Research Article Safety Monitoring Index of High Concrete

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 732325 14 pageshttpdxdoiorg1011552013732325

Research ArticleSafety Monitoring Index of High Concrete Gravity DamBased on Failure Mechanism of Instability

Shaowei Wang123 Chongshi Gu123 and Tengfei Bao123

1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai University Nanjing 210098 China2National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety Hohai UniversityNanjing 210098 China

3 College of Water-Conservancy and Hydropower Hohai University Nanjing 210098 China

Correspondence should be addressed to Shaowei Wang shaowei2006nanjing163com

Received 8 September 2013 Revised 14 November 2013 Accepted 14 November 2013

Academic Editor Xiao-Wei Ye

Copyright copy 2013 Shaowei Wang 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

Traditional methods of establishing dam safety monitoring index are mostly based on the observation data According to theperformance of dam-foundation system under the experienced loads alarm values and extreme values are predicted formonitoringquantities As for some dams the potential most unfavorable loads may not yet have appeared and dam bearing capacity mayalso decrease over time Therefore monitoring index determined by these methods can not reflect whether the dam will breakor not Based on the finite element method to study the progressive instability failures of high concrete gravity dams under thefailure modes of material strength degradation or uncertainty and extreme environmental loads during operation methods ofstrength reduction and overloading are respectively used Typical stages in the instability processes are identified by evaluationindicators of dam displacement the connectivity of yield zones and the yield volume ratio of dam concretes then instability safetymonitoring indexes are hierarchically determined according to these typical symptoms At last a case study is performed to give amore detailed introduction about the process of establishing safety monitoring index for high concrete gravity dams based on thefailure mechanism of instability and three grades of monitoring index related to different safety situations are established for thisgravity dam

1 Introduction

With the implementation of the National West to East PowerTransmission Project a large number of high dams are con-structed or under construction in western China in whichconcrete gravity dams are frequently adopted The specialmountain valleys in western China provide advantageoustopographic conditions for the construction of high damsHowever dam safety becomes an important issue in thewestern area due to the complicated geological conditions aswell as strong earthquakes of high frequency

Structure safety monitoring is more frequently designedand implemented on civil engineering structures such asdams bridges and high buildings Meanwhile analysis andback-analysis of the monitoring data are performed to eval-uate the performance of these structures in time [1ndash5] Asfor dams dam failure is a progressive process in which local

damages accumulate firstly then lead to the deteriorationof dam safety situation and finally cause the dam failureTherefore to avoid dam failure it is necessary to monitor thedams and their foundations and timely detect and analyzedam abnormal symptoms according to the observation data[6] To ensure the normal operation monitoring quantityshould not exceed its allowable value namely the safetymonitoring index Hence monitoring index is defined asthe extreme value of each monitoring quantities before damfailure which is used to evaluate and monitor dam safety [7]Before the nineteen sixties engineers had not realized theimportance of observation data in dam safetymanagement sothat further analyseswere ignored let alone the establishmentof monitoring index and ternperatwre alarm so dam safetymonitoring system was not fully utilized The failures ofMalpasset arch dam and Vajont arch dam are both closelyrelated to the absence of monitoring index [8]Themeasured

2 Mathematical Problems in Engineering

displacement of Malpasset arch dam four mouths beforeits failure is significantly larger than the theoretical valueand the closer to dam bottom the more serious Landslideson the left bank of Vajont arch dam began to creep slowlyafter the impoundment of upstream reservoir in 1960 themeasured total displacement at the dam crest came up to429 cm on October 7 1963 and increased at an amazingspeed of 483mmd during the last 12 days before failureTernperatwre alarms were not made for the occurrence ofabnormities so that both dam failures occurred without anyengineering or nonengineering measures so the absenceof monitoring index for Malpasset arch dam and Vajontarch dam restricted the function of their safety monitoringsystems The situation that monitoring quantity exceeds itsmonitoring index probably means the abnormity of damsafety so it is a key problem for managers to determine themonitoring index scientifically

As for gravity dams dam failures are mainly caused bythe instability of dam-foundation systems and the failureprocess depends on failure modes [9 10] Due to the com-plexity and specificity of each dam-foundation system failuremechanisms and failure processes are different from damto dam even if under the same failure mode Therefore itis necessary to simulate the real failure process and studythe failure mechanism of instability under different failuremodes and the instability safety monitoring index of highconcrete gravity dams should be determined according to thetypical symptoms in the simulated failure process

This paper firstly makes a brief summary about the cur-rent theories and methods of establishing dam safety mon-itoring indexes in which disadvantages of each methodare analyzed Then based on the traditional finite elementstructural analysis method considering the most probablepotential failure modes of material degradation or uncer-tainty and extreme external environmental loads during damoperation methods of strength reduction and overloadingare respectively used in this paper to study the progressiveinstability failure process of high concrete gravity damsTypical stages in the instability processes are identified byevaluation indicators of dam displacement the connectivityof yield zones and the yield volume ratio of dam concretesthen instability safety monitoring index of high concretegravity dams is determined according to these typical symp-toms At last the proposedmethod for establishing instabilitysafety monitoring index of high concrete gravity dams isstudied in detail with a practical engineering

2 Research Situation of Dam SafetyMonitoring Index

Current dam safety monitoring items are deformation stressuplift pressure seepage crack opening and so on Moni-toring indexes for dam stress uplift pressure and seepageare determined according to the hydraulic specifications andthese items are often established for local areas where themonitoring quantities should be controlled strictly Especiallyfor dam stress the stress-controllable areas such as damheel and dam toe are also the stress concentration areas in

the finite element method (FEM) so it is difficult to deter-mine a reasonable stress control standard for these areas byFEM simulation [11] As for the crack opening it is not easy todetermine the monitoring index by hydraulic specificationsdue to the complex opening mechanism of cracks Howevercrack opening is the same as other monitoring items thatonly local damages may appear when its monitoring index isexceeded and obvious abnormality will be directly reflectedon dam deformation even if the rapid development of theselocal damages will result in the dam failure Among all thesemonitoring items deformation can directly reflect the globalsafety and the progressive failure process of dam-foundationsystem so monitoring index for dam deformation is mostlydetermined as dam safety monitoring index [12]

The reasonablemonitoring index can be used in analyzingand evaluating the situation of dam safety However due tothe complexity of dam structures and the different materialvariation characteristics comprehensive demonstration bydifferent methods should be conducted to determine damsafety monitoring index The mostly used methods forestablishing the monitoring index at present are confidenceinterval method typical low probability method limit statemethod and structural analysis method [13] These methodsare all without taking dam failure modes into considerationlet alone the instabilitymechanism and the progressive failureprocess under different failure modes Therefore advantagesand disadvantages of these methods are analyzed beforeestablishing the safety monitoring index of high concretegravity dam based on failure mechanism of instability

21 Confidence Interval Method The basic principle of confi-dence interval method is the little probability event in statis-tics According to the observation data mathematical models(such as statistical model hybrid model and deterministicmodel) are established between monitoring effect quantitiesand environmental variables and these models are used incalculating the deviations (119910 minus 119910) between the calculatedvalues (119910) and the measured values 119910 of monitoring effectquantities in the domain of dam experienced loads If thedeviations are within the confidence band of Δ = plusmn 120573120590 withthe probability of 1 minus 120572 (120572 is the significance level which isfrequently determined as 1sim5) and no obvious tendencyvariations are reflected on the monitoring effect quantitiesthen this dam is considered to be in normal conditionTherefore dam monitoring index is established as follows

120575

119898= 119910 + Δ = 119910 plusmn 120573120590 (1)

where 120573 is related to the significance level 120572 and 120590 is theresidual standard deviation of the mathematical model

The frequently used confidence interval method andtypical lowprobabilitymethod are both based on the observa-tion data According to the performance of dam-foundationsystem under the experienced loads bearing capacities underthe potential loads are evaluated and the correspondingalarm values and extreme values are predicted for differentmonitoring effect quantities However dam safety informa-tion contained in the observation data varies from dam todam due to the different experienced loads especially for

Mathematical Problems in Engineering 3

some dams which have never experienced the potential mostunfavorable loads [14] Meanwhile the bearing capacity ofdam-foundation system is changing during dam operationTherefore monitoring index based on the observation data iswithout considering the real condition of dam safety insteadof really reflecting whether the dam will break or not it onlycan be used as the warning index to identify the abnormalityof monitoring quantities [15ndash17]

Based on the aforementioned analyses disadvantages ofthe confidence interval method are as follows (1) If theobservation data under the most unfavorable load combina-tion are absent monitoring index based on the confidenceinterval method may be unreliable it is just the alarmingvalue for the experienced loads rather than the extreme valuesfor dam failure (2) The residual standard deviation 120590 ofthe mathematical model varies with the selected observationdata sequences for the same monitoring points and thesignificance level is determined with arbitrariness more orless (3) Instead of associating with dam structural state andfailure mechanism the confidence interval method is totallydependent on statistical theories so it is lack of physicalconcepts

22 Typical Low Probability Method The typical low proba-bility method is the same as the confidence interval methodthat totally depends on the observation data differencesare that the former qualitatively associates with the con-trolling conditions of strength and stability by selectingthe monitoring effect quantity (119910

119898119894) or its component in

mathematical models under the unfavorable load conditions(namely the typical monitoring effect quantities) Accordingto different dam types and the actual situation 119910

119898119894is

selected annually and a random sample is constituted as119910 = 119910

1198981 119910

1198982 119910

119898119899 Characteristics of the sample are

described as follows

119910 =

1

119899

119899

sum

119894=1

119910

119898119894 (2)

120590

119864=

radic

1

119899 minus 1

(

119899

sum

119894=1

119910

2

119898119894minus 119899119910

2

) (3)

The probability density function 119891(119910) (such as normaldistribution logarithmic normal distribution and extreme-I distribution) of sample 119910 is determined by statistical testsAssuming that 119910

119898(119910max or 119910min) is the extreme value of

the monitoring quantity or its loading component damabnormality occurs if 119910 gt 119910max or 119910 lt 119910min and the proba-bility is

119875 (119910 gt 119910max) = 119875

119886= int

+infin

119910max

119891 (119910

(max)) 119889119910 upper limit (4)

or

119875 (119910 lt 119910min) = 119875

119886= int

119910min

minusinfin

119891 (119910

(min)) 119889119910 lower limit (5)

Dam failure probability 119875

119886is determined according to the

importance of each dam Then dam safety monitoring

indexes are established according to 119875

119886and 119891(119910) (119891(119910

(max))or 119891(119910

(min)))Monitoring indexes established by the typical low prob-

ability method can be determined as the extreme value ofthe whole dam operation period just on the condition thatthe dam has experienced all kinds of unfavorable condi-tions (including unfavorable load combinations and materialdegradation) Another problem is that the controlling condi-tions of strength and stability are only qualitatively associatedwhile quantitative analysis is ignored

23 Limit State Method It is assumed by the limit statemethod that each dam failure modes are corresponding to acertain load combination and dam failures are mainly boileddown to the failuremodes of strength stability cracks and soon The limit state equation is defined as follows

119885 = 119877 minus 119878 ge 0 (6)

where 119877 is the structure resistance which is defined asmaterial tension strength compression strength and shearstrength for the evaluation of strength and the antislidingforce and fracture toughness for the evaluation of stabilityand cracking respectively 119878 is the load effect which is deter-mined as extreme stress sliding force and stress intensityfactor for the evaluation of strength stability and crackingrespectively

The limit state method shows a relatively clear physicalconcept by quantificationally contacting with dam strengthand stability However dam strength is based on the pointfailure criterion which cannot reflect the global safety ofdam-foundation system as for dam stability sliding surfaceshould be assumed in advance for the overall sliding failurecriterion and the stability cannot be directly reflected by themonitoring quantities

24 Traditional Structural Analysis Method As for the tra-ditional structural analysis method it respectively connectsthe three safety states (normal abnormal and dangerous)in dam safety monitoring standard with three structuralbehaviors (linear elastic elastic-plastic and failure) and threelevels of safety monitoring index are established as followsMonitoring index of grade one

120575

1= 119865(120590

119905lt [120590

119905] 120590

119888lt [120590

119888] 119870 =

119877

1198981

119878

ge [119870]) (7)

Monitoring index of grade two

120575

2= 119865 (120590

119905lt 120590

119905119877 120590

119888lt 120590

119888119877 119878 le 119877

1198982 119870

119888le [119870

119888]) (8)

Monitoring index of grade three

120575

3= 119865 (120590

119905lt 120590

119905119898 120590

119888lt 120590

119888119898 119878 le 119877

1198983) (9)

where 120590

119905and 120590

119888are tensile stress and compression stress

of controlling areas [120590

119905] 120590

119905119877 and 120590

119905119898are the allowable

stress yield strength and ultimate strength of dam materialsin the state of tension respectively [120590

119888] 120590119888119877 and 120590

119888119898are

the allowable stress yield strength and ultimate strength of


dam materials in the state of compression respectively 119878

is the sliding force on the assumed sliding surface 119870 and[119870] are antislide stability safety coefficients of the actualvalue and the allowable value respectively 119877

1198981 1198771198982 and

119877

1198983are antisliding forces which are respectively calculated

by material shear strength of sliding surface in states ofproportion limit yield limit and the peak value119870

119888and [119870

119888]

are stress intensity factor and fracture toughness respectivelyIt is the same as the limit state method that the afore-

mentioned three levels of dam safety monitoring index areall based on the point failure criterion and the prior assumedsliding surfaceHowever due to the huge volumeof dambodyas well as the complicated geological condition in foundationstructural behaviors for each parts of the dam-foundationsystem are not the same If fixed proportions of dammaterialin stages of linear elastic elastic-plastic and failure are used todecide the global structural behavior of dams it is not easy todetermine the proportions reasonably for different complexconstructions Therefore it is unreasonable to determinethe dam safety monitoring index based on the mechanicalproperty ofmaterials and the failuremechanismof instabilityunder different failure modes cannot be reflected by thetraditional structural analysis method

3 Simulation of the Progressive Failure ofHigh Concrete Gravity Dam

Thekey problem of high concrete gravity dams is the stabilityPractical experiences show that instability failure of gravitydams on rock foundation may occur in two modes [18] (1)strength degradation caused by seepage or some originalweak structural surfaces so dam failure occurs once theresistance force along some weak surfaces cannot stand upto the sliding force Here the sliding surfaces are usuallythe foundation plane construction interfaces in dam bodyand some weak structural surfaces in bedrocks (2) Underthe action of extreme environmental loads pull broken areasand crushed areas in bedrocks of dam heel and dam toe arerespectively performed and dam failure of instability occursaccompanied with toppling The construction interfaces indam body can be avoided if dam concretes are poured ingood quality namely the probability of instability failurein dam body is mostly decreased As for the sliding alongweak structural surfaces in bedrocks or the toppling-slidingfailure it mainly depends on the geological conditions Thespecial mountain valleys provide advantageous topographicconditions for the construction of high dams However thesedams are often threatened by the complicated geologicalconditions as well as strong earthquakes of high frequencyTherefore monitoring index for these high gravity damsmust be determined according to the failure mechanism ofinstability under different potential failure modes

Due to the complexity of bedrocks slidingmodes of grav-ity dams cannot be identified directly Different combinationsof foundation weak surfaces result in different sliding modesAccording to the spatial distribution of foundation weaksurfaces sliding modes of gravity dams can be summarizedinto four types which are single inclined plane sliding double

inclined plane sliding crushed failure or bulged failure of thetail rock resistance block [19] According to the dip angle offoundation weak surfaces the aforementioned four modescan be summarized into two types namely the double orpotential double inclined plane sliding and the translationalsliding which is shown in Figure 1 If the foundation weakstructural surfaces respectively incline to the upstream anddownstream directions and intersect at the bedrocks justbelow the foundation plane the double inclined plane slidingoccurs along the surface of ABC As for the single inclinedweak surface such as the upstream direction inclined of B1015840Cor the downstream direction inclined of AB10158401015840 failure areasof tension-shear or compression-shear may firstly appear atdam heel and dam toe and the potential double inclinedplane sliding occurs along the surface of AB1015840C and AB10158401015840CrespectivelyThe translational sliding occurs on the conditionthat the nearly horizontal gentle inclined weak structuralsurfaces are contained in bedrocks Dam body and parts ofbedrocks above the weak surface slide to the downstreamintegrally and the tail rock resistance block tends to becrushed or bulged according to the buried depth of the weaksurfaces and the mechanical property of upper rocks

The stress field and displacement field of dam-foundationsystem can be calculated by FEM and it is more reasonableto automaticly search the sliding surface according to damdeformation On the other hand methods of strength reduc-tion and overloading can be respectively used to simulatematerial degradation or uncertainty and extreme externalenvironmental loads during the service period Hence theFEM simulation is frequently used in studying the globalsafety of gravity dams [19 20] and arch dams [21ndash23]

31 Overloading Method To study the overloading capacityof gravity dam-foundation systems overloading method isconducted under the assumption of unchangeable materialproperties of dam concretes and bedrocks Under the normalload combination external loads are increased until the damfailure by elevating the upstream water level or increasingthe upstream reservoir water density in which water densityoverloading method is commonly used by engineers Withthe enlargement of upstream reservoir water density to 119870

119901

times (for normal load condition the overloading parameter119870

119901= 1) stress field and displacement field are calculated

by FEM and the variation of dam safety is identified bythe development of displacement and stress of typical pointsas well as the connectivity of plasticity yield zones of dam-foundation system Hence the overloading method canbetter simulate dam failures under the potential abnormalenvironmental loads which are caused by overtopping superearthquake and the landslide of reservoir bank

Taking a gravity dam section of unit width as an examplethe dam height is 160m and the widths at dam crest andbottom are 16m and 125m respectively The unit widthdam section is designed with a vertical upstream damsurface and the downstream surface at a gradient of 1 075According to the current Chinese specifications for seismicdesign of hydraulic structures DL5073-2000 [24] as for thetraditional pseudo-static method earthquake hydrodynamicpressure and inertial force are respectively calculated and


Gravity dam

Foundation rock

A

B

C

Nature structural surface

Foundation plane

Pull broken or

crushed area Failu

re zo

ne of

com

pres

sion-

shea

r

B998400 B998400998400middot

Envi

ronm

ent l

oad

(a)

Gravity dam

Foundation plane

Envi

ronm

ent l

oad

Nature structural surface Pull broken areas

Foundation rock

Translational slip

Slip

Slip

Uplifted areas caused by compression-shear

(b)

Figure 1 Sliding modes of gravity dam (a) double or potential double inclined plane sliding (b) translational sliding

Table 1 The equivalent water density overloading parameter ofearthquakes

Peak acceleration of design earthquakes 01 g 02 g 04 gStatic water pressure of upstream (107 N) 116Earthquake hydrodynamic pressure (107 N) 038 076 151Earthquake inertial force (107 N) 113 226 451The total dynamic forcestatic water pressure 013 026 052Overloading parameter of water density119870

119875113 126 152

Notes g is the gravitational acceleration the normal water depth of upstreamreservoir is 154m

shown in Table 1 It can be seen that the equivalent waterdensity overloading parameter119870

119901comes up to 152 when the

peak acceleration of earthquakes reaches 04 g As for theactual situation extreme external loads caused by strongearthquakes or landslidesmay bemore serious than this suchas the failure of Vajont arch dam later studies show that thehuge water pressure caused by the landslide of reservoir bankis about 8 times of the designed loads

32 Strength Reduction Method Strength reduction methodmainly considers the strength degradation during the serviceperiod and the uncertainty of material strength Underthe normal load combination strengths of dam concretesand bedrocks are gradually reduced until the dam failureEspecially for bedrocks due to the complexity of rock genesisand geotectonic movement various faults joints and cracksare distributed complicatedly so it is possible to make bigdifferences of material properties in local small areas thatcannot be systematically represented in the geological surveyBased on the Drucker-Prager yield criterion the originalshear strength parameters are denoted as 119888 and119891 for cohesionand friction angle respectively Hence the reduced param-eters are denoted as 119888119870

119904and 119891119870

119904(for normal condition

the strength reduction parameter 119870119904= 1) and the gradually

reduced shear strength is used by FEM simulation until thedam failure

33 Comprehensive Method Instead of the single actionof overloading or strength degradation dam failure is aprogressive process from local damage to global failure underthe comprehensive action of these two actors The com-prehensive method is the combination of overloading andstrength reduction so it seems more reasonable to simulatethe dam failure However due to the specificity of damprojects how to reasonably combine these two methods isstill an unfathomed problem for engineers and this situationlimits the development of the comprehensive method in thestudying of dam global safety

34 Dam Safety Evaluation Indicators inthe Progressive Failure

341 Dam Displacement The global instability failure ofgravity dams mainly resulted from the rapid development ofinfinite deformation caused by material strength degradationor abnormal environmental loads No matter the slidingmodes of inclined plane sliding or the translational slidingdam displacements are all gradually increased before the damfailure On the other hand the progressive failure process ofgravity dams under different failure modes can be simulatedby FEM and the theoretical displacements of typical stages indam failure process can be determined as the instability safetymonitoring indexes of gravity dams The comparison of theobservation displacement and itsmonitoring index shows thecurrent situation of dam safety as well as the safety margin

The simulation of dam failure by the geomechanicalmodel test shows that when the parameters of strengthreduction or overloading come up to a large amplitudethe rapidly increased nonlinear deformation results in thecatastrophe of dam displacement and the bearing capacity ofdam-foundation system loses immediately The developmentof dam displacement in the FEM simulation is similar to this


so the catastrophe of dam displacement can be defined as thesign of losing bearing capacity for gravity dam-foundationsystems and the theoretical displacement at this moment isdetermined as the safety monitoring index of dam failure

342 The Connectivity of Yield Zones With the strengthreduction or overloading yield zones of dam-foundationsystem extend and join and these yield zones are finallyconnected in dam body along the foundation plane or inbedrocks Here yield zones are defined as the zones where theequivalent plastic strain is larger than a certain magnitudeand the equivalent plastic strain is defined as follows [25]

120576

119901

= int

120576

119901

119889119905 = int(

2

3

120576

119901

119894119895120576

119901

119894119895)

12

119889119905(10)

where

120576

119901 is the equivalent plastic strain ratePlastic strain of tension compression and shear are all

included in the equivalent plastic strain by integrating theequivalent plastic strain rate Research results [21 23] showthat it is more suitable to set the amplitude of the totalequivalent plastic strain at 10

minus4 to determine whether theconcrete and bedrock are yielding or not

Instead of the elastic-perfectly plastic material bothbedrock and dam concrete have the potential bearing capac-ity after yielding so there is no obvious relationship betweenthe connectivity of yield zones and the dam failure Zhenget al [26] pointed out that the connectivity of yield zonesin soil is the necessary condition of soil sliding failurenot the sufficient condition and the sign of soil slidingfailure is identified as the rapid development of infinitedeformation Although the connectivity of yield zones doesnot immediately result in the dam failure it still meansthe approach of ultimate bearing capacity If engineeringor nonengineering measures are not taken immediately tostop the deterioration of dam safety dam deformation willincrease sustainably and result in the dam failure at last

343 The Yield Volume Ratio of Dam Body Various dis-advantageous weak structural surfaces are frequently dis-tributed in dam foundation and the working principle ofgravity dams is that using the friction force caused by damself-weight to resist the upstream horizontal water pressureto guarantee the stability Meanwhile yield zones of damconcretes mainly appeared at local areas of dam heel damtoe or the turning points of dam upstream and downstreamsurfaces Therefore if dam concretes are poured in goodquality to ensure the designed strength and stiffness globalfailure of gravity dams is unlikely to be caused by the yieldof dam concretes However as for some high concrete damswhich are constructed on the ideal bedrocks that the strengthand stiffness are both guaranteed dam concrete degradationor the abnormal environmental loads may result in a largeproportion of yield concretes and the rapidly increasedinfinite deformation of dam body determines the loss ofbearing capacity of dam-foundation systems For these highconcrete gravity dams catastrophe of the yield volume ratioof dam concretes can be determined as the sign of losingbearing capacity

4 Determination of Instability SafetyMonitoring Index of Gravity Dams

To establish the instability safety monitoring index for highconcrete gravity dams according to the actual conditionssuch as the geological condition environmental conditionand the degradation of dam concretes it is necessary tofirstly study the failure mechanism of instability under dif-ferent potential failure modes By simulating the progressivefailures typical stages in the instability failure process areidentified by evaluation indicators of dam displacement theconnectivity of yield zones and the yield volume ratio ofdam concretes Then considering the condition that some ofthe failure conditions may not appear during dam operationso these typical stages are analyzed and compared andfrom the view of most unfavorable for dam safety severaltypical stages are selected for hierarchically determiningdam instability safety monitoring indexes Finally accordingto dam displacement fields at these typical stages safetymonitoring indexes are established for different dam safetygradesThe flow chart of establishing safetymonitoring indexfor high gravity dams based on the failure mechanism ofinstability is shown in Figure 2

5 Case Study

A concrete gravity dam is located in the west of Chinawith a maximum dam height of 1600m a crest elevationof 14240m and a crest axis length of 6400m The highestdam section on the riverbed is selected to study the failuremechanism of instability and establish safety monitoringindex There are two nearly horizontal weak interlayersdistributed in foundation bedrocks with the average burieddepths of 30m and 80m and the thicknesses of 165mand 233m which are respectively denoted as 1199051

119887and 1199051

119886

According to the boundaries of 1199051119887and 1199051

119886 foundation rocks

are divided into three categories which are respectivelydenoted as rock I rock II and rock III from the groundsurface to the deeper The range of the FEM model is abouttwo times of the maximum dam height in the upstreamdownstream and downward directions according to the damheel and dam toe Thicknesses of the weak interlayer inthe FEM model are determined as the actual value Thegravity dam-foundation system is discretized into eight-nodeand six-node solid elements with 15932 elements and 19056nodes in which the dam body contains 3549 elements and4432 nodesThe FEMmodel is shown in Figure 3(a)Materialparameters for dam body and its foundation are listed inTable 2

To study the failure mechanism of instability by methodsof strength reduction overloading and the comprehensivemethod evaluation indicators of dam displacement theconnectivity of yield zones and the yield volume ratio of dambody are used to identify the safety variation of this highconcrete gravity dam-foundation system in the progressivefailure process Five observation points of the plumb line inthe monitoring system are determined as the typical pointsof dam displacement and the elevations are 14240m (damcrest) 13590m 13200m 12920m and 12640m (foundation


Establish the FEM model of high concrete gravity dam

Structure characteristics Material property Geological condition

Simulation of the progressive failure under different potential failure modes

Material degradationExtreme external environmental loads

Strength reduction methodOverloading method Comprehensive method

Failure modes

Study on the rule of different progressive failures

Identify the typical failure stages and analyze the corresponding

dam instability risk

Dam displacement

Connectivity of yield zones

Yield volume ratio of dam body

From the view of most unfavorable for gravity dam safety comprehensively determine the typical stages that are used for

establishing dam instability safety monitoring indexes

Determine the safety monitoring indexes for different dam safety grades

Dam

safe

tyev

alua

tion

indi

cato

r

Figure 2The flow chart of establishing safety monitoring index for high concrete gravity dams based on the failure mechanism of instability

Table 2 Material parameters for dam body and its foundation

Elastic modulus119864 (GPa)

Poissonrsquos ratio]

Density120588 (kgm3)

Cohesion119888 (MPa)

Friction angle119891

Dam body 25 0167 2400 27 133Rock I 4 027 2600 07 095Rock II 8 027 2600 10 115Rock III 10 027 2600 13 135Weak interlayer 2 03 2500 04 073

plane) respectively Distribution of the typical points isshown in Figure 3(b)

51MaterialModel andYield Criterion Drucker-Prager yieldcriterion is commonly used for concretes and rocks as it canyield a smooth failure surface and is determined correspond-ing to the hydrostatic stress Hence the Drucker-Prager yieldcriterion is adopted in studying the failure mechanism ofinstability of high concrete gravity dams which is presentedas follows

119891 = 120572119868

1+ radic119869

2minus 119870 = 0

(11)

where 119868

1 1198692are the first invariant of stress tensor and the

second invariant of deviatoric stress tensor respectively 120572and 119870 are parameters related to the material shear strengthas follows

120572 =

sin120593

radic3radic3 + sin2120593

(12)

119870 =

3119888 cos120593


(13)


Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)

Figure 3 Integral FEMmodel and the typical points (a) FEMmodel (b) typical displacement points

52 Simulation of the Progressive Failure under DifferentFailure Modes Considering that the most probable potentialfailure modes are material degradation and extreme externalenvironmental loads during the service period hence toestablish dam safety monitoring index based on the risk ofdam failure methods of strength reduction and overloadingare used in studying the failure mechanism of instabilityand the progressive failure process at first Then safetymonitoring indexes are hierarchically determined accordingto the typical stages of the progressive failure and the actualdam situation

521 Analysis Results of the Strength Reduction MethodThe strength reduction method is used to simulate thematerial strength degradation and uncertainty The constantload condition is the combination of upstream hydrostaticpressure (with the normal water level of 14180m) dam self-weight silt pressure and uplift pressure The elevation ofsilt sedimentation is 13350m the silt submerged unit weightand the friction angle are 12 kNm3 and 23∘ respectivelyThe uplift pressure reduction coefficient of dam foundationimpervious curtain is 025

The progressive failure process of this gravity dam-foundation system under the simulation method of strengthreduction is shown in Figure 4 in which the black zones arethe failure regions where the total equivalent plastic strain isbeyond the amplitude of 10minus4 and it has the samemeaning inFigure 7

Due to the existence of the stream direction horizontalweak interlayer under the normal load condition yield zonesfirstly appeared at the dam toe and its nearby bedrocksof the shallowly buried 1199051

119887interlayer When the reduction

parameter 119870

119904reaches 12 the connectivity of yield zones

is formed at the dam toe between the foundation planeand the 1199051

119887interlayer namely the potential downstream

sliding surface is developedWith the continual increments of

the reduction parameter yield zones rapidly extend towardsthe upstream direction along the foundation plane and the1199051

119887interlayer When 119870

119904= 20 the connectivity of yield

zones from upstream to downstream is partly formed atthe shallowly buried 1199051

119887interlayer on the right side of this

dam section and when 119870

119904= 22 this yield zones are

totally connected between the foundation plane and the 1199051

119887

interlayer from dam heel to dam toe Therefore one of thepotential slidingmodes of this gravity dam is the translationalsliding with three sliding surfaces which are composed of thetension-shear crack zones at the dam heel the 1199051

119887interlayer

and the compression-shear crushed zones at the dam toeWhen 119870

119904= 30 the connected yield zones extend to the

1199051

119886interlayer which is deeply buried with a depth of 80m

Meanwhile the strength reduction results in the connectivityof dam concretes between the dam heel and the turning pointof the downstream dam surface Thus the connectivity ofyield zones both appeared in dambody and foundation rocksand the rapidly increased infinite deformation results in thecatastrophe of dam displacement and the loss of bearingcapacity at last

The developments of dam displacement and dam bodyyield volume ratio with the strength reduction parameterare shown in Figures 5 and 6 and it is perfectly in accor-dance with the aforementioned progressive failure processIt can be seen from Figure 5 that when 119870

119904is less than 22

the stream displacement of the selected five typical pointsremains largely unchanged and yield zones rarely appearedin dam body The relatively stable relationship betweendam displacement and the reduction parameter indicatesthe unchanged stable status of this gravity dam Then damconcrete yields over a large area while dam displacementslowly increases with a small amplitude Reasons may beconcluded as follows the first one is that the connectivity ofyield zones in dam body is not formed before119870

119904reaches 30

The other important reason is that the translational sliding


(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30

Figure 4 The progressive failure process of dam-foundation system under strength reduction

along the weak interlayer is restricted by the downstreambedrocks It seems that the totally connected yield zonesbetween the foundation plane and the 1199051

119887interlayer from

dam heel to dam toe will result in the rapid development oftranslational sliding of dam body and parts of the bedrocksafter 119870

119904reaches 22 However the 1199051

119887interlayer is buried

at an average depth of 30m and horizontally distributed inthe stream direction so the development of the translationalsliding is largely limited by the tail rock resistance blocks andthis phenomenon is better explained by one of the selectedtypical points which is on the foundation plane When 119870

119904

exceeds 30 due to the existence of the downstream free

surface of dam body the connected yield zones in dam bodyresult in the rapidly increased deformation at the upper of thisdam Therefore catastrophes are shown on the displacementrelation curves of the upper located typical points

522 Analysis Results of the Overloading Method Materialstrength of dam concretes and bedrocks are designed as theoriginal values in the overloading method Load condition isthe same as that of the strength reduction method the onlydifference is that the water density of upstream reservoir isincreased to 119870

119901times when the overloading parameter 119870

119901

is larger than 10 namely only the upstream water pressure


255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

Figure 5 Relation curves between the stream displacement of dambody and the strength reduction parameter

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

Figure 6 Relation curve between the yield volume ratio of dambody and the strength reduction parameter

is increased when overloading The overloading simulationprocess is that dam self-weight is firstly applied to modelthe pouring of dam concretes then water pressure siltpressure and uplift pressure under the normal load conditionare added and the overloading is finally conducted by thecontinual increments of water density at an interval of 02times

The progressive failure process under the overloadingmethod is shown in Figure 7 which is similar to the strengthreduction method As for the dam deformation of typicalstages such as the connectivity of plastic yield zones inbedrocks along the 1199051

119887interlayer from upstream to down-

stream dam displacement by the overloading method isobviously larger than that of the strength reduction methodat the same stage When 119870

119901= 20 the connectivity of

yield zones completely appeared between the foundationplane and the 1199051

119887interlayer Due to the existence of the

folded slope of dam upstream surface the total water weightson the upstream dam surface are also increased with theincrements of upstream water density which results in thatthe compression-shear yield zones are largely distributed inthe bedrocks right below the dam heel The strength of damconcretes is significantly higher than that of bedrocks henceexcept for some small parts of dam concretes close to thefoundation plane yield zones in dam body firstly appearedat the dam toe and the turning points of the upstream anddownstream dam surface until 119870

119901comes up to 28 With

the continual increments of the overloading parameter yieldzones extend to the internal of dam body and dam concretesat the turning point of the upstreamdam surface yield rapidly

When119870

119901= 36 yield zones are connected in dam body from

upstream to downstreamFigure 8 shows the relation curves between the stream

displacement of dam body and the overloading parameter Itcan be seen that dam stream displacements of typical pointsat the elevation of 14240m and 13590m increase rapidlyafter 119870

119901reaches 36 Reasons are that the connectivity of

yield zones is formed in dam body when 119870

119901= 36 and

this yield zone works as a plastic hinge for the existenceof the downstream dam free surface Hence the nonlineardeformation develops rapidly at the upper of the dam body

It can be concluded from Figures 7 and 8 that theconnectivity of yield zones already completely appearedbetween the foundation plane and the 1199051

119887interlayer when

119870

119901= 20 However displacement increasing rate of the five

selected typical points is smaller until 119870119901reaches 30 (dam

concretes begin to yield rapidly when 119870

119901= 30) Therefore

for this concrete gravity dam the connectivity of yield zonesin dam foundation does notmean the loss of bearing capacity

The relation curve between the yield volume ratio of dambody and the overloading parameter is shown in Figure 9 Itcan be seen that when119870

119901= 24 the yield volume ratio begins

to increase with a smaller increasing rate When 119870

119901= 30

dam concretes yield rapidly and the yield volume ratio hasincreased from 012 to 077 with the overloading parameterthat ranges from 30 to 46 Water pressure on the top of theupstream dam surface increases slowly in the water densityoverloading method so yield zones extend slowly to the damcrest after 119870

119901= 46 and the yield volume ratio of dam body

remains largely unchanged

523 Analysis Results of the ComprehensiveMethod To studythe failuremechanism of instability under the comprehensivecondition of abnormal environmental loads and materialstrength degradation or uncertainty the comprehensivemethod has been conducted and the simulation analysisresults are concluded as follows

Relation curves of stream displacement-overloadingparameter at the foundation plane and dam crest are shownin Figures 10 and 11 respectively The bigger strength reduc-tion the smaller overloading parameter is allowed whennonconvergence occurs so these curves only reflect damdisplacements before the overloading parameter 119870

119901reaches

34 The development rule of displacement of the other threetypical points are similar to this Although for differentstrength reduction parameters dam displacement changesstably and keeps almost the same values before119870

119901reaches 20

Therefore under the comprehensive condition of abnormalenvironmental loads and a certain percentage of materialstrength degradation displacement of this gravity dam willincrease at a certain amplitude while dam failure will notdirectly occur if the strength degradation and environmentalloads are properly controlled

Relation curves between the yield volume ratio of dambody and the overloading parameter under different strengthreduction parameters are shown in Figure 12 It can be seenthat strength reduction results in a reduced bearing capacityand the earlier occurrence of the catastrophe of concrete


(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60

Figure 7 The progressive failure process of dam-foundation system under overloading

0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74

Overloading parameter

Disp

lace

men

t (m

m)

Figure 8 Relation curves between the stream displacement of dambody and the overloading parameter

yield volume ratio Dam overloading failures under differentstrength reduction conditions show that catastrophes of theyield volume ratio of dam concretes all appeared next to theconnectivity of plastic yield zones between the foundationplane and the 1199051

119887interlayer and before the catastrophe of dam

displacementTherefore catastrophe of the yield volume ratio

Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1

Figure 9 Relation curve between the yield volume ratio of dambody and the overloading parameter

of dam concretes does not mean the loss of bearing capacityfor this concrete gravity dam which should be determinedaccording to whether the excessive plastic deformation willresult in the catastrophe of dam displacement or not

53 Instability Safety Monitoring Indexes The progressivefailure processes of this gravity dam section under thesimulation methods of strength reduction and water densityoverloading are both represented as follows plastic yield


0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)

Figure 10 Relation curves between the stream displacement of thefoundation plane and the overloading parameter under differentstrength reduction parameters

0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250

Figure 11 Relation curves between the stream displacement of thedam crest and the overloading parameter under different strengthreduction parameters

zones are firstly connected in bedrocks along the 1199051

119887weak

interlayer then yield zones rapidly extend to dam bodyand result in the catastrophe of yield volume ratio of damconcretes the rapidly increased excessive plastic deformationin dam body and foundation rocks results in the catastropheof dam displacement and the gravity dam loses the bearingcapacity due to the failure of instability finally

The aforementioned analyses show that catastrophes ofthe yield volume ratio of dam concretes in both simulationmethods all appeared closely next to the connectivity ofplastic yield zones between the foundation plane and the1199051

119887interlayer Therefore there are two typical stages that

can be defined in both failure processes the first one isthe connectivity of plastic yield zones along the 1199051

119887weak

interlayer in bedrocks the second one is the catastrophe ofdam displacement

During the designed service period the potential mostunfavorable conditions of dams are concluded as materialstrength degradation and extreme external environmentalloads Hence methods of strength reduction and over-loading can be respectively used in studying the failuremechanism of high concrete gravity dams under these twounfavorable conditions Based on the dam safety monitoringsystem dam theoretical displacements of typical points at

07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Figure 12 Relation curves between the yield volume ratio ofdam body and the overloading parameter under different strengthreduction parameters

the aforementioned two typical stages can be determinedas the safety monitoring indexes Dam failure mechanismunder the comprehensive method is similar to that of justoverloading and differences are only represented on thedeformation that it is bigger for the same environmental loadswhen the material strength is reduced Therefore from theview of safety the smaller displacement at the same typicalstage is determined as the dam safety monitoring indexnamely monitoring indexes are hierarchically determinedaccording to the theoretical results of strength reduction andoverloading

Research results of the strength reduction method showthat the resisting force of the tail rock resistance block canbe ensured due to the buried depth of 30m and 80m for 1199051

119887

and 1199051

119886 respectively Therefore although there are two weak

interlayers distributed in bedrocks the connectivity of plasticyield zones along the 1199051

119887interlayer will not result in the rapid

development of the translational sliding Dam displacementstend to be rapidly increased until dam concretes yield overlarge areas when 119870

119904reaches 30 However material property

of dam concretes is easy to be identified and varies slightly forthe better construction quality so it is not inconsistent withthe actual situation that the strength of all dam concretes canbe determined as 13 of the original value due to the strengthdegradation or uncertainty On the other hand strength ofbedrocks is usually weaker than that of dam concretes andthe strength degradation of bedrocks and weak structuralsurfaces are more serious than dam concretes for the obviousseepage in dam foundation Theoretically speaking damfailure of instability caused by material strength degradationor uncertainty will occur in dam foundation firstlyThereforebased on the aforementioned analyses catastrophe of damdisplacement in the strength reduction method is not iden-tified as the sign of losing bearing capacity for this concretegravity dam

Due to the complexity of rock genesis and geotectonicmovement various faults joints and cracks are complicat-edly distributed in dam foundation so big differences ofmaterial properties may appear in local small areas thatcannot be systematically represented in geological surveyTherefore under the normal condition large deformation


Table 3 Monitoring indexes of dam stream displacement (unitmm)

Elevation Dam instability safety monitoring indexesGrade one Grade two Grade three

1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526

which seems abnormal may also take place due to theuncertainty of rock properties especially for the strength ofweak structural surfaces and dam safety will be threatened ifand only if this uncertainty is beyond the range of acceptableTherefore the connectivity of yield zones along the 1199051

119887

interlayer in the strength reduction method is defined as thevariation sign of normal operation for this concrete gravitydam and the corresponding damdisplacement is determinedas dam instability safetymonitoring index of grade oneAs forthe connectivity of yield zones along the 1199051

119887interlayer caused

by overloading if engineering or nonengineering measuresare not taken to stop the rapidly increased deformation(caused by the continual increments of environmental loadsor the creep effect of bedrocks and dam concretes) it mayresult in the instability sliding of this gravity dam-foundationsystem For the same typical stage of the connectivity of yieldzones along the 1199051

119887interlayer the risk level under overloading

is more serious than that of strength degradation so thesecond dam instability safetymonitoring index is determinedby the overloadingmethod at the aforementioned dam failurestage

Based on the aforementioned failure mechanism of insta-bility three grades of instability safety monitoring indexesare hierarchically determined for this high concrete gravitydam The corresponding typical stages in the simulated damfailure process are identified as follows (1) the first gradethe connectivity of plastic yield zones along the 1199051

119887interlayer

from dam heel to dam toe by the strength reduction methodwith119870

119904= 22 (2) the second grade the connectivity of plastic

yield zones along the t1119887interlayer from dam heel to dam toe

by the overloadingmethodwith119870

119901= 20 (3) the third grade

catastrophe of dam displacement by the overloading methodwith119870

119901= 36 Monitoring indexes for the observation points

of the plumb line are shown in Table 3 Here the monitoringindexes of dam displacement are determined in terms of thefoundation plane

6 Conclusions

Aiming at the potential failure modes of material strengthdegradation and extreme external environmental loads dur-ing the service period based on the FEM structural analysismethod failure mechanisms and the progressive failureprocess of high concrete gravity dams are studied in this paperby methods of strength reduction and overloading Typicalstages in the failure process are identified by evaluationindicators of dam displacement the connectivity of yield

zones and the yield volume ratio of dam concretes theninstability safety monitoring index of high concrete gravitydams is determined according to these typical symptomsAt last failure mechanism of a high concrete gravity damis studied and according to different dam safety situationsthree grades of dam instability safety monitoring index ofdam displacement are hierarchically established which arerespectively at the stages of the connectivity of yield zonesalong the weak interlayer by methods of strength reductionand overloading and the catastrophe of dam displacementby the overloading method

Acknowledgments

This work was supported by the Research Fund for theDoctoral Program of Higher Education of China (Grantsnos 20120094110005 and 20120094130003) the NationalNatural Science Foundation of China (Grants nos 5137906851139001 51279052 51209077 and 51179066) the Programfor New Century Excellent Talents in University (Grant noNCET-11-0628) and the Ministry of Water Resources PublicWelfare Industry Research Special Fund Project (Grants nos201201038 and 201101013)

References

[1] C S Gu B Li G L Xu andH Yu ldquoBack analysis ofmechanicalparameters of roller compacted concrete damrdquo Science ChinaTechnological Sciences vol 53 no 3 pp 848ndash853 2010

[2] H Yu Z R Wu T F Bao and L Zhang ldquoMultivariate analysisin dammonitoring data with PCArdquo Science China TechnologicalSciences vol 53 no 4 pp 1088ndash1097 2010

[3] Y Q Ni X W Ye and J M Ko ldquoMonitoring-based fatiguereliability assessment of steel bridges analytical model andapplicationrdquo Journal of Structural Engineering vol 136 no 12pp 1563ndash1573 2010

[4] X W Ye Y Q Ni K Y Wong and J M Ko ldquoStatistical analysisof stress spectra for fatigue life assessment of steel bridges withstructural health monitoring datardquo Engineering Structures vol45 pp 166ndash176 2012

[5] X W Ye Y Q Ni and Y X Xia ldquoDistributed strain sensor net-works for in-construction monitoring and safety evaluation ofhigh-rise buildingrdquo International Journal of Distributed SensorNetworks vol 2012 Article ID 685054 13 pages 2012

[6] C S Gu E F Zhao Y Jin and H Z Su ldquoSingular valuediagnosis in dam safetymonitoring effect valuesrdquo Science ChinaTechnological Sciences vol 54 no 5 pp 1169ndash1176 2011

[7] L Chen Mechanics Performance With Parameters Changingin Space and Monitoring Models of Roller Compacted ConcreteDam College of Water Conservancy and Hydropower Engi-neering Hohai University Nanjing China 2006 (Chinese)

[8] P Lei Study on theTheory andMethod of DeformationMonitor-ing Index of Concrete Dam College of Water Conservancy andHydropower Engineering Hohai University Nanjing China2008 (Chinese)

[9] H Z Su J Hu J Y Li and Z R Wu ldquoDeep stability evaluationof high-gravity dam under combining action of powerhouseand damrdquo International Journal of Geomechanics vol 13 no 3pp 257ndash272 2013


[10] H Z Su J Hu and Z P Wen ldquoService life predicting of damsystems with correlated failure modesrdquo Journal of Performanceof Constructed Facilities vol 27 no 3 pp 252ndash269 2013

[11] S L Fan J Y Chen and J Y Guo ldquoApplication of finite elementequivalent stressmethod to analyze the strength of gravity damrdquoJournal of Hydraulic Engineering vol 38 no 6 pp 754ndash7662007 (Chinese)

[12] H Z Su Z R Wu Y C Gu J Hu and Z P Wen ldquoGamemodel of safety monitoring for arch dam deformationrdquo Sciencein China E vol 51 no 2 pp 76ndash81 2008

[13] C S Gu and Z R Wu Safety Monitoring of Dams and DamFoundations-Theories amp Methods and Their Application HohaiUniversity Press Nanjing China 2006 (Chinese)

[14] Z Z Shen M Ma and X X Tu ldquoEarly warning index of defor-mation for gravity dam based on discontinuous deformationanalysisrdquo Journal of Hydraulic Engineering vol 38 supplementpp 94ndash99 2007 (Chinese)

[15] D J Zheng Z Y Huo and B Li ldquoArch-dam crack deformationmonitoring hybrid model based on XFEMrdquo Science ChinaTechnological Sciences vol 54 no 10 pp 2611ndash2617 2011

[16] P Lei X L Chang F Xiao G J Zhang and H Z Su ldquoStudyon early warning index of spatial deformation for high concretedamrdquo Science China Technological Sciences vol 54 no 6 pp1607ndash1614 2011

[17] Y C Gu and S J Wang ldquoStudy on the early-warning thresholdof structural instability unexpected accidents of reservoir damrdquoJournal of Hydraulic Engineering vol 40 no 12 pp 1467ndash14722009 (Chinese)

[18] C S Shen S X Wang Y C Lin and X Q Liu HydraulicStructure China Water Power Press Beijing China 2008(Chinese)

[19] X L Chang HWangW Zhou andC B Zhou ldquoMechanism oftwo sliding failure modes in gravity dam and method for safetyevaluationrdquo Journal of Hydraulic Engineering vol 40 no 10 pp1189ndash1195 2009 (Chinese)

[20] F Jin W Hu J W Pan J Yang J T Wang and C HZhang ldquoFailure analysis of high-concrete gravity dam based onstrength reserve factor methodrdquo Computers and Geotechnicsvol 35 no 4 pp 627ndash636 2008

[21] F Jin W Hu J W Pan J Yang J T Wang and C H ZhangldquoComparative study procedure for the safety evaluation of higharch damsrdquo Computers and Geotechnics vol 38 no 3 pp 306ndash317 2011

[22] G X Zhang Y Liu and Q J Zhou ldquoStudy on real workingperformance and overload safety factor of high arch damrdquoScience in China E vol 51 no 2 pp 48ndash59 2008

[23] D J Zheng and T Lei ldquoInstability criteria for high archdams using catastrophe theoryrdquo Chinese Journal of GeotechnicalEngineering vol 33 no 1 pp 23ndash27 2011 (Chinese)

[24] State Economic and Trade Commission of China [SETCC]Specifications for seismic design of hydraulic structuresDL5073-2000 2001 (in Chinese)

[25] MSC Software CorporationMSCMarc Vol ATheory and UserInformationMSCSoftwareCorporation SantaAna Calif USA2005

[26] Y R Zheng S Y Zhao W X Kong and C J Deng ldquoGeotech-nical engineering limit analysis using finite element methodrdquoRock and Soil Mechanics vol 26 no 1 pp 163ndash168 2005(Chinese)

Submit your manuscripts athttpwwwhindawicom

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Differential EquationsInternational Journal of

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

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Stochastic AnalysisInternational Journal of


displacement of Malpasset arch dam four mouths beforeits failure is significantly larger than the theoretical valueand the closer to dam bottom the more serious Landslideson the left bank of Vajont arch dam began to creep slowlyafter the impoundment of upstream reservoir in 1960 themeasured total displacement at the dam crest came up to429 cm on October 7 1963 and increased at an amazingspeed of 483mmd during the last 12 days before failureTernperatwre alarms were not made for the occurrence ofabnormities so that both dam failures occurred without anyengineering or nonengineering measures so the absenceof monitoring index for Malpasset arch dam and Vajontarch dam restricted the function of their safety monitoringsystems The situation that monitoring quantity exceeds itsmonitoring index probably means the abnormity of damsafety so it is a key problem for managers to determine themonitoring index scientifically

As for gravity dams dam failures are mainly caused bythe instability of dam-foundation systems and the failureprocess depends on failure modes [9 10] Due to the com-plexity and specificity of each dam-foundation system failuremechanisms and failure processes are different from damto dam even if under the same failure mode Therefore itis necessary to simulate the real failure process and studythe failure mechanism of instability under different failuremodes and the instability safety monitoring index of highconcrete gravity dams should be determined according to thetypical symptoms in the simulated failure process

This paper firstly makes a brief summary about the cur-rent theories and methods of establishing dam safety mon-itoring indexes in which disadvantages of each methodare analyzed Then based on the traditional finite elementstructural analysis method considering the most probablepotential failure modes of material degradation or uncer-tainty and extreme external environmental loads during damoperation methods of strength reduction and overloadingare respectively used in this paper to study the progressiveinstability failure process of high concrete gravity damsTypical stages in the instability processes are identified byevaluation indicators of dam displacement the connectivityof yield zones and the yield volume ratio of dam concretesthen instability safety monitoring index of high concretegravity dams is determined according to these typical symp-toms At last the proposedmethod for establishing instabilitysafety monitoring index of high concrete gravity dams isstudied in detail with a practical engineering

2 Research Situation of Dam SafetyMonitoring Index

Current dam safety monitoring items are deformation stressuplift pressure seepage crack opening and so on Moni-toring indexes for dam stress uplift pressure and seepageare determined according to the hydraulic specifications andthese items are often established for local areas where themonitoring quantities should be controlled strictly Especiallyfor dam stress the stress-controllable areas such as damheel and dam toe are also the stress concentration areas in

the finite element method (FEM) so it is difficult to deter-mine a reasonable stress control standard for these areas byFEM simulation [11] As for the crack opening it is not easy todetermine the monitoring index by hydraulic specificationsdue to the complex opening mechanism of cracks Howevercrack opening is the same as other monitoring items thatonly local damages may appear when its monitoring index isexceeded and obvious abnormality will be directly reflectedon dam deformation even if the rapid development of theselocal damages will result in the dam failure Among all thesemonitoring items deformation can directly reflect the globalsafety and the progressive failure process of dam-foundationsystem so monitoring index for dam deformation is mostlydetermined as dam safety monitoring index [12]

The reasonablemonitoring index can be used in analyzingand evaluating the situation of dam safety However due tothe complexity of dam structures and the different materialvariation characteristics comprehensive demonstration bydifferent methods should be conducted to determine damsafety monitoring index The mostly used methods forestablishing the monitoring index at present are confidenceinterval method typical low probability method limit statemethod and structural analysis method [13] These methodsare all without taking dam failure modes into considerationlet alone the instabilitymechanism and the progressive failureprocess under different failure modes Therefore advantagesand disadvantages of these methods are analyzed beforeestablishing the safety monitoring index of high concretegravity dam based on failure mechanism of instability

21 Confidence Interval Method The basic principle of confi-dence interval method is the little probability event in statis-tics According to the observation data mathematical models(such as statistical model hybrid model and deterministicmodel) are established between monitoring effect quantitiesand environmental variables and these models are used incalculating the deviations (119910 minus 119910) between the calculatedvalues (119910) and the measured values 119910 of monitoring effectquantities in the domain of dam experienced loads If thedeviations are within the confidence band of Δ = plusmn 120573120590 withthe probability of 1 minus 120572 (120572 is the significance level which isfrequently determined as 1sim5) and no obvious tendencyvariations are reflected on the monitoring effect quantitiesthen this dam is considered to be in normal conditionTherefore dam monitoring index is established as follows

120575

119898= 119910 + Δ = 119910 plusmn 120573120590 (1)

where 120573 is related to the significance level 120572 and 120590 is theresidual standard deviation of the mathematical model

The frequently used confidence interval method andtypical lowprobabilitymethod are both based on the observa-tion data According to the performance of dam-foundationsystem under the experienced loads bearing capacities underthe potential loads are evaluated and the correspondingalarm values and extreme values are predicted for differentmonitoring effect quantities However dam safety informa-tion contained in the observation data varies from dam todam due to the different experienced loads especially for







119898119894is


1198981 119910

1198982 119910



119910 =

1

119899

119899

sum

119894=1

119910

119898119894 (2)

120590

119864=

radic

1

119899 minus 1

(

119899

sum

119894=1

119910

2

119898119894minus 119899119910

2

) (3)




119875 (119910 gt 119910max) = 119875

119886= int

+infin

119910max

119891 (119910

(max)) 119889119910 upper limit (4)

or

119875 (119910 lt 119910min) = 119875

119886= int

119910min

minusinfin

119891 (119910

(min)) 119889119910 lower limit (5)





119886and 119891(119910) (119891(119910

(max))or 119891(119910




119885 = 119877 minus 119878 ge 0 (6)




120575

1= 119865(120590

119905lt [120590

119905] 120590

119888lt [120590

119888] 119870 =

119877

1198981

119878

ge [119870]) (7)


120575

2= 119865 (120590

119905lt 120590

119905119877 120590

119888lt 120590

119888119877 119878 le 119877

1198982 119870

119888le [119870

119888]) (8)


120575

3= 119865 (120590

119905lt 120590

119905119898 120590

119888lt 120590

119888119898 119878 le 119877

1198983) (9)

where 120590

119905and 120590



119905] 120590

119905119877 and 120590



119888] 120590119888119877 and 120590

119888119898are





1198981 1198771198982 and

119877



119888and [119870

119888]









119901






Gravity dam

Foundation rock

A

B

C


Foundation plane

Pull broken or

crushed area Failu

re zo

ne of

com

pres

sion-

shea

r

B998400 B998400998400middot

Envi

ronm

ent l

oad

(a)

Gravity dam

Foundation plane

Envi

ronm

ent l

oad


Foundation rock

Translational slip

Slip

Slip


(b)




119875113 126 152






119904and 119891119870











120576

119901

= int

120576

119901

119889119905 = int(

2

3

120576

119901

119894119895120576

119901

119894119895)

12

119889119905(10)

where

120576








5 Case Study


119887and 1199051

119886











Failure modes




Dam displacement






Dam

safe

tyev

alua

tion

indi

cato

r











119891 = 120572119868

1+ radic119869

2minus 119870 = 0

(11)

where 119868



120572 =

sin120593


(12)

119870 =

3119888 cos120593


(13)


Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)







parameter 119870













119887


119887interlayer



1199051






119904reaches 30



(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















119898119894is


1198981 119910

1198982 119910



119910 =

1

119899

119899

sum

119894=1

119910

119898119894 (2)

120590

119864=

radic

1

119899 minus 1

(

119899

sum

119894=1

119910

2

119898119894minus 119899119910

2

) (3)




119875 (119910 gt 119910max) = 119875

119886= int

+infin

119910max

119891 (119910

(max)) 119889119910 upper limit (4)

or

119875 (119910 lt 119910min) = 119875

119886= int

119910min

minusinfin

119891 (119910

(min)) 119889119910 lower limit (5)





119886and 119891(119910) (119891(119910

(max))or 119891(119910




119885 = 119877 minus 119878 ge 0 (6)




120575

1= 119865(120590

119905lt [120590

119905] 120590

119888lt [120590

119888] 119870 =

119877

1198981

119878

ge [119870]) (7)


120575

2= 119865 (120590

119905lt 120590

119905119877 120590

119888lt 120590

119888119877 119878 le 119877

1198982 119870

119888le [119870

119888]) (8)


120575

3= 119865 (120590

119905lt 120590

119905119898 120590

119888lt 120590

119888119898 119878 le 119877

1198983) (9)

where 120590

119905and 120590



119905] 120590

119905119877 and 120590



119888] 120590119888119877 and 120590

119888119898are





1198981 1198771198982 and

119877



119888and [119870

119888]









119901






Gravity dam

Foundation rock

A

B

C


Foundation plane

Pull broken or

crushed area Failu

re zo

ne of

com

pres

sion-

shea

r

B998400 B998400998400middot

Envi

ronm

ent l

oad

(a)

Gravity dam

Foundation plane

Envi

ronm

ent l

oad


Foundation rock

Translational slip

Slip

Slip


(b)




119875113 126 152






119904and 119891119870











120576

119901

= int

120576

119901

119889119905 = int(

2

3

120576

119901

119894119895120576

119901

119894119895)

12

119889119905(10)

where

120576








5 Case Study


119887and 1199051

119886











Failure modes




Dam displacement






Dam

safe

tyev

alua

tion

indi

cato

r











119891 = 120572119868

1+ radic119869

2minus 119870 = 0

(11)

where 119868



120572 =

sin120593


(12)

119870 =

3119888 cos120593


(13)


Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)







parameter 119870













119887


119887interlayer



1199051






119904reaches 30



(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1198981 1198771198982 and

119877



119888and [119870

119888]









119901






Gravity dam

Foundation rock

A

B

C


Foundation plane

Pull broken or

crushed area Failu

re zo

ne of

com

pres

sion-

shea

r

B998400 B998400998400middot

Envi

ronm

ent l

oad

(a)

Gravity dam

Foundation plane

Envi

ronm

ent l

oad


Foundation rock

Translational slip

Slip

Slip


(b)




119875113 126 152






119904and 119891119870











120576

119901

= int

120576

119901

119889119905 = int(

2

3

120576

119901

119894119895120576

119901

119894119895)

12

119889119905(10)

where

120576








5 Case Study


119887and 1199051

119886











Failure modes




Dam displacement






Dam

safe

tyev

alua

tion

indi

cato

r











119891 = 120572119868

1+ radic119869

2minus 119870 = 0

(11)

where 119868



120572 =

sin120593


(12)

119870 =

3119888 cos120593


(13)


Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)







parameter 119870













119887


119887interlayer



1199051






119904reaches 30



(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Gravity dam

Foundation rock

A

B

C


Foundation plane

Pull broken or

crushed area Failu

re zo

ne of

com

pres

sion-

shea

r

B998400 B998400998400middot

Envi

ronm

ent l

oad

(a)

Gravity dam

Foundation plane

Envi

ronm

ent l

oad


Foundation rock

Translational slip

Slip

Slip


(b)




119875113 126 152






119904and 119891119870











120576

119901

= int

120576

119901

119889119905 = int(

2

3

120576

119901

119894119895120576

119901

119894119895)

12

119889119905(10)

where

120576








5 Case Study


119887and 1199051

119886











Failure modes




Dam displacement






Dam

safe

tyev

alua

tion

indi

cato

r











119891 = 120572119868

1+ radic119869

2minus 119870 = 0

(11)

where 119868



120572 =

sin120593


(12)

119870 =

3119888 cos120593


(13)


Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)







parameter 119870













119887


119887interlayer



1199051






119904reaches 30



(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












120576

119901

= int

120576

119901

119889119905 = int(

2

3

120576

119901

119894119895120576

119901

119894119895)

12

119889119905(10)

where

120576








5 Case Study


119887and 1199051

119886











Failure modes




Dam displacement






Dam

safe

tyev

alua

tion

indi

cato

r











119891 = 120572119868

1+ radic119869

2minus 119870 = 0

(11)

where 119868



120572 =

sin120593


(12)

119870 =

3119888 cos120593


(13)


Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)







parameter 119870













119887


119887interlayer



1199051






119904reaches 30



(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















Failure modes




Dam displacement






Dam

safe

tyev

alua

tion

indi

cato

r











119891 = 120572119868

1+ radic119869

2minus 119870 = 0

(11)

where 119868



120572 =

sin120593


(12)

119870 =

3119888 cos120593


(13)


Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)







parameter 119870













119887


119887interlayer



1199051






119904reaches 30



(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Dam body

Rock I

Rock II

Rock III

t1b

t1a

(a)

1424 m

1359 m

1320 m

1292 m

1264 m

(b)







parameter 119870













119887


119887interlayer



1199051






119904reaches 30



(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) 119870119904= 12 (b) 119870

119904= 18

(c) 119870119904= 20

(d) 119870119904= 22

(e) 119870119904= 28 (f) 119870

119904= 30








119904





119901



255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










255075

100125150175200225

Disp

lace

men

t (m

m)

142413591320

12921264

1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter


1 12 14 16 18 2 22 24 26 28 3 32 34

Reduction parameter

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)












When119870






119901= 36 and




119870









119901= 30






119901reaches


119901reaches 20




(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) 119870119901= 10 (b) 119870

119901= 20

(c) 119870119901= 32 (d) 119870

119901= 36

(e) 119870119901= 46 (f) 119870

119901= 60


0100020003000400050006000

142413591320

12921264

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


Disp

lace

men

t (m

m)





Ratio

of p

lasti

cvo

lum

e (

)

1

14

18

22

26 3

34

38

42

46 5

54

58

62

66 7

74


0

02

04

06

08

1





0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0100200300400500600700800900

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m)


0

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36


Disp

lace

men

t (m

m) 2250

2000

1750

1500

1250

1000

750

500

250



119887weak





119887weak



07

06

05

04

03

02

01

0

Ratio

of p

lasti

cvo

lum

e (

)

101214

1618

1 12 14 16 18 2 22 24 26 28 3 32 34 36





119887

and 1199051











1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1424m 2606 7616 399611359m 1889 4486 213601320m 1279 2568 102831292m 700 1243 4526


119887







119887interlayer









6 Conclusions



Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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Research Article Safety Monitoring Index of High Concrete