motion parameters and the
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response of a soil-pile system is investigated using a number of selected near-fault and far-fault ground motions. Twenty-three ground motion parameters (see Appendix A) are compared before PGV is
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identified as the best parameter in characterizing the behavior of the soil-pile system in liquefying ground, and possible reasons why PGV is a suitable parameter are discussed. Finally, conclusions are
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drawn.
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2. Numerical modeling
It is difficult to explore the effect of ground motion characteristics on the seismic response of a pile
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by means of a large number of earthquake ground motions using experimental techniques, because it is costly and time consuming. Meanwhile in recent years numerical modeling has increasingly emerged as a versatile tool to study this issue (Elgamal et al. 2008; Liyanapathirana and Poulos 2005). In this
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section, a three-dimensional FE nonlinear analysis was carried out to simulate a centrifuge experiment on the dynamic behavior of a pile foundation in liquefied ground. 2.1. Centrifuge test
A centrifuge test (event F in test Csp2) was performed by Wilson (1998) to study the dynamic response of a pile foundation in liquefying sand (Fig. 1). All values described below are presented in prototype scale, which is based on the theory of centrifuge test described in detail by Taylor (2003). The soil model consisted of two layers of saturated Nevada sand (fine, and uniformly graded; see Fig. 1). A pipe pile with a diameter of 670 mm and a wall thickness of 19 mm was partially embedded in the soil (Fig. 1). The embedded length of the pile was 16.8 m. The pile top, which was 3.8 m above the ground surface, was applied with a superstructure load of 500 kN.
ACCEPTED MANUSCRIPT 2.2. Finite element modeling All FE simulations were performed using OpenSees, a software framework for simulating the seismic response of structural and geotechnical systems (http://opensees.berkeley.edu, Mazzoni et al. 2006). The FE mesh depicted in Fig. 2(a) was used to model the centrifuge experiment. Only half of the model has been meshed along the center-line of the pile (parallel to the shaking direction) for numerical
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analysis due to symmetry. The two-phase material response of saturated sand was formulated based on
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a u-p formulation (Chan 1988), and the Newmark implicit method was used for time integration. Loose and dense sand were simulated with a multi-yield-surface plasticity constitutive model (Yang et al.
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2003). The soil constitutive model was developed based on the multi-surface plasticity theory for frictional cohesionless soils proposed by Prevost (1985). This model was developed with emphasis on
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simulating the volumetric strain accumulation mechanism in clean cohesionless soils due to cyclic shear strain (Yang et al. 2003). A bilinear material “Steel01” with kinematic hardening illustrated in
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Fig. 2(b) was selected to describe the nonlinear response of the pile (Mazzoni et al. 2006). The pile was simulated using nonlinear beam-column elements, which had six degrees of freedom
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(DOFs) at each node: three for translational displacements and three for rotations (Mazzoni et al. 2006). The soil domain was discretised into 8-node, effective-stress solid-fluid fully coupled brick
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elements (Biot 1955; Lu et al. 2011), which was based on the solid-fluid formulation for saturated soil (Biot 1955; Chan 1988). Each node of this type of brick element had four DOFs: three for translational displacements of soil skeleton and one for pore water pressure. The superstructure was represented as a
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lumped mass at the pile head.
In order to represent the geometric space occupied by the pile [Fig. 2(c)], rigid beam-column links were used in the direction normal to the pile vertical axis (Elgamal et al. 2008). These rigid links acted together as a rigid body (at each horizontal plane where links are located). The soil domain 3D brick elements are connected to the pile geometric configuration at the outer nodes of these rigid links. The soil-pile interface was simulated by the zero-length interface element (i.e., Zerolength element in OpenSees), which could describe the slippage between the pile and soil. More specifically, the zerolength interface element was defined by two nodes (Rigid link node and Soil node) at the same location where the rigid beam-column link was connected to the surrounding soil [Fig. 2(c)]. Moreover, due to the difference between the DOFs at the rigid link node and soil node, an additional node (at the same
ACCEPTED MANUSCRIPT location with soil node) was added to connect the zero-length interface element [Fig. 2(c)]. An elasticperfectly plastic material model was utilized for the interface elements. Young’s modulus and yielding strain of this material were selected to be 2 MPa and 0.04 respectively (Rahmani and Pak 2012). The boundary conditions imposed on the FE model were given below: (1) at any given depth, displacement degrees of freedom of the both side boundary planes (perpendicular to the excitation direction) are tied together (in the horizontal and vertical directions) to
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reproduce laminar box boundary effects (Parra 1996) using the OpenSees equalDOF command; (2) at the side planes parallel to the shaking direction, nodes are restrained from movement in the
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traverse y direction;
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(3) the base and lateral boundaries were impervious (due to symmetry);
(4) the soil surface was stress free, with zero prescribed pore pressure; and
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(5) the vertical deformations at the base was restrained and the recorded base acceleration (Fig. 3) in
2.3. Validation of the numerical model
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the test was applied to the base of the FE model as a uniform accelerat ion boundary condition.
Soil properties employed in the FE simulations are listed in Table 1 (Lu et al. 2006), which are
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obtained based on an earlier calibration process by Elgamal et al. (2002). The permeability of the sand is from the measured values for Nevada sand (Popescu and Prevost 1993). Properties of the pile are
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given in Table 2 (Wilson 1998). The strain hardening ratio b is 0.1 (Bhattacharya 2003). The excess pore pressure (u e) and acceleration time histories (computed and experimental) in the free field are presented in Figs. 4 and 5. It is noted that the onset of liquefaction condition is attained when the
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excess pore pressure ratio ru , defined as the ratio of u e to overburden effective stress, reaches a value close to unity (Wilson 1998). For the loose sand, after an initial rise, a peak is achieved and then the liquefaction-level of the u e is maintained until the end of the shaking process, while the dense sand does not liquefy. The superstructure acceleration (Fig. 6) and pile bending moment resposne (Fig. 7) obtained from the numerical model agree reasonably well with the experimental measurements. Overall, the results obtained from the numerical model agree reasonably well with the experimental data.
3. Ground motion database Earthquake ground motion is an intricate phenomenon which resulted from the sudden energy
ACCEPTED MANUSCRIPT release caused by fault rupture, and the ground motion recorded at stations located within the near-fault region of an earthquake is significantly different from the usual far-fault ground motion observed at a large distance (Davoodi et al. 2013; Zhang et al. 2013). Near-fault ground motion is characterized by a pulse-type wave shape, long pulse period, abundant long-period components, a high ratio of peak ground velocity to peak ground acceleration (PGV/PGA ) and possible significant permanent ground displacement (Davoodi et al. 2013). Therefore, the ground motion database compiled for nonlinear
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analyses constitutes a representative number of near-fault and far-fault ground motions.
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From these databases (Consortium of Organizations for Strong-Motion Observation Systems http://cosmos-eq.org/ and the Pacific Earthquake Engineering Research Center
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http://peer.berkeley.edu/), a total of 16 ground motions were selected to cover a range of frequency content, duration and amplitude (Table 3). All the selected recordings were obtained from Northridge
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(1994), Imperial Valley (1979), Loma Prieta (1989), and Chi-Chi (1999) earthquakes and are related to large ground failures and extensive liquefaction phenomena (Zhang and Wang 2013). Eight ground
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motions, recorded at closest fault distance in range of 0.0-10 km, are selected to represent the features of near-fault ground motions. For all the near-fault ground motions, the velocity pulse duration is larger
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than 1.0 sec, and the PGV/PGA is over 0.1 sec (Table 3). On the other hand, another set of ground motions, recorded from the same earthquake events with site far away from the epicenter (in range of
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15-40 km), is used to represent the far-fault ground motions. All the earthquake records, as shown in Fig. 8(a), are scaled to a PGA of 0.2 g for initial comparison (the influence of PGA will be discussed in Section 4.3). The acceleration response spectrum with a damping ratio of 5% for all selected ground
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motion records are shown in Fig. 8(b). The elastic acceleration response spectra is computed by means of time-integration of the equation of motion of a series of single-degree-of-freedom systems, from which the acceleration response quantities are then obtained and plotted in period vs. amplitude graphs [Fig. 8(b)], using the computer program SeismoSignal (2016). It is observed that the long period response of a near-fault ground motion is more substantial than a far-fault ground motion. Note that all the ground motion parameters used in this study are calculated according to the method described in Appendix A (Kramer 1996), using SeismoSignal (2016). Moreover, the motion at ground surface is
used as the input motion in this study. It is a common practice to use ground surface motion as the input motion in soil liquefaction FE modelling (Asgari et al. 2013; Haldar and Babu 2010; Liyanapathirana and Poulos 2005) since it is difficult to obtain the input motion as the site
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4. Results and discussions In order to find the influence of near-fault ground motions on the soil-pile system, the performance of soil-pile system subjected to both selected NF-P and NF-NP ground motions is examined using the calibrated FE model.
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4.1. Free-field soil response
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Liquefaction is a phenomenon that is associated with a buildup of u e. Free-field u e time histories of loose sand at the depth of 4.55 m for the near-fault and far-fault ground motions are presented in Fig. 9.
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It is observed that soil liquefied in all the cases studied. The peak u e is reached after an initial rise and then the liquefaction-level u e is maintained until the end of shaking. Moreover, the u e distribution under
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the near-fault ground motions shows sharp pore pressure decrease (dilation spikes) which is due to soil dilation, and it leads to an increase in the shear strength of the soil due to the increase in mean effective
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stress. Nevertheless, only slight fluctuations in the u e is observed in the far-fault ground motion cases. In order to provide better insights into the influences of acceleration, velocity, displacement and
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energy of ground motion on soil response, the time histories of free-field u e and lateral displacement at 4.55 m depth when the model is subjected to Nos. 15 and 16 ground motions are showed in Fig. 10.
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Ground motion energy is defined based on the Arias intensity (Ia ). It is noted that the peak soil lateral displacement and dilation spikes could be caused by ground motions with less input energy and acceleration. On the other hand, the peak soil lateral displacement and dilation spikes occur almost at
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the same time with PGV. As similar results were obtained for all the earthquake ground motions used, only the results of Nos. 15 and 16 ground motions are presented here. It can be inferred that PGV has a significant influence on the response of liquefied soil. 4.2. Pile response
The loss of soil strength and stiffness caused by liquefaction under strong shaking will lead to substantial deformation in pile foundation. In this section, the seismic behavior of pile in liquefying ground is evaluated by considering two different criteria: (a) strength criterion expressed in terms of bending moment envelopes along the pile; and (b) damage criterion expressed in terms of maximu m lateral displacement.
ACCEPTED MANUSCRIPT Figs. 11 and 12 show maximu m pile bending moment and maximu m pile lateral displacement envelopes, respectively. It is clear from Fig. 11 that the maximu m bending moment invariably develops at the depth corresponding to the interface between liquefiable (loose sand) and non-liquefiable (dense sand) layers (i.e., 9.1 m depth), and the maximu m lateral displacement is attained at the pile head (Fig. 12). The values of maximu m pile bending moment and lateral displacement when the model is subjected to near-fault ground motions are generally greater than those under far-fault ground motions
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although the PGA of all ground motions used are the same. This demonstrates that pile in liquefying
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ground is more susceptible to damage when subjected to near-fault ground motions.
The effects of acceleration, velocity, displacement and Arias intensity of a ground motion on the
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bending moment and lateral displacement when the model is subjected to Nos. 5 and 6 ground motions are shown in Fig. 13. Similar to soil response, the maximu m pile bending moment and lateral
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displacement also occur at the time of PGV but not at peak acceleration amplitude, peak displacement amplitude or maximu m accumulated input energy. Similar observations can be found for other ground
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motions used.
4.3. Effect of PGV on the response of soil-pile system
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Based on the findings above (Figs. 10 and 13), it can be concluded that peak response of soil and pile occur at the time of PGV. To further investigate of the effect of PGV on the response of soil-pile
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system, each earthquake time acceleration data are scaled to 0.1-, 0.2-, 0.3-, 0.4- and 0.5-g peak acceleration values, respectively.
The influences of PGV on maximu m pile bending moment, pile lateral displacement, and soil lateral
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displacement under various PGA are presented in Fig. 14. A linear relationship is found between PGV and these maximum pile and soil response with good correlation where the linear correlation coefficients (R2 ) obtained are 0.89, 0.89, and 0.87 for maximu m pile bending moment, pile lateral displacement, and soil lateral displacement, respectively. The interesting finding of the relationship between PGV and maximu m soil lateral displacement may explain the differences of dilation phenomena between near-fault and far-fault ground motions. As reported by Asgari et al. (2013), the dilation response could be strongly influenced by the soil lateral displacement. This is also observed in Fig. 10, the dilation spikes occur almost at the same time as the peak soil lateral displacement reaches. Meanwhile, a linear relationship was found between PGV and
ACCEPTED MANUSCRIPT maximu m soil lateral displacement [Fig. 14(c)], and the near-fault ground motions have a much larger PGV than the far-fault ground motions (Table 3). Therefore, it would be logical to conclude that the dilation phenomena were observed more prevalently in the cases of near-fault ground motions. Based on the findings of the relationship between PGV and pile response, the relationship between PGV and the normalized maximu m moment could be expressed as:
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M max / M y k1 PGV (1)
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where PGV is expressed in units of m/sec, Mmax is the maximu m pile moment, My is the yield moment of pile, k 1 is the slope of the line, the mean of k 1 is 0.76 and the standard deviation of k 1 is 0.23.
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Similarly, the relationship between PGV and the normalized maximu m displacement can also be expressed by Equation (2):
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ymax / D k2 PGV
(2)
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where PGV is expressed in units of m/sec, ymax is the maximu m pile displacement, D is pile diameter, k 2 is the slope of the line. The mean of k 2 is 0.82 and the standard deviation of k 2 is 0.29. The results from seven centrifuge tests which were performed by Wilson (1998) as shown in Table 4, were used to
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verify these relationships. As shown in Fig. 15, the test results agree well with the mean line. Therefore, these relationships can be used to estimate the maximu m moment and displacement of pile which is
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located in the similar site conditions as this study. 4.4. PGV versus other ground motion parameters To identify an appropriate ground motion parameter to characterize the behavior of the soil-pile
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system, the effect of a total of 23 ground motion parameters (Appendix A) were compared in this study. The coefficient of correlation between the ground motion parameters and the response of the soil-pile system is listed in Table 5. The top three parameters PGV, vRMS , and SMV are closely related to each other (R2 : 0.80-0.89) and these parameters are all velocity-related parameters. This implies that velocity is a reliable parameter to deduce the level of strain produced due to the ground motion. While PGV has the best correlation on both dynamic behavior of soil and pile, it is suggested that PGV is the best ground motion parameter to characterize the response of a soil-pile system in liquefying ground. One possible reason for the good performance of velocity related parameters is that the effect on the dynamic behavior of soil and pile is closely related to the strain level of the soil. Although the strain is
ACCEPTED MANUSCRIPT related to displacement gradient, it is the accumulation of velocity gradient. In this relatively simple case, the displacement distribution is almost linear along the pile (e.g., Fig. 12), therefore the strain experienced by the soil and pile is directly related to the displacement. From Figs. 10 and 13, it can be seen that, despite the many peaks for the acceleration trace, there is only one distinct peak pile displacement and one PGV. It would be logical to infer that the higher the PGV, the higher the peak pile displacement which leads to the higher bending moment in the pile. Therefore, PGV turns out to be a
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better indicator for peak pile displacement and maximu m bending moment in the pile and PGV has a
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very good correlation with all these quantities for a wide range of earthquake input motions. To investigate whether PGV is also a suitable parameter to characterize the response of pile in the
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non-liquefied soils, the DOFs for pore water pressure in each soil node were fixed in the numerical model. The coefficients of linear correlation between ground motion parameters and the response of the
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soil-pile system are listed in Table 5. It is found that the parameter with the best correlation for nonliquefied soil is HI which can capture important aspects of the amplitude and frequency content of a
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ground motion and it relates to some form of displacement, while for liquefied soil it is PGV which is an amplitude parameter of ground motion. Therefore, PGV is a better parameter to characterize the
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response of the soil-pile system in liquefying soil than in the non-liquefied soil though PGV is still performing reasonably well for non-liquefying soil. Moreover, it should be noted that the top three
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parameters for the non-liquefied soils (i.e., VSI, HI, and PGV) are also velocity-related parameters. Therefore, it can be concluded that the velocity-related parameters have a better correlation with the soil-pile system in both liquefied and non-liquefied ground.
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Site effect is a major issue in the field of earthquake engineering since the seismic motion could be strongly modified in some specific sites, and it is mainly affected by the site conditions (De Ferrari et al. 2017). Therefore, it is necessary to investigate the influence of the s ite effects on the findings of the relationship between PGV and the response of pile-soil system. In this study, the selected motions are recorded from different stations with different site conditions , and each earthquake time acceleration data are scaled to 0.1-, 0.2-, 0.3-, 0.4- and 0.5-g peak acceleration values, respectively. As shown in Fig. 14, the linear relationship is found between PGV and the maximu m pile and soil response for each case with different PGA. And it is also found the PGV has a better correlation with the soil-pile system in both liquefied and non-liquefied soils (Table 5). So the site effects may not alter the relationship between PGV and the response of pile-soil system. To further investigate the influence of site effect on
ACCEPTED MANUSCRIPT the findings in this study, the material parameters for the loose sand in the numerical model has been changed to medium sand and medium-dense sand. These parameters, as listed in Table 1, are suggested by Lu et al. (2006). The correlation between PGV and maximu m pile displacement for the case of PGA=0.2 g are shown in Fig. 16. It can be clearly observed that PGV is still good for different soil conditions. Therefore, it could be concluded that the site effect s will not alter the findings of the relationship between PGV and the response of pile-soil system.
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For any correlation index method, there will be an uncertainty band as it does not consider a lot of finer details. Therefore, additional experimental data, along with related numerical analyses, should be
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examined to verify if this correlation between PGV and the response of soil-pile system in liquefied
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limited information from this one physical configuration.
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soil applies to other physical settings , and also to derive a better physical explanations as we have
5. Conclusions
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This study provides a better insight into the seismic performance of a pile foundation in liquefied soil. In this regard, three-dimensional FE method was employed to simulate a centrifuge test. Based on the calibrated FE model, effect of PGV on the dynamic behavior of a pile foundation in liquefied soil
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conclusions are as follows:
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was invsetigated by carrying out eighty nonlinear time history analyses at five intensity levels. Main
(1) The numerical model is effective in simulating the nonlinear response of the soil-pile system in liquefying ground.
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(2) PGV is the most reliable ground motion parameter for predicting the dynamic performance of the soil-pile system in liquefying ground. Increase of PGV will cause larger soil lateral displacement, pile bending moment and pile lateral displacement. It is likely because, despite there are many peaks in the acceleration traces that are the same in magnitude of PGA, there is only one distinct peak in velocity time history and the same can be concluded for soil lateral displacement, pile bending moment and pile lateral displacement. Furthermore, these peak values occurred at the same time approximately. Therefore, it can be inferred that these peak values are correlated well with each other. (3) Velocity-related parameters have a better correlation with the soil-pile system in both liquefied and non-liquefied soils. PGV is the best parameter for the liquefying ground cases, and Housner Intensity is the best parameter for the non-liquefied soil cases.
ACCEPTED MANUSCRIPT (4) Relative to far-fault ground motions, sharp excess pore pressure spikes caused by soil dilation, easy to occur in near-fault ground motion cases. Moreover, near-fault ground motions can create larger pile bending moment and lateral displacement than those under far-fault ground motions although PGA used for the records are the same.
Acknowledgments
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The presented research work was funded by the National Key R&D Program of China (Grant No. 2016YFE0205100), the National Natural Science Foundation of China (Grant No. 51578195), the
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Open Research Fund of State Key Laboratory of Geo mechanics and Geotechnical Engineering,
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Institute of Rock and So il Mechanics, Chinese Academy of Sciences (Grant No. Z016007), the Special Project Fund of Taishan Scholars of Shandong Province, Ch ina (Grant No. 2015 -212), the Natural
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Science Foundation of Heilongjiang Province of China (Grant No. E2015017), and the Opening Fund
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for Innovation Platform of China (Grant No. 2016YJ004).
Appendi x A. Description of ground motion parameters Detailed description for all the ground motion parameters used in this study can be found in
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Kramer (1996). Only a brief description of these parameters is provided below due to space limitations. PGA: Peak ground acceleration
2.
PGV: Peak ground velocity
3.
PGD: Peak ground displacement
4.
PGV/PGA : The ratio of peak ground velocity to peak ground acceleration
5.
a RMS : Acceleration RMS aRMS
7.
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6.
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1.
1 Td
vRMS : Velocity RMS vRMS
Ia : Arias Intensity I a
2g
1 Td
Td
[a(t )] dt where Td is the duration of the strong motion 2
0
Td
[v(t )] dt 2
0
Td
[a(t )] dt 2
0
3
8.
Ic: Characteristic Intensity I c (aRMS ) 2 Td
9.
SED: Specific Energy Density SED [v(t )]2 dt
Td
0
ACCEPTED MANUSCRIPT 10. CAV: Cumulative Absolute Velocity CAV
Td
a(t ) dt 0
11. ASI: Acceleration Spectrum Intensity. The area under the acceleration response spectrum between periods of 0.1 sec and 0.5 sec 12. VSI: Velocity Spectrum Intensity. The area under the velocity response spectrum between periods of 0.1 sec and 0.5 sec
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13. HI: Housner Intensity. The area under the pseudo-velocity response spectrum between periods of 0.1 sec and 2.5 sec
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14. SMA: Sustained Maximum Acceleration. This parameter gives the sustained maximum
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acceleration during three cycles, and is defined as the third highest absolute value of acceleration in the time-history (note: in order for an absolute value to be considered as a
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"maximu m", it must be larger than values 20 steps before and 20 steps after). 15. SMV: Sustained Maximum Velocity. This parameter gives the sustained maximum velocity
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during three cycles, and is defined as the third highest absolute value of velocity in the timehistory.
16. EDA: Effective Design Acceleration. This parameter corresponds to the peak acceleration
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value found after lowpass filtering the input time history with a cut -off frequency of 9 Hz. 17. A95 : The acceleration level below which 95% of the total Arias intensity is contained.
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18. Tp : Predominant Period. This is the period at which the maximu m spectral acceleration occurs in an acceleration response spectrum calculated at 5% damping.
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Ci 2 f i 19. Tm : Mean Period Tm Ci 2
20. Du : Uniform Duration. The total time during which the acceleration is larger than a given threshold value (5% of PGA). 21. DB : Bracketed Duration. The total time elapsed between the first and the last excursions of a specified level of acceleration (5% of PGA). 22. DS : Significant Duration. The interval of time over which a proportion (percentage) of the total Arias Intensity is accumulated (the interval between the 5% and 95% thresholds). 23. DE : Effective Duration. It is based on the significant duration concept but both the start and end of the strong shaking phase are identified by absolute criteria.
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Table 1 Parameters for the soil model (after Lu et al., 2006; Popescu and Prevost, 1993)
3
2100 kg/m3
Medium sand
Mass density
1700 kg/m3
1900 kg/m
Low-strain shear modulus, Gr
55.5 MPa
75 MPa
100 MPa
130.0 MPa
Reference confining pressure, Pr
80 kPa
80 kPa
80 kPa
80 kPa
Friction angle,
29°
33°
37°
40°
Liquefaction yield strain, y
1%
1%
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Dense sand
Loose sand
1%
0
Contraction parameter, c1
0.21
0.07
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Mediumdense sand
Parameters
0.05
0.03
Phase transformation angle, PT
29°
27°
27°
27°
Dilation parameter, d 1
0
0.4
3.0
0.8
Dilation parameter, d 2
0
5.0
5.0
Permeability, k
6.6×10-5 m/s
2000 kg/m
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6.6×10 m/s
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3
-5
6.05×10 m/s
3.7×10-5 m/s
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Table 2 Pile properties (Wilson, 1998) Value
Young’s modulus
7.0×104 MPa
Yield stress
290 MPa
Moment of inertia
6.1×10-3 m4
Yield moment
5.3×103 kN-m
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Parameters
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Table 3 Shaking events employed in this study (after Zhang and Wang, 2013) No.
Motion type
Earthquake
Fault distance (km)
Station
Magnitude
PGA (g)
PGV (m/sec)
1
Near-fault
Northridge 1994
8.6
Los Angeles Reservoir
6.7
0.32
0.44
2
Far-fault
Northridge 1994
18.4
Los Angeles, CA - Fire Station 108
6.7
0.59
3
Near-fault
Northridge 1994
7.1
Newhall, CA - Los Angeles County Fire
6.7
0.59
4
Far-fault
Northridge 1994
29.4
Warm Springs
6.7
5
Near-fault
Imperial Valley 1979
5.2
El Centro, CA - Array Sta 5
6.5
6
Far-fault
Imperial Valley 1979
29.5
Plaster City, CA
7
Near-fault
Imperial Valley 1979
8.8
Holtville, CA - Post Office
8
Far-fault
Imperial Valley 1979
21.8
Superstition Mtn, CA - Camera Site
9
Near-fault
Loma Prieta 1989
6.3
Gilroy Array Sta 3
10
Far-fault
Loma Prieta 1989
22.7
11
Near-fault
Loma Prieta 1989
7.9
12
Far-fault
Loma Prieta 1989
16.9
13
Near-fault
Chi-Chi 1999
8.9
14
Far-fault
Chi-Chi 1999
32.0
15
Near-fault
Chi-Chi 1999
16
Far-fault
Chi-Chi 1999
37.2
Ia (m/sec)
Tm (sec)
DB (sec)
0.39
0.14
1.37
0.80
24.64
0.05
2.85
0.33
22.30
0.42
0.17
5.61
0.70
59.29
0.23
I R
1.20
0.14
0.07
0.06
0.22
0.26
19.81
0.37
0.98
0.77
0.27
1.63
1.28
36.45
0.04
0.03
0.01
0.08
0.03
0.36
17.62
6.5
0.25
0.52
0.75
0.21
0.85
0.64
28.90
6.5
0.19
0.08
0.07
0.05
0.19
0.25
21.00
6.9
0.37
0.44
0.16
0.12
1.29
0.65
31.56
Gilroy Array Sta 7
6.9
0.32
0.16
0.05
0.05
0.82
0.39
26.87
Gilroy Array Sta 4
6.9
0.22
0.39
0.10
0.18
0.97
0.78
36.51
Coyote Lake Dam, CA
6.9
0.48
0.38
0.14
0.08
1.48
0.61
18.75
Taichung, Taiwan
7.6
0.15
0.34
0.50
0.24
0.84
0.76
108.06
Ilan, Taiwan
7.6
0.20
0.12
0.09
0.06
0.60
0.41
42.42
Taichung, Taiwan
7.6
0.34
0.61
0.41
0.18
3.53
0.50
111.40
Chiayi, Taiwan
7.6
0.26
0.23
0.06
0.09
1.69
0.55
54.81
D E
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A M
T P
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C A 3.2
PGV/PGA (sec)
6.5
0.30 0.96
PGD (m)
T P
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PGA (g)
PGV (m/sec)
D
Kobe
0.04
0.05
E
Santa Cruz
0.49
0.33
F
Kobe
0.22
0.25
G
Santa Cruz
0.1
0.07
H
Kobe
0.1
0.11
J
Santa Cruz*
0.45
0.27
K
Santa Cruz*
0.12
0.07
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Table 5 Linear correlation coefficients (R2 ) between ground motion parameters and response of soilpile system Maximum pile displacement
Maximum pile moment
Maximum soil displacement
Liquefied
Non-liquefied
Liquefied
Non-liquefied
Liquefied
Non-liquefied
PGA
0.24
0.45
0.22
0.37
0.22
0.57
PGV
0.89
0.75
0.89
0.78
0.87
PGD
0.71
0.38
0.74
0.38
0.76
0.19
PGV/PGA
0.58
0.28
0.58
0.33
a RMS
0.28
0.47
0.27
0.42
vRMS
0.87
0.65
0.87
Ia
0.33
0.43
0.33
Ic
0.38
0.58
SED
0.47
0.29
CAV
0.28
0.30
ASI
0.36
0.57
VSI
0.54
HI
0.67
SMA
0.28
SMV EDA
0.53
0.58
0.08
0.24
0.53
0.65
0.86
0.41
0.42
0.34
0.53
0.38
0.55
0.37
0.68
0.50
0.29
0.52
0.19
0.28
0.29
0.30
0.37
0.36
0.49
0.34
0.65
0.92
0.55
0.88
0.52
0.73
0.92
0.68
0.90
0.64
0.67
0.59
0.27
0.51
0.26
0.67
0.87
0.66
0.85
0.68
0.86
0.46
0.25
0.46
0.23
0.38
0.23
0.59
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Ground motion parameters
A95
0.23
0.44
0.22
0.36
0.21
0.57
Tp
0.05
0.17
0.05
0.15
0.05
0.09
0.40
0.29
0.40
0.28
0.38
0.07
DU
0.06
0.02
0.06
0.02
0.08
0.02
DB
0.11
0.05
0.13
0.06
0.14
0.02
DS
0.02
0.00
0.02
0.00
0.03
0.00
DE
0.03
0.00
0.03
0.00
0.04
0.01
Tm
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3.8 m
Ground surface 9.1 m loose sand (Dr =35%)
16.8 m
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11.4 m dense sand (Dr =80%)
Pore pressure
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Acceleration
Strain
Displacement
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Z Z
Y Y
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20.5 m
XX
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Stress or force
(a) Finite element mesh
b×E 0
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-F y
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b×E 0
(b) Stress-strain relationship of Steel01 in OpenSees (Mazzoni et al. 2006)
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Soil elements
Pile element
Rigid link node
Zerolength element
Pile node Rigid beam-column link
Rigid beam-column links Pile elements
Interface elements
(c) Connection between pile and soil elements Fig. 2. Finite element modeling
Additional node node Soil node EqualDOF
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Fig. 3. Base input motion (Wilson, 1998)
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Fig. 4. Computed and experimental free-field excess pore pressure time histories
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Fig. 5. Computed and experimental free-field acceleration time histories
PT
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Fig. 6. Computed and experimental acceleration time histories at the pile head
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Fig. 7. Computed and experimental pile bending moment time histories
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(a)
0.2
No. 1
No. 5
No. 9
No. 13
No. 2
No. 6
No. 10
No. 14
No. 3
No. 7
No. 11
No. 15
No. 4
No. 8
No. 12
No. 16
0.0 -0.2
Acceleration (g)
0.2 0.0 -0.2 0.2 0.0
0.2 0.0 -0.2 6
12
18
24 0
7
14
21
28 0
10
1.2
No. 1 No. 3 No. 5 No. 7 No. 9 No. 11 No. 13 No. 15
0.6
0.3
0.0
40 0
20
40
60
0.9
80 100
No. 2 No. 4 No. 6 No. 8 No. 10 No. 12 No. 14 No. 16
Far-fault
NU
0.9
1.2
0.6
0.3
0.1
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Spectral acceleration (g)
Near-fault
30
SC
Time (sec)
(b)
20
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0
PT
-0.2
1
ED
Period (sec)
0.0
0.1
1 Period (sec)
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Fig. 8. The ground motions used in this study (scaled to a PGA of 0.2 g): (a) acceleration time histories; and (b) acceleration response spectra (5% damping ratio)
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Fig. 9. Free-field excess pore pressure time histories at 4.55-m depth for the shaking events of (a) Northridge; (b) Imperial Valley; (c) Loma Prieta; and (d) Chi-Chi earthquakes
Acceleration (g)
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Base input motion (x-direction) Time of PGV (No. 16)
Velocity (m/sec)
Time of PGV (No. 5)
PT
Displacement (m)
Base input motion (x-direction)
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Excess pore pressure, ue Displacement Arias Intensity (m) (%) (kPa)
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Base input motion (x-direction)
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Base input motion
4.55 m depth (x-direction)
4.55 m depth
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Fig. 10. Free-field excess pore pressure and displacement time histories along with the acceleration, velocity, displacement and Arias intensity time histories of Nos. 15 and 16 base input motions for comparison
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Fig. 11. Maximum pile bending moment profiles for: (a) near-fault ground motions; and (b) far-fault ground motions
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Fig. 12. Maximum pile lateral displacement profiles for: (a) near-fault ground motions; and (b) far-fault ground motions
Acceleration (g)
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Base input motion (x-direction)
Velocity (m/sec)
Time of PGV (No. 5)
Time of PGV (No. 6)
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Displacement (m)
Base input motion (x-direction)
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Arias Intensity (%)
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Base input motion (x-direction)
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Displacement (m)
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Moment (×103 kN-m)
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Base input motion
9.1 m depth (x-direction)
Pile head (x-direction)
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Fig. 13. Pile bending moment and lateral displacement time histories along with the acceleration, velocity, displacement, and Arias intensity time histories of Nos. 5 and 6 base input motions for comparison
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Fig. 14. Effect of PGV on: (a) maximu m pile bending moment; (b) maximu m pile lateral displacement; and (c) maximu m soil lateral displacement
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Fig. 15. Comparison of the mean line with the centrifuge tests: (a) normalized maximu m moment;
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Fig. 16. Effect of PGV on maximum pile lateral displacement: (a) medium sand; and (b) medium-
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A 3D FEM was employed to simulate a seismic soil-pile interaction centrifuge test Influence of ground motion parameters on soil-pile system is investigated
PGV is a reliant parameter to characterize the response of soil-pile system
Near-fault ground motions could result in more severe damage to the pile
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