J. Cent. South Univ. (2016) 23: 906−918 DOI: 10.1007/s11771-016-3138-5

Numerical analysis on seismic behavior of railway earth embankment: A case study

LIN Yu-liang(林宇亮)1, SHI Feng(石峰)1, YANG Xiao(杨啸)1, 2, YANG Guo-lin(杨果林)1, LI Li-min(李丽民)3

1. School of Civil Engineering, Central South University, Changsha 410075, China; 2. Department of Civil Engineering, Monash University, Melbourne 3800, Australia;

3. School of Civil and Environmental Engineering, Hunan University of Science and Engineering, Yongzhou 425199, China

© Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: A numerical case study on the seismic behavior of embankment was carried out based on a prototype of earth embankment in Yun−Gui Railway (from Kunming City to Nanning City) in southwest of China. A full-scale model of earth embankment was established by means of numerical simulation with FLAC3D code. The numerical results were verified by shaking table test. The seismic behaviors of earth embankment were studied, including the horizontal acceleration response, the vertical acceleration response, the dynamic displacement response, and the block state of earth embankment. Results show that the acceleration magnification near the embankment slope is larger than that in internal earth embankment body. With the increase of input peak acceleration, the horizontal acceleration magnification presents a decreasing trend. The horizontal acceleration response at the top of embankment is more sensitive to the intensity of ground motion than that at the bottom of embankment. The embankment presents an obvious nonlinear-plastic characteristic when the input horizontal peak acceleration is larger than 0.3 g. The maximum residual deformation occurs in the middle of embankment slope surface instead of at the top of embankment. The upper part of embankment experiences tension failure without shear failure, and area at the bottom of embankment around the symmetry-axis of embankment mainly presents shear failure under the earthquake loading. The tension failure and shear failure repeatedly occur along the slope surface of earth embankment. Key words: earth embankment; numerical analysis; seismic behavior; earthquake 1 Introduction

In recent years, large earthquake frequently struck many areas all over the world, which triggered a large number of earth embankment or slope failures. In 2004, the Mid Niigata Prefecture earthquake (Mw 6.5) in Japan induced more than 1000 landslides, which widely distributed on steep slopes [1]. After three years in 2007, Niigata Chuetsu-Oki earthquake (Mw 6.6) struck the city of Kashiwazaki in southern Niigata Prefecture in Japan again, and triggered hundreds of landslides [2]. In 2008, a large earthquake (Mw 7.9 or Ms 8.0) occurred in Sichuan Province, China, which was named as Wenchuan Earthquake. The Wenchuan Earthquake induced more than 60000 landslides, which subsequently resulted in about 20000 casualties [3−8]. In Yushu, China earthquake (Mw 6.9) of April 14, 2010, at least 2036 co-seismic landslides with a total coverage area of 1.194 km2 were mapped by XU and XU [9]. The traditional seismic design method, which takes the

pseudo-static method for seismic stability assessment of earth embankment or slope [10−12], needs to be verified or improved to create a safe seismic design of earth embankment or slope.

The test method related to the seismic behavior of earth embankment or slope mainly includes shaking table test [13−16] and dynamic centrifuge test [17−20], by which it is possible to reveal the seismic behavior of earth embankment or slope in laboratory. However, including the huge cost of the tests, there are still some shortcomings both for shaking table test and dynamic centrifuge test. In shaking table test, the test model is commonly established with a reduced-scale in geotechnical engineering while the 1g gravity field can not be changed. Consequently, the similar law cannot be well met in shaking table test. The dynamic centrifuge system can simulate the gravity field as expected, but the size of the test model is still limited due to the carrying capacity of dynamic centrifuge.

The numerical analysis provides an economical way to study the seismic behavior of earth embankment or

Foundation item: Project(51308551) supported by the National Natural Science Foundation of China; Project(2012M511760) supported by the China

Postdoctoral Science Foundation; Project(13JJ4017) supported by the Hunan Provincial Natural Science Foundation of China Received date: 2015−02−09; Accepted date: 2015−06−05 Corresponding author: LIN Yu-liang, PhD, Associate Professor; Tel: +86−13508477813; E-mail: linyuliang11@163.com

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slope effectively with the rapid development of computer technology. The full-scale analysis model can be established, and the imposed load can be changed or repeated as expected in numerical analysis. Consequently, the numerical analysis method is widely taken for extensive analysis in geotechnical engineering [21−26]. HUANG et al [27] presented a numerical analysis on the seismic behavior of an earth embankment on liquefiable foundation soils, and the results showed that the numerical model captured the fundamental liquefaction aspects of embankment foundation system reasonable well. EVANGELISTA et al [28] studied the behavior of a cantilever retaining wall by means of numerical analysis with FLAC2D code to validate the stress plasticity solution for evaluating the gravitational and dynamic active earth pressure. PITILAKIS et al [29] studied the soil-structure interaction phenomena with a foundation- structure system by numerical analysis and shaking table test. In PITILAKIS’ research, the numerical simulation captured many important aspects of soil-structure interaction that are apparent in the shaking table test, and the numerical model was shown to be adequate for practical engineering design purpose.

In this work, based on a prototype of an earth embankment in Yun−Gui Railway (from Kunming City to Nanning City) in southwest of China, a full-scale model of earth embankment was established by means of numerical simulation with FLAC3D code to study the seismic behavior of embankment under earthquake loading. The Wenchuan excitations with different intensities were performed in numerical analysis. The numerical results were verified by shaking table test. The seismic behaviors of earth embankment, including the horizontal and the vertical acceleration responses, the dynamic displacement response, and the block state of earth embankment during the earthquake loading, were studied effectively. The aim of this work is to provide more details about the seismic behavior of earth

embankment under the earthquake loading, and to create a safe seismic design for Yun−Gui Railway. 2 Numerical model 2.1 Model of embankment

The Yun−Gui Railway is now under construction in southwest of China. The total length of the railway is about 710 km. The Yun−Gui Railway goes across the mountain areas with the seismic intensity of above 8 degree. The railway embankment with average height of 9 m is widely under construction in many areas of the railway line. A photograph about the construction of embankment in Yun−Gui Railway is shown in Fig. 1. Consequently, the seismic behavior of high embankment under strong seismic excitation becomes an important aspect for creating a safe seismic design.

Fig. 1 A photograph about construction of earth embankment in Yun−Gui Railway

Based on a prototype of embankment with a rock foundation below in Yun−Gui Railway, a full-scale numerical model of embankment was established, as shown in Fig. 2. The total height of earth embankment body is 9 m. A block with the height of 6 m is established to simulate the rock foundation at the bottom of earth embankment. Three surfaces are taken from the profile

Fig. 2 Embankment model in numerical study

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of embankment for typical study, which are named as surfaces A, B, and C respectively. The typical points in these three surfaces are marked as A1−A6, B1−B6, and C1−C6, respectively, as shown in Fig. 2. 2.2 Input ground motion and excitation events

The structure will be more vulnerable to near-field ground motion [30−33]. In this work, the Wenchuan ground motion, which was recorded at the nearest station in Wenchuan Earthquake in 2008, is selected for numerical study. The acceleration time history of original recorded Wenchuan ground motion as well as its Fourier spectrum is shown in Fig. 3. It is seen that the original Wenchuan ground motion lasts 150 s with two intensive impulsions. In numerical study, the dynamic analysis requires a large amount of computer storage space, and the computation time is very long while inputting a long-time pulse. To simplify the numerical analysis, the first 50 s of original Wenchuan ground motion, which covers two intensive impulsions, is taken as input seismic excitation. With this treatment, the spectrum characteristic of Wenchuan ground motion is not changed, as shown in Fig. 4.

Generally, the frequency components of the recorded ground motion are very complex. The

Fig. 3 Time history (a) and Fourier spectrum (b) of original recorded Wenchuan ground motion

Fig. 4 Time history (a) and Fourier spectrum (b) of Wenchuan ground motion in numerical analysis propagation of seismic wave will be affected by the frequency characteristic of the input ground motion as well as the dynamic characteristic of the structure. When the high frequency of input ground motion increases, the grid size of the numerical model should be small enough to satisfy the requirement of wave propagation, which subsequently increases the calculating time significantly in dynamic numerical analysis. Consequently, to make the dynamic numerical analysis successful, the high frequency components of the original ground motion should be filtered out. Meanwhile, a range of frequency components corresponding to the majority of wave energy should be retained to avoid the distortion of original ground motion. In this study, the high frequency component of Wenchuan ground motion, which is larger than 15 Hz, is filtered out because the frequency band of Wenchuan ground motion mainly concentrates at 0−15 Hz, as shown in Fig. 4(b).

Figure 5 shows the adjustment of the baseline of Wenchuan ground motion. The original time histories of velocity and displacement can be determined by making integral on the acceleration time history of Wenchuan ground motion, as shown in Figs. 5 (a), (c) and (e). However, it is seen that the final velocity and final

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Fig. 5 Baseline adjustment of displacement of original Wenchuan ground motion (a, c, e) and adjusted Wenchuan ground motion (b, d, f): (a, b) Acceleration; (c, d) Velocity; (e, f) Displacement displacement, especially for the final displacement, deviate from the baseline at the end of time history curve. To avoid such deviation, the original acceleration time history of Wenchuan ground motion can be adjusted by adding a low frequency waveform in polynomial or periodic forms. The adjusted time histories of acceleration, velocity and displacement of Wenchuan ground motion are shown in Figs. 5 (b), (d) and (f), respectively. Subsequently, the residual deformation of embankment induced by earthquake loading can be determined by the offset of the last point of displacement response curve.

The seismic excitations were performed in bi- direction in numerical study. According to the definition

of seismic fortification in “Code for Seismic Design of Railway Engineering” (GB 50111—2006) in China, the peak values of input horizontal acceleration (i.e. x direction) are adjusted to 0.1g, 0.2g, 0.3g, 0.4g, 0.6g, 0.8g, and 1.0g, respectively. The intensity of vertical excitation (i.e. z direction) is adjusted to 2/3 of that of horizontal excitation for each excitation event. The excitation events are code-named as WC1−WC7, as listed in Table 1. 2.3 Model grid size and model parameters

The embankment model grid in small size will greatly prolong the computing time in dynamic numerical analysis. On the other hand, according to the

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Table 1 Excitation events in numerical analysis

Serial number

Code name of excitation

events

Peak acceleration/g Remark

x direction z direction

1 WC1 0.1 0.067 Seismic fortification of 7°

2 WC2 0.2 0.133 Seismic fortification of 8º

3 WC3 0.3 0.200 Seismic fortification of 8º

4 WC4 0.4 0.267 Seismic fortification of 9º

5 WC5 0.6 0.400 Seismic

fortification above 9º

6 WC6 0.8 0.533 Seismic

fortification above 9º

7 WC7 1.0 0.667 Seismic

fortification above 9º

research of KUHLEMEYER and LYSMER [34], the grid size of the model should be less than 1/8−1/10 of the wavelength of input ground motion to present an accurate seismic wave propagation characteristic, which can be expressed as

∆l ≤ (1/8−1/10)λ (1) where ∆l refers to the grid size of the model; λ refers to the wavelength of the input ground motion corresponding to the maximum frequency. It is seen that the size of model grid is determined by the high frequency component of input ground motion as well as the stiffness of the structure. It is previously mentioned that the high frequency component of Wenchuan ground motion larger than 15 Hz is filtered out. Besides, the values of the shear wave velocity of embankment filler and rock foundation are 150 m/s and 400 m/s, respectively, according to the data of engineering geology in Yun−Gui Railway. Consequently, it is determined by Eq. (1) that the permitted maximum model grid sizes of embankment body and rock

foundation are 1.00−1.25 m and 2.67−3.34 m, respectively. In numerical model, the maximum grid sizes of embankment body and rock foundation are 0.375 m and 1.5 m, respectively, which are smaller than permitted maximum model grid sizes, as listed in Table 2. The embankment filler is simulated by Mohr-Coulomb model, and the rock foundation is simulated by elastic model in dynamic numerical analysis. Based on the information of embankment prototype in Yun−Gui Railway, the values of embankment model parameters in numerical analysis are presented in Table 3. The deformation at the interface between the embankment body and the rock foundation is neglected, and the interface-element is not attached in numerical analysis model. 2.4 Dynamic boundary condition and damping setting

The seismic wave propagation in embankment body is influenced by the wave reflection at the boundary of embankment model in dynamic numerical analysis. To obtain accurate results in numerical analysis, the numerical model should be established as large as possible, which will subsequently result in an enormous computational burden. In this work, the free field method is taken to avoid the wave reflection at the boundary of embankment model. The free field boundary conditions are created by generating one-dimensional or two- dimensional grids along the boundary of embankment model. The main grids at the boundary of embankment model couple with the free field grids by damper, and the unbalanced forces of free field grids are applied to the main grids. The free field provides a boundary effect like an infinite field, and the surface wave does not distort or reflect at the boundary of embankment model. The free field method is now widely taken in numerical analysis by many scholars for its effectiveness [35−36].

The structure damping mainly derives from the internal friction or the energy consumption on possible sliding surface. The rayleigh damping, the local damping, and the hysteretic damping are widely used to describe

Table 2 Permitted maximum grid size in embankment model in dynamic analysis

Item Maximum

frequency of input ground motion/Hz

Velocity of shear wave/(m·s−1)

Wavelength corresponding to the

maximum frequency/m

Permitted maximum model grid size/m

Maximum model grid size in numerical

analysis/m Embankment body 15 150 10.0 1.00−1.25 0.375

Rock foundation 15 400 26.7 2.67−3.34 1.5

Table 3 Values of embankment model parameters in numerical analysis

Item Element type Constitutive model Density/ (kg·m−3)

Elastic modulus/MPa

Poisson ratio

Cohesion, c/kPa

Internal friction angle, φ/(º)

Rock foundation Brick Elastic model 2500 28080 0.20 — —

Embankment body Brick Mohr-Coulomb model 1900 48 0.39 24.5 27.2

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the damping characteristics of structure in dynamic numerical analysis [37]. In this work, the local damping is adopted to describe the damping characteristic of embankment because the local damping coefficient is independent of the natural frequency of embankment. Meanwhile, the time step of dynamic calculation will not be shorten when the local damping is used. The local damping coefficient is determined as αL=πD (2) where αL refers to the local damping coefficient; D refers to the critical damping ratio. The critical damping ratio of embankment is set to 5% in this work based on the specification in “Code for Seismic Design of Railway Engineering” (GB 50111—2006) in China. 3 Verification of numerical results

The shaking table test on embankment slope was previously carried out in China Merchants Chongqing Communications Research and Design Institute Co. Ltd.. The dimension of embankment shaking model was 2.0 m in height, 3.6 m in length and 1.5 m in width. A rock foundation with the height of 0.4 m was set at the bottom of model. The total height of embankment shaking model was about 1.5 m with a compaction degree of 95%. The Wenchuan excitations were mainly performed in shaking table test in both horizontal and vertical directions. The peak values of input horizontal acceleration (Axmax) were adjusted to 0.1g, 0.2g, 0.4g and 0.6g. The peak value of input vertical acceleration was about 2/3 of that of horizontal acceleration for each case. More details about the shaking table test were described by LIN and YANG [38].

Corresponding to the shaking table test, a full- scaled model of embankment slope was established in numerical analysis with the same seismic excitations. In seismic analysis, acceleration magnification is widely used to study the seismic behavior of embankment or slope. The acceleration magnification is defined as the ratio of the peak acceleration in embankment body to the peak value of the acceleration on foundation. Consequently, the results of acceleration magnification, which are obtained by shaking table test and numerical study, are compared, as listed in Tables 4 and 5, in which the relative height refers to the ratio of the height of test point to the total height of embankment body. It is seen that the values of horizontal acceleration magnification determined by numerical study coincide well with those investigated in shaking table test. The results of vertical acceleration magnification determined by these two methods differ a little for several points due to the uncertainty of shaking table test. However, the numerical results capture the general regulation of vertical acceleration magnification that is apparent in shaking table test. The proposed numerical method is an effective way to study the seismic behavior of embankment under earthquake loading. 4 Numerical results and analysis

The embankment reaches the force balance under self-weight before applying the seismic excitation. In this study, the residual velocity and displacement of embankment caused by self-weigh are removed to analyze only the dynamic response of embankment induced by seismic excitation.

Table 4 Results of horizontal acceleration magnification determined by numerical study and shaking table test

Relative height of test point

Axmax=0.1g Axmax=0.2g Axmax=0.4g Axmax=0.6g

Test value Numerical value Test value Numerical

value Test value Numerical value Test value Numerical

value 0.13 1.212 1.515 1.043 1.663 1.013 1.379 0.958 1.192

0.47 1.818 1.836 1.614 1.816 1.370 1.756 1.332 1.565

0.80 2.414 2.619 2.305 2.525 2.069 2.302 1.531 2.114

1.00 2.889 3.157 2.767 2.904 2.481 2.478 2.450 2.488

Table 5 Results of vertical acceleration magnification determined by numerical study and shaking table test

Relative height of test point

Axmax=0.1g Axmax=0.2g Axmax=0.4g Axmax=0.6g

Test value Numerical value Test value Numerical

value Test value Numerical value Test value Numerical

value 0.13 1.614 1.469 1.669 1.168 1.615 1.320 1.665 1.257

0.47 1.514 1.691 1.715 1.366 1.926 1.694 2.230 1.479

0.80 1.757 2.580 2.115 2.073 2.807 2.167 3.008 1.821

1.00 1.957 3.778 2.085 3.194 3.507 3.392 4.400 3.917

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4.1 Horizontal acceleration response

The typical study on the time history of horizontal acceleration response is performed by selecting several points in embankment body under WC4 (Axmax=0.4g) excitation event, as shown in Fig. 6. Points A2 and A5 are both in slope surface (i.e. Surface A) of embankment, and the heights of them are 1 m and 7 m, respectively. The points A5, B5 and C5 are in the same height of 7 m in embankment profile, as shown in Fig. 2. It is seen that the time histories of horizontal acceleration response present a similar basic shape, but the amplitude of horizontal acceleration response differs greatly for different points. The peak value of horizontal acceleration response of Point A2 is 0.559g, and it is 0.956g for point A5. It is seen that the input acceleration is greatly amplified when the seismic waves transmits upwards through the embankment. The peak horizontal accelerations of points A5, B5, and C5 are 0.956g, 0.874g and 0.816g, respectively, with a ratio of 1.17:1.07:1, which shows a decreasing trend. The points near the embankment slope tend to be more active than the points in internal embankment body under earthquake loading because the areas near the embankment slope surface subject to less constraint. The similar results were also observed in shaking table test [15] and dynamic centrifuge test [19−20].

Figure 7 compares the distributions of horizontal acceleration magnification in embankment slope surface

(i.e. Surface A) and another two surfaces in internal embankment body (i.e. Surface B and Surface C) under WC4 (Axmax=0.4g) excitation event. Horizontal acceleration magnification increases nonlinearly along the height of embankment, and it reaches the maximum value at the top of embankment. The horizontal acceleration magnification is always larger than 1.0 under WC4 excitation event, which means that the ground motion is amplified when the seismic wave transmits through the embankment. The results of horizontal acceleration magnification are quite different from the specification in “Code for Seismic Design of Railway Engineering” (GB 50111—2006) in China, which ignore the magnified effect of acceleration when the height of retaining wall is less than 12 m. The value of horizontal acceleration magnification differs in different profile surfaces, which corresponds to the results of the time history of horizontal acceleration response for different points in Fig. 6. The acceleration magnification near the embankment slope surface is larger than that in internal embankment body. The ranges of horizontal acceleration magnification in surfaces A, B, and C are 1.30−3.10, 1.05−2.51, and 0.97−2.38, respectively. Consequently, the slope surface should be specially protected or restricted to improve the seismic stability of embankment.

Figure 8 shows the distributions of horizontal acce lerat ion magnificat ion along the he ight o f

Fig. 6 Time histories of horizontal acceleration response for typical points in embankment: (a) Point A2; (b) Point A5; (c) Point B5; (d) Point C5

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Fig. 7 Horizontal acceleration magnification distributions in different slope surfaces

Fig. 8 Horizontal acceleration magnification distributions under different shaking events embankment under different shaking events. The horizontal acceleration magnification is greatly affected by the intensity of input ground motion. With the increase of input peak acceleration, the horizontal acceleration magnification shows a decreasing trend, and the shapes of the horizontal acceleration magnification distribution curves change. When the input horizontal peak acceleration is large than 0.8g (i.e. WC6 and WC7 excitation events), the horizontal acceleration magnification is even less than 1.0. With the increase of the intensity of input ground motion, the filler of embankment will be loosened. In this case, both the shear strain and damping ratio of embankment increase obviously, and subsequently induce a great filter effect on input seismic excitation. Consequently, the horizontal acceleration magnification decreases under strong seismic excitation. Nevertheless, such phenomenon is beneficial to the seismic stability of embankment or slope.

According to the research of LIN and YANG [38], logarithmic formula is used to describe the relationship between the acceleration magnification and the intensity of input ground motion, which is expressed as follows:

RHAM=alnAxmax+b (3) where RHAM refers to the horizontal acceleration magnification; Axmax refers to the peak value of input horizontal acceleration; both a and b are fitting parameters. The fitting results for different points are shown in Fig. 9. The values of fitting parameters with R2 (R refers to the correlation coefficient) are shown in Table 6. The values of R2 for all points are larger than 0.850, which means that the fitting results determined by logarithmic formula are reliable. The absolute value of fitting parameter a reflects the decreasing speed of the horizontal acceleration magnification with the increase of the intensity of ground motion. The absolute value of a for the area near the top of embankment is generally larger than that of the points near the bottom of embankment. For example, the absolute value of a for Point A5 is 0.986, and it decreases to 0.362 for Point A2. The zone at the top of embankment is more sensitive to the intensity of ground motion than the area at the bottom of embankment.

Fig. 9 Fitting results on relationship between acceleration magnification and horizontal peak acceleration by logarithmic formula for different points Table 6 Fitting results of relationship between horizontal acceleration magnification and input peak horizontal acceleration by logarithmic formula

Point a b R2 A2 −0.362 0.835 0.855 A3 −0.443 0.740 0.878

A4 −0.726 0.748 0.982

A5 −0.986 0.961 0.956

A6 −0.842 1.725 0.850

4.2 Vertical acceleration response

Vertical acceleration is another main factor, inducing embankment or slope failure [39]. Likewise, taking the case under WC4 (Axmax=0.4g) excitation event

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for typical study, the time histories of vertical acceleration response for several points (i.e. points A2, A5, B5, and C5) are presented in Fig. 10. Like horizontal acceleration response, the amplitude of vertical acceleration response differs for different points. The peak values of vertical acceleration response of Points A2 and A5 are 0.311g and 0.535g, respectively. The point at high elevation shows stronger vertical acceleration response. The amplitude of vertical acceleration response presents a decreasing trend from the area near the embankment slope surface to the zone in internal embankment body, and the decreasing trend is more obvious than that of horizontal acceleration response. For example, the peak values of vertical acceleration response for points A5, B5, and C5 are 0.535g, 0.453g and 0.394g with the ratio of 1.36:1.15:1, which is larger than the ratio of horizontal acceleration response (1.17:1.07:1).

The distributions of vertical acceleration magnification in surfaces A, B, and C of embankment are presented in Fig. 11. The vertical acceleration magnification increases along the height of embankment, and the increasing trend is more obvious at the top of embankment due to less vertical stress. Like horizontal acceleration magnification, the value of vertical acceleration magnification in slope surface is much larger than that in internal embankment body. The ranges of the vertical acceleration magnification in surfaces A, B,

and C are 1.41−3.71, 0.78−2.89, and 0.81−2.66, respectively, which presents a more obvious decreasing trend than horizontal acceleration magnification.

Figure 12 shows the distributions of vertical acceleration magnification under different excitation events. Figure 13 shows the change of the vertical acceleration magnification with the increase of input vertical peak acceleration. Unlike horizontal acceleration magnification, the distributions of vertical acceleration magnification does not change greatly under different excitation events, and the vertical acceleration magnification do not present obvious decreasing or increasing trend with the increase of input peak acceleration, neither. The vertical acceleration response is less sensitive to the intensity of ground motion than horizontal acceleration response. A linear-elastic system will perform a constant value of acceleration magnification regardless of the intensity of ground motion. Consequently, the nonlinear characteristic of acceleration response in vertical direction is not as obvious as that in horizontal direction. 4.3 Deformation behavior of embankment

The horizontal deformation response is typically studied on several points (i.e. points A2, A4, and A6) in slope surface of embankment under WC3 (Axmax=0.3g) excitation event, as shown in Fig. 14. The heights of points A2, A4, and A6 are 1 m, 5 m and 9 m, respectively,

Fig. 10 Time histories of vertical acceleration response for typical points in embankment: (a) Point A2; (b) Point A5; (c) Point B5; (d) Point C5

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Fig. 11 Vertical acceleration magnification distributions in different slope surfaces

Fig. 12 Distributions of vertical acceleration magnification under different excitation events

Fig. 13 Change of vertical acceleration magnification with increase of input vertical peak acceleration as shown in Fig. 2. Corresponding to the deformation time history of input Wenchuan excitation (see Fig. 5(f)), the deformation response of embankment presents two fluctuations. The first fluctuation occurs in the range of negative value, and the other one mainly occurs in positive range. The last point of deformation response curve deviates from the baseline of deformation time

Fig. 14 Time history of deformation response for several points under WC3 (Axmax=0.3g) excitation event history, which means that the residual deformation of embankment is induced by Wenchuan excitation. The residual deformation of Point A4 is larger than that of points A2, and A6, which coincides with the residual deformation contour of embankment, as shown in Fig. 15. The maximum residual deformation occurs in the middle of embankment slope surface instead of at the top of embankment. Besides, it is noted that residual deformation contour is asymmetric in the symmetric profile of embankment. The deformation characteristic of embankment under earthquake loading is much different from that under static load condition.

Fig. 15 Residual deformation contour of embankment under WC3 (Axmax=0.3g) excitation event (Unit: mm)

Figure 16 shows the time history of deformation response of Point A4 under different excitation events. Figure 17 shows the change of residual deformation of several points in embankment slope surface with the increase of input horizontal peak acceleration. When the input horizontal peak acceleration is less than 0.3g, the deformation response of embankment mainly presents an elastic characteristic, and the maximum residual deformation of embankment is about 41 mm. When the input horizontal peak acceleration is larger than 0.3g, the time history of deformation response fluctuates within the range of negative value. The embankment presents obvious nonlinear plastic characteristics and the residual deformation of embankment increases obviously. The increasing speed of residual deformation also increases with the increase of input horizontal peak acceleration. Besides, it is seen that residual deformation of the upper

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Fig. 16 Time history of deformation response of Point A4 under different excitation events part of embankment (both points A4 and A6) increases more quickly than that at the bottom of embankment (see Point A2) with the increase of input horizontal peak acceleration.

Fig. 17 Change of residual deformation of several points in slope surface with increase of input horizontal peak acceleration 4.4 Embankment state during excitation

Figure 18 shows the block state of earth embankment during the WC7 (Axmax=1.0g) excitation, in

Fig. 18 State of embankment body during WC7 (Axmax=1.0g) excitation: (a) t=5 s; (b) t=10 s; (c) t=15 s; (d) t=20 s; (e) t=35 s; (f) t=50 s

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which “None” means that there is neither tension failure nor shear failure in embankment block; “Shear” and “Tension” refer to shear failure and tension failure, respectively; “N” means that the failure is now on; “P” means that the failure occurred in the past time; t refers to the excitation time.

At the beginning of seismic excitation (t=5 s), the tension failure occurs at the top of embankment as well as along the slope surface, and no shear failure is observed in embankment body. When t=10 s, the embankment experiences the first intensive excitation. Except the upper part of embankment, the area along the slope surface, which has already experienced tension failure and shear failure, is now experiencing another tension failure and shear failure. At the bottom of embankment, the area around the symmetry-axis of embankment mainly presents shear failure without tension failure. When t=20 s, a large areas marked with “Shear-P, Tension-P” are observed from the bottom to the middle of embankment. Consequently, it is inferred that the tension failure and shear failure repeatedly occur along the slope surface during the seismic excitation. When t=35 s, the embankment experiences the second intensive excitation. The tension failure is occurring along the slope surface of earth embankment once again. Consequently, based on the above analysis, the general conclusions are drawn as follow:

1) The upper part of embankment presents tension failure without shear failure during the seismic excitation.

2) At the bottom of embankment, the area around the symmetry-axis of embankment mainly presents shear failure without tension failure.

3) Except the upper part of embankment, tension failure and shear failure repeatedly occur along the slope surface during the seismic excitation. 5 Conclusions

1) The ground motion is amplified when the seismic wave transmits through the embankment for most excitation events. The acceleration magnification near the embankment slope surface is larger than that in internal embankment body. The zone at the top of embankment is more sensitive to the intensity of ground motion than the area at the bottom of embankment. The horizontal acceleration magnification shows a decreasing trend with the increase of input peak acceleration. The vertical acceleration response is less sensitive to the intensity of ground motion than the horizontal acceleration response. The nonlinear characteristic of acceleration response in vertical direction is not as obvious as that in horizontal direction.

2) The maximum residual deformation occurs in the

middle of embankment slope surface instead of at the top of embankment. The embankment presents obvious nonlinear plastic characteristics and the residual deformation of embankment increases obviously when the input horizontal peak acceleration is larger than 0.3g. The residual deformation at the upper part of embankment increases more quickly than that at the bottom of embankment with the increase of input horizontal peak acceleration.

3) The upper part of embankment experiences tension failure without shear failure, and area at the bottom of embankment around the symmetry-axis of embankment mainly presents shear failure under the earthquake loading. Except the upper part of embankment, tension failure and shear failure repeatedly occur along the embankment slope surface. References [1] CHIGIRA M, YAGI H. Geological and geomorphological

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(Edited by YANG Hua)