Research Article New Developments in Geotechnical...

Research ArticleNew Developments in Geotechnical Earthquake Engineering

Yang Changwei1 Su Tianbao2 Zhang Jianjing1 and Du Lin1

1 School of Civil Engineering Key Laboratory of Transportation Tunnel Engineering Ministry of EducationSouthwest Jiaotong University Chengdu 610031 China

2Henan University of Urban Construction Pingdingshan Henan 467036 China

Correspondence should be addressed to Zhang Jianjing yangchangwei56163com

Received 21 February 2014 Revised 31 March 2014 Accepted 17 April 2014 Published 7 July 2014

Academic Editor George Z Kyzas

Copyright copy 2014 Yang Changwei et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Based on the review on the advances of several important problems in geotechnical seismic engineering the authors propose theinitial analysis theory of time-frequency-amplitude (known as TFA for short) in an effort to realize the organic combination of timeand frequency information and develop a groundbreaking concept to the traditional idea in the geotechnical seismic engineeringarea

1 Review on the Present Main Defect inthe Geotechnical Earthquake Engineering

Geotechnical seismic engineering is an important area ingeotechnical engineering and its topic is to resolve theseismic problems related to geotechnical engineering Withdevelopment for more than 50 years the time domainanalysis theory and the frequency analysis theory have beengenerally established in the geotechnical seismic engineering[1ndash6] However a common problem still exists in the timedomain analysis theory and the frequency domain theorywhich is that the research methods for geotechnical seismicengineering are still the separate application of time domainor frequency domain and no combination of above twois considered [7ndash11] For example time domain analysistheory can only consider the time histories of accelerationvelocity and displacement but not the frequency contents ofground motions Frequency domain analysis theory can onlyconsider the frequency contents of ground motions whiletime histories of acceleration velocity and displacement arenot included Seismic wave is however a very complex non-stationary signal whose amplitudes and frequencies changewith time Present outcomes in the time domain theory andthe frequency domain theory cannot reflect synthetically thecharacteristics of geotechnical seismic engineering very closeto an oldChinese saying ldquoTheblindman feels an elephantmdashto

take a part for the wholerdquo Therefore research on the time-frequency-amplitude analysis theory considering the timefrequency and amplitude can be an important task whichwill be a new direction of geotechnical seismic engineering

2 Brief Introduction of the SignalAnalysis Technologies

Fourier transform and wavelet transform are two seis-mic signal analysis technologies [12] Fourier transformis a steady-state analysis technology and suitable for fre-quency domain analysis Wavelet transform has some time-frequency domain resolution ability but it is hard to carryout an accurate time-frequency analysis [13] because ofuncertainty principle Based on theHilbert transformHuanget al proposed a new signal analysis method for nonsta-tionary signal [14] called Hilbert-Huang transform (HHT)The approach can perform linearized and stabilized analysisfor nonlinear and nonstationary signals initial data in theanalysis can be retained and energy leaking can be avoidedStudies in the past showed that the results from HHTcan reflect true cases The concrete calculation principle ofHilbert-Huang transform is shown as follows generally anonstationary signal can be decomposed into a series of

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2014 Article ID 902690 7 pageshttpdxdoiorg1011552014902690

2 Advances in Materials Science and Engineering

The figure of investigated routes in disaster areas

Earthquake fault zoneInvestigated routeSeismic influenced areaCountry roadProvince roadMunicipal governmentCounty governmentDamaged spots

Figure 1 Roads investigated and seismic intensity

intrinsic mode function (known as IMF for short) com-ponents by using ensemble empirical mode decomposition(known as EEMD for short) method The instantaneousfrequency of each IMF will be derived by the Hilbert-Huangtransform and then the Hilbert spectrumwill be obtained byintegrating all the instantaneous frequency spectrums Theanalytical signal amplitude function phase function andinstantaneous frequency function can be obtained by usingthe Hilbert-Huang transform The computational formulasare shown in

119885 (119905) = 119888 (119905) + 119895119867 [119888 (119905)] = 119886 (119905) 119890119895120601(119905)

119886 (119905) = radic1198882 (119905) + 1198672 [119888 (119905)]

120601 (119905) = arctan 119867[119888 (119905)]

119888 (119905)

119891 (119905) =1

2120587

119889120601 (119905)

119889 (119905)

(1)

From the above formulas it is known that both amplitudeand frequency are the function of time If the amplitude iscalculated by using a combined time and frequency domainapproach the Hilbert spectrum can be obtained as shown in(2) The marginal spectrum and the instantaneous frequencyspectrum can be obtained by using (3) and (4) The Hilbertspectrum can be obtained by integrating amplitude squaredas shown in (5)

Consider

119867(120596 119905) = Re119899

sum

119894=1

119886119894 (119905) 119890119895120601119894(119905) (2)

ℎ (120596) = int

119879

0

119867(120596 119905) 119889119905 (3)

119868119864 (119905) = int120596

119867(120596 119905) 119889119905 (4)

119864119878 (120596) = int

119879

0

1198672(120596 119905) 119889119905 (5)

3 New Development in the GeotechnicalEarthquake Engineering

Up to now our team has conducted a field investigationalong the road and railway nearly 3000 km in 512 Wenchuanearthquake-stricken areas (see Figure 1) a number of fieldmonitoring of typical slopes more than twenty shaking tabletests a number of numerical simulations and theoreticalstudies [15 16] some shaking tabletest models are shown inFigures 2 3 4 5 and 6

On the basis of extensive studies several importantproblems in the geotechnical seismic engineering are studiedincluding analysis methods of seismic responses of the siteanalysis methods of seismic responses and seismic stabilityof the retaining structures analysis methods of seismicresponses of the slope analysis methods of the landslidemechanism and the analysis method of seismic stability ofthe slope With the help of above-mentioned signal analysisskills in the aerospace area and signal analysis area (egHilbert-Huang transform) our team has conducted a seriesof analyses on civil structure depending on the proposedtime-frequency-amplitude (known as TFA for short) analysistheories which are comprised of horizontal layers inclined

Advances in Materials Science and Engineering 3

Figure 2 Shaking table test of site under nonuniform seismicexcitation

Figure 3 Shaking table test of rock slope

layers gravity retainingwall reinforced retainingwall slopesand landslide mechanism [17 18] Our team gives the initialprototype of TFA analysis theories in geotechnical seismicengineering which realizes the organic combination of timeand frequency information and develops a groundbreakingconcept to the traditional idea in the geotechnical seismicengineering area

4 Essence of the Time-Frequency-AmplitudeAnalysis Theories

The time-frequency-amplitude analysis theories give reason-able considerations to the time-frequency characteristics ofseismic waves mainly reflected in the elastic displacementmagnitude and the frequency of the wave vector This timethis paper selects Wolong earthquake wave (as shown inFigure 7) to make an explanation procedures are as followsfirst Wo-Long wave is decomposed into intrinsic modefunctions (IMF) using the empirical mode decomposition(EMD) method The acceleration time histories of each IMFcan be seen in Figure 8 and the instant frequency timehistories of each IMF can be seen in Figure 9 Based onthe acceleration time histories and instant frequency timehistories of each IMF bring them into the related formulasin order to get the stress time histories of each IMF finallysum the stress time histories together in order to obtain thetotal results

Figure 4 Shaking table test of retaining wall

Figure 5 Shaking table test of antisliding pile

5 Advantages of the Time-Frequency AnalysisMethod of Seismic Safety of the Rock Slope

Comparisons with pseudostatic methods using the variouscountriesrsquo earthquake resistant design codes TFA analysistheory of seismic stability of rock slope is capable of consider-ing the time frequency and amplitude of seismic wave andthen a brief introduction of the above-mentioned theory ismade as follows

In the TFA analysis theory of seismic stability of rockslope the calculated model is shown in Figures 10 and 11 Inthe model the sliding mass was divided into seven slices andan angle of 120579 between the tangent and horizontal directionsat any point A was obtained at the middle of a slice Figure 11shows the reflection and refraction model at point A Themechanical parameters in the upper medium (bedrock) are120588111986211990111198621199041 and1198661 (density 119875wave speed 119878wave speed andshearmodulus) and 120588211986211990121198621199042 and1198662 in the lowermedium(colluvial soils) and the I-I stands for the sliding surfaceWhen transverse wave 1198781 reaches the I-I surface some newwaves are produced for example reflected transverse wave1198782 reflected longitudinal wave 1198783 refracted transverse wave1198784 and refracted longitudinal wave 119878

5 1205721 12057210158401 1205731 and 120573

10158401

stand for the incident angle of the incident transverse wavethe reflected angle of the reflected longitudinal wave therefracted angle of the refracted transverse wave and therefracted angle of the refracted longitudinal wave Note thatthe reflected angle of the reflected transverse wave is the sameas the incident angle of the incident transverse wave

After the derivation the stress state at any point can becalculated according to (6) and (7) And then the stress stateat whole sliding surface can be calculated according to (8) At


Figure 6 Simulation test of fault slip

Trial license5 10 15 20 25 30 35

Time (s)

minus5000

5001000

Acce

lera

tion

(g)

Figure 7 Time history of the Wenchuan-Wolong seismic wave

5 10 15 20 25 30 35minus500

0500

1000150020002500300035004000450050005500

Acce

lera

tion

(cm

ss

)

Trial license

Time (s)

Figure 8 Acceleration time history of IMF

Trial license5 10 15 20 25 30 35

Time (s)

0

500

1000

1500

2000

2500

3000

3500

(cm

ss

)

Figure 9 Instant frequency time history of IMF

Sliding mass

BedrockA

Figure 10 Generalized model of the bedrock-regolith slope

A

1205721

1205731

S1

S2

S4

S5

S3

1205729984001

1205739984001

X

Z

Figure 11 Analysis model of reflection and refraction at any pointA

last the seismic stability of slope can be estimated accordingto (9)

Consider

120591s = 1205910 + 1205831 [11987810 sdot 11989611119911 sdot cos1205721 minus 119878

20 sdot 11989621119911 sdot cos1205721

+ 11987830 sdot 11989631119911 sdot sin12057210158401 minus 119878

10 sdot 11989611119909 sdot sin1205721 minus 119878

20 sdot 11989621119909

sdot sin1205721 minus 11987830 sdot 11989631119909 sdot cos12057210158401]

(6)

1205900 tan120593 + 119862

= 1205821 [11987810 sdot 11989611119909 sdot cos1205721 minus 119878

20 sdot 11989621119909

sdot cos1205721 + 11987830 sdot 11989631119909 sdot sin12057210158401] + (1205821 + 21205831)

times [minus11987810 sdot 11989611119911 sdot sin1205721 minus 119878

20 sdot 11989621119911 sdot sin1205721

minus 11987830 sdot 11989631119911 sdot cos12057210158401] + 1205900 tan120593 + 119862

(7)

In (6) and (7) 11987810 stand for the displacement of incidenttransverse wave 11987820 stand for the displacement of reflectedtransverse wave 11987830 stand for the displacement of reflectedlongitudinal wave 11987840 stand for the displacement of refractedtransverse wave and 119878

50 stand for the displacement of

refracted longitudinal wave 1198961198941119909 1198961198941119911 stand for the wave vectors

in the 119883 and 119885 directions of the incident reflected and the


Figure 12 Calculated model

0 5 10 15 20 25 30 35 40

Acce

lera

tion

(g)

Time (s)

minus200E minus 01minus150E minus 01minus100E minus 01minus500E minus 02000E + 00500E minus 02100E minus 01150E minus 01200E minus 01

Figure 13 Time history of sine wave

refracted waves respectively119862 stand for the cohension of thesliding mass and 120593 stand for the internal friction angle

Consider

119865119904 =

119899

sum

119894=1

120591119904119894 sdot 119889119860 119894

119865119903 =

119899

sum

119894=1

(1205900119894 sdot tan120593119894 + 119862119894) sdot 119889119860 119894

(8)

119870 =119865119903

119865119904

lt 1198700 risk

119870 =119865119903

119865119904

gt 1198700 safety(9)

In (8) and (9) 120591119904119894 represents the sliding shear stress at point 119894119860 119894 = 05 (119871 119894minus1 + 119871 119894+1) times 1 is the slice area 119871 119894minus1 is the widthof the 119894 minus 1th slice and 119871 119894+1 is the width of the 119894 + 1th slice1205900119894 represents the normal stress at point 119894 120593119894 represents thefrictional angle at point 119894 119862119894 represents the cohesion at point119894

According to the above-mentioned method a simpleexample is used to illustrate the advantage of the TFAanalysis theory model for calculation is shown in Figure 12Figures 13 and 14 give the adopted sine wave whose instan-taneous frequencies gradually increase with time and thecalculated parameters can be seen in Table 1

After the calculation is done results of TFA analysismethod are shown in Figure 15 indicating that the slopewould fail after 119879 = 100 s The result of pseudostatic methodshows that the surplus sliding force is minus47 kN andmeans thatthe slope is stable While the slope is proven to fail in thenumerical simulation which is consistent with the result of

0

0005

001

0015

002

0025

Trial license

5 10 15 20 25 30 35 40Time (s)

0

5

10

15

20

25

Freq

uenc

y (H

z)

Figure 14 Hilbert spectrum of sine wave

Time (s)

minus60

minus40

minus20

0

20

40

60

0 5 10 15 20 25 30 35 40

Surp

lus s

hear

forc

e (kN

)

Figure 15 Result of TFA analysis method

TFA analysis method shown in Figure 16 this phenomenoncan be elucidated as follows

(i) At 119879 = 100 s the instantaneous frequency of theseismic wave is 49Hz and the natural frequencycalculated according to the literature [17] is 68Hzwith both being very close to each other leadingto a further resonance However the instantaneousfrequency of the input seismic wave reaches 68Hzat 119879 = 182 s and the resonance shows the strongestvalue which leads to the maximum surplus shearforce Then the resonance gradually decreases withdifference between the frequencies of the input waveand the natural frequency goes up and the surplusshear force gradually decreases in response

(ii) Time-frequency analysis method and numericalmethod both not only can consider the effect of PGAon the seismic stability of slope but also consider theeffect of frequency on the seismic stability of slopeBut pseudo-staticmethod only can consider the effectof PGA on the seismic stability of slope which leadsto the difference between the calculated results

Synthesizes the above analysis we can know that thereforethe TFA analysis method can solve the fundamental flawexisting in the analysis method using the codes


Table 1 Physical and mechanics parameters of bedrock soil layer and structural plane

Model Gravity Shear wave velocity Longitudinal wave velocity Lame coefficients Shear modulusBedrock 30 kNm3 82619ms 3240ms 88189MPa 204724MPaSlip mass 19 kNm3 9921ms 14534ms 630MPa 630MPaSliding surface Normal stiffness Shear stiffness Internal friction angle Tensile strength Cohesion

4500MPa 2300 32∘ 23 kPa 50 kPa

3856e minus 0033435e minus 0033015e minus 0032595e minus 0032175e minus 0031755e minus 0031335e minus 0039144e minus 0044942e minus 0047402e minus 005minus3462e minus 004minus7663e minus 004minus4616e minus 003minus5475e minus 002minus1049e minus 001minus1550e minus 001minus2051e minus 001

Figure 16 Results of numerical simulation

6 Application in Practice

Up to now the TFA analysis theory has been already usedto direct the aseismic designs of geotechnical engineeringcontaining several kilometers of YaLe expressway and thecontribution to several traffic lines opening

7 Conclusions and Future Works

Themain conclusions of this study are as follows

(i) Based on the above analysis this paper gives an initialprototype of time-frequency-amplitude analysis the-ory in the geotechnical seismic engineeringThis the-ory realizes the organic combination of time informa-tion and frequency information and gives reasonableconsiderations to the time-frequency characteristicsof seismic waves which mainly is reflected in theelastic displacement magnitude and the frequency ofthe wave vector and that is the core content of TFAanalysis theories

(ii) Comparing to the results of TFA analysis theoryof rock slope pseudostatic method and numericalanalysis method shows that the TFA analysis theorycan consider the effect of the time and frequencyof the input wave on the seismic stability of slopewhich solves the fundamental flaw existing in theanalysis method using the codes At the same timeaccording to the derivation results we can know thatthe time-frequency analysis method of rock slope hassome universalization and comprehensiveness whichcan consider some factors reasonably as follows (1)initial geostress field (2) the inner frictional angle thecohesion the reflection coefficients and the refrac-tion coefficients (3) the physical and mechanicalproperties of the bedrock and the regolith and (4)the instantaneous frequency the incidence angle the

time histories of the acceleration the velocity thedisplacement and so forth

(iii) The time-frequency-amplitude analysis theory is builtin compliance with the elastic wave theory andgeotechnical seismic engineering in which the elasticstate of the system is considered The next worksare making the further studies based on the presentoutcomes time-frequency-amplitude analysis theorycan be thus proposed to consider the nonlinear of thegeotechnical engineering and earthquake wave

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This study is supported in part by the National Science Foun-dation of China (Contract no 41030742) NBRP of China(973 Program 2011CB013605) and Construction and Scienceand Technology Project of the Ministry of Communications(Contract no 2013318800020)

References

[1] D K Keefer ldquoLandslides caused by earthquakesrdquo GeologicalSociety of America Bulletin vol 95 pp 406ndash421 1984

[2] J N Hutchinson ldquoMechanism producing large displacementsin landslides on preexisting shearsrdquo Memoir of the Society ofGeology of China vol 9 pp 175ndash200 1987

[3] K Sassa ldquoPrediction of earthquake induced landslidesrdquo inProceedings of the 7th International Symposium on LandslidesK Senneset Ed vol 1 pp 115ndash132 Balkema Rotterdam TheNetherlands 1996

[4] A Prestininzi and R Romeo ldquoEarthquake-induced groundfailures in Italyrdquo Engineering Geology vol 58 no 3-4 pp 387ndash397 2000

[5] M Lin and K Wang ldquoSeismic slope behavior in a large-scaleshaking table model testrdquo Engineering Geology vol 86 no 2-3pp 118ndash133 2006

[6] M Chigira X Wu T Inokuchi and G Wang ldquoLandslidesinduced by the 2008 Wenchuan earthquake Sichuan ChinardquoGeomorphology vol 118 no 3-4 pp 225ndash238 2010

[7] JWasowski andV Del Gaudio ldquoEvaluating seismically inducedmass movement hazard in Caramaico Terme (Italy)rdquo Engineer-ing Geology vol 58 no 3-4 pp 291ndash311 2000

[8] H B Havenith D Jongmans E Faccioli K Abdrakhmatovand P Bard ldquoSite effect analysis around the seismically induced


Ananevo rockslide Kyrgyzstanrdquo Bulletin of the SeismologicalSociety of America vol 92 no 8 pp 3190ndash3209 2002

[9] H-B Havenith A Strom D Jongmans K Abdrakhmatov DDelvaux andP Trefois ldquoSeismic triggering of landslides part Afield evidence from the Northern Tien Shanrdquo Natural Hazardsand Earth System Science vol 3 no 1-2 pp 135ndash149 2003

[10] S A Sepulveda W Murphy R W Jibson and D N PetleyldquoSeismically induced rock slope failures resulting from topo-graphic amplification of strong ground motions the case ofPacoima Canyon Californiardquo Engineering Geology vol 80 no3-4 pp 336ndash348 2005

[11] A L Che and X R Ge ldquoEarthquake-induced toppling failuremechanism and its evaluationmethod of slope in discontinuousrock massrdquo International Journal of Applied Mechanics vol 4no 3 Article ID 1250036 15 pages 2012

[12] Z Zuwu and Y Lingkan ldquoSeismic waves scattering in rockinterface and energy dissipation characteristicsmdashtaking M80Wenchuan Earthquake as an examplerdquo Journal of Catastrophol-ogy no 1 pp 5ndash9 2011

[13] S XuW Zheng Y Liu D Xi and G Li ldquoA preliminary analysisof scale effect of elastic wave propagation in rockmassrdquo ChineseJournal of Geotechnical Engineering vol 33 no 9 pp 1348ndash13562011

[14] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquoTheRoyal Society of LondonA vol 454 pp 903ndash995 1998

[15] J Zhang H Qu Y Liao and Y Ma ldquoSeismic damage ofearth structures of road engineering in the 2008 Wenchuanearthquakerdquo Environmental Earth Sciences vol 65 no 4 pp987ndash993 2012

[16] Y Changwei and Z Jianjing ldquoA predictionmodel for horizontalrun-out distance of landslides triggered by Wenchuan Earth-quakerdquo Earthquake Engineering and Engineering Vibration vol12 no 2 pp 201ndash208 2013

[17] C Yang J Zhang and D Zhou ldquoResearch on time-frequencyanalysis method for seismic stability of rock slope subjected toSV waverdquo Chinese Journal of Rock Mechanics and Engineeringvol 32 no 3 pp 483ndash491 2013

[18] C Yang and J Zhang ldquoLandslide responses of high steephill with two-side slopes under ground shakingrdquo Journal ofSouthwest Jiaotong University vol 48 no 3 pp 415ndash422 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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NanoparticlesJournal of



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Biomaterials


NanoscienceJournal of

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Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


The figure of investigated routes in disaster areas

Earthquake fault zoneInvestigated routeSeismic influenced areaCountry roadProvince roadMunicipal governmentCounty governmentDamaged spots

Figure 1 Roads investigated and seismic intensity

intrinsic mode function (known as IMF for short) com-ponents by using ensemble empirical mode decomposition(known as EEMD for short) method The instantaneousfrequency of each IMF will be derived by the Hilbert-Huangtransform and then the Hilbert spectrumwill be obtained byintegrating all the instantaneous frequency spectrums Theanalytical signal amplitude function phase function andinstantaneous frequency function can be obtained by usingthe Hilbert-Huang transform The computational formulasare shown in

119885 (119905) = 119888 (119905) + 119895119867 [119888 (119905)] = 119886 (119905) 119890119895120601(119905)

119886 (119905) = radic1198882 (119905) + 1198672 [119888 (119905)]

120601 (119905) = arctan 119867[119888 (119905)]

119888 (119905)

119891 (119905) =1

2120587

119889120601 (119905)

119889 (119905)

(1)

From the above formulas it is known that both amplitudeand frequency are the function of time If the amplitude iscalculated by using a combined time and frequency domainapproach the Hilbert spectrum can be obtained as shown in(2) The marginal spectrum and the instantaneous frequencyspectrum can be obtained by using (3) and (4) The Hilbertspectrum can be obtained by integrating amplitude squaredas shown in (5)

Consider

119867(120596 119905) = Re119899

sum

119894=1

119886119894 (119905) 119890119895120601119894(119905) (2)

ℎ (120596) = int

119879

0

119867(120596 119905) 119889119905 (3)

119868119864 (119905) = int120596

119867(120596 119905) 119889119905 (4)

119864119878 (120596) = int

119879

0

1198672(120596 119905) 119889119905 (5)

3 New Development in the GeotechnicalEarthquake Engineering

Up to now our team has conducted a field investigationalong the road and railway nearly 3000 km in 512 Wenchuanearthquake-stricken areas (see Figure 1) a number of fieldmonitoring of typical slopes more than twenty shaking tabletests a number of numerical simulations and theoreticalstudies [15 16] some shaking tabletest models are shown inFigures 2 3 4 5 and 6

On the basis of extensive studies several importantproblems in the geotechnical seismic engineering are studiedincluding analysis methods of seismic responses of the siteanalysis methods of seismic responses and seismic stabilityof the retaining structures analysis methods of seismicresponses of the slope analysis methods of the landslidemechanism and the analysis method of seismic stability ofthe slope With the help of above-mentioned signal analysisskills in the aerospace area and signal analysis area (egHilbert-Huang transform) our team has conducted a seriesof analyses on civil structure depending on the proposedtime-frequency-amplitude (known as TFA for short) analysistheories which are comprised of horizontal layers inclined












5 1205721 12057210158401 1205731 and 120573

10158401





Trial license5 10 15 20 25 30 35

Time (s)

minus5000

5001000

Acce

lera

tion

(g)


5 10 15 20 25 30 35minus500

0500

1000150020002500300035004000450050005500

Acce

lera

tion

(cm

ss

)

Trial license

Time (s)


Trial license5 10 15 20 25 30 35

Time (s)

0

500

1000

1500

2000

2500

3000

3500

(cm

ss

)


Sliding mass

BedrockA


A

1205721

1205731

S1

S2

S4

S5

S3

1205729984001

1205739984001

X

Z



Consider


20 sdot 11989621119911 sdot cos1205721



20 sdot 11989621119909


(6)

1205900 tan120593 + 119862


20 sdot 11989621119909



20 sdot 11989621119911 sdot sin1205721


(7)







0 5 10 15 20 25 30 35 40

Acce

lera

tion

(g)

Time (s)




Consider

119865119904 =

119899

sum

119894=1

120591119904119894 sdot 119889119860 119894

119865119903 =

119899

sum

119894=1

(1205900119894 sdot tan120593119894 + 119862119894) sdot 119889119860 119894

(8)

119870 =119865119903

119865119904

lt 1198700 risk

119870 =119865119903

119865119904





0

0005

001

0015

002

0025

Trial license

5 10 15 20 25 30 35 40Time (s)

0

5

10

15

20

25

Freq

uenc

y (H

z)


Time (s)

minus60

minus40

minus20

0

20

40

60

0 5 10 15 20 25 30 35 40

Surp

lus s

hear

forc

e (kN

)









4500MPa 2300 32∘ 23 kPa 50 kPa













Acknowledgments


References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials














5 1205721 12057210158401 1205731 and 120573

10158401





Trial license5 10 15 20 25 30 35

Time (s)

minus5000

5001000

Acce

lera

tion

(g)


5 10 15 20 25 30 35minus500

0500

1000150020002500300035004000450050005500

Acce

lera

tion

(cm

ss

)

Trial license

Time (s)


Trial license5 10 15 20 25 30 35

Time (s)

0

500

1000

1500

2000

2500

3000

3500

(cm

ss

)


Sliding mass

BedrockA


A

1205721

1205731

S1

S2

S4

S5

S3

1205729984001

1205739984001

X

Z



Consider


20 sdot 11989621119911 sdot cos1205721



20 sdot 11989621119909


(6)

1205900 tan120593 + 119862


20 sdot 11989621119909



20 sdot 11989621119911 sdot sin1205721


(7)







0 5 10 15 20 25 30 35 40

Acce

lera

tion

(g)

Time (s)




Consider

119865119904 =

119899

sum

119894=1

120591119904119894 sdot 119889119860 119894

119865119903 =

119899

sum

119894=1

(1205900119894 sdot tan120593119894 + 119862119894) sdot 119889119860 119894

(8)

119870 =119865119903

119865119904

lt 1198700 risk

119870 =119865119903

119865119904





0

0005

001

0015

002

0025

Trial license

5 10 15 20 25 30 35 40Time (s)

0

5

10

15

20

25

Freq

uenc

y (H

z)


Time (s)

minus60

minus40

minus20

0

20

40

60

0 5 10 15 20 25 30 35 40

Surp

lus s

hear

forc

e (kN

)









4500MPa 2300 32∘ 23 kPa 50 kPa













Acknowledgments


References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Trial license5 10 15 20 25 30 35

Time (s)

minus5000

5001000

Acce

lera

tion

(g)


5 10 15 20 25 30 35minus500

0500

1000150020002500300035004000450050005500

Acce

lera

tion

(cm

ss

)

Trial license

Time (s)


Trial license5 10 15 20 25 30 35

Time (s)

0

500

1000

1500

2000

2500

3000

3500

(cm

ss

)


Sliding mass

BedrockA


A

1205721

1205731

S1

S2

S4

S5

S3

1205729984001

1205739984001

X

Z



Consider


20 sdot 11989621119911 sdot cos1205721



20 sdot 11989621119909


(6)

1205900 tan120593 + 119862


20 sdot 11989621119909



20 sdot 11989621119911 sdot sin1205721


(7)







0 5 10 15 20 25 30 35 40

Acce

lera

tion

(g)

Time (s)




Consider

119865119904 =

119899

sum

119894=1

120591119904119894 sdot 119889119860 119894

119865119903 =

119899

sum

119894=1

(1205900119894 sdot tan120593119894 + 119862119894) sdot 119889119860 119894

(8)

119870 =119865119903

119865119904

lt 1198700 risk

119870 =119865119903

119865119904





0

0005

001

0015

002

0025

Trial license

5 10 15 20 25 30 35 40Time (s)

0

5

10

15

20

25

Freq

uenc

y (H

z)


Time (s)

minus60

minus40

minus20

0

20

40

60

0 5 10 15 20 25 30 35 40

Surp

lus s

hear

forc

e (kN

)









4500MPa 2300 32∘ 23 kPa 50 kPa













Acknowledgments


References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





0 5 10 15 20 25 30 35 40

Acce

lera

tion

(g)

Time (s)




Consider

119865119904 =

119899

sum

119894=1

120591119904119894 sdot 119889119860 119894

119865119903 =

119899

sum

119894=1

(1205900119894 sdot tan120593119894 + 119862119894) sdot 119889119860 119894

(8)

119870 =119865119903

119865119904

lt 1198700 risk

119870 =119865119903

119865119904





0

0005

001

0015

002

0025

Trial license

5 10 15 20 25 30 35 40Time (s)

0

5

10

15

20

25

Freq

uenc

y (H

z)


Time (s)

minus60

minus40

minus20

0

20

40

60

0 5 10 15 20 25 30 35 40

Surp

lus s

hear

forc

e (kN

)









4500MPa 2300 32∘ 23 kPa 50 kPa













Acknowledgments


References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






4500MPa 2300 32∘ 23 kPa 50 kPa













Acknowledgments


References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Research Article New Developments in Geotechnical...

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