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Finite element modeling of soil-pile response subjected to liquefaction-induced lateral spreading in a large-scale shake table experiment
Soil Dynamics and Earthquake Engineering 92 (2017) 573–584
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Finite element modeling of soil-pile response subjected to liquefactioninduced lateral spreading in a large-scale shake table experiment Gangjin Li, Ramin Motamed
crossmark
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Department of Civil and Environmental Engineering, University of Nevada Reno, Reno, NV 89557, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Lateral spreading 2D effective stress analysis OpenSees Soil-pile response Mitigation measure
This paper presents two-dimensional (2D) nonlinear dynamic finite element (FE) modeling of a large-scale shake table test conducted at the E-Defense shake table facility in Japan. This study explores the efficiency of 2D effective stress analyses to predict the behavior of soil-pile systems subjected to liquefaction and lateral spreading using the library of existing constitutive models and the prescribed parameters. The coupled soilwater FE model was developed in OpenSees and the analysis results are compared with measured data from the shake table experiment with the main emphasis on the response of liquefied soil and the demand applied to the piles as well as the sheet-pile quay wall. By examining the numerical analysis results, it is demonstrated that the FE model was able to reproduce the shake table model behavior with reasonable accuracy. Lastly, a mitigation strategy was modeled to investigate its effectiveness to reduce the demand on the soil-pile system.
1. Introduction In recent earthquakes such as the 2010 Haiti, the 2010 Chile, the 2010–2011 Canterbury Sequence and the 2011 Great Tohoku earthquakes, extensive damage in pile foundations has been observed due to liquefaction-induced lateral spreading. Many researchers have investigated the basic mechanisms of this phenomenon through physical modeling including shake table experiments [1–5] and centrifuge tests [6–9]. In addition, a number of numerical simulations have been carried out based on physical experiments for validation and application using different modeling techniques [10–14]. In March 2006, a large-scale test on lateral spreading of liquefied sand behind a sheet-pile quay wall was performed at the E-Defense facility in Japan. The experimental data was analyzed by Motamed et al. [2], which studied the soil-pile interaction in laterally spreading grounds in detail. The experiment included a simple structure model supported on a 2×3 pile group located adjacent to a sheet-pile quay wall as shown in Fig. 1. The model was heavily instrumented to measure the dynamic response of the soil-pile system. Liquefactioninduced lateral spreading was achieved and the soil moved laterally about 1.1 m behind the quay wall. Based on the shake table experiment, a 2D numerical model was developed in this study using OpenSees [15] framework employing available constitutive models in its material library. The constitutive soil model used in this study was developed for granular materials subjected to cyclic loading with emphasis to undrained cases [16–18]. The suggested parameters of
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the constitutive model were calibrated for Nevada sand, which was significantly different from the sand used in the shake table experiment as explained in Section 3.1 in this paper. The numerical modeling produced comparable results to the experimental data and the details are presented hereafter. In addition to modeling the behavior of the pile group subjected to the lateral flow of liquefied soil based on the large-scale experiment, this research explores the effectiveness of a mitigation measure to reduce seismic demands on the soil and the pile group. Motamed and Towhata [19] carried out a series of 1 g small-scale shake table model tests on a 3×3 pile group located behind a sheet-pile quay wall subjected to liquefaction-induced large ground deformation which was basically a 1/10 scale of the E-Defense shake table experiment. Three remedial techniques were explored in Motamed and Towhata [19], among which one of the studied mitigation measures was selected to be explored in this study. The selected mitigation strategy included installation of a mitigating sheet-pile with fixed-base boundary condition in between the pile group and the quay wall. This paper discusses the effectiveness of this method to reduce seismic demands using the OpenSees model and compared with the experimental results reported by Motamed and Towhata [19]. Lastly, a parametric study was performed to investigate the remedial effects of various types of mitigating sheet piles with different sectional properties, which are commonly used in engineering practice.
Corresponding author. E-mail addresses: [email protected] (G. Li), [email protected] (R. Motamed).
http://dx.doi.org/10.1016/j.soildyn.2016.11.001 Received 4 December 2015; Received in revised form 21 October 2016; Accepted 1 November 2016 Available online 11 November 2016 0267-7261/ © 2016 Elsevier Ltd. All rights reserved.
Soil Dynamics and Earthquake Engineering 92 (2017) 573–584
G. Li, R. Motamed
4.5
11.5
1.0
0.6 1.0
Weights (12 t)
0.5
0.5 0.8
Water
Footing (10 t)
Pile
L. 3.5
D. 0.15
Liquefiable ground
4.5
3.5
3.2
Sheet pile 1.0
B2
Cross section view
A2 16.0 m
Rear Front row row 1.2 1.2
4.5
1.0
8.1D
A3 A2 A1
2×4D
1.6
4.0
Plan view
B3 B2 B1
8.9
1.6
Fig. 2. Acceleration time histories of input motion.
Fig. 1. Schematic illustration of large scale shake table test at E-Defense facility (unit: m) (Motamed et al. [2]).
2. Description of E-Defense shake table experiment The shake table model of the soil-pile system was constructed in a large semi-rigid box with the dimensions of 16 m×5 m×4 m, and the soil configuration was a horizontal ground consisted of uniform liquefiable Albany Silica sand with the relative density of 60% underlain by a thin denser sand layer (Dr=70%). The basic properties of the soil profile are listed in Table 1 [20,21]. Similar to Kazama et al. [21], uniform shear wave velocity (VS) of 120 m/s and Possion's ratio (γ) of 0.3 were adopted in this study. A LSP-2 type steel sheet pile quay wall was used, which deformed laterally and triggered the liquefactioninduced lateral spreading. Behind the quay wall, six hollow steel piles with outer diameters of 0.1524 m and thicknesses of 0.002 m were connected to the base using a hinge connection (i.e. zero displacement and moment). The piles were used to support the 12 t weight of the superstructure and the 10 t weight of the pile cap as illustrated in Fig. 1. The large-scale model was subjected to two-directional ground motions (i.e. longitudinal and vertical) as presented in Fig. 2. The records obtained at the JR Takatori station during the 1995 Kobe earthquake were scaled down by 20% and chosen as the input motions. The maximum amplitudes of the horizontal and vertical components were 0.6g and 0.23g, respectively. More details on the shake table experiment can be found in Motamed et al. [2].
Fig. 3. FE model discretization of shake table experiment.
illustrated in Fig. 3. The maximum allowable soil element size of 0.5 m was determined to fit 20 elements within one shortest wavelength, i.e. 10 m, of the propagating shear wave [23,24]. In this manner, the propagating waves can be well captured in the analysis. The shortest wavelength within soil profile was calculated using the shear wave velocity of 120 m/sec and the maximum frequency content, i.e. 12 Hz, of the ground motion. Additionally, a convergence study was carried out to investigate the possibility of using finer mesh schemes with maximum element sizes of 0.25 m or 0.1 m. However, these models with refined discretization encountered convergence problem during dynamic analysis due to the fact they had redundant elements within one wavelength as reported by Zerwer et al. [23]. This finding reflects that the discretization of our model was sufficiently fine.
3. OpenSees numerical model
3.1. Elements, materials and boundary conditions
The 2D numerical model was built using OpenSees framework, which is an open source finite element software developed by UC Berkeley for earthquake engineering simulation [15] and post-processing was performed with GiD [22]. The discretization of the model is
In the FE model, the saturated soil was simulated as a two-phase material using QuadUP elements [18] based on the Biot's theory [25] for porous media, in which displacement of the soil skeleton (u) and pore pressure (p) are the primary unknowns (u-p formulation). The out-of-plane thickness of the soil elements was set to be the same as the width of the container in the shake table test (i.e. 4 m) in order to capture the pinning effects around the piles when the soil is liquefied. The constitutive behavior of the soil was captured by the PressureDependMultiYield02 (PDMY02) material [16–18] available in OpenSees to simulate the response characteristics of sand. The parameters needed for the constitutive soil model as presented in Table 2 were selected based on a combination of recommended values from the constitutive model developer [18] and correlations with the measured parameters from the shake table experiment [20,21]. The low strain shear modulus of soil (Gmax) was calculated based on
Table 1 Soil properties of Albany silica sand [20,21]. Depth (m)
0.0 - 4.0
4.0 - 4.5
Relative density, Dr (%) Density, ρ (t/m3) Vs (m/sec) Permeability, k (m/sec) Void ratio, e Possion's ratio, γ
60 1.67
70 1.70 120 8.50E−05 0.558 0.3
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the matching node on the pile cap. The superstructure was simplified as a concentrated mass of 12 t at the center of gravity to reproduce the actual mass. The structure columns were simulated to represent the natural period of a uniform stiffness column with fixed boundary conditions and natural period of 1.54 s. The group included 6 piles in the shake table experiment (i.e. 2 rows in total and 3 piles in each row) and was represented by two piles in the 2D model, each having three times the bending and cap connection stiffness of a single actual pile to approximate the exact stiffness of the 3D model in a 2D format [11]. In the numerical model, the pile and soil elements were connected using zero-length elements with nonlinear p-y springs represented by the PyLiq1 material [6,8,27,28], which has been used by other researchers for the study of soil-pile interaction in liquefied and laterally spreading ground in OpenSees [11,28,29]. The spring properties were determined based on American Petroleum Institute (API) formulas [30] as described by Boulanger et al. [6,8,28]. And the drag resistance ratio (Cd) of the gap component of the p-y springs was set to 0.3 similar to Boulanger et al. [6]. The connection of piles at the bottom was modeled by a hinge connection to the container similar to the experiment setup. Because of the constraints at the base of the piles, i.e. rotation was allowed and no vertical movement was permitted, the t-z and q-z springs were not implemented in the numerical model. The PyLiq1 springs were also attached to the top and bottom of the pile cap to capture its interaction with the surrounding soil [27,28,31]. Along the interface between the soil and the sheet pile, a kinematic condition was specified that required the sheet pile and the adjacent soil to share identical displacements in both the horizontal and vertical directions [12,13]. The container employed in the experiment had semi-rigid boundaries and was approximated in the OpenSees model using 2D linear elastic isotropic materials and quad elements [15]. The drainage was prevented at the container bottom similar to Chang et al. [11]. The bottom of the model was fixed in such a way that no relative movement was allowed in both vertical and horizontal directions to represent a fully reflecting boundary condition of the semi-rigid container. The displacements of the model on both lateral sides were tied together with periodic boundary conditions, meaning the container sides shared the same displacement. The hydrostatic pressures from the ponded water were modeled as distributed pressures applied on the surrounding soil elements [11]. Furthermore, to incorporate the dynamic effects of the ponded water without altering the effective stresses in the soil elements, each node on the boundary of the mesh, which was below the ponded water, was assigned a nodal mass using the mass command [15] in OpenSees. The horizontal mass was set to zero and the vertical mass was set as the mass of the volume of water supported by the node [32]. In this way, the dynamic effect of the ponded water was approximated by the induced inertial forces of the water mass under the shaking.
Table 2 PDMY02 model parameters for Albany silica sand at different relative densities. Dr (%)
60
70
Pref (kPa) Gr (MPa) γmax, r Br (MPa) d φ' φPT c1
101 23.1 0.1 50.0 0.5 35° 26° 0.03
c2
5
c3 d1
0.05 0.1
0 0.3
d2 d3
3 0.05
0
liq1
1
liq2
0
cs1 cs2 cs3 NYS c (kPa)
0.9 0.02 0.7 20 0.1
27.4 53.9
0.01
Description Reference effective confining pressure Reference low-strain shear modulus Maximum octahedral shear strain Bulk modulus Pressure dependency coefficient Friction angle Phase transformation angle Non-negative parameter that controls the shearinduced volumetric change Non-negative parameter that reflects contraction tendancy based on the dilation history or fabric damage Accounts for the overburden stress effect Reflects the dilation tendancy (along with friction angle and phase transformation angle) above phase transformation angle Reflects fabric damage (stress history) Accounts for overburden stress effect; this effect can be accounted by c3 solely Damage parameter to define accumulated permanent shear strain as a function of dilation history Damage parameter to define biased accumulation of permanent shear strain as a function of load reversal history Parameters defining a straight critical-state line ec in e-p′ space Number of yield surface Cohesion
measured shear wave velocity using Gmax =ρVs2 . The reference shear modulus (Gr) was determined by Gr =Gmax (pref / p)d , where p, pref, and d represent effective confining pressure, reference mean effective confining pressure, and pressure dependent coefficient, respectively. The friction angle (ϕ’) was estimated using the correlation ⎛ σ′ ⎞ φ′=3.9° [Vs ⎜ σ v0 ⎟ ]0.44 proposed by Mayne [26], where σ′v0 and σatm are ⎝ atm ⎠ effective overburden pressure and atmospheric pressure, respectively. The remaining parameters listed in Table 2 were suggested by the constitutive model developer. It is noteworthy the parameters of PDMY02 material were originally calibrated for the Nevada sand, whereas Albany silica sand was used in the shake table experiment. The properties of these two types of soils drastically differ in many ways such as particle shape. Specifically, the Nevada sand is an angular material while the Albany silica sand is very round. This factor could result in some misfits between the numerical and experimental results as explained in Section 4. Elastic beam-column elements [15] were utilized for the simulation of the sheet pile, pile cap and superstructure. On the other hand, the piles were modeled utilizing nonlinear displacement-based beamcolumn element [15]. And elastoplastic pile section behavior was incorporated using a fiber section object [15]. The properties of the aforementioned structural components are listed in Table 3. The pile cap was modeled using rigid beam column elements with high flexural stiffness and masses lumped at the nodes. The pile-to-cap connection was modeled as rigid in rotation, and the nodes at the top of the piles were constrained to have the same displacement degrees of freedom as
3.2. Analysis sequence The FE analysis sequence is consisted of a few steps as described below.
•
Table 3 Properties of foundation, quay wall and structural components. Component
E (kPa)
I (m4)
A (m2)
Mass (ton)
Sheet pile Piles Pile cap Superstructure
2.06E+08 2.06E+08 1.00E+09 2.06E+08
4.28E−06 8.02E−06 1.00E+01 6.53E−04
3.02E−02 2.84E−03 8.00E−01 1.91E−02
/ / 10 12
575
Step 1: the soil, container and sheet pile mesh were built and soil permeability was set artificially large to facilitate consolidation. The materials were assigned elastic properties, and then the static gravity of the model and hydrostatic pore pressure from the ponded water were applied to establish the initial stress states in the soil. During this step of soil deposition and ground preparation, two phases were distinguished with regard to prescribing the boundary condition of the sheet pile. In the first stage, the sheet pile was fixed horizontally and soil underwent consolidation. In the second stage, the sheet pile was released horizontally and tied together with adjacent soil nodes both horizontally and vertically as aforementioned using the master/slave node technique [15] in OpenSees. And lateral earth pressures from the backfill soil and the submerged sand
Soil Dynamics and Earthquake Engineering 92 (2017) 573–584
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• •
were applied to the sheet pile. Step 2: the piles, superstructure, and soil spring elements were incorporated into the model. The self-weight of the superstructure and pile cap were loaded as nodal vertical forces. Step 3: Soil permeability was updated to its desired values, the soil and soil springs materials were set to plastic stage, and dynamic loading was applied to the fixed nodes at the base of the soil and container meshes using the UniformExcitation command [15] in OpenSees. The Newmark method was used to integrate the dynamic response with γ=0.6 and β=0.3025 for convergence. An assumed 3% Rayleigh damping for the soil-pile-structure was used to apply some damping at low strain level. The mass proportional damping (am) and stiffness proportional damping (ak) were set as am=0.0 and ak=0.006 according to the estimated first mode frequency of 9.09 Hz to ensure numerical stability in the analysis. Moreover, energy increment test [15] with the tolerance of 1.0e-4 was utilized to judge whether the convergence had been achieved.
4. Analysis results and discussions The response of the soil, piles and the sheet pile are presented in this section and compared with the recorded data of the shake table experiment. It is worth mentioning that the bottom connection of the front row piles (piles A1, A2, A3 in Fig. 1) were unexpectedly broken during the shaking in the experiment and the footing with the superstructure tilted 20 degrees toward the land. As a result, some sensors were hit and even disconnected by the tilted footing around 10.2 s, which resulted in some irregular recordings. Fig. 5. Lateral displacement time histories of soil at various depths beside the pile group.
4.1. Soil deformation The computed lateral soil displacement time histories at various depths behind the sheet pile (Line C in Fig. 3) and beside the pile group (Line D in Fig. 3) are compared with experimental counterparts [2] as presented in Figs. 4 and 5. The predicted response is highly sensitive to
the dynamic characteristics of the soil constitutive model used, which are discussed in another paper by the authors [33]. In general, the numerical model yielded, as shown in Figs. 4 and 5, lower displacements than the recorded data, though the overall behavior was reproduced fairly well. According to Figs. 6 and 7, which display the soil lateral displacement profiles behind the sheet pile (Line C in Fig. 3)
Fig. 4. Lateral displacement time histories of soil at various depths behind the quay wall.
Fig. 6. Lateral displacement profile of soil at various depths behind the quay wall.
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fairly reasonable. It is noteworthy that the soil element at surface was pulled up by the sheet pile as can be seen in Fig. 8, which is unrealistic compared to the experiment. This phenomenon was possibly caused by the assumed interface boundary condition of perfect bounding between the quay wall and the adjacent soil nodes. This simplification of the soil-sheet pile interface can be considered acceptable for this simulation since the overall deformation pattern agreed fairly well with the experimental observations. Another simplified alternative approach to model soil-sheet pile interface boundary condition is to utilize zerolength elements coupled with 1D elastic-no tension material [15]. The authors explored this alternative approach, however the pulling-up of the ground surface still persisted. In addition, the accuracy of the simulated lateral deformations was reduced. Therefore, the first simple interface modeling method was employed in this paper similar to some other published research (e.g. [12,13]). The soil stress-strain loops at various depths at two locations (see Lines E and F in Fig. 3) are presented in Fig. 9. It appears that cyclic mobility occurred at all depths as the shear strains became quite large (as high as about 18%) and the inelastic behavior of soil was highly prominent. Lateral spreading led to shear strain accumulation and strong dilative response in the seaward direction. This observation validates that the FE model successfully captured the characteristic behaviors of soil subjected to liquefaction-induced lateral spreading. Overall, the large ground deformations due to the extensive liquefaction and lateral spreading were reproduced fairly well by the dynamic FE model in this study. However, it should be noted that the numerical analysis generally underestimated the maximum displacement recorded in the experiment. In order to explore the sensitivity of the soil constitutive model to the selected parameters, a comprehensive sensitivity analysis was carried out to understand the effects of the internal angle of friction and small strain shear modulus on the lateral displacement of liquefied soil [33]. Due to the page limitation, the analyses results are not presented in this paper, however a summary of the findings are presented herein. The sensitivity study found that the effects of internal friction angle and small-strain shear modulus on liquefied soil deformations were significant. As a result, a careful selection of these parameters in developing numerical models seems to be critical.
Fig. 7. Lateral displacement profile of soil at various depths beside the pile group.
and beside the pile group (Line D in Fig. 3), the predicted soil lateral displacement at various depths agreed with the recorded values quite well until 10 s. However, the underestimation of the soil lateral displacement by the FE model became pronounced after 15 s at both locations. Fig. 8(a) illustrates the overall horizontal deformation and residual displacement pattern of the FE model which shows that the sheet pile quay wall was predicted to move laterally 1.04 m toward the water, which was very close to the measured 1.1 m seaward displacement in the experiment. In general, the simulated deformation pattern illustrated that the soil lateral deformation decreased as the distance from the quay wall increased toward the land, which was consistent with the experimental observations. Moreover, as shown in Fig. 8(b), the ground settled about 0.31 m on the landside while it heaved about 0.36 m on the seaside as computed by the numerical model. Compared to the experimental results of 0.24 m settlement on the landside and 0.34 m bulging on the seaside, the numerical results were proved to be
4.2. Excess pore water pressure buildup In order to monitor the generation, redistribution and dissipation of excess pore water pressure (PWP), the physical model was instrumented with PWP sensors inside the ground at different depths [2]. For comparison, the recorded and predicted excess PWP data on the landside at two locations (see Lines E and F in Fig. 3) and three different depths are presented in Fig. 10. Numerically and experimentally, the liquefaction state in the ground was achieved soon after shaking started likely because of several pronounced peaks in the input motion (Fig. 2). At few locations, recordings of excess PWP were overall slightly higher than computed values since the sensors sunk into the ground during the liquefaction state. In addition, the excess PWP of the experimental model built up faster and dissipated slightly slower than the dynamic FE model. This difference became more pronounced at deeper depths. Moreover, the measured excess PWP exhibited profound fluctuations before 20 s during some loading cycles while the numerical model failed to reproduce such a strong cyclic mobility response. Besides, the excess PWP contour toward the end of shaking (about 30 s) is presented in Fig. 11. As it displays, the largest excess PWP was 49.4 kPa in the landside compared to the initial effective stress of 50.4 kPa, which indicates the liquefaction status had been achieved in the soil.
Fig. 8. Deformed shape and residual displacements of the numerical model (a) horizontal residual deformation (b) vertical residual deformation.
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Fig. 9. Stress-strain loops of soil at various depths along lines E and F.
was not available for the whole duration of the shaking for some of the records such as at the depth of 0.55 m in Fig. 12. Overall, it seems the simulation results of the piles responses were in less agreement with the experimental data compared to the soil response. This discrepancy can be attributed to several factors such as the three-dimensional nature of the experiment and disconnection of the pile bottom connection during the experiment.
4.3. Response of piles Bending strains along the piles were recorded during the experiment by several pairs of strain gauges attached to the piles in the direction of liquefied soil lateral flow [2]. The bending strains of the piles recorded during the shake table experiment were then converted into bending moment using Eq. (1) assuming elastic linear behavior for the piles.
M =EIε / y
4.4. Response of sheet-pile quay wall
(1)
The measured bending strain data along the sheet-pile quay wall were translated into bending moment using Eq. (1) and the results are presented in Fig. 13. As shown in Fig. 13, the bending moment time histories of the sheet pile produced by the numerical modeling and experiment were in reasonable agreement except at deeper depths. Large negative bending moments were predicted to develop at the depth of 2.5 m throughout the shaking for the sheet-pile by the OpenSees model, whereas the experimental data did not present the same phenomenon. This could be due to the fact that the sheet-pile was free at both ends in the experiment, whereas it was tied to the adjacent soil nodes horizontally and vertically in the FE model. Fig. 14 shows the bending moment profile of the sheet-pile for both numerical and experimental models. It can be found that the magnitude of the bending moments was not properly captured by the numerical model at the deeper depths.
in which
M Bending moment (KN∙m) E Modulus of elasticity of sheet pile or piles (KN/m2) I Area moment of inertia of sheet pile or piles (m4) ε Bending strain y Radius of pile or distance between the neutral axis and the centroid for the sheet pile (m) The computed and measured time histories of bending moments in the piles (pile A at front row and pile B at rear row in Fig. 3) are compared in Fig. 12. The bending moment time histories appeared to be comparable in magnitude and phasing up to a depth of 2.5 m, whereas comparison at the depth of 3.9 m were not satisfactory. The reason behind inconsistency between measured and predicted bending moments at deeper depths is contributed to the sudden breakage of the bottom connection of the front row piles in the experiment, while the hinge connection in the FE model was sustained throughout the analysis. Please note due to the disconnection of some strain gauge cables during the experiment as a result of large deformations, the data
4.5. Investigation of failure modes of piles In order to investigate the failure mechanism of the pile foundation 578
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Fig. 10. Excess pore water pressure time history response of soil.
predicted that the front row pile (pile A) received 92% higher shear forces and thus more vulnerable to shear failure than the rear row pile (pile B) at the estimated time (about 10.2 s) when the breakage occurred in the shake table experiment. In addition, there could be some other unknown factors contributing to the occurrence of the breakage such as fabrication deficit or installation issues, which makes this phenomenon difficult to be simulated in the FE model. Fig. 11. Contour plot of excess PWP on deformed shape at 30 s of the shaking.
5. Evaluation of a mitigation measure
exhibited in the shake table experiment, we evaluated the shear forces imposed to the piles by the lateral flow of the liquefied soil. In the shake table experiment, all piles were observed to yield at the heads as shown in Fig. 15. Based on linear elastic assumption, Motamed et al. [2] back-calculated the experimental shear force from the bending moment along the piles up to 6.2 s before the plastic deformation was initiated. In addition, Motamed et al. [2] identified the yielding moment of piles was 8.74 kN∙m considering the axial load in each pile (i.e. 36 kN), from which the yielding shear force at pile heads can be determined as 2.19 kN. The numerical and experimental monotonic shear forces at the heads of the front and rear row piles are compared in Fig. 16. As can be seen, the predicted shear forces at the heads of piles A and B were higher than the threshold value indicating the onset of plastic deformation and in good agreement with those of piles A3 and B3 in the experiment, respectively, at 6.2 s. This could possibly explain the exhibition of the yielding failure at pile heads in the shake table experiment. Regarding the unexpected disconnection at the base of the front row piles in the shake table experiment, this breakage was not meant to occur by the original design. As illustrated in Fig. 17, the FE model
In the previous sections, the response of a soil-pile-quay wall system when subjected to liquefaction-induced lateral spreading was investigated through FE modeling and the results were compared to a large-scale shake table experiment. Since the lateral flow of liquefied soil applied significant lateral forces on the piles and the quay wall, in this section the effects of a mitigation measure to reduce the seismic demands in the piles and the quay wall is explored. The selection of the mitigation method was based on a series of small-scale 1 g shake table experiments performed by the second author [19] in which the approach was to limit the soil displacements behind the quay-wall. This mitigation philosophy provided promising results in the smallscale experiments and is investigated in this study using numerical modeling. As a mitigation strategy, this paper investigates the installation of a sheet-pile with a fixed-end base connection in between the quay wall and the pile group to decrease the demand on different components using FE modeling. This remedial measure can be used as a retrofitting technique for the existing pile foundations near the waterfront structures with minimum disruption to the performance of these elements. The dynamic FE model discussed in the preceding sections 579
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Fig. 12. Bending moment time histories of piles.
5.1.1. Reduction in soil displacement Fig. 19 presents time histories of surface ground displacement behind the quay wall as well as in front of the pile group, corresponding to points P2 and P1 in Fig. 18, which illustrates the efficiency of the proposed countermeasure especially toward the end of shaking. Furthermore, reduction factors were calculated for the maximum soil displacement at these locations and the results are compared with the experimental findings [19] as exhibited in Fig. 20. The comparison illustrates that the mitigation strategy simulated by the FE model moderately reduced the liquefied soil displacement at P1 by 38%, which agreed well with the experimental displacement reduction of 31% at P1 [19]. However, the FE model only predicted a relatively small reduction of the liquefaction-induced lateral soil deformation at P2 (RF=39%) compared to the noticeable improvement (RF=70%) at P2 observed in the small-scale shake table experiment [19] employing the same countermeasure. The observed inconsistency in the extent of reductions in soil displacements between numerical model and shake table experiment seems to be attributed to the differences in scale (i.e. size), even though both approaches indicated overall improvements in reducing the soil deformations.
was further modified to incorporate a mitigating sheet-pile right in between the quay wall and the pile group as shown in Fig. 18. The mitigating sheet pile was vertically placed and extended upright from the bottom of the container to the ground surface. In addition, all other features and configurations of the OpenSees model remained identical to the previous model without any countermeasure. The mitigating sheet pile was fixed at the base and acted as a cantilever beam. Besides, the interface connections between the mitigating sheet-pile and the adjacent soil nodes were employed in the same way as the quay wall. Regarding the mitigating sheet pile properties, a parametric study was carried out to examine the remedial effects of mitigation sheet piles with different flexural stiffness (EI). As a benchmark case, the typeof the mitigating sheet-pile was picked to be the same as the quay wall. And four more commonly used types of sheet pile in Japan [34], as presented in Table 4, were selected and investigated. 5.1. Benchmark case In this section, only the benchmark mitigation case is discussed. And the efficiency of the proposed countermeasure on several parameters such as lateral soil displacements, pile cap displacement, and displacement and tilting of the quay wall are evaluated and compared with the available experimental results [19]. For comparison, a parameter called Reduction Factor (RF) is introduced to quantitatively describe the effectiveness of the remedial technique (Eq. (2)).
⎛ parameterwithmitigation ⎞ RFparameter =⎜1 − ⎟ ×100 paramterwithoutmitigation ⎠ ⎝
5.1.2. Reduction in pile cap displacement Fig. 21(a) presents the reduction factor values for both maximum and residual pile cap displacements of the OpenSees model and the shake table experiment [19] which demonstrates the extent of reduction in both models. As can be seen, the experiment demonstrated the fixed-end mitigating sheet pile could significantly alleviate the pile cap displacements (RF=60% for maximum value and RF=65% for residual
(2) 580
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Fig. 15. Photo of yielding at pile heads .
Fig. 13. Bending moment time histories of sheet pile.
Fig. 16. Comparison of monotonic components of shear force at pile heads .
Fig. 17. Time histories of predicted monotonic shear force at pile bases .
5.1.3. Reduction in quay wall movement Two parameters characterizing the movement of the quay wall, i.e. tilting and displacement, are introduced in this section. The tilting of the quay wall was defined as the rotation of the bottom of the quay wall. On other hand, the lateral movement of the top of the quay wall was denoted as the displacement of the quay wall.
Fig. 14. Bending moment profile of sheet pile.
value). On the other hand, the numerical model displayed a fairly comparable improvement in pile cap displacement reduction (RF=40% and 42%).
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Fig. 18. FE model discretization with mitigation sheet pile. Table 4 Properties of mitigation sheet piles [34]. Sheet Pile Type
Thickness (mm)
E (kPa)
I (m4)
A (m2)
LSP-2 (Benchmark) LSP-1 LSP-2* LSP-3B LSP-3D
5 4 4 5 6
2.06E+08
4.28E−06 2.56E−06 3.40E−06 2.54E−05 9.92E−05
3.02E−02 2.12E−02 2.41E−02 3.30E−02 3.56E−02
Note: the LSP-2* type has a different thickness of 4 mm from the benchmark LSP-2 type with the thickness of 5 mm.
Fig. 21. Comparison between reduction factors for the numerical (benchmark case) and experimental models with mitigation measure in terms of (a) pile cap displacement (b) quay wall residual movements (horizontal displacement and tilting).
Fig. 21(b) compares the reduction factors for the quay wall movement computed from the numerical and the experimental results [19]. It is shown that the OpenSees model was able to pretty well reproduce the moderate remedial impact of the fixed-end sheet pile on reducing the quay wall displacement (RF=42% in the numerical model against RF=36% in the physical model) and the quay wall tilting (RF=38% in the numerical model against RF=42% in the physical model). Fig. 19. Comparison between surface ground displacements behind quay wall w/o and w mitigation measure (benchmark case).
5.2. Parametric study This section focuses on the parametric study of the mitigating sheet pile. Fig. 22 illustrates time histories of lateral surface soil displacement of different mitigation cases at point P2 in Fig. 18. With the inclusion of the mitigation sheet pile, the ground lateral spreading can
Fig. 20. Comparison between reduction factors for the numerical (benchmark case) and experimental models with mitigation measure in terms of lateral soil displacement. Fig. 22. Comparison between surface ground displacements behind quay wall of different mitigation cases.
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Sports, Science, and Technology (MEXT). These supports are greatly appreciated. The authors also acknowledge the constructive comments provided by two anonymous reviewers which improved this paper. References [1] Tokimatsu K, Suzuki H, Tabata K, Sato M. Three-dimensional shaking table tests on soil-pile structure models using E-Defense facility. In: Proceedings of the 4th International Conference on Earthquake Geotechnical Engineering. Paper No. 1529; 2007. [2] Motamed R, Towhata I, Honda T, Yasuda S, Tabata K, Nakazawa H. Behavior of pile group behind a sheet pile quay wall subjected to liquefaction-induced large ground deformation observed in shaking test in E-Defense project. Soils Found 2009;49(3):459–75. [3] Suzuki H, Tokimatsu K. Effects of soil-structure interaction on stress distribution within a pile group under multi-dimensional loading. In: Proceedings of the 5th International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. Paper No.5.50a; 2010. [4] Motamed R, Towhata I. Shaking table model tests on pile groups behind quay walls subjected to lateral spreading. J Geotech Geoenviron Eng ASCE 2010;136(3):477–89. [5] Motamed R, Towhata I, Honda T, Tabata K, Abe A. Pile group response to liquefaction-induced lateral spreading: e-defense large shake table test. Soil Dyn Earthq Eng 2013;51:35–46. [6] Boulanger RW, Curras CJ, Kutter BL, Wilson DW. Seismic soil-pile-structure interaction experiments and analyses. J Geotech Geoenviron Eng ASCE 1999;125:750–9. [7] Abdoun T, Dobry R. Evaluation of pile foundation response to lateral spreading. Soil Dyn Earthq Eng 2002;22(9):1051–8. [8] Boulanger RW, Kutter BL, Brandenberg SJ, Singh P, Chang D. Pile Foundations in Liquefied and Laterally Spreading Ground During Earthquakes: Centrifuge Experiments & Analyses [PEER report No. UCD/CGM-03/01]Pacific Earthquake Engineering Research Center. Berkeley: University of California; 2003. [9] Brandenberg SJ. Behavior of pile foundations in laterally spreading ground [Ph.D. Thesis]. Davis: University of California; 2005. [10] Mohammed AMY, Okhovat MR, Maekawa K. Numerical investigation on damage evolution of piles inside liquefied soil foundation: dynamic loading experiments. Int J World Acad Sci, Eng Technol 2012;71:1796–803. [11] Chang D, Boulanger RW, Brandenberg SJ, Kutter BL. FEM analysis of dynamic soil-pile-structure interaction in liquefied and laterally spreading ground. Earthq Spectra 2013;29(3):733–55. [12] Cubrinovski M, Uzuoka R, Sugita H, Tokimatsu K, Sato M, Ishihara K, Tsukamoto Y, Kamata T. Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: shaking in the direction of ground flow. Soil Dyn Earthq Eng 2008;28(6):421–35. [13] Uzuoka R, Cubrinovski M, Sugita H, Sato M, Tokimatsu K, Sento N, Kazama M, Zhang F, Yashima A, Oka F. Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: shaking in the direction perpendicular to ground flow. Soil Dyn Earthq Eng 2008;28(6):436–52. [14] Zhou YH, Tokimatsu K, Suzuki H, Yoshida H, Nukui Y. Numerical study of threedimensional nonlinear behavior of soil-pile-structure system under strong input motion. In: Proceedings of the 15th World Conference on Earthquake Engineering, 24-28 September 2012, Lisbon, Portugal. 12362-12370; 2012. [15] Mazzoni S, McKenna F, Scott MH, Fenves GL. Open System for Earthquake Engineering Simulation user Manual. Berkeley: University of California; 2009 〈http://opensees.berkeley.edu〉. [16] Elgamal A, Yang Z, Parra E. Computational modeling of cyclic mobility and postliquefaction site response. Soil Dyn Earthq Eng 2002;22(4):259–71. [17] Yang ZH, Elgamal A, Parra E. Computational model for cyclic mobility and associated shear deformation. J Geotech Geoenviron Eng 2003;129(12):1119–27. [18] Yang ZH, Lu JC, Elgamal A. OpenSees soil models and solid-fluid fully coupled elements: user's manual [available at]. San Diego: Department of Structural Engineering, University of California; 2008, [available at] 〈http://cyclic.ucsd.edu〉. [19] Motamed R, Towhata I. Mitigation measures for pile groups behind quay walls subjected to lateral flow of liquefied soil: shake table model tests. Soil Dyn Earthq Eng 2010;30(2010):1043–60. [20] MEXT and NIED. Research Theme No.2, Annual Report of the Fiscal Year 2005, Special Project for Earthquake Disaster Mitigation in Urban Areas, Ministry of Education and Culture Sports Science and Technology and National Research Institute for Earth Science and Disaster Prevention (in Japanese); 2006. [21] Kazama M, Ryosuke U, Noriaki S, Kabasawa Y, Kamiya K, Oka F, Yashima A, Zhang F. Three-dimensional numerical prediction and analysis of the foundation experiment (lateral flow analysis, part I). As a part of E-Defense working group report, website: 〈http://www.bosai.go.jp/hyogo/ddt-pj/report/result17/re-index.htm〉 (in Japanese); 2005. [22] Website: 〈http://www.gidhome.com〉 [23] Zerwer A, Cascante G, Hutchinson J. Parameter estimation in finite element simulations of Rayleigh waves. J Geotech Geoenviron Eng 2002;128(3):250–61. [24] McGann C, Arduino P. Site response analysis of a layered soil column (total stress analysis). OpenSees wiki example, website: 〈http://opensees.berkeley.edu/wiki/ index.php/Site_Response_Analysis_of_a_Layered_Soil_Column_(Total_Stress_ Analysis)〉; 2011. [25] Biot MA. Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 1962;33(4):1482–98.
Fig. 23. Maximum soil lateral displacements at P1 and P2 of different mitigation cases.
be diminished. Specifically, when LSP-3D type sheet pile was adopted, the lateral soil displacement was remarkably reduced compared to the scenario without mitigation measure. Also it is observed that the horizontal ground deformation varies significantly with the choice of mitigation sheet pile. In addition, Fig. 23 exhibits maximum soil lateral displacement at points P1 and P2 in Fig. 18 of different mitigation cases. Overall, the increase of EI makes mitigation sheet pile more effective in reducing the lateral soil deformation in both points. 6. Conclusions This study evaluates the accuracy and effectiveness of using existing constitutive models in the OpenSees framework to reproduce the response characteristics of liquefaction-induced lateral spreading of pile foundations based on the results of a large-scale shake table experiment. Considering the involved complications, it can be said that an overall agreement was reached concerning the dynamic response of the soil. However, the 2D FE model was unable to accurately predict the seismic demands on the piles and the sheet-pile, though the overall behavior was effectively captured. Because of the limitations and uncertainties involved in the numerical model, considerable differences were observed between the predicted and measured response of the piles and the quay wall. There are a number of possible reasons for this inconsistency including, but not limited to, the unexpected disconnection of the front row piles in the experiment and induced overturning of the pile cap, the uncertainty in the soil constitutive model parameters used in the FE model, differences between the 3D physical model and the 2D approximation, and the complexity of soil-structure interaction problems. Finally, the efficiency of a mitigation measure which included the installation of a fixed-end sheet-pile in between the pile group and the quay wall on the response of soil-pile-quay wall system was assessed and the results were compared with the small-scale shake table test results deploying the same countermeasure. And a parametric study on flexural stiffness of mitigating sheet pile was performed. In conclusion, it is demonstrated that the 2D OpenSees model was able to qualitatively capture the reduction effects of the proposed remedial strategy, which demonstrates the robustness of the OpenSees modeling. Acknowledgement The large-scale experiment described in this paper was carried out at the National Research Institute for Earth Science and Disaster Prevention (NIED), Hyogo Earthquake Engineering Research Center and was sponsored by the Japan Ministry of Education, Culture, 583
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Petroleum Institute; 1993. [31] Chang D. Inertial and lateral spreading demands on soil-pile-structure systems in liquefied and laterally spreading ground during earthquakes [Ph.D Thesis] Department of Civil Engineering. Davis: University of California; 2007. [32] McGann C, Arduino P. Dynamic 2D effective stress analysis of slope. OpenSees wiki example, website: 〈http://opensees.berkeley.edu/wiki/index.php/Dynamic_2D_ Effective_Stress_Analysis_of_Slope〉; 2011. [33] Li GJ, Motamed R. Numerical modeling of pile group response subjected to liquefaction-induced large ground deformations in E-Defense shake table test. 6th International Conference on Earthquake Geotechnical Engineering, 1-4 November 2015, Christchurch, New Zealand. Paper No.173; 2015. [34] Website: 〈http://www.ns-kenzai.co.jp/cmsdesigner/dlfile.php?Entryname=dl_ doboku & entryid=00002 & fileid=00000041 & ./C044.pdf〉
[26] Mayne PW. Interpretation of geotechnical parameters from seismic piezocone tests. In: Proceedings of the 3rd international symposium on cone pentrometer testing, CPT (Vol. 14, pp. 47–73; 2014. [27] Curras CJ, Boulanger RW, Kutter BL, Wilson DW. Dynamic experiments and analyses of a pile-group-supported structure. J Geotech Geoenviron Eng 2001;127(7):585–96. [28] Brandenberg SJ, Zhao M, Boulanger RW, Wilson DW. p-y plasticity model for nonlinear dynamic analysis of piles in liquefiable soil. J Geotech Geoenviron Eng 2012;139(8):1262–74. [29] Khosravifar A, Boulanger RW, Kunnath SK. Design of extended pile shafts for the effects of liquefaction. Earthq Spectra 2014;30(4):1775–99. [30] American Petroleum Institute (API) . Recommended practice for planning, design, and constructing fixed offshore platforms. API RP 2A-WSD, 20th edition. American
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Contents lists available at ScienceDirect
Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Finite element modeling of soil-pile response subjected to liquefactioninduced lateral spreading in a large-scale shake table experiment Gangjin Li, Ramin Motamed
crossmark
⁎
Department of Civil and Environmental Engineering, University of Nevada Reno, Reno, NV 89557, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Lateral spreading 2D effective stress analysis OpenSees Soil-pile response Mitigation measure
This paper presents two-dimensional (2D) nonlinear dynamic finite element (FE) modeling of a large-scale shake table test conducted at the E-Defense shake table facility in Japan. This study explores the efficiency of 2D effective stress analyses to predict the behavior of soil-pile systems subjected to liquefaction and lateral spreading using the library of existing constitutive models and the prescribed parameters. The coupled soilwater FE model was developed in OpenSees and the analysis results are compared with measured data from the shake table experiment with the main emphasis on the response of liquefied soil and the demand applied to the piles as well as the sheet-pile quay wall. By examining the numerical analysis results, it is demonstrated that the FE model was able to reproduce the shake table model behavior with reasonable accuracy. Lastly, a mitigation strategy was modeled to investigate its effectiveness to reduce the demand on the soil-pile system.
1. Introduction In recent earthquakes such as the 2010 Haiti, the 2010 Chile, the 2010–2011 Canterbury Sequence and the 2011 Great Tohoku earthquakes, extensive damage in pile foundations has been observed due to liquefaction-induced lateral spreading. Many researchers have investigated the basic mechanisms of this phenomenon through physical modeling including shake table experiments [1–5] and centrifuge tests [6–9]. In addition, a number of numerical simulations have been carried out based on physical experiments for validation and application using different modeling techniques [10–14]. In March 2006, a large-scale test on lateral spreading of liquefied sand behind a sheet-pile quay wall was performed at the E-Defense facility in Japan. The experimental data was analyzed by Motamed et al. [2], which studied the soil-pile interaction in laterally spreading grounds in detail. The experiment included a simple structure model supported on a 2×3 pile group located adjacent to a sheet-pile quay wall as shown in Fig. 1. The model was heavily instrumented to measure the dynamic response of the soil-pile system. Liquefactioninduced lateral spreading was achieved and the soil moved laterally about 1.1 m behind the quay wall. Based on the shake table experiment, a 2D numerical model was developed in this study using OpenSees [15] framework employing available constitutive models in its material library. The constitutive soil model used in this study was developed for granular materials subjected to cyclic loading with emphasis to undrained cases [16–18]. The suggested parameters of
⁎
the constitutive model were calibrated for Nevada sand, which was significantly different from the sand used in the shake table experiment as explained in Section 3.1 in this paper. The numerical modeling produced comparable results to the experimental data and the details are presented hereafter. In addition to modeling the behavior of the pile group subjected to the lateral flow of liquefied soil based on the large-scale experiment, this research explores the effectiveness of a mitigation measure to reduce seismic demands on the soil and the pile group. Motamed and Towhata [19] carried out a series of 1 g small-scale shake table model tests on a 3×3 pile group located behind a sheet-pile quay wall subjected to liquefaction-induced large ground deformation which was basically a 1/10 scale of the E-Defense shake table experiment. Three remedial techniques were explored in Motamed and Towhata [19], among which one of the studied mitigation measures was selected to be explored in this study. The selected mitigation strategy included installation of a mitigating sheet-pile with fixed-base boundary condition in between the pile group and the quay wall. This paper discusses the effectiveness of this method to reduce seismic demands using the OpenSees model and compared with the experimental results reported by Motamed and Towhata [19]. Lastly, a parametric study was performed to investigate the remedial effects of various types of mitigating sheet piles with different sectional properties, which are commonly used in engineering practice.
Corresponding author. E-mail addresses: [email protected] (G. Li), [email protected] (R. Motamed).
http://dx.doi.org/10.1016/j.soildyn.2016.11.001 Received 4 December 2015; Received in revised form 21 October 2016; Accepted 1 November 2016 Available online 11 November 2016 0267-7261/ © 2016 Elsevier Ltd. All rights reserved.
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4.5
11.5
1.0
0.6 1.0
Weights (12 t)
0.5
0.5 0.8
Water
Footing (10 t)
Pile
L. 3.5
D. 0.15
Liquefiable ground
4.5
3.5
3.2
Sheet pile 1.0
B2
Cross section view
A2 16.0 m
Rear Front row row 1.2 1.2
4.5
1.0
8.1D
A3 A2 A1
2×4D
1.6
4.0
Plan view
B3 B2 B1
8.9
1.6
Fig. 2. Acceleration time histories of input motion.
Fig. 1. Schematic illustration of large scale shake table test at E-Defense facility (unit: m) (Motamed et al. [2]).
2. Description of E-Defense shake table experiment The shake table model of the soil-pile system was constructed in a large semi-rigid box with the dimensions of 16 m×5 m×4 m, and the soil configuration was a horizontal ground consisted of uniform liquefiable Albany Silica sand with the relative density of 60% underlain by a thin denser sand layer (Dr=70%). The basic properties of the soil profile are listed in Table 1 [20,21]. Similar to Kazama et al. [21], uniform shear wave velocity (VS) of 120 m/s and Possion's ratio (γ) of 0.3 were adopted in this study. A LSP-2 type steel sheet pile quay wall was used, which deformed laterally and triggered the liquefactioninduced lateral spreading. Behind the quay wall, six hollow steel piles with outer diameters of 0.1524 m and thicknesses of 0.002 m were connected to the base using a hinge connection (i.e. zero displacement and moment). The piles were used to support the 12 t weight of the superstructure and the 10 t weight of the pile cap as illustrated in Fig. 1. The large-scale model was subjected to two-directional ground motions (i.e. longitudinal and vertical) as presented in Fig. 2. The records obtained at the JR Takatori station during the 1995 Kobe earthquake were scaled down by 20% and chosen as the input motions. The maximum amplitudes of the horizontal and vertical components were 0.6g and 0.23g, respectively. More details on the shake table experiment can be found in Motamed et al. [2].
Fig. 3. FE model discretization of shake table experiment.
illustrated in Fig. 3. The maximum allowable soil element size of 0.5 m was determined to fit 20 elements within one shortest wavelength, i.e. 10 m, of the propagating shear wave [23,24]. In this manner, the propagating waves can be well captured in the analysis. The shortest wavelength within soil profile was calculated using the shear wave velocity of 120 m/sec and the maximum frequency content, i.e. 12 Hz, of the ground motion. Additionally, a convergence study was carried out to investigate the possibility of using finer mesh schemes with maximum element sizes of 0.25 m or 0.1 m. However, these models with refined discretization encountered convergence problem during dynamic analysis due to the fact they had redundant elements within one wavelength as reported by Zerwer et al. [23]. This finding reflects that the discretization of our model was sufficiently fine.
3. OpenSees numerical model
3.1. Elements, materials and boundary conditions
The 2D numerical model was built using OpenSees framework, which is an open source finite element software developed by UC Berkeley for earthquake engineering simulation [15] and post-processing was performed with GiD [22]. The discretization of the model is
In the FE model, the saturated soil was simulated as a two-phase material using QuadUP elements [18] based on the Biot's theory [25] for porous media, in which displacement of the soil skeleton (u) and pore pressure (p) are the primary unknowns (u-p formulation). The out-of-plane thickness of the soil elements was set to be the same as the width of the container in the shake table test (i.e. 4 m) in order to capture the pinning effects around the piles when the soil is liquefied. The constitutive behavior of the soil was captured by the PressureDependMultiYield02 (PDMY02) material [16–18] available in OpenSees to simulate the response characteristics of sand. The parameters needed for the constitutive soil model as presented in Table 2 were selected based on a combination of recommended values from the constitutive model developer [18] and correlations with the measured parameters from the shake table experiment [20,21]. The low strain shear modulus of soil (Gmax) was calculated based on
Table 1 Soil properties of Albany silica sand [20,21]. Depth (m)
0.0 - 4.0
4.0 - 4.5
Relative density, Dr (%) Density, ρ (t/m3) Vs (m/sec) Permeability, k (m/sec) Void ratio, e Possion's ratio, γ
60 1.67
70 1.70 120 8.50E−05 0.558 0.3
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the matching node on the pile cap. The superstructure was simplified as a concentrated mass of 12 t at the center of gravity to reproduce the actual mass. The structure columns were simulated to represent the natural period of a uniform stiffness column with fixed boundary conditions and natural period of 1.54 s. The group included 6 piles in the shake table experiment (i.e. 2 rows in total and 3 piles in each row) and was represented by two piles in the 2D model, each having three times the bending and cap connection stiffness of a single actual pile to approximate the exact stiffness of the 3D model in a 2D format [11]. In the numerical model, the pile and soil elements were connected using zero-length elements with nonlinear p-y springs represented by the PyLiq1 material [6,8,27,28], which has been used by other researchers for the study of soil-pile interaction in liquefied and laterally spreading ground in OpenSees [11,28,29]. The spring properties were determined based on American Petroleum Institute (API) formulas [30] as described by Boulanger et al. [6,8,28]. And the drag resistance ratio (Cd) of the gap component of the p-y springs was set to 0.3 similar to Boulanger et al. [6]. The connection of piles at the bottom was modeled by a hinge connection to the container similar to the experiment setup. Because of the constraints at the base of the piles, i.e. rotation was allowed and no vertical movement was permitted, the t-z and q-z springs were not implemented in the numerical model. The PyLiq1 springs were also attached to the top and bottom of the pile cap to capture its interaction with the surrounding soil [27,28,31]. Along the interface between the soil and the sheet pile, a kinematic condition was specified that required the sheet pile and the adjacent soil to share identical displacements in both the horizontal and vertical directions [12,13]. The container employed in the experiment had semi-rigid boundaries and was approximated in the OpenSees model using 2D linear elastic isotropic materials and quad elements [15]. The drainage was prevented at the container bottom similar to Chang et al. [11]. The bottom of the model was fixed in such a way that no relative movement was allowed in both vertical and horizontal directions to represent a fully reflecting boundary condition of the semi-rigid container. The displacements of the model on both lateral sides were tied together with periodic boundary conditions, meaning the container sides shared the same displacement. The hydrostatic pressures from the ponded water were modeled as distributed pressures applied on the surrounding soil elements [11]. Furthermore, to incorporate the dynamic effects of the ponded water without altering the effective stresses in the soil elements, each node on the boundary of the mesh, which was below the ponded water, was assigned a nodal mass using the mass command [15] in OpenSees. The horizontal mass was set to zero and the vertical mass was set as the mass of the volume of water supported by the node [32]. In this way, the dynamic effect of the ponded water was approximated by the induced inertial forces of the water mass under the shaking.
Table 2 PDMY02 model parameters for Albany silica sand at different relative densities. Dr (%)
60
70
Pref (kPa) Gr (MPa) γmax, r Br (MPa) d φ' φPT c1
101 23.1 0.1 50.0 0.5 35° 26° 0.03
c2
5
c3 d1
0.05 0.1
0 0.3
d2 d3
3 0.05
0
liq1
1
liq2
0
cs1 cs2 cs3 NYS c (kPa)
0.9 0.02 0.7 20 0.1
27.4 53.9
0.01
Description Reference effective confining pressure Reference low-strain shear modulus Maximum octahedral shear strain Bulk modulus Pressure dependency coefficient Friction angle Phase transformation angle Non-negative parameter that controls the shearinduced volumetric change Non-negative parameter that reflects contraction tendancy based on the dilation history or fabric damage Accounts for the overburden stress effect Reflects the dilation tendancy (along with friction angle and phase transformation angle) above phase transformation angle Reflects fabric damage (stress history) Accounts for overburden stress effect; this effect can be accounted by c3 solely Damage parameter to define accumulated permanent shear strain as a function of dilation history Damage parameter to define biased accumulation of permanent shear strain as a function of load reversal history Parameters defining a straight critical-state line ec in e-p′ space Number of yield surface Cohesion
measured shear wave velocity using Gmax =ρVs2 . The reference shear modulus (Gr) was determined by Gr =Gmax (pref / p)d , where p, pref, and d represent effective confining pressure, reference mean effective confining pressure, and pressure dependent coefficient, respectively. The friction angle (ϕ’) was estimated using the correlation ⎛ σ′ ⎞ φ′=3.9° [Vs ⎜ σ v0 ⎟ ]0.44 proposed by Mayne [26], where σ′v0 and σatm are ⎝ atm ⎠ effective overburden pressure and atmospheric pressure, respectively. The remaining parameters listed in Table 2 were suggested by the constitutive model developer. It is noteworthy the parameters of PDMY02 material were originally calibrated for the Nevada sand, whereas Albany silica sand was used in the shake table experiment. The properties of these two types of soils drastically differ in many ways such as particle shape. Specifically, the Nevada sand is an angular material while the Albany silica sand is very round. This factor could result in some misfits between the numerical and experimental results as explained in Section 4. Elastic beam-column elements [15] were utilized for the simulation of the sheet pile, pile cap and superstructure. On the other hand, the piles were modeled utilizing nonlinear displacement-based beamcolumn element [15]. And elastoplastic pile section behavior was incorporated using a fiber section object [15]. The properties of the aforementioned structural components are listed in Table 3. The pile cap was modeled using rigid beam column elements with high flexural stiffness and masses lumped at the nodes. The pile-to-cap connection was modeled as rigid in rotation, and the nodes at the top of the piles were constrained to have the same displacement degrees of freedom as
3.2. Analysis sequence The FE analysis sequence is consisted of a few steps as described below.
•
Table 3 Properties of foundation, quay wall and structural components. Component
E (kPa)
I (m4)
A (m2)
Mass (ton)
Sheet pile Piles Pile cap Superstructure
2.06E+08 2.06E+08 1.00E+09 2.06E+08
4.28E−06 8.02E−06 1.00E+01 6.53E−04
3.02E−02 2.84E−03 8.00E−01 1.91E−02
/ / 10 12
575
Step 1: the soil, container and sheet pile mesh were built and soil permeability was set artificially large to facilitate consolidation. The materials were assigned elastic properties, and then the static gravity of the model and hydrostatic pore pressure from the ponded water were applied to establish the initial stress states in the soil. During this step of soil deposition and ground preparation, two phases were distinguished with regard to prescribing the boundary condition of the sheet pile. In the first stage, the sheet pile was fixed horizontally and soil underwent consolidation. In the second stage, the sheet pile was released horizontally and tied together with adjacent soil nodes both horizontally and vertically as aforementioned using the master/slave node technique [15] in OpenSees. And lateral earth pressures from the backfill soil and the submerged sand
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• •
were applied to the sheet pile. Step 2: the piles, superstructure, and soil spring elements were incorporated into the model. The self-weight of the superstructure and pile cap were loaded as nodal vertical forces. Step 3: Soil permeability was updated to its desired values, the soil and soil springs materials were set to plastic stage, and dynamic loading was applied to the fixed nodes at the base of the soil and container meshes using the UniformExcitation command [15] in OpenSees. The Newmark method was used to integrate the dynamic response with γ=0.6 and β=0.3025 for convergence. An assumed 3% Rayleigh damping for the soil-pile-structure was used to apply some damping at low strain level. The mass proportional damping (am) and stiffness proportional damping (ak) were set as am=0.0 and ak=0.006 according to the estimated first mode frequency of 9.09 Hz to ensure numerical stability in the analysis. Moreover, energy increment test [15] with the tolerance of 1.0e-4 was utilized to judge whether the convergence had been achieved.
4. Analysis results and discussions The response of the soil, piles and the sheet pile are presented in this section and compared with the recorded data of the shake table experiment. It is worth mentioning that the bottom connection of the front row piles (piles A1, A2, A3 in Fig. 1) were unexpectedly broken during the shaking in the experiment and the footing with the superstructure tilted 20 degrees toward the land. As a result, some sensors were hit and even disconnected by the tilted footing around 10.2 s, which resulted in some irregular recordings. Fig. 5. Lateral displacement time histories of soil at various depths beside the pile group.
4.1. Soil deformation The computed lateral soil displacement time histories at various depths behind the sheet pile (Line C in Fig. 3) and beside the pile group (Line D in Fig. 3) are compared with experimental counterparts [2] as presented in Figs. 4 and 5. The predicted response is highly sensitive to
the dynamic characteristics of the soil constitutive model used, which are discussed in another paper by the authors [33]. In general, the numerical model yielded, as shown in Figs. 4 and 5, lower displacements than the recorded data, though the overall behavior was reproduced fairly well. According to Figs. 6 and 7, which display the soil lateral displacement profiles behind the sheet pile (Line C in Fig. 3)
Fig. 4. Lateral displacement time histories of soil at various depths behind the quay wall.
Fig. 6. Lateral displacement profile of soil at various depths behind the quay wall.
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fairly reasonable. It is noteworthy that the soil element at surface was pulled up by the sheet pile as can be seen in Fig. 8, which is unrealistic compared to the experiment. This phenomenon was possibly caused by the assumed interface boundary condition of perfect bounding between the quay wall and the adjacent soil nodes. This simplification of the soil-sheet pile interface can be considered acceptable for this simulation since the overall deformation pattern agreed fairly well with the experimental observations. Another simplified alternative approach to model soil-sheet pile interface boundary condition is to utilize zerolength elements coupled with 1D elastic-no tension material [15]. The authors explored this alternative approach, however the pulling-up of the ground surface still persisted. In addition, the accuracy of the simulated lateral deformations was reduced. Therefore, the first simple interface modeling method was employed in this paper similar to some other published research (e.g. [12,13]). The soil stress-strain loops at various depths at two locations (see Lines E and F in Fig. 3) are presented in Fig. 9. It appears that cyclic mobility occurred at all depths as the shear strains became quite large (as high as about 18%) and the inelastic behavior of soil was highly prominent. Lateral spreading led to shear strain accumulation and strong dilative response in the seaward direction. This observation validates that the FE model successfully captured the characteristic behaviors of soil subjected to liquefaction-induced lateral spreading. Overall, the large ground deformations due to the extensive liquefaction and lateral spreading were reproduced fairly well by the dynamic FE model in this study. However, it should be noted that the numerical analysis generally underestimated the maximum displacement recorded in the experiment. In order to explore the sensitivity of the soil constitutive model to the selected parameters, a comprehensive sensitivity analysis was carried out to understand the effects of the internal angle of friction and small strain shear modulus on the lateral displacement of liquefied soil [33]. Due to the page limitation, the analyses results are not presented in this paper, however a summary of the findings are presented herein. The sensitivity study found that the effects of internal friction angle and small-strain shear modulus on liquefied soil deformations were significant. As a result, a careful selection of these parameters in developing numerical models seems to be critical.
Fig. 7. Lateral displacement profile of soil at various depths beside the pile group.
and beside the pile group (Line D in Fig. 3), the predicted soil lateral displacement at various depths agreed with the recorded values quite well until 10 s. However, the underestimation of the soil lateral displacement by the FE model became pronounced after 15 s at both locations. Fig. 8(a) illustrates the overall horizontal deformation and residual displacement pattern of the FE model which shows that the sheet pile quay wall was predicted to move laterally 1.04 m toward the water, which was very close to the measured 1.1 m seaward displacement in the experiment. In general, the simulated deformation pattern illustrated that the soil lateral deformation decreased as the distance from the quay wall increased toward the land, which was consistent with the experimental observations. Moreover, as shown in Fig. 8(b), the ground settled about 0.31 m on the landside while it heaved about 0.36 m on the seaside as computed by the numerical model. Compared to the experimental results of 0.24 m settlement on the landside and 0.34 m bulging on the seaside, the numerical results were proved to be
4.2. Excess pore water pressure buildup In order to monitor the generation, redistribution and dissipation of excess pore water pressure (PWP), the physical model was instrumented with PWP sensors inside the ground at different depths [2]. For comparison, the recorded and predicted excess PWP data on the landside at two locations (see Lines E and F in Fig. 3) and three different depths are presented in Fig. 10. Numerically and experimentally, the liquefaction state in the ground was achieved soon after shaking started likely because of several pronounced peaks in the input motion (Fig. 2). At few locations, recordings of excess PWP were overall slightly higher than computed values since the sensors sunk into the ground during the liquefaction state. In addition, the excess PWP of the experimental model built up faster and dissipated slightly slower than the dynamic FE model. This difference became more pronounced at deeper depths. Moreover, the measured excess PWP exhibited profound fluctuations before 20 s during some loading cycles while the numerical model failed to reproduce such a strong cyclic mobility response. Besides, the excess PWP contour toward the end of shaking (about 30 s) is presented in Fig. 11. As it displays, the largest excess PWP was 49.4 kPa in the landside compared to the initial effective stress of 50.4 kPa, which indicates the liquefaction status had been achieved in the soil.
Fig. 8. Deformed shape and residual displacements of the numerical model (a) horizontal residual deformation (b) vertical residual deformation.
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Fig. 9. Stress-strain loops of soil at various depths along lines E and F.
was not available for the whole duration of the shaking for some of the records such as at the depth of 0.55 m in Fig. 12. Overall, it seems the simulation results of the piles responses were in less agreement with the experimental data compared to the soil response. This discrepancy can be attributed to several factors such as the three-dimensional nature of the experiment and disconnection of the pile bottom connection during the experiment.
4.3. Response of piles Bending strains along the piles were recorded during the experiment by several pairs of strain gauges attached to the piles in the direction of liquefied soil lateral flow [2]. The bending strains of the piles recorded during the shake table experiment were then converted into bending moment using Eq. (1) assuming elastic linear behavior for the piles.
M =EIε / y
4.4. Response of sheet-pile quay wall
(1)
The measured bending strain data along the sheet-pile quay wall were translated into bending moment using Eq. (1) and the results are presented in Fig. 13. As shown in Fig. 13, the bending moment time histories of the sheet pile produced by the numerical modeling and experiment were in reasonable agreement except at deeper depths. Large negative bending moments were predicted to develop at the depth of 2.5 m throughout the shaking for the sheet-pile by the OpenSees model, whereas the experimental data did not present the same phenomenon. This could be due to the fact that the sheet-pile was free at both ends in the experiment, whereas it was tied to the adjacent soil nodes horizontally and vertically in the FE model. Fig. 14 shows the bending moment profile of the sheet-pile for both numerical and experimental models. It can be found that the magnitude of the bending moments was not properly captured by the numerical model at the deeper depths.
in which
M Bending moment (KN∙m) E Modulus of elasticity of sheet pile or piles (KN/m2) I Area moment of inertia of sheet pile or piles (m4) ε Bending strain y Radius of pile or distance between the neutral axis and the centroid for the sheet pile (m) The computed and measured time histories of bending moments in the piles (pile A at front row and pile B at rear row in Fig. 3) are compared in Fig. 12. The bending moment time histories appeared to be comparable in magnitude and phasing up to a depth of 2.5 m, whereas comparison at the depth of 3.9 m were not satisfactory. The reason behind inconsistency between measured and predicted bending moments at deeper depths is contributed to the sudden breakage of the bottom connection of the front row piles in the experiment, while the hinge connection in the FE model was sustained throughout the analysis. Please note due to the disconnection of some strain gauge cables during the experiment as a result of large deformations, the data
4.5. Investigation of failure modes of piles In order to investigate the failure mechanism of the pile foundation 578
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Fig. 10. Excess pore water pressure time history response of soil.
predicted that the front row pile (pile A) received 92% higher shear forces and thus more vulnerable to shear failure than the rear row pile (pile B) at the estimated time (about 10.2 s) when the breakage occurred in the shake table experiment. In addition, there could be some other unknown factors contributing to the occurrence of the breakage such as fabrication deficit or installation issues, which makes this phenomenon difficult to be simulated in the FE model. Fig. 11. Contour plot of excess PWP on deformed shape at 30 s of the shaking.
5. Evaluation of a mitigation measure
exhibited in the shake table experiment, we evaluated the shear forces imposed to the piles by the lateral flow of the liquefied soil. In the shake table experiment, all piles were observed to yield at the heads as shown in Fig. 15. Based on linear elastic assumption, Motamed et al. [2] back-calculated the experimental shear force from the bending moment along the piles up to 6.2 s before the plastic deformation was initiated. In addition, Motamed et al. [2] identified the yielding moment of piles was 8.74 kN∙m considering the axial load in each pile (i.e. 36 kN), from which the yielding shear force at pile heads can be determined as 2.19 kN. The numerical and experimental monotonic shear forces at the heads of the front and rear row piles are compared in Fig. 16. As can be seen, the predicted shear forces at the heads of piles A and B were higher than the threshold value indicating the onset of plastic deformation and in good agreement with those of piles A3 and B3 in the experiment, respectively, at 6.2 s. This could possibly explain the exhibition of the yielding failure at pile heads in the shake table experiment. Regarding the unexpected disconnection at the base of the front row piles in the shake table experiment, this breakage was not meant to occur by the original design. As illustrated in Fig. 17, the FE model
In the previous sections, the response of a soil-pile-quay wall system when subjected to liquefaction-induced lateral spreading was investigated through FE modeling and the results were compared to a large-scale shake table experiment. Since the lateral flow of liquefied soil applied significant lateral forces on the piles and the quay wall, in this section the effects of a mitigation measure to reduce the seismic demands in the piles and the quay wall is explored. The selection of the mitigation method was based on a series of small-scale 1 g shake table experiments performed by the second author [19] in which the approach was to limit the soil displacements behind the quay-wall. This mitigation philosophy provided promising results in the smallscale experiments and is investigated in this study using numerical modeling. As a mitigation strategy, this paper investigates the installation of a sheet-pile with a fixed-end base connection in between the quay wall and the pile group to decrease the demand on different components using FE modeling. This remedial measure can be used as a retrofitting technique for the existing pile foundations near the waterfront structures with minimum disruption to the performance of these elements. The dynamic FE model discussed in the preceding sections 579
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Fig. 12. Bending moment time histories of piles.
5.1.1. Reduction in soil displacement Fig. 19 presents time histories of surface ground displacement behind the quay wall as well as in front of the pile group, corresponding to points P2 and P1 in Fig. 18, which illustrates the efficiency of the proposed countermeasure especially toward the end of shaking. Furthermore, reduction factors were calculated for the maximum soil displacement at these locations and the results are compared with the experimental findings [19] as exhibited in Fig. 20. The comparison illustrates that the mitigation strategy simulated by the FE model moderately reduced the liquefied soil displacement at P1 by 38%, which agreed well with the experimental displacement reduction of 31% at P1 [19]. However, the FE model only predicted a relatively small reduction of the liquefaction-induced lateral soil deformation at P2 (RF=39%) compared to the noticeable improvement (RF=70%) at P2 observed in the small-scale shake table experiment [19] employing the same countermeasure. The observed inconsistency in the extent of reductions in soil displacements between numerical model and shake table experiment seems to be attributed to the differences in scale (i.e. size), even though both approaches indicated overall improvements in reducing the soil deformations.
was further modified to incorporate a mitigating sheet-pile right in between the quay wall and the pile group as shown in Fig. 18. The mitigating sheet pile was vertically placed and extended upright from the bottom of the container to the ground surface. In addition, all other features and configurations of the OpenSees model remained identical to the previous model without any countermeasure. The mitigating sheet pile was fixed at the base and acted as a cantilever beam. Besides, the interface connections between the mitigating sheet-pile and the adjacent soil nodes were employed in the same way as the quay wall. Regarding the mitigating sheet pile properties, a parametric study was carried out to examine the remedial effects of mitigation sheet piles with different flexural stiffness (EI). As a benchmark case, the typeof the mitigating sheet-pile was picked to be the same as the quay wall. And four more commonly used types of sheet pile in Japan [34], as presented in Table 4, were selected and investigated. 5.1. Benchmark case In this section, only the benchmark mitigation case is discussed. And the efficiency of the proposed countermeasure on several parameters such as lateral soil displacements, pile cap displacement, and displacement and tilting of the quay wall are evaluated and compared with the available experimental results [19]. For comparison, a parameter called Reduction Factor (RF) is introduced to quantitatively describe the effectiveness of the remedial technique (Eq. (2)).
⎛ parameterwithmitigation ⎞ RFparameter =⎜1 − ⎟ ×100 paramterwithoutmitigation ⎠ ⎝
5.1.2. Reduction in pile cap displacement Fig. 21(a) presents the reduction factor values for both maximum and residual pile cap displacements of the OpenSees model and the shake table experiment [19] which demonstrates the extent of reduction in both models. As can be seen, the experiment demonstrated the fixed-end mitigating sheet pile could significantly alleviate the pile cap displacements (RF=60% for maximum value and RF=65% for residual
(2) 580
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Fig. 15. Photo of yielding at pile heads .
Fig. 13. Bending moment time histories of sheet pile.
Fig. 16. Comparison of monotonic components of shear force at pile heads .
Fig. 17. Time histories of predicted monotonic shear force at pile bases .
5.1.3. Reduction in quay wall movement Two parameters characterizing the movement of the quay wall, i.e. tilting and displacement, are introduced in this section. The tilting of the quay wall was defined as the rotation of the bottom of the quay wall. On other hand, the lateral movement of the top of the quay wall was denoted as the displacement of the quay wall.
Fig. 14. Bending moment profile of sheet pile.
value). On the other hand, the numerical model displayed a fairly comparable improvement in pile cap displacement reduction (RF=40% and 42%).
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Fig. 18. FE model discretization with mitigation sheet pile. Table 4 Properties of mitigation sheet piles [34]. Sheet Pile Type
Thickness (mm)
E (kPa)
I (m4)
A (m2)
LSP-2 (Benchmark) LSP-1 LSP-2* LSP-3B LSP-3D
5 4 4 5 6
2.06E+08
4.28E−06 2.56E−06 3.40E−06 2.54E−05 9.92E−05
3.02E−02 2.12E−02 2.41E−02 3.30E−02 3.56E−02
Note: the LSP-2* type has a different thickness of 4 mm from the benchmark LSP-2 type with the thickness of 5 mm.
Fig. 21. Comparison between reduction factors for the numerical (benchmark case) and experimental models with mitigation measure in terms of (a) pile cap displacement (b) quay wall residual movements (horizontal displacement and tilting).
Fig. 21(b) compares the reduction factors for the quay wall movement computed from the numerical and the experimental results [19]. It is shown that the OpenSees model was able to pretty well reproduce the moderate remedial impact of the fixed-end sheet pile on reducing the quay wall displacement (RF=42% in the numerical model against RF=36% in the physical model) and the quay wall tilting (RF=38% in the numerical model against RF=42% in the physical model). Fig. 19. Comparison between surface ground displacements behind quay wall w/o and w mitigation measure (benchmark case).
5.2. Parametric study This section focuses on the parametric study of the mitigating sheet pile. Fig. 22 illustrates time histories of lateral surface soil displacement of different mitigation cases at point P2 in Fig. 18. With the inclusion of the mitigation sheet pile, the ground lateral spreading can
Fig. 20. Comparison between reduction factors for the numerical (benchmark case) and experimental models with mitigation measure in terms of lateral soil displacement. Fig. 22. Comparison between surface ground displacements behind quay wall of different mitigation cases.
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Sports, Science, and Technology (MEXT). These supports are greatly appreciated. The authors also acknowledge the constructive comments provided by two anonymous reviewers which improved this paper. References [1] Tokimatsu K, Suzuki H, Tabata K, Sato M. Three-dimensional shaking table tests on soil-pile structure models using E-Defense facility. In: Proceedings of the 4th International Conference on Earthquake Geotechnical Engineering. Paper No. 1529; 2007. [2] Motamed R, Towhata I, Honda T, Yasuda S, Tabata K, Nakazawa H. Behavior of pile group behind a sheet pile quay wall subjected to liquefaction-induced large ground deformation observed in shaking test in E-Defense project. Soils Found 2009;49(3):459–75. [3] Suzuki H, Tokimatsu K. Effects of soil-structure interaction on stress distribution within a pile group under multi-dimensional loading. In: Proceedings of the 5th International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. Paper No.5.50a; 2010. [4] Motamed R, Towhata I. Shaking table model tests on pile groups behind quay walls subjected to lateral spreading. J Geotech Geoenviron Eng ASCE 2010;136(3):477–89. [5] Motamed R, Towhata I, Honda T, Tabata K, Abe A. Pile group response to liquefaction-induced lateral spreading: e-defense large shake table test. Soil Dyn Earthq Eng 2013;51:35–46. [6] Boulanger RW, Curras CJ, Kutter BL, Wilson DW. Seismic soil-pile-structure interaction experiments and analyses. J Geotech Geoenviron Eng ASCE 1999;125:750–9. [7] Abdoun T, Dobry R. Evaluation of pile foundation response to lateral spreading. Soil Dyn Earthq Eng 2002;22(9):1051–8. [8] Boulanger RW, Kutter BL, Brandenberg SJ, Singh P, Chang D. Pile Foundations in Liquefied and Laterally Spreading Ground During Earthquakes: Centrifuge Experiments & Analyses [PEER report No. UCD/CGM-03/01]Pacific Earthquake Engineering Research Center. Berkeley: University of California; 2003. [9] Brandenberg SJ. Behavior of pile foundations in laterally spreading ground [Ph.D. Thesis]. Davis: University of California; 2005. [10] Mohammed AMY, Okhovat MR, Maekawa K. Numerical investigation on damage evolution of piles inside liquefied soil foundation: dynamic loading experiments. Int J World Acad Sci, Eng Technol 2012;71:1796–803. [11] Chang D, Boulanger RW, Brandenberg SJ, Kutter BL. FEM analysis of dynamic soil-pile-structure interaction in liquefied and laterally spreading ground. Earthq Spectra 2013;29(3):733–55. [12] Cubrinovski M, Uzuoka R, Sugita H, Tokimatsu K, Sato M, Ishihara K, Tsukamoto Y, Kamata T. Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: shaking in the direction of ground flow. Soil Dyn Earthq Eng 2008;28(6):421–35. [13] Uzuoka R, Cubrinovski M, Sugita H, Sato M, Tokimatsu K, Sento N, Kazama M, Zhang F, Yashima A, Oka F. Prediction of pile response to lateral spreading by 3-D soil–water coupled dynamic analysis: shaking in the direction perpendicular to ground flow. Soil Dyn Earthq Eng 2008;28(6):436–52. [14] Zhou YH, Tokimatsu K, Suzuki H, Yoshida H, Nukui Y. Numerical study of threedimensional nonlinear behavior of soil-pile-structure system under strong input motion. In: Proceedings of the 15th World Conference on Earthquake Engineering, 24-28 September 2012, Lisbon, Portugal. 12362-12370; 2012. [15] Mazzoni S, McKenna F, Scott MH, Fenves GL. Open System for Earthquake Engineering Simulation user Manual. Berkeley: University of California; 2009 〈http://opensees.berkeley.edu〉. [16] Elgamal A, Yang Z, Parra E. Computational modeling of cyclic mobility and postliquefaction site response. Soil Dyn Earthq Eng 2002;22(4):259–71. [17] Yang ZH, Elgamal A, Parra E. Computational model for cyclic mobility and associated shear deformation. J Geotech Geoenviron Eng 2003;129(12):1119–27. [18] Yang ZH, Lu JC, Elgamal A. OpenSees soil models and solid-fluid fully coupled elements: user's manual [available at]. San Diego: Department of Structural Engineering, University of California; 2008, [available at] 〈http://cyclic.ucsd.edu〉. [19] Motamed R, Towhata I. Mitigation measures for pile groups behind quay walls subjected to lateral flow of liquefied soil: shake table model tests. Soil Dyn Earthq Eng 2010;30(2010):1043–60. [20] MEXT and NIED. Research Theme No.2, Annual Report of the Fiscal Year 2005, Special Project for Earthquake Disaster Mitigation in Urban Areas, Ministry of Education and Culture Sports Science and Technology and National Research Institute for Earth Science and Disaster Prevention (in Japanese); 2006. [21] Kazama M, Ryosuke U, Noriaki S, Kabasawa Y, Kamiya K, Oka F, Yashima A, Zhang F. Three-dimensional numerical prediction and analysis of the foundation experiment (lateral flow analysis, part I). 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Fig. 23. Maximum soil lateral displacements at P1 and P2 of different mitigation cases.
be diminished. Specifically, when LSP-3D type sheet pile was adopted, the lateral soil displacement was remarkably reduced compared to the scenario without mitigation measure. Also it is observed that the horizontal ground deformation varies significantly with the choice of mitigation sheet pile. In addition, Fig. 23 exhibits maximum soil lateral displacement at points P1 and P2 in Fig. 18 of different mitigation cases. Overall, the increase of EI makes mitigation sheet pile more effective in reducing the lateral soil deformation in both points. 6. Conclusions This study evaluates the accuracy and effectiveness of using existing constitutive models in the OpenSees framework to reproduce the response characteristics of liquefaction-induced lateral spreading of pile foundations based on the results of a large-scale shake table experiment. Considering the involved complications, it can be said that an overall agreement was reached concerning the dynamic response of the soil. However, the 2D FE model was unable to accurately predict the seismic demands on the piles and the sheet-pile, though the overall behavior was effectively captured. Because of the limitations and uncertainties involved in the numerical model, considerable differences were observed between the predicted and measured response of the piles and the quay wall. There are a number of possible reasons for this inconsistency including, but not limited to, the unexpected disconnection of the front row piles in the experiment and induced overturning of the pile cap, the uncertainty in the soil constitutive model parameters used in the FE model, differences between the 3D physical model and the 2D approximation, and the complexity of soil-structure interaction problems. Finally, the efficiency of a mitigation measure which included the installation of a fixed-end sheet-pile in between the pile group and the quay wall on the response of soil-pile-quay wall system was assessed and the results were compared with the small-scale shake table test results deploying the same countermeasure. And a parametric study on flexural stiffness of mitigating sheet pile was performed. In conclusion, it is demonstrated that the 2D OpenSees model was able to qualitatively capture the reduction effects of the proposed remedial strategy, which demonstrates the robustness of the OpenSees modeling. Acknowledgement The large-scale experiment described in this paper was carried out at the National Research Institute for Earth Science and Disaster Prevention (NIED), Hyogo Earthquake Engineering Research Center and was sponsored by the Japan Ministry of Education, Culture, 583
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Petroleum Institute; 1993. [31] Chang D. Inertial and lateral spreading demands on soil-pile-structure systems in liquefied and laterally spreading ground during earthquakes [Ph.D Thesis] Department of Civil Engineering. Davis: University of California; 2007. [32] McGann C, Arduino P. Dynamic 2D effective stress analysis of slope. OpenSees wiki example, website: 〈http://opensees.berkeley.edu/wiki/index.php/Dynamic_2D_ Effective_Stress_Analysis_of_Slope〉; 2011. [33] Li GJ, Motamed R. Numerical modeling of pile group response subjected to liquefaction-induced large ground deformations in E-Defense shake table test. 6th International Conference on Earthquake Geotechnical Engineering, 1-4 November 2015, Christchurch, New Zealand. Paper No.173; 2015. [34] Website: 〈http://www.ns-kenzai.co.jp/cmsdesigner/dlfile.php?Entryname=dl_ doboku & entryid=00002 & fileid=00000041 & ./C044.pdf〉
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