research article application of effective stress model to...

Research ArticleApplication of Effective Stress Model to Analysis of Liquefactionand Seismic Performance of an Earth Dam in China

Changqing Qi Wei Lu Jimin Wu and Xing Liu

School of Earth Sciences and Engineering Hohai University Nanjing 210098 China

Correspondence should be addressed to Changqing Qi chqi79gmailcom

Received 17 February 2015 Accepted 17 June 2015

Academic Editor Francesco Tornabene

Copyright copy 2015 Changqing Qi et al This 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

Earthquake-induced liquefaction is one of the major causes of catastrophic earth dam failure In order to assess the liquefactionpotential and analyze the seismic performance of an earth dam in Fujian SoutheasternChina the in situ shear wave velocity test wasfirstly carried out Results indicate that the gravelly filling is a type of liquefiable soil at present seismic setting Then the effectivestress model was adopted to thoroughly simulate the response of the soil to a proposed earthquake Numerical result generallycoincides with that of the empirical judgment based on in situ test Negative excess pore pressure developed in the upper part ofthe saturated gravelly filling and positive excess pore pressure developed in the lower part The excess pore pressure ratio increaseswith depth until it reaches a maximum value of 045The displacement of the saturated gravelly soil is relatively small and tolerableResults show that the saturated gravelly filling cannot reach a fully liquefied state The dam is overall stable under the proposedearthquake

1 Introduction

Earth dams usually have better seismic performance duringearthquakes According to statistics seldom earth dams havebeen totally out of service after earthquakes in the past fewdecades inChina [1] But when the dam contains or is situatedon liquefiable materials earthquake-induced liquefactionmay cause considerable reduction in stiffness and strengthof soil resulting in dam failure [2] A number of damfailures or damages have been reported due to seismicallyinduced liquefaction The most classic example is the lowerSan Fernando damduring the 1971 San Fernando earthquakeLiquefaction induced flow slide on the upstream side of thedam nearly caused the dam to be out of service [3] Theliquefaction slide of Baihe dam of Miyun Reservoir duringthe 1976 Tangshan earthquake was another representativeexample The estimated 015 million m3 volumetric slide inthe upstream part of the dam aroused great panic at that time[4] Several dam failures in Chilean [5] Japan [6] and India[7] were also reported causing great damage

In sight of its immense economic damage and loss oflife earth dam failures due to liquefaction have drawn greatconcern in the past half century Several types of approacheshave been developed to study this problem The empirical

relationships based on tested indexes are commonly usedmethods at present [8ndash10] The empirical relationship meth-ods can give an overall and quick judgment on liquefactionpotential of gravelly soil But for thoroughly understandingthe response of coarse soil to cyclic shear loads numericalmodeling technique is better [11ndash13] The seismic response ofsoil has a direct relation to the progressive build-up of porepressure during an earthquake The increasing pore pressureand decreasing effective stress control the resistance of thesoil to deformation [14] Thus assessment on progressivedegradation of soil strength is important in dynamic soilliquefaction analysis

The effective stress method is a useful tool in modelingthe progressive loss of soil strength caused by development ofpore pressure Liyanapathirana and Poulos [15] summarizedfourmain categories of liquefactionmodels based on effectivestress analysis method which are (1) models based onplasticity theory (2) stress path methods (3) correlationsbetween pore pressure response and plastic volume changetendency and (4) use of experimentally observed undrainedpore pressure response The model of the third categorywhich is often referred to as the Finn model is explicitand has a lesser number of parameters The model can takeinto account stiffness and strength degradation due to pore

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 404712 7 pageshttpdxdoiorg1011552015404712

2 Mathematical Problems in Engineering

pressure development and was used in this paper for damliquefaction and seismic performance assessment

2 Methodology

The strength and stiffness of soil are primarily governed byeffective stress and so it is desirable to evaluate seismicresponse of soil in terms of effective stress For saturated gran-ular material adopted numerical model should reflect thevariation of pore pressure and thus can predict the effectivestress level

For saturated soil under undrained conditions Martin etal [16] suggested that the pore pressure increment is relatedto the change of plastic volumetric strain of the soil skeleton

Δ119906 = minus1119862119887

Δ120576V119889 (1)

whereΔ119906 is pore pressure increment119862119887is bulk compressibil-

ity and Δ120576V119889 is the plastic volumetric strain increment Thereferred model can adequately reflect the response of porepressure until liquefaction triggering point [17] and thus isan effective tool for assessment of soil liquefaction risk

Theplastic volumetric strain increment could be obtainedby various constitutive theories In this paper the expressionpresented by Byrne [18] was adopted The plastic volumetricstrain increment was expressed as follows

Δ120576V119889

120574= 1198621 exp(minus1198622

120576V119889

120574) (2)

where 120574 is the shear strain in the current cycle 120576V119889 is theaccumulated volumetric strain from prior cycles and 1198621 and1198622 are constants that depend on the relative density119863

119903

1198621 = 7600 (119863119903)minus25

1198622 =041198621

(3)

In this paper the model was incorporated into the finitedifference computer program Flac3D to perform a nonlinearfully coupled dynamic analysis Flac3D is based on a con-tinuum finite difference discretization using the Lagrangianapproach [19] The equations of motion are utilized to obtainthe velocities and displacements when dynamic load isexcreted The equation of motion can be expressed as

120588120597V119894

120597119905=

120597120590119894119895

120597119909119894

+120588119887119894 (4)

where 120588 is material density 119905 is time domain 119909119894is coordinate

vector 120590119894119895is stress tensor and 119887

119894is body force

For a fully nonlinear method any given function can beused in dynamic analysis of Flac3D The general constitutiveequation is expressed as

120590119894119895= 119872(120590

119894119895 120576119894119895 120581) (5)

where 120590119894119895is stress rate tensor 120576

119894119895is strain rate tensor 120581 is the

parameter taking the loading history into account and 119872 isthe given functional expression

The Mohr-Coulomb elastic-perfectly plastic constitutiverelation is the commonly used constitutive models for soilIn order to adapt the model for dynamic analysis severalmodifications have been achieved In this paper the modifi-cation defined by Puebla et al [20] was usedThe secant shearmodulus119866 and bulk modulus 119861were considered to be stress-dependent and given as follows

119866 = kg sdotPa sdot (1205901015840119898Pa)119899

119861 = kb sdotPa sdot (1205901015840119898Pa)119898

(6)

where kg and kb are shear and bulk modulus numbers 119899 and119898 aremodulus exponents 1205901015840

119898is themean effective stress and

Pa is atmospheric pressure

3 Statement of Dam Conditions

Dongzhen reservoir located about 60 km upstream PutianCity in Fujian Province Southeastern China has a normalstorage capacity of 435 millionm3 The reservoir has acomprehensive function of flood control irrigation andpower generation The water retaining dam has an irregulargeometry (Figure 1) The longitudinal profile of the dam hasan asymmetric U-shape which is steep on the right flank andgentle on the left (Figure 2(a)) The dam is a core-wall earthdam with a maximum height of 586mThe normal dammedwater level is about 81m to the dam crest (Figure 2(b)) Thecore wall made of lean clay and the filling is gravelly soil Alayer of rock blocks revetment was placed on the surface toprotect the slope The thickness of the blocks revetment onthe upstream surface is about 20m

Thedamwas built in the 1950s when there was no seismicdesign standard in China The study area is located in thecoast of Taiwan Channel Caused by the movement of thePacific Plate a series of NNE and NW fault zones can befound in this area (Figure 3) The area is currently within theregion with seismic intensity of 7 based on Chinese Standard[21] According to the seismic safety analysis completedby Fujian Provincial Institute of Geological EngineeringInvestigation the equivalent earthquake magnitude whichaffects the dam area is Ms 65 and the epicenter distance isabout 50 kmThe peak bedrock acceleration of themaximumcredible earthquake is about 158 gal Owing to the high publicinterest and the large amount of potentially affected personsquestions about the seismic stability of the dam are importantto study in detail

4 Shear Wave Velocity Test

In order to study the seismic stability of the dam the firststep is to evaluate the liquefaction potential of gravelly soils[11] The usually available field test methods are the standardpenetration test (SPT) the cone penetration test (CPT) insitu shear wave velocity measurement (119881

119904) and the Becker

penetration test (BPT) [22] Among these approaches theshear wave velocity measurement is more feasible in gravellysoil field because this type of soil is difficult to penetrate[10 22 23] A three-component geophone setup was placedin a 30m deep borehole to obtain the shear wave velocity

Mathematical Problems in Engineering 3

Spillway

0 100(m)

N

DongzhenReservoir

70

7060

60

6070

80

4050

50

8080

Dam body

Figure 1 Plane view of Dongzhen Reservoir dam

0 100(m)

Dam body

NW

Bedrock

Spillway

(a)

0 40(m)

UpstreamDesign retaining water level

Downstream

Clay coreSand and gravel shell

Cut-off wall

Clay

Sand and gravel shellRock block

Bedrock

Rock block A1A2A3A4A5A6A7A8wall

1 201 25

1 32

1 29

1 30

(b)

Figure 2 Longitudinal (a) and cross (b) section of DongzhenReservoir dam A1ndashA8 denote the location for excess pore pressureratio analysis

at different depths According to Chinese Standard [24] thesoils can be determined as nonliquefiable when themeasuredshear wave velocity is greater than calculated limit shear wavevelocity The limit shear wave velocity can be calculated fromthe following empirical equation

119881119904119905

= 291 sdot radic119870ℎsdot 119885 sdot 119903119889 (7)

where 119881119904119905is the limit shear wave velocity 119870

ℎis the peak

acceleration coefficient the value is 01 for the field with

0 100(km)

F1 Eastern Taiwan Strait fault zoneF2 Seashore fault zoneF3 Changle-Shaoan fault zoneF4 Zhenghe-Haifeng fault zoneF5 Minjiang river fault zoneF6 Shaxian-Nanri island fault zoneF7 Yongan-Jinjiang river fault zoneF8 Jiulong river fault zoneF9 Shaxian-Lianjiang river fault zoneF10 Zhangping-Putian fault zoneF11 Nanjing-Xiamen fault zoneI Taiwan upwelling zoneII Taiwan Strait subsiding zoneIII Wuyi-Daiyun upwelling zone

Earthquake epicenter

Fuzhou

Dam site

Putian

Taiwan Strait

118∘

119∘

120∘

26∘

25∘

26∘

25∘

Quaternary formationCretaceous formationJurassic formationTriassic formationGranite

III3 Western Fujian upwelling zoneIII2 Central Fujian upwelling zoneIII1 Eastern Fujian upwelling zone

Figure 3 Geological map of the study area

seismic intensity of 7 119885 refers to the depth and 119903119889can be

calculated as follows119903119889= 10minus 001119885 when 119885 = 0 sim 10m

119903119889= 11minus 002119885 when 119885 = 10 sim 20m

119903119889= 09minus 001119885 when 119885 = 20 sim 30m

(8)

The measured and calculated results are listed in Table 1It can be concluded that the upstream gravelly filling has thepossibility of liquefaction below the depth of 120m

5 Liquefaction Assessment andDeformation Analysis

51 Numerical Modeling and Parameters The detailed seis-mic response of Dongzhen Reservoir dam was simulated


Table 1 Liquefaction judgment using shear wave velocity test

Number Depth (m) Measured shear wavevelocity (ms)

Limit shear wavevelocity (ms)

Primary liquefactionestimation

1 2ndash4 315 157 Nonliquefiable2 4ndash6 292 201 Nonliquefiable3 6ndash8 305 235 Nonliquefiable4 8ndash10 315 263 Nonliquefiable5 10ndash12 296 286 Nonliquefiable6 12ndash14 300 304 Liquefiable7 14ndash16 285 319 Liquefiable8 16ndash18 314 331 Liquefiable9 18ndash20 287 340 Liquefiable10 20ndash22 302 350 Liquefiable11 22ndash24 303 361 Liquefiable12 24ndash26 304 371 Liquefiable13 26ndash28 304 380 Liquefiable14 28ndash30 288 387 Liquefiable

using software Flac3D A three-dimensional modeling of thedam was established (Figure 4) 119909-axis of the model wasset along the river 119910-axis was set perpendicular to theriver center line and the positive 119911-axis was set upward Afield seismic wave provided by Fujian Provincial Institute ofGeological Engineering Investigation was used in this paperfor dam seismic response analysis The seismic wave wasselected from historical seismic wave database consideringsimilar field condition and potential influence of the epicen-ter The seismic acceleration was recorded from the Ms 66Imperial Valley Earthquake in 1979 at an epicenter distanceof 576 km The peak seismic acceleration is 189 gal Thehorizontal acceleration time history was shown in Figure 5The viscous absorb boundary developed by Lysmer andKuhlemeyer [25] was used to absorb the unbalanced energyat the boundary In view of the large permeability differencebetween the clay and gravelly soil the clay core wall wasconsidered as impermeable layerThe phreatic water level wasused and normal retaining water level of the reservoir was81m below the dam crestThe hydrostatic pressure caused bythe retaining water was applied to the upper stream surface ofthe dam

The analysis was conducted in two steps First the staticanalysis was carried out The Mohr-Coulomb model withstress-dependent materials properties was used for all theparts of the dam The materials properties of the dam aregiven in Table 2 In the second step the effective stress modelwas applied to the upstream gravelly soil and the Mohr-Coulomb model was still used for the rest parts The relativedensity (119863

119903) of the upstream gravelly soil used in the Byrne

model was obtained by field test and the mean value is 675In order to illustrate the liquefaction degree of the gravelly

soil the excess pore pressure ratio 119877119906was defined and

denoted as

119877119906=

119880119890

1205901015840

1198980 (9)

where 119880119890is the excess pore pressure during the earthquake

and 1205901015840

1198980is the mean effective stress in the static condition

Block groupClayGravelly

Block

XY

Z

Figure 4 Three-dimensional finite difference mesh of DongzhenReservoir dam

0 5 10 15 20 25 30

minus200

minus150

minus100

minus50

0

50

100

150

200

Acce

lera

tion

(gal

)

Time (s)

Figure 5 Input earthquake acceleration record

119877119906

= 10 represents a fully liquefied state and 119877119906

= 00

represents a static condition


0 5 10 15 20 25 30minus08

minus06

minus04

minus02

00

02

04

Time (s)

A1

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(a)

0 5 10 15 20 25 30minus06

minus04

minus02

00

02

04

06

08

Time (s)

A2

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(b)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A3

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(c)

0 5 10 15 20 25 30

minus02

00

02

04

06

Time (s)

A4

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(d)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A5

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(e)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A6

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(f)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A7

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(g)

0 5 10 15 20 25 30

minus015

minus010

minus005

000005010015020025

Exce

ss p

ore p

ress

ure r

atio

(Pa)

Time (s)

A8

(h)

Figure 6 Excess pore pressure ratio of upstream gravelly soil at points A1 to A8 The location of points A1 to A8 is shown in Figure 2(b)


Table 2 Properties of the soils used in the numerical modeling

Material UnitweightkNm3

Shear modulusnumbers

Shear modulusexponent

Bulk modulusnumbers

Bulk modulusexponents CohesionkPa Friction

angle∘Permeability

coefficient cmsClay 195 490 050 1470 050 480 240 750 times 10

minus6

Gravel 200 1200 063 3600 063 00 370 522 times 10minus2

Block 220 1050 069 3150 069 00 450 055

52 Result of the Analyses The responses of the saturatedgravelly soil in terms of excess pore pressure ratio (119877

119906)

at different depths are presented in Figure 6 The relativepositions selected for illustration are shown in Figure 2 Thedistance of the positions is about 50m and the depth ofpoint A1 is about 20m which is just below the rock blockrevetment layer Figure 6 indicates that negative excess porepressure ratio developed in the upper part of the saturatedgravelly filling which means a decrease of pore pressure andincrease of effective stress This phenomenon coincides withthe dynamic behavior research of moderate dense granularmaterial with low confining stress [26] The increase of effec-tive stress prevents the occurrence of potential liquefaction inthis rangeThis conclusion also coincides with the result of insitu shear wave test Below the depth of 120m only positiveexcess pore pressures were built up during the earthquakeThe excess pore pressures ratios increase sharply in the time75 to 10 s corresponding to the period of strong shakingand then level off The permanent mean excess pore pressureratio increases with depth and then decreasesThemaximumpermanent mean excess pore pressure ratio is less than 045which means that upstream saturated gravelly filling cannotreach a fully liquefied state

Figure 7 illustrates the time history of the maximumhorizontal displacement in the upstream gravelly soil of thedam We can observe that the permanent displacement isrelatively small The maximum horizontal displacement ofthe upstream filling occurs at middle slope with a valueabout 73 cmThe deformations are tolerable and do not havesignificant influence on the service function of thewhole damaccording to Hynes-Griffin and Franklin [27]

6 Conclusion and Discussion

Soil liquefaction resulting from earthquake shaking is amajorcause of damage in earth dam engineering The field of soilliquefaction research is now only semimaturedThe generallyused liquefaction assessment methods include laboratorytest empirical relationships base on in situ test indexes andnumericalmodeling analyses Laboratory tests sometimes aretoo complicated and expensive to be used in engineeringAlso undisturbed test samples are difficult to collect andstore These two aspects restrict the wide use of laboratorytests The empirical judgments only need several in situ testindexes Empirical relationships were established based onnumerous field cases and accordingly can give a reasonableresult in liquefaction estimation Thus the empirical judg-ment is the dominated method at present But the empiricalmethods can only provide overall seismic response estima-tion The history of soil strength and deformation during

0 5 10 15 20 25 30minus010

minus008

minus006

minus004

minus002

000

002

Hor

izon

tal d

ispla

cem

ent (

m)

Time (s)

Figure 7 Time history of maximum horizontal displacement inupstream gravelly soil

earthquake cannot be reflected in empirical relationshipsOppositely numerical modeling can adopt more complexgeometrical stress history and constitutive models and caneasily give the results of effective stress shear strain anddeformation at any time So it is more feasible for detailedseismic performance analysis

Dongzhen Reservoir water retaining dam is only 60 kmupstream the Putian City The stability of the dam has drawngreat concerns The result of in situ shear wave velocitytest demonstrates that the gravelly filling has liquefactionpotential under an earthquake of intensity 7 In order tothoroughly investigate the seismic response of the dam three-dimensional finite difference technique was adopted in thispaper The results suggest that negative excess pore pressuredeveloped in the upper part of the saturated gravelly fillingwhichmeans that the gravelly soil is not likely to liquefy abovethe depth of 120m Below this depth positive excess porepressure developed and the maximum excess pore pressureratio appears at the depth of about 220m The maximumexcess pore pressure ratio rises to about 045 This meansthat the gravelly soil cannot reach a fully liquefied stateThe displacement in upstream saturated gravelly filling isrelatively small and tolerable The deformation would nothave significant impact on the overall stability of the damThegravelly filling still can maintain its seismic resistance

Conflict of Interests

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


Acknowledgments

The authors would like to gratefully acknowledge the finan-cial support provided by National Natural Science Founda-tion of China (no 41272328) The authors also wish to thankthe reviewers for their instructive comments

References

[1] J G Gao ldquoEarthquake-caused-damages of reservoirs in Chinaand countermeasures against themrdquo Journal of Disaster Pre-vention and Mitigation Engineering vol 23 pp 81ndash91 2003(Chinese)

[2] H B Seed P A De Alba and F I Makdisi ldquoPerformance ofearth dams during earthquakesrdquo Journal of the GeotechnicalEngineering Division vol 104 pp 967ndash994 1978

[3] H B Seed K L Lee I M Idriss and F I Makdisi ldquoThe slidesin the San Fernando dams during the earthquake of February 91971rdquo Journal of the Geotechnical Engineering Division vol 101no 7 pp 651ndash688 1975

[4] X Z Ling L X Wang and H Zhou ldquoAscertainment of sandliquefaction arising from earthquake by the method of compre-hensive stress taking seismic damage to Baihe principal dam ofMiyun reservoir in Beijing China as an examplerdquo EarthquakeEngineering and Engineering Vibration vol 21 pp 99ndash104 2001(Chinese)

[5] R Dobry and L Alavarez ldquoSeismic failures of Chilean tailingsdamsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 93 pp 237ndash260 1967

[6] S Okusa and S Anma ldquoSlope failures and tailings dam dam-age in the 1978 Izu-Ohshima-Kinkai earthquakerdquo EngineeringGeology vol 16 no 3-4 pp 195ndash224 1980

[7] E L Krinitzsky andM E Hynes ldquoThe Bhuj India earthquakelessons learned for earthquake safety of dams on alluviumrdquoEngineering Geology vol 66 no 3-4 pp 163ndash196 2002

[8] H A Taiebat and J P Carter ldquoA semi-empirical method forthe liquefaction analysis of offshore foundationsrdquo InternationalJournal for Numerical and Analytical Methods in Geomechanicsvol 24 no 13 pp 991ndash1011 2000

[9] R D Andrus P Piratheepan B S Ellis J Zhang and C HJuang ldquoComparing liquefaction evaluationmethods using pen-etration-VS relationshipsrdquo Soil Dynamics and Earthquake Engi-neering vol 24 no 9-10 pp 713ndash721 2004

[10] I M Idriss and R W Boulanger ldquoSemi-empirical proceduresfor evaluating liquefaction potential during earthquakesrdquo SoilDynamics and Earthquake Engineering vol 26 no 2ndash4 pp 115ndash130 2006

[11] H B Seed K O Cetin R E S Moss et al ldquoRecent advances insoil liquefaction engineering a unified and consistent frame-workrdquo in Proceedings of the 26th Annual ASCE Los Ange-les Geotechnical Spring Seminar Keynote Presentation LongBeach Calif USA 2003

[12] Z-L Wang F I Makdisi and J Egan ldquoPractical applications ofa nonlinear approach to analysis of earthquake-induced lique-faction and deformation of earth structuresrdquo Soil Dynamics andEarthquake Engineering vol 26 no 2ndash4 pp 231ndash252 2006

[13] J-M Zhang and G Wang ldquoLarge post-liquefaction deforma-tion of sand part I physical mechanism constitutive descrip-tion and numerical algorithmrdquo Acta Geotechnica vol 7 no 2pp 69ndash113 2012

[14] W F Marcuson ldquoDefinition of terms related to liquefactionrdquoJournal of the Geotechnical Engineering Division vol 104 pp1197ndash1200 1978

[15] D S Liyanapathirana andH G Poulos ldquoA numerical model fordynamic soil liquefaction analysisrdquo Soil Dynamics and Earth-quake Engineering vol 22 no 9ndash12 pp 1007ndash1015 2002

[16] G R Martin W D L Finn and H B Seed ldquoFundamentalsof liquefaction under cyclic loadingrdquo ASCE Journal of the Geo-technical Engineering Division vol 101 no 5 pp 423ndash438 1975

[17] P M Byrne E Naesgaard and M Seid-Karbasi ldquoHardy lec-turemdashanalysis and design of earth structures to resist seismicsoil liquefactionrdquo in Proceedeings of the 59th Canadian Geotech-nical Conference pp 1ndash24 Vancouver Canada 2006

[18] P Byrne ldquoA cyclic shear-volume coupling and pore-pressuremodel for sandrdquo in Proceedings of the 2nd International Confer-ence onRecentAdvances inGeotechnical Earthquake Engineeringand Soil Dynamics pp 47ndash55 Geotechnical Special RublicationSt Louis Mo USA 1991

[19] Itasca Consulting Group FLAC3119863-Fast Lagrangian Analysis ofContinua inThree DimensionsmdashUserrsquos Guide Itasca ConsultingGroup 2005

[20] H Puebla P M Byrne and R Phillips ldquoAnalysis of CANLEXliquefaction embankments prototype and centrifuge modelsrdquoCanadian Geotechnical Journal vol 34 no 5 pp 641ndash657 1997

[21] GBT 18306 Seismic Ground Motion Parameter Map of China2001 (Chinese)

[22] T L Youd and S K Noble ldquoLiquefaction criteria based on sta-tistical and probabilistic analysesrdquo in Proceedings of the NCEERWorkshop on Evaluation of Liquefaction Resistance of Soils pp201ndash205 1997

[23] R D Andrus and K H Stokoe ldquoLiquefaction resistance ofsoils from shear-wave velocityrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 126 no 11 pp 1015ndash10252000

[24] GB 50487Code for EngineeringGeological Investigation ofWaterResources and Hydropower China Plan Publishing CompanyBeijing China 2008 (Chinese)

[25] J Lysmer and R L Kuhlemeyer ldquoFinite dynamic model forinfinite mediardquo Journal of the Engineering Mechanics Divisionvol 95 no 4 pp 859ndash878 1969

[26] M R Madhav and A M Krishna ldquoLiquefaction mitigation ofsand deposits by granular pilesmdashan overviewrdquo in Geotech-nical Engineering for Disaster Mitigation and RehabilitationProceedings of the 2nd International Conference GEDMAR08Nanjing China 30 Maymdash2 June 2008 pp 66ndash79 SpringerBerlin Germany 2008

[27] M E Hynes-Griffin and A G Franklin ldquoRationalizing the seis-mic coefficient methodrdquo Miscellaneous Paper GL-84-13 USArmy Corps of Engineers Waterways Experiment StationVicksburg Miss USA 1984

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pressure development and was used in this paper for damliquefaction and seismic performance assessment

2 Methodology

The strength and stiffness of soil are primarily governed byeffective stress and so it is desirable to evaluate seismicresponse of soil in terms of effective stress For saturated gran-ular material adopted numerical model should reflect thevariation of pore pressure and thus can predict the effectivestress level

For saturated soil under undrained conditions Martin etal [16] suggested that the pore pressure increment is relatedto the change of plastic volumetric strain of the soil skeleton

Δ119906 = minus1119862119887

Δ120576V119889 (1)

whereΔ119906 is pore pressure increment119862119887is bulk compressibil-

ity and Δ120576V119889 is the plastic volumetric strain increment Thereferred model can adequately reflect the response of porepressure until liquefaction triggering point [17] and thus isan effective tool for assessment of soil liquefaction risk

Theplastic volumetric strain increment could be obtainedby various constitutive theories In this paper the expressionpresented by Byrne [18] was adopted The plastic volumetricstrain increment was expressed as follows

Δ120576V119889

120574= 1198621 exp(minus1198622

120576V119889

120574) (2)

where 120574 is the shear strain in the current cycle 120576V119889 is theaccumulated volumetric strain from prior cycles and 1198621 and1198622 are constants that depend on the relative density119863

119903

1198621 = 7600 (119863119903)minus25

1198622 =041198621

(3)

In this paper the model was incorporated into the finitedifference computer program Flac3D to perform a nonlinearfully coupled dynamic analysis Flac3D is based on a con-tinuum finite difference discretization using the Lagrangianapproach [19] The equations of motion are utilized to obtainthe velocities and displacements when dynamic load isexcreted The equation of motion can be expressed as

120588120597V119894

120597119905=

120597120590119894119895

120597119909119894

+120588119887119894 (4)

where 120588 is material density 119905 is time domain 119909119894is coordinate

vector 120590119894119895is stress tensor and 119887

119894is body force

For a fully nonlinear method any given function can beused in dynamic analysis of Flac3D The general constitutiveequation is expressed as

120590119894119895= 119872(120590

119894119895 120576119894119895 120581) (5)

where 120590119894119895is stress rate tensor 120576

119894119895is strain rate tensor 120581 is the

parameter taking the loading history into account and 119872 isthe given functional expression

The Mohr-Coulomb elastic-perfectly plastic constitutiverelation is the commonly used constitutive models for soilIn order to adapt the model for dynamic analysis severalmodifications have been achieved In this paper the modifi-cation defined by Puebla et al [20] was usedThe secant shearmodulus119866 and bulk modulus 119861were considered to be stress-dependent and given as follows

119866 = kg sdotPa sdot (1205901015840119898Pa)119899

119861 = kb sdotPa sdot (1205901015840119898Pa)119898

(6)

where kg and kb are shear and bulk modulus numbers 119899 and119898 aremodulus exponents 1205901015840

119898is themean effective stress and

Pa is atmospheric pressure

3 Statement of Dam Conditions

Dongzhen reservoir located about 60 km upstream PutianCity in Fujian Province Southeastern China has a normalstorage capacity of 435 millionm3 The reservoir has acomprehensive function of flood control irrigation andpower generation The water retaining dam has an irregulargeometry (Figure 1) The longitudinal profile of the dam hasan asymmetric U-shape which is steep on the right flank andgentle on the left (Figure 2(a)) The dam is a core-wall earthdam with a maximum height of 586mThe normal dammedwater level is about 81m to the dam crest (Figure 2(b)) Thecore wall made of lean clay and the filling is gravelly soil Alayer of rock blocks revetment was placed on the surface toprotect the slope The thickness of the blocks revetment onthe upstream surface is about 20m

Thedamwas built in the 1950s when there was no seismicdesign standard in China The study area is located in thecoast of Taiwan Channel Caused by the movement of thePacific Plate a series of NNE and NW fault zones can befound in this area (Figure 3) The area is currently within theregion with seismic intensity of 7 based on Chinese Standard[21] According to the seismic safety analysis completedby Fujian Provincial Institute of Geological EngineeringInvestigation the equivalent earthquake magnitude whichaffects the dam area is Ms 65 and the epicenter distance isabout 50 kmThe peak bedrock acceleration of themaximumcredible earthquake is about 158 gal Owing to the high publicinterest and the large amount of potentially affected personsquestions about the seismic stability of the dam are importantto study in detail

4 Shear Wave Velocity Test

In order to study the seismic stability of the dam the firststep is to evaluate the liquefaction potential of gravelly soils[11] The usually available field test methods are the standardpenetration test (SPT) the cone penetration test (CPT) insitu shear wave velocity measurement (119881

119904) and the Becker

penetration test (BPT) [22] Among these approaches theshear wave velocity measurement is more feasible in gravellysoil field because this type of soil is difficult to penetrate[10 22 23] A three-component geophone setup was placedin a 30m deep borehole to obtain the shear wave velocity


Spillway

0 100(m)

N

DongzhenReservoir

70

7060

60

6070

80

4050

50

8080

Dam body


0 100(m)

Dam body

NW

Bedrock

Spillway

(a)

0 40(m)


Downstream


Cut-off wall

Clay


Bedrock


1 201 25

1 32

1 29

1 30

(b)



119881119904119905



ℎis the peak


0 100(km)



Fuzhou

Dam site

Putian

Taiwan Strait

118∘

119∘

120∘

26∘

25∘

26∘

25∘






119903119889= 11minus 002119885 when 119885 = 10 sim 20m

119903119889= 09minus 001119885 when 119885 = 20 sim 30m

(8)















denoted as

119877119906=

119880119890

1205901015840

1198980 (9)


and 1205901015840



Block

XY

Z


0 5 10 15 20 25 30

minus200

minus150

minus100

minus50

0

50

100

150

200

Acce

lera

tion

(gal

)

Time (s)


119877119906


= 00



0 5 10 15 20 25 30minus08

minus06

minus04

minus02

00

02

04

Time (s)

A1

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(a)

0 5 10 15 20 25 30minus06

minus04

minus02

00

02

04

06

08

Time (s)

A2

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(b)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A3

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(c)

0 5 10 15 20 25 30

minus02

00

02

04

06

Time (s)

A4

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(d)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A5

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(e)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A6

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(f)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A7

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(g)

0 5 10 15 20 25 30

minus015

minus010

minus005

000005010015020025

Exce

ss p

ore p

ress

ure r

atio

(Pa)

Time (s)

A8

(h)







Bulk modulusnumbers




minus6


Block 220 1050 069 3150 069 00 450 055


119906)





0 5 10 15 20 25 30minus010

minus008

minus006

minus004

minus002

000

002

Hor

izon

tal d

ispla

cem

ent (

m)

Time (s)







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Spillway

0 100(m)

N

DongzhenReservoir

70

7060

60

6070

80

4050

50

8080

Dam body


0 100(m)

Dam body

NW

Bedrock

Spillway

(a)

0 40(m)


Downstream


Cut-off wall

Clay


Bedrock


1 201 25

1 32

1 29

1 30

(b)



119881119904119905



ℎis the peak


0 100(km)



Fuzhou

Dam site

Putian

Taiwan Strait

118∘

119∘

120∘

26∘

25∘

26∘

25∘






119903119889= 11minus 002119885 when 119885 = 10 sim 20m

119903119889= 09minus 001119885 when 119885 = 20 sim 30m

(8)















denoted as

119877119906=

119880119890

1205901015840

1198980 (9)


and 1205901015840



Block

XY

Z


0 5 10 15 20 25 30

minus200

minus150

minus100

minus50

0

50

100

150

200

Acce

lera

tion

(gal

)

Time (s)


119877119906


= 00



0 5 10 15 20 25 30minus08

minus06

minus04

minus02

00

02

04

Time (s)

A1

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(a)

0 5 10 15 20 25 30minus06

minus04

minus02

00

02

04

06

08

Time (s)

A2

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(b)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A3

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(c)

0 5 10 15 20 25 30

minus02

00

02

04

06

Time (s)

A4

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(d)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A5

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(e)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A6

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(f)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A7

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(g)

0 5 10 15 20 25 30

minus015

minus010

minus005

000005010015020025

Exce

ss p

ore p

ress

ure r

atio

(Pa)

Time (s)

A8

(h)







Bulk modulusnumbers




minus6


Block 220 1050 069 3150 069 00 450 055


119906)





0 5 10 15 20 25 30minus010

minus008

minus006

minus004

minus002

000

002

Hor

izon

tal d

ispla

cem

ent (

m)

Time (s)







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















denoted as

119877119906=

119880119890

1205901015840

1198980 (9)


and 1205901015840



Block

XY

Z


0 5 10 15 20 25 30

minus200

minus150

minus100

minus50

0

50

100

150

200

Acce

lera

tion

(gal

)

Time (s)


119877119906


= 00



0 5 10 15 20 25 30minus08

minus06

minus04

minus02

00

02

04

Time (s)

A1

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(a)

0 5 10 15 20 25 30minus06

minus04

minus02

00

02

04

06

08

Time (s)

A2

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(b)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A3

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(c)

0 5 10 15 20 25 30

minus02

00

02

04

06

Time (s)

A4

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(d)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A5

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(e)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A6

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(f)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A7

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(g)

0 5 10 15 20 25 30

minus015

minus010

minus005

000005010015020025

Exce

ss p

ore p

ress

ure r

atio

(Pa)

Time (s)

A8

(h)







Bulk modulusnumbers




minus6


Block 220 1050 069 3150 069 00 450 055


119906)





0 5 10 15 20 25 30minus010

minus008

minus006

minus004

minus002

000

002

Hor

izon

tal d

ispla

cem

ent (

m)

Time (s)







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 5 10 15 20 25 30minus08

minus06

minus04

minus02

00

02

04

Time (s)

A1

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(a)

0 5 10 15 20 25 30minus06

minus04

minus02

00

02

04

06

08

Time (s)

A2

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(b)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A3

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(c)

0 5 10 15 20 25 30

minus02

00

02

04

06

Time (s)

A4

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(d)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A5

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(e)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A6

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(f)

0 5 10 15 20 25 30minus04

minus02

00

02

04

06

08

Time (s)

A7

Exce

ss p

ore p

ress

ure r

atio

(Pa)

(g)

0 5 10 15 20 25 30

minus015

minus010

minus005

000005010015020025

Exce

ss p

ore p

ress

ure r

atio

(Pa)

Time (s)

A8

(h)







Bulk modulusnumbers




minus6


Block 220 1050 069 3150 069 00 450 055


119906)





0 5 10 15 20 25 30minus010

minus008

minus006

minus004

minus002

000

002

Hor

izon

tal d

ispla

cem

ent (

m)

Time (s)







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Bulk modulusnumbers




minus6


Block 220 1050 069 3150 069 00 450 055


119906)





0 5 10 15 20 25 30minus010

minus008

minus006

minus004

minus002

000

002

Hor

izon

tal d

ispla

cem

ent (

m)

Time (s)







Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article application of effective stress model to...

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