Numerical earthquake response analysis of the Liyutan earth ......Z. Feng et al.: Numerical earthquake response analysis 1271 1.0E+09 8 T2 Station (EL 304 m) T4 Station (EL 205 m)

Nat. Hazards Earth Syst. Sci., 10, 1269–1280, 2010www.nat-hazards-earth-syst-sci.net/10/1269/2010/doi:10.5194/nhess-10-1269-2010© Author(s) 2010. CC Attribution 3.0 License.

Natural Hazardsand Earth

System Sciences

Numerical earthquake response analysis of the Liyutan earthdam in Taiwan

Z. Feng1, P. H. Tsai2, and J. N. Li3

1Department of Soil and Water Conservation, National Chung Hsing University, Taichung 402, Taiwan2Department of Construction Engineering, Chaoyang University of Technology, Taichung, Taiwan3Kingfeng County Government, Taitung, Taiwan

Received: 30 March 2010 – Revised: 21 May 2010 – Accepted: 27 May 2010 – Published: 17 June 2010

Abstract. The dynamic response of the Liyutan earth damto the 1999 Chi-Chi earthquake (ML=7.3) in Taiwan was nu-merically analyzed. First, the staged construction of the damwas simulated. Then, seepage analysis, considering a 60-mwater level, was performed. After seepage analysis, the ini-tial static stress (prior to dynamic loading) was established inthe dam. Both the horizontal and vertical acceleration timehistories recorded at the base of the dam were used in thenumerical simulations. The dynamic responses of the damwere analyzed for 50 s in the time domain. The simulated re-sults were in agreement with the monitored data. The trans-fer function analysis and Hilbert-Huang Transform (HHT)were used to compare the results and to perceive the responsecharacteristics of the dam. In particular, the time-frequency-energy plots of the HHT can reveal the timing and time frameof the dominant frequencies of the dynamic response. Theinfluences of the initial shear modulus and uni-axial earth-quake loading were also investigated.

1 Introduction

The 21 September 1999 Chi-Chi earthquake (ML=7.3) in-duced by the Chelunpu fault fracture caused very strongshaking in central Taiwan. The Liyutan earth dam expe-rienced the earthquake and showed damage and deforma-tion. A crack near the left abutment of the dam was ob-served. An inspection pit was excavated to a depth of ap-proximately 2.5 m for examination. Based on the exami-nation, the damage seemed to be manageable and minor.Strong motion records of the earth dam were captured dur-

Correspondence to:Z. Feng([email protected])

ing the earthquake. This dam is the closest earth dam to theChelunpu thrust fault in Taiwan that has complete strong mo-tion records (Fig. 1). Therefore, this dam presents a rare op-portunity to simulate the strong earthquake response of anearth dam using a complete set of recorded data for compa-rison.

The earthquake performance of an earth dam is a very im-portant safety issue. Seismic response evaluations of everyearth dam in Taiwan are carried out at regular 5-year inter-vals. Recently, various approaches to the dynamic responseanalysis of earth dams have been applied. Cascone and Ram-pello (2003) used the equivalent linear method to accountfor non-linear soil behavior for the two-dimensional finiteelement (FE) dynamic analyses of an earth dam. They ac-counted for synthetic and real acceleration histories as the in-put motions. Rampello et al. (2009) analyzed the dynamic re-sponse for the same dam using the finite element method witha hardening soil model, and they back-analyzed the earthdam construction. Psarropoulos and Tsompanakis (2008)evaluated a tailing dam using a FEM code, PLAXIS, to studystatic and seismic loading. Parish et al. (2009) used a fi-nite difference code, FLAC3D, to evaluate the seismic re-sponse of a 3-D earth dam for elastic and plastic responsesby comparing velocity spectra. However, the input seis-mic velocity history at the foundation base was only uni-axial in the horizontal direction, and therefore, their anal-ysis is still a 2-D model. In addition, the shear modulusand elastic modulus did not change with effective confiningstress and remained constant throughout the analyses. Siyahiand Arslan (2008a, b) adopted a finite element framework,OpenSees, with pressure-dependent multi-yield materials toinvestigate the dynamic behavior, failure modes and mech-anisms of failure of a dam. Hwang et al. (2007) studiedthe 42 earthquake records of the Liyutan earth dam and sug-gested the shear modulus of the dam. Their suggested shear

Published by Copernicus Publications on behalf of the European Geosciences Union.

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1270 Z. Feng et al.: Numerical earthquake response analysis

7

1 2 3 Figure 1 Location of the Liyutan earth dam and distribution of East-West peak ground 4 acceleration (PGA) during the 1999 Chi-Chi earthquake. (Note: The PGA data are after 5 Central Weather Bureau Taiwan.) 6

Fig. 1. Location of the Liyutan earth dam and distribution of East-West peak ground acceleration (PGA) during the 1999 Chi-Chiearthquake. (Note: the PGA data are after Central Weather BureauTaiwan.)

modulus is referenced in this study for the purpose of com-parison. Hwang et al. (2007) performed a frequency domaindynamic analysis using the FLUSH program (Lysmer et al.,1975) with an equivalent linear soil model for the dam forvarious peak ground accelerations (PGAs) up to 0.7 g. Thestudies mentioned above involved only uni-axial earthquakeloading. Previously, we performed a preliminary dynamicresponse study of the Liyutan earth dam with bi-axial earth-quake loading in the time domain (Feng et al., 2006); thatdynamic response is investigated further and in more detailin this paper.

This study focuses on the dynamic response of the Liyu-tan earth dam during the 1999 Chi-Chi strong earthquake.Many of prior dynamic analyses were done in the frequencydomain or with uni-axial loading. This study, however, per-forms time domain dynamic response analysis with bi-axialloading. Transfer function analysis and the Hilbert-HuangTransform (HHT; Huang et al., 1998) are adopted to present

the differences between the simulated results of this studyand the data from the monitored records. The HHT canclearly show the detailed dynamic responses of the dam inthe frequency and time-frequency domains to compare andexamine dynamic response characteristics. The analyzed re-sults of the dam subjected to the Chi-Chi earthquake are vali-dated by the monitored records. In addition to the validation,this study demonstrates that a higher initial shear modulusassignment to the dam produces a stronger response at highfrequencies and predicts smaller deformation of the dam.The authors also prove with the analyzed results that bi-axialloading shows a stronger response, and thus, for dams closeto a fault, the vertical earthquake loading should not be ig-nored. The simulation process of the Liyutan earth dam andinterpretations of results presented in this study are straight-forward and can be easily followed by researchers/engineersto perform dynamic earth dam analysis.

2 Site description and input motion

2.1 Description of the Liyutan earth dam

The Liyutan earth dam forms an off-channel reservoir lo-cated downstream of the Jing-Shan River in Miaoli, Taiwan.It is a roller-compacted earth dam measuring 96 m high and235 m long with a top width of 10 m. A cross section of thedam, which illustrates its material composition, is shown inFig. 2. Basically, the core is composed of impermeable ma-terial, and the shells are composed of semi-permeable ma-terial. The foundation materials are mostly sandstone, siltsandstone and shale, which are much stiffer than the dammaterials and are not considered in the numerical model.

2.2 Material properties for numerical analysis

The material properties of the dam are simplified for numer-ical analysis in this study. The dam is divided into the up-stream shell, downstream shell and the core. The core ofthe dam is mainly composed of impermeable clayey materialand is classified as clay (CL), silty sand (SM), silt (ML) andclayey gravel (GC) by the Unified Soil Classification Sys-tem. The shells are composed of excavated rocks and aresemi-permeable. The filter, which is mainly present betweenthe core and the downstream shell, is composed of gravelfrom the riverbed, and its properties are very close to thoseof the downstream shell. Therefore, for simplicity, the filteris merged into the downstream shell in the numerical model.

The initial shear modulus,Gmax, in the numerical modelwas assigned according to shear seismic field test results, asshown in Fig. 3 (Central Water Resources Office, 1995), re-ferring to the initial static stress state obtained previously. Wealso adopted theGmax suggested by Hwang et al. (2007) tocompare the influence of the shear modulus of dam materialson the dynamic responses of the Liyutan earth dam.

Nat. Hazards Earth Syst. Sci., 10, 1269–1280, 2010 www.nat-hazards-earth-syst-sci.net/10/1269/2010/

Z. Feng et al.: Numerical earthquake response analysis 1271

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T2 Station (EL 304 m)

T4 Station (EL 205 m)200

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Cross Section of the Liyutan Earth Dam

2: semi-permeable shell 1A 1B: impermeable core (SM, CL, ML, GC)

3A: permeable material (riverbed gravel; < 30 cm)

4A: core of temporal dam (riverbed material < 15 cm)4B: filter (riverbed material < 3.75 cm )

3B: semi-permeable shell (< 30 cm; laterite, GW)

3B

1 2 Figure 2 Central cross-section and material zones of the Liyutan earth dam (re-plotted, 3 Central Water Resources Office, 2000b). 4

Fig. 2. Central cross-section and material zones of the Liyutan earth dam (re-plotted, Central Water Resources Office, 2000b).

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Gm

ax( P

a )

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This studyHwang (2007)

3 Figure 3 Initial shear modulus, Gmax. The solid line indicates test results for the Liyutan earth 4 dam (after Central Water Resources Office, 1995). The dashed line presents a synthetic trend, 5 deduced from Hwang et al. (2007). 6 Fig. 3. Initial shear modulus,Gmax. The solid line indicates testresults for the Liyutan earth dam (after Central Water ResourcesOffice, 1995). The dashed line presents a synthetic trend, deducedfrom Hwang et al. (2007).

For the numerical analysis, the shells and core of the earthdam are assumed to satisfy the Mohr-Coulomb model. Fieldand laboratory tests were performed during and after con-struction by the Central Water Resources Office in Taiwan toevaluate the material properties of the dam. The evaluatedproperties for numerical simulations are listed in Table 1.Note that the shear modulus shown in Table 1 is only used toestablish the initial static stress state during the simulation ofdam construction. The initial shear modulus assigned in thedynamic analysis of each element will be re-calculated ac-cording to the mean effective stress and the curve presentedin Fig. 3.

Table 1. Material parameters of the earth dam based on test data(Central Water Resources Office, 1995).

Zone Shear Perme- Poisson’s c′, φ′,modulus, ability, Ratio,

G, Pa K, cm/s υ kPa deg

Upstream shell 5.0E8 5E-6 0.34 94 41Core 3.5E8 1E-7 0.45 34 27Downstream shell 6.0E8 5E-6 0.3 82 35

2.3 Shear modulus degradation and damping

The four-parameter sigmoidal (Sig4) model (Itasca, 2008) isadopted to fit the S-shaped shear modulus degradation curvesof the shell and core materials. The model has proper asymp-totic behavior. The equation of secant modulus,Ms, for theSig4 model is

Ms= y0+a

1+exp(−(L−x0)/b)(1)

whereL is the logarithmic strain,L = log10(γ ), andγ is thecyclic strain. The valuesa, b, x0 andy0 are the four modelparameters. The four parameters can be curve fitted by trial-and-error in a spreadsheet to resemble the normalized shearmodulus reduction curves from material test results.

This study adopted the normalized shear modulus reduc-tion curves obtained from the test results of the dam materi-als (Central Water Resources Office in Taiwan, 1995). Thenormalized shear modulus reduction (G/Gmax) versus shearstrain curves with the fittings of the Sig4 model are demon-strated in Fig. 4. The fitted parameters of the sigmoidalmodel are listed in Table 2.

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Shear strain, γ

Upstream shell -Test dataUpstream shell - Sig4Core - Test dataCore - Sig4Downstream shell - Test dataDownstream shell - Sig4

3 Figure 4 Shear modulus reduction curves fitted by the Sig4 model for each zone. 4 Fig. 4. Shear modulus reduction curves fitted by the Sig4 model foreach zone.

Table 2. Parameters of the sigmoidal (Sig4) model for the shellsand core.

Zone a b x0 y0

Upstream shell 0.995 –0.55 –1.5 0.02Core 0.963 –0.52 –1.15 0.045Downstream shell 0.9789 –0.485 –1.3 0.027

The material damping ratios of the Liyutan earth dam ob-tained from the test results show that damping ratios are higheven at a low cyclic strain level of 1×10−6. Furthermore, thesigmoidal model dissipates almost no energy at a low cyclicshear strain level (Itasca, 2008). Additionally, when theMohr-Coulomb material yields and undergoes plastic flow,both the 5% Rayleigh damping and the sigmoidal model willbe “switched off” (Itasca, 2008). Therefore, to account forthe high damping of the dam materials at low strain level,an additional 5% Rayleigh damping has been added in thedynamic analysis.

2.4 Input motion

The Chi-Chi earthquake acceleration time histories recordedat the T4 station at the base and central sections of the Liyu-tan earth dam were selected as the input motion for this study.The horizontal and vertical monitored acceleration time his-tories of the Chi-Chi earthquake were simultaneously consid-ered as the bi-axial input to the base of the dam for a durationof 45 s in the dynamic analyses. The horizontal accelerationcomponent is perpendicular to the longitudinal axis of thedam. In the Chi-Chi earthquake, the horizontal and verticalpeak accelerations monitored at the base of the dam were0.149 g and 0.108 g, respectively.

The displacement of the earth at the base should be zeroafter the earthquake, at which time the authors assume nopermanent ground movement occurs. However, double in-

tegration of an acceleration record may not be zero due tonoise or the threshold of the seismic instrument. Therefore,a baseline correction is applied for the two input acceler-ation time histories. The vertical and horizontal baseline-corrected acceleration time histories are shown in Fig. 5 withtheir respective Fourier spectra. The dominant frequencies ofhorizontal acceleration were approximately 0.244, 0.69, and0.87 Hz. For vertical acceleration, the dominant frequencywas approximately 0.255 Hz.

3 Analysis methods

The Fast Lagrangian Analysis of Continua (FLAC) 6.0 code(Itasca, 2008) is adopted in this study. The mid-section ofthe Liyutan earth dam was modeled as a 2-D grid. Thereare 1101 elements in the mesh, as shown in Fig. 6. Both thehorizontal and vertical acceleration of the earthquake wereapplied to the dam. The acceleration and displacement timehistories and permanent displacement of the dam can be ob-tained from the numerical results. The results were com-pared to the field measurement and to the acceleration histo-ries recorded at the T2 station at the top of the dam.

3.1 Static analysis

To establish a reasonable stress state for the dam before dy-namic analysis, the initial static equilibrium stress state wasobtained. The staged construction was simulated by sequen-tially adding 20 layers of dam construction materials beforewater impounding. When a layer was added, a new staticequilibrium for that stage of the dam construction was com-puted. This process was repeated until the full dam structurewas formed. After the stage construction analysis, the dis-placements at each node of the mesh were reset to zero. Theretaining water level of the Liyutan earth dam was 60 m whenthe Chi-Chi earthquake struck. Therefore, the steady stateseepage analysis of the dam for a 60-m water level was per-formed. The seepage analysis was uncoupled from the me-chanical analysis. The initial static stress state (prior to theearthquake) was then computed. The dam showed a slightmovement to the upstream direction due to buoyancy forcesin the upstream shell. The stress state at this stage is the ini-tial stress condition of the dam before dynamic loading.

These static analyses yielded the following results: 1) thestress distribution after dam construction, 2) the pore waterpressure distribution for steady state seepage, and 3) the ini-tial stress state prior to the earthquake.

3.2 Dynamic analysis

By using the initial stress state obtained in the previous staticanalysis, the dam was modeled using the Chi-Chi earth-quake bi-axial acceleration time history as a dynamic forcingterm. The horizontal and vertical acceleration time-historyrecorded at the base of the dam are input simultaneously. The



(a)

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1 Figure 5a The recorded horizontal acceleration time history for the Chi-Chi earthquake at the 2 T4 station at the base of the Liyutan dam. 3

FFT: T4 Horizontal Acc.

0.1 1 10frequency ( Hz )

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Figure 5b Fourier spectra of the recorded horizontal acceleration of the earthquake at the T4 5

station. 6

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7 Figure 5c The recorded vertical acceleration time history for the Chi-Chi earthquake at the T4 8 station at the base of the Liyutan dam. 9

FFT: T4 Vertical Acc.


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Figure 5d Fourier spectra of the recorded vertical acceleration of the earthquake at the T4 11

station. 12

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Fig. 5. (a)The recorded horizontal acceleration time history for the Chi-Chi earthquake at the T4 station at the base of the Liyutan dam.(b)Fourier spectra of the recorded horizontal acceleration of the earthquake at the T4 station.(c) The recorded vertical acceleration time historyfor the Chi-Chi earthquake at the T4 station at the base of the Liyutan dam.(d) Fourier spectra of the recorded vertical acceleration of theearthquake at the T4 station.

duration of the dynamic analysis is 50 s, which is five secondsmore than the recorded input acceleration (45 s). The addi-tional 5 s allows for attenuation of the transient response ofthe dam to the earthquake vibration.

3.3 Transfer function and Hilbert-Huang Transform

Transfer function analysis is employed in this study to com-pare the dynamic response of the dam in the frequency do-main. Following Hwang et al. (2007), the transfer function isdefined as the ratio of the Fourier amplitude response spec-trum (RFRS) of the acceleration history of the crest dividedby that of the base. The recorded acceleration at the base isdefined as the input, and the acceleration response at the crestis the output.

For the time-frequency domain, the HHT is applied to ob-tain the acceleration time-frequency-energy spectra for com-parison. HHT is a powerful method because of its adaptive

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Figure 6 The mesh for numerical analyses of the Liyutan earth dam. 9

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0 1 00m

-2.500 -1.500 -0.500 0.500 1.500 2.500

(*10^2)0

0

100

Fig. 6. The mesh for numerical analyses of the Liyutan earth dam.

and time efficiency. It is very good for analyzing nonlinearand non-stationary signals. Signals are first decomposed intointrinsic mode functions (IMFs) by the empirical mode de-composition method. The IMFs are then transformed usingthe Hilbert transform to obtain their instantaneous frequen-cies as a function of time. For details of the HHT method,readers should refer to Huang et al. (1998). The timing andtime frame of the dominant frequencies of the dynamic re-sponse of a dam can be clearly revealed by HHT.



Table 3. Comparisons of the calculated permanent displacements at the surface of the dam with the measured data (unit: cm).

Upstream shell Upstream shell Top of crest Top of crest Downstream shell Downstream shell(mid-height) (mid-height) (mid-height) (mid-height)

Horiz. Vert. Horiz. Vert. Horiz. Vert.

Measured displacement1 –2.7∼−3.9 –5.4∼−6.8 –0.7∼−4.3 –5.0∼−7.9 1.8∼2.9 –2.6∼−3.4Calculated displacement –2.0 1.3 –5.5 –5.8 –0.4 0.2

1 Survey results after the Chi-Chi earthquake from the Central Water Resources Office (1999).2 Negative signs (–) represent horizontal leftward displacement or vertical downward displacement.

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Figure 7 The pore pressure distribution derived from the seepage analysis. The dotted line 10

shows the in-situ measured phreatic surface. Height of retained water is 60 m. 11

12

Pore pressure contours 0.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05 6.00E+05Contour interval= 5.00E+04

(Unit: Pa)

The measured phreatic surface

60 m

Fig. 7. The pore pressure distribution derived from the seepageanalysis. The dotted line shows the in-situ measured phreatic sur-face. Height of retained water is 60 m.

4 Results and discussion

4.1 Seepage analysis

The result of the steady state seepage calculation is shown inFig. 7. The largest static pore water pressure was found to be600 kPa. The phreatic surface depresses quickly in the down-stream shell. Overall, the trends of the calculated phreaticsurface are reasonable and close to field measurement data(Central Water Resources Office, 2000a) with the exceptionof those in the core zone. The field measurement of thephreatic surface in the core zone is higher because the seep-age remains in a transient state, as opposed to steady state.In addition, the materials in the core zone are relatively im-permeable, whereas the shell materials are semi-permeable.Therefore, the lowering of the phreatic surface in the corezone occurs more slowly than in the shells. This study con-siders only steady state seepage, which may overestimate theeffective stress distribution in the core zone and slightly over-estimate theGmax in the core zone. Further study on transientseepage in the core zone may improve the accuracy of the es-timations.

4.2 Deformation of the dam

The exaggeratedly deformed mesh (after the 50-s earth-quake) is shown in Fig. 8. The displacements are the perma-nent deformation after the earthquake simulation. The dam

mostly deformed toward the upstream side with a maximumdisplacement of 8.7 cm. A potential sliding surface is locatedat two-thirds of the height of the dam in the upstream shell.The upstream shell is mostly submerged under water, andits shear strength is smaller due to a lower effective stress.Overall, the calculated displacements are fairly close to thefield-measured data (Table 3). The simulated displacementat the dam crest was the best fit with the field data; however,larger discrepancies appear at the mid-height of the upstreamand downstream shells. These discrepancies could be causedby use of the triangular mesh for the dam, which is fixedat the base and thus constrains the deformability of the damand prevents sliding at the base of the dam. Relative hori-zontal and vertical displacement differences between the topand base of the dam during the earthquake simulation are de-picted in Fig. 9. The maximum relative horizontal displace-ment is 14.9 cm toward upstream. The permanent horizontaldisplacement is 5.5 cm. The maximum relative vertical dis-placement is 6.2 cm downward, and the permanent verticaldisplacement is 5.8 cm.

4.3 Distribution of the maximum accelerationof each element

The maximum accelerations of each element during the 50 sof earthquake simulation were calculated. The distributionsof the maximum horizontal and vertical accelerations are de-picted in Fig. 10a and b. For horizontal movement, higher ac-celerations are mainly located at the top portion of the dam.For vertical movement, higher accelerations are located at themid-height of the upstream and downstream shells. Appar-ently, horizontal accelerations are generally larger than verti-cal acceleration for most elements.

4.4 Acceleration response at the crest

The calculated acceleration time histories at the crest of thedam and its RFRS and HHT spectra are discussed. Corre-sponding plots of the recorded data are presented for com-parison in Figs. 11–14. The computed horizontal and ver-tical peak accelerations are 0.269 g and 0.133 g, which areclose to the recorded peak accelerations of 0.24 g and 0.15 g,



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Relative Horiz. Disp.Relative Verti. Disp.

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ativ

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Figure 9 Relative horizontal and vertical displacements between the crest and base of the 3

dam. 4

Fig. 8. Exaggerated grid distortion after shaking. Maximum displacement = 8.7 cm; displacement magnification = 100 times. The dotted linerepresents the sliding surface of the displaced block. The movement is toward the upstream side of the dam.

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Figure 9 Relative horizontal and vertical displacements between the crest and base of the dam. 3

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Fig. 9. Relative horizontal and vertical displacements between the crest and base of the dam.

respectively; refer to Figs. 11a, b and 12a, b. For horizontalvibration, the transfer functions (RFRS) versus frequency areshown in Fig. 11c for the calculated results and Fig. 11d forthe recorded data. The frequencies of the “peaks” in RFRSare similar to those shown in Fig. 11c and d. When the fre-quency is lower than 5 Hz, the two RFRS fit well. Whenthe frequency is greater than 5 Hz, the RFRS of the recordeddata are generally larger than those of the calculated result.The amplification of the high frequency region is not obviousin the numerical calculation, which may be due to limitationof the element size. Similar results are observed for verticalvibration, as shown in Fig. 12c and d. The RFRS of the cal-culated result are smaller than the RFRS of the recorded datawhen the frequency is greater than 5 Hz.

The time-frequency-energy spectra of the Hilbert-HuangTransform of the accelerations at the dam crest can be eval-uated from Figs. 13 and 14. In these figures, higher en-ergy instantaneous frequencies are shown in dark red, andlower energy frequencies are presented in a lighter color. TheHHT spectra of the calculated results and recorded data at theT2 station are qualitatively similar. For the horizontal vibra-tion at the dam crest, the dominant frequencies with higherenergy are approximately 0.6∼1.2 Hz and vary with time(Fig. 13). At 0.244 Hz and 0.69 Hz, the dominant frequencyof the input horizontal acceleration at the base shows high en-ergy (Fig. 13a and b). Energy above 3 Hz is insignificant, asshown in Fig. 13. For vertical vibration at the crest (Fig. 14),the energy is much lower than the energy of the horizontalshaking. The input vertical acceleration at the base, with adominant frequency of 0.255 Hz, controls the response. Ver-tical vibration energy near this frequency is stronger alongthe time axis from 15 to 25 s (Fig. 14).

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Figure 10a The maximum horizontal acceleration distribution of the dam during the 45 11

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Figure 10b The maximum vertical acceleration distribution of the dam during the 45 seconds 22

of earthquake simulation. 23

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Contour interval= 5.00E-01

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Figure 10a The maximum horizontal acceleration distribution of the dam during the 45 11

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Figure 10b The maximum vertical acceleration distribution of the dam during the 45 seconds 22

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Unit: m/sec2

(b)

Fig. 10. (a)The maximum horizontal acceleration distribution ofthe dam during the 45 s of earthquake simulation.(b) The maxi-mum vertical acceleration distribution of the dam during the 45 s ofearthquake simulation.

4.5 Influence ofGmax

This study assigns the initial shear modulus,Gmax, of thedam materials according to field and laboratory test resultsfrom the Central Water Resources Office. The initial shearmodulus is assigned to each element according to the effec-tive mean stress of that element. Hwang et al. (2007) recom-mended a higher initial shear modulus of the dam (Fig. 3),



(a)

17

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2

Acce

lera

tion,

m/s

ec^2

1 a) Calculated horizontal acceleration at the crest 2

3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2

Acce

lera

tion,

m/s

ec^2

4 b) Recorded T2 horizontal acceleration at the crest 5

6

Top Crest / T4 Station

1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S

7 c) Transfer function (RFRS) between the horizontal response of the calculated result and the 8

recorded T4 station 9

10

T2 Station / T4 Station

1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S

11 d) Transfer function (RFRS) between the recorded horizontal response at the T2 and T4 12

station 13

Figure 11 Comparison of the horizontal acceleration response at the crest and recorded T2 14

station. 15

(b)

17

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2

Acce

lera

tion,

m/s

ec^2


3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2

Acce

lera

tion,

m/s

ec^2


6


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S



10


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S


station 13


station. 15

(c)

17

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2

Acce

lera

tion,

m/s

ec^2


3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2Ac

cele

ratio

n, m

/sec

^2


6


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S



10


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S


station 13


station. 15

(d)

17

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2

Acce

lera

tion,

m/s

ec^2


3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

0

2

Acce

lera

tion,

m/s

ec^2


6


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S



10


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S


station 13


station. 15

Fig. 11.Comparison of the horizontal acceleration response at the crest and recorded T2 station.(a) Calculated horizontal acceleration at thecrest.(b) Recorded T2 horizontal acceleration at the crest.(c) Transfer function (RFRS) between the horizontal response of the calculatedresult and the recorded T4 station.(d) Transfer function (RFRS) between the recorded horizontal response at the T2 and T4 stations.

and this suggestion is used to evaluate the influence ofGmaxon the dynamic response of the dam in this study. The trans-fer functions (RFRS) obtained from the data recorded at theT2 and T4 stations are compared in Fig. 15. For the RFRS ofhorizontal acceleration (Fig. 15a), this study fits the recordedRFRS better in the 1.1∼1.5 Hz band than the results obtainedusing theGmax from Hwang et al. (2007). This frequencyrange is near the fundamental frequency of the dam duringthe Chi-Chi earthquake. The horizontal fundamental fre-quency of the dam during the Chi-Chi earthquake is approx-imately 1.30 Hz, as suggested by Hwang et al. (2007). For0.5∼1.0 Hz, the RFRS results obtained using theGmax fromHwang et al. (2007) match the recorded RFRS better thanthe RFRS obtained using theGmax estimated in this study.At a higher frequency range, 2.5∼3 Hz, the RFRS resultsobtained using theGmax suggested by Hwang et al. (2007)show a stronger response than those using theGmax esti-mated in this study. It is possibly due to the high initial shearmodulus assignment. The same phenomenon is observed in

Fig. 15b for the RFRS of the vertical response in the fre-quency range 2.6∼3 Hz. For the vertical response, the ver-tical fundamental frequency of the dam during the Chi-Chiearthquake is approximately 2.04 Hz, as indicated by Hwanget al. (2007), while the vertical fundamental frequency isnear 1.95∼2 Hz based upon the RFRS of the recorded datapresented in Fig. 15b. The RFRS results obtained using thetwo Gmax assignments match the recorded RFRS quite wellfor low frequencies below 1.9 Hz. For the displacement as-pect, the maximum permanent displacement found in thisstudy is 8.7 cm, while the maximum permanent displace-ment obtained using the higher initial shear moduli accord-ing to Hwang et al. (2007) is only 2.9 cm. This value is muchsmaller than that found in the field survey data, as indicatedin Table 3.

Therefore, assigning a higher initial shear modulus to thedam materials could cause a stronger response in the higherfrequency range, which will predict less deformation of thedam.



(a)

18

5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2

Acce

lera

tion,

m/s

ec^2

1 a) Calculated vertical acceleration at the crest 2

3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2

Acce

lera

tion,

m/s

ec^2

4 b) Recorded T2 vertical acceleration at crest 5

6


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S

7 c) Transfer function (RFRS) between the vertical response of the calculated result and the 8



1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S

10 d) Transfer function (RFRS) between the recorded vertical response at the T2 and T4 11

stations 12

Figure 12 Comparison of the vertical acceleration response at the crest and recorded T2 13

station. 14

(b)

18

5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2

Acce

lera

tion,

m/s

ec^2


3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2

Acce

lera

tion,

m/s

ec^2


6


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S




1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S


stations 12


station. 14

(c)

18

5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2

Acce

lera

tion,

m/s

ec^2


3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2Ac

cele

ratio

n, m

/sec

^2


6


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S




1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S


stations 12


station. 14

(d)

18

5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2

Acce

lera

tion,

m/s

ec^2


3

0 5 10 15 20 25 30 35 40 45 50time ( sec )

-2

-1

0

1

2

Acce

lera

tion,

m/s

ec^2


6


1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S




1 2 3 4 5 6 7 8 9 10frequency ( Hz )

0

10

20

30

RFR

S


stations 12


station. 14

Fig. 12. Comparison of the vertical acceleration response at the crest and recorded T2 station.(a) Calculated vertical acceleration at thecrest.(b) Recorded T2 vertical acceleration at crest.(c) Transfer function (RFRS) between the vertical response of the calculated result andthe recorded T4 station.(d) Transfer function (RFRS) between the recorded vertical response at the T2 and T4 stations.

19

0 5 10 15 20 25 30 35 40 45Time (sec) )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uenc

y ( H

z )

1 a) HHT time-frequency-energy spectra for the calculated horizontal acceleration at the crest 2

0 5 10 15 20 25 30 35 40 45Time ( sec )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uen

cy (

Hz

)

3 b) HHT time-frequency-energy spectra for the horizontal acceleration of the T2 station at the 4

crest 5

6

Figure 13 Comparison of the HHT time-frequency spectra for the calculated horizontal 7

acceleration at the crest and that of the recorded T2 station. 8

19

0 5 10 15 20 25 30 35 40 45Time ( sec )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uen

cy (

Hz

)

1 a) HHT time-frequency-energy spectra for the calculated horizontal acceleration at the crest 2

0 5 10 15 20 25 30 35 40 45Time ( sec)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uenc

y ( H

z )

3 b) HHT time-frequency-energy spectra for the horizontal acceleration of the T2 station at the 4

crest 5

6

Figure 13 Comparison of the HHT time-frequency spectra for the calculated horizontal 7

acceleration at the crest and that of the recorded T2 station. 8

(a) (b)

Fig. 13. Comparison of the HHT time-frequency spectra for the calculated horizontal acceleration at the crest and that of the recordedT2 station.(a) HHT time-frequency-energy spectra for the calculated horizontal acceleration at the crest.(b) HHT time-frequency-energyspectra for the horizontal acceleration of the T2 station at the crest.



20

0 5 10 15 20 25 30 35 40 45Time (sec) )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uenc

y ( H

z )

1 a) HHT time-frequency-energy spectra for the calculated vertical acceleration at the crest 2

0 5 10 15 20 25 30 35 40 45Time ( sec )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uen

cy (

Hz

)

3 b) HHT time-frequency-energy spectra for the vertical acceleration of the T2 station at the 4

crest 5

6

Figure 14 Comparison of HHT time-frequency spectra for the calculated vertical acceleration 7

at the crest and that of the recorded T2 station. 8

20

0 5 10 15 20 25 30 35 40 45Time ( sec )

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uen

cy (

Hz

)

1 a) HHT time-frequency-energy spectra for the calculated vertical acceleration at the crest 2

0 5 10 15 20 25 30 35 40 45Time ( sec)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Freq

uenc

y ( H

z )

3 b) HHT time-frequency-energy spectra for the vertical acceleration of the T2 station at the 4

crest 5

6

Figure 14 Comparison of HHT time-frequency spectra for the calculated vertical acceleration 7

at the crest and that of the recorded T2 station. 8

(a) (b)

Fig. 14. Comparison of HHT time-frequency spectra for the calculated vertical acceleration at the crest and that of the recorded T2 station.(a) HHT time-frequency-energy spectra for the calculated vertical acceleration at the crest.(b) HHT time-frequency-energy spectra for thevertical acceleration of the T2 station at the crest.

2

This studyRecorded ( T2 / T4 )Hwang et al. ( 2007 )

0.5 1 1.5 2 2.5 3frequency ( Hz )

0

5

10

15

20

25

30

RFR

S

1

2


0.5 1 1.5 2 2.5 3frequency ( Hz )

0

5

10

15

20

25

30

RFR

S

3 (b)

4

Fig. 15. Comparison of transfer function (RFRS) to illustrate the influence of Gmax 5

assignment. (a) Comparison of transfer function (RFRS) for horizontal acceleration. (b) 6

Comparison of transfer function (RFRS) for vertical acceleration. 7

(a)

2


0.5 1 1.5 2 2.5 3frequency ( Hz )

0

5

10

15

20

25

30

RFR

S

1

(b) 2

Fig. 15. Comparison of transfer function (RFRS) to illustrate the influence of Gmax 3

assignment. (a) Comparison of transfer function (RFRS) for horizontal acceleration. (b) 4

Comparison of transfer function (RFRS) for vertical acceleration. 5

6

Please exchange the Fig 15. (b). 7

(b)

Fig. 15. Comparison of transfer function (RFRS) to illustrate theinfluence ofGmax assignment.(a) Comparison of transfer func-tion (RFRS) for horizontal acceleration.(b) Comparison of transferfunction (RFRS) for vertical acceleration.

4.6 Influence of uni-axial and bi-axial earthquakeloading

A simulation that only accounted for horizontal accelera-tion as the input earthquake loading was performed as a uni-axial case to evaluate the difference in response between uni-axial and bi-axial earthquake loading. The transfer functions(RFRS) of the horizontal acceleration between the two cases

3

Bi-axial EQ loadingUni-axial EQ loading

0.5 1 1.5 2 2.5 3frequency ( Hz )

0

5

10

15

20

25

30

RFR

S

1

(a) 2


0.5 1 1.5 2 2.5 3frequency ( Hz )

0

5

10

15

20

25

30

RFR

S

3

(b) 4

Fig. 16. Comparison of responses between bi-axial and uni-axial EQ loading. (a) Comparison 5

of transfer function (RFRS) between bi-axial and uni-axial EQ loading for horizontal 6

acceleration. (b) Comparison of transfer function (RFRS) between bi-axial and uni-axial EQ 7

loading for vertical acceleration. 8

9

(a)

3


0.5 1 1.5 2 2.5 3frequency ( Hz )

0

5

10

15

20

25

30

RFR

S

1

(a) 2


0.5 1 1.5 2 2.5 3frequency ( Hz )

0

5

10

15

20

25

30

RFR

S

3

(b) 4

Fig. 16. Comparison of responses between bi-axial and uni-axial EQ loading. (a) Comparison 5

of transfer function (RFRS) between bi-axial and uni-axial EQ loading for horizontal 6

acceleration. (b) Comparison of transfer function (RFRS) between bi-axial and uni-axial EQ 7

loading for vertical acceleration. 8

9

(b)

Fig. 16. Comparison of responses between bi-axial and uni-axialEQ loading.(a) Comparison of transfer function (RFRS) betweenbi-axial and uni-axial EQ loading for horizontal acceleration.(b)Comparison of transfer function (RFRS) between bi-axial and uni-axial EQ loading for vertical acceleration.

are almost identical (Fig. 16a); however, the bi-axial caseshowed a stronger response. For vertical acceleration, largedifferences are obvious when the frequency is smaller than1.5 Hz (Fig. 16). For frequencies higher than 1.5 Hz, theRFRS between the two cases are fairly close because thevertical acceleration response of the dam crest in uni-axialloading is caused by the reflection of waves in the dam body



generated by horizontal vibration. The permanent displace-ment of the uni-axial loading case is 7.0 cm, which is 1.7 cmsmaller than that of the bi-axial loading case.

In this study, the vertical acceleration of the Chi-Chiearthquake is not obvious because the vertical PGA is only0.108 g; therefore, the horizontal responses of the uni-axialand biaxial loading cases are very similar. If only the hori-zontal vibration component of the dam is required, the ver-tical acceleration input may be omitted. However, if a damis close to a fault, the vertical shaking could be serious, andvertical acceleration should not be ignored.

5 Conclusions and suggestions

The aim of this study was to simulate the dynamic responseof the Liyutan earth dam when it was struck by the 1999Chi-Chi earthquake (ML=7.3). The response of the dam wasanalyzed in the time domain using bi-axial earthquake load-ing. The results were presented for comparison in the formof the transfer functions (RFRS) and HHT. The influence ofthe initial shear modulus was investigated, and the responseof the dam to uni-axial earthquake loading was compared.

The following conclusions can be drawn from this study:

1. The simulation process used in this study includes thedam construction phase, steady state seepage, initialstatic stress state and dynamic analysis. This simula-tion process is straightforward, and, when the resultsare compared with the recorded data, they are validatedwith satisfaction.

2. The steady state seepage analysis result represents thephreatic surface quite well, with the exception of thecore zone. Thus, the effective stress and shear modulusmay be slightly over-estimated in the core zone.

3. A potential sliding surface moving toward the upstreamside was found, located at two-thirds of the height ofthe dam. The calculated displacements are fairly closeto the field-measured data, and the permanent displace-ments at the dam crest fit well with the in-situ surveydata. The maximum permanent displacement of thedam from the numerical simulation is 8.7 cm.

4. Higher horizontal accelerations are located at the topportion of the dam. However, higher vertical acceler-ations are located at the mid-height of the upstream anddownstream shells, as indicated by the results of theanalysis.

5. Based upon comparison of the transfer functions(RFRS), the simulated acceleration at the crest fit wellwhen compared to the recorded data, with the excep-tion of the high-frequency region. The HHT spectra canshow which periods have high energy in the dominantfrequencies during earthquake shaking. The transfer

function analysis and Hilbert-Huang Transform providetools to reveal the details of the response characteristicsof the dam.

6. For the two initial shear modulus assignments, thetransfer functions match the recorded ones fairly well,with the exception of some frequency ranges. Gen-erally, a higher initial shear modulus assignment pro-duces a stronger response at high frequencies and pre-dicts smaller deformation of the dam.

7. The transfer functions (RFRS) of horizontal accelera-tion between the uni-axial and bi-axial loading are al-most the same. However, the bi-axial case shows astronger response. The vertical acceleration responseof the crest in uni-axial loading is caused by the reflec-tion of waves generated by the horizontal vibration andis present at frequencies higher than 1.5 Hz. Verticalacceleration loading should not be omitted in dynamicanalysis for those dams subjected to high vertical shak-ing.

In this study, the equivalent linear sigmoidal model with theMohr-Coulomb model was used. Therefore, the excess porewater pressure generated during the earthquake was not pre-dicted. Further study of the earth dam can be focused onapplying a nonlinear cyclic plasticity model for the dam ma-terials, especially for the upstream shell, which has a higherliquefaction potential. In addition, further parametric studycan be useful for detailed examination of the dynamic re-sponse of an earth dam. It can be considered by varying theretaining water level, buck modulus, shear modulus, materialdamping, input motion, and peak ground acceleration.

Acknowledgements.This study was funded by the NationalScience Foundation of Taiwan (NSC-93-2211-E-005-11-), andtheir support is highly appreciated. Also, the authors would liketo acknowledge the Central Water Resources Office in Taiwan forproviding the monitored data and reports of the Liyutan dam.

Edited by: M. E. ContadakisReviewed by: M. Sadek and H. Arslan

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Central Water Resources Office: Regular monitoring and anal-ysis report of Liyutan dam, Central Water Resources Office,Taichung, Taiwan, 1995 (in Chinese).

Central Water Resources Office: Chi-Chi earthquake analysis re-port of Liyutan dam, Central Water Resources Office, Taichung,Taiwan, 1999 (in Chinese).

Central Water Resources Office: Regular monitoring and anal-ysis report of Liyutan dam, Central Water Resources Office,Taichung, Taiwan, 2000a (in Chinese).



Central Water Resources Office: Report on earthquake monitoringand equipment maintenance of Liyutan dam, Central Water Re-sources Office, Taichung, Taiwan, 2000b (in Chinese).

Feng, Z., Tsai, P. H., Chang, Y. H., and Li, J. N.: Dynamic responseof Liyutan earthdam subjected to the 1999 Chi-Chi earthquakein Taiwan. FLAC and Numerical Modeling in Geomechanics-2006, in: Proceedings of the 4th International FLAC Sympo-sium, Madrid, Spain, 29–31 May 2006.

Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., et al.: The empiricalmode decomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysis, Proc. R. Soc. Lon. Ser.-A,454, 903–995, 1998.

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Parish, Y., Sadek, M., and Shahrour, I.: Review Article: Nu-merical analysis of the seismic behaviour of earth dam, Nat.Hazards Earth Syst. Sci., 9, 451–458, doi:10.5194/nhess-9-451-2009, 2009.

Psarropoulos, P. N. and Tsompanakis, Y.: Stability of tailings damsunder static and seismic loading, Can. Geotech. J., 45, 663–675,2008.

Rampello, S., Cascone, E., and Grosso, N.: Evaluation of the seis-mic response of a homogeneous earth dam, Soil Dyn. Earthq.Eng., 29, 782–798, 2009.

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Numerical earthquake response analysis of the Liyutan earth ......Z. Feng et al.: Numerical earthquake response analysis 1271 1.0E+09 8 T2 Station (EL 304 m) T4 Station (EL 205 m)