Overall Stability Analysis of Xiluodu High Arch Dam Based ...

Research ArticleOverall Stability Analysis of Xiluodu High Arch Dam Based onFine Three-Dimension Numerical Modeling

Tianhui Ma 1 Zhiqiang Feng 1 Chunrsquoan Tang1 Peng Lin2 and Kedar Prasad Yadav1

1State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology Dalian Liaoning 116024 China2Department of Water Resources and Hydropower Engineering Tsinghua University Beijing 100000 China

Correspondence should be addressed to Zhiqiang Feng fengzq136653maildluteducn

Received 22 November 2020 Revised 25 December 2020 Accepted 15 January 2021 Published 29 January 2021

Academic Editor Zhigang Zhang

Copyright copy 2021 Tianhui Ma et al -is 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

-e RFPA3D is used to establish a fine finite element model of 663 million elements which realizes the fine simulation of thestability of the Xiluodu arch dam under layered overall multiworking conditions and multistress fields and the cracking andfailure process under overload-e structural design scheme of the arch dam and the corresponding foundation treatment designare evaluated -e model fully reflects the measures of dam shape structure design angle fitting structure design and foundationconcrete replacement in the Xiluodu arch dam technical design stage -e RFPA3D adopts the mesoelement elastic damagemodel which considers the MohrndashCoulomb criterion of shear fracture and the maximum tensile failure criterion and assumesthat the mechanical properties of the element satisfy Weibull distribution to consider its heterogeneity -e simulation resultsshow that under normal load conditions the dam foundation surface after comprehensive reinforcement has better overallstability the stress and deformation of the dam body have good symmetry and the overload factor of crack initiation underoverload calculation K1 2P0 (P0 is normal water load) the nonlinear deformation overload factor K2 35ndash4P0 and the limitload factorK3 75ndash80P0 dam safety can be satisfied-e RFPA3D is used to establish a superlarge finemodel to study the overallstability of the high arch dam which provides an effective method for analysis and research of other large hydraulic projects inthe world

1 Introduction

A series of major projects related to national economicconstruction in China such as water conservancy and hy-dropower industry tend to be large-scale comprehensiveand complex A large number of dam foundation-bankstructures that are complete in process or proposed aregenerally facing the challenges of construction and opera-tional safety under complex unpredictable and extremeload conditions Among super-high dams the arch damstransfer loads to the dam foundations and abutmentsthrough the effect of the beam and the arching effect so thatthe dam body is mainly compressed and hence the com-pressive performance of concrete materials can be fullyrealized It has become an extremely beneficial dam type ofsuper-high dams because of its advantages of high safetystrong seismic capacity large dam discharge and small

concrete quantities [1ndash5] However as most of the load istransferred to the rock on both sides of the dam highstability and strength of the rock are required If the geo-logical conditions of the foundation are not good or thesymmetry is poor the arch dam will be prone to stressconcentration dam instability and other problems whichcan result in cracking and even damage to the dam body-esafe operation of dams has a profound impact on socialenergy efficiency and the lives of downstream residents-ere have been many incidents of arch dam damage in theworld [6 7] which have greatly hindered the safe operationof the project -erefore it is particularly important toreasonably evaluate the stability of the arch dams in thedesign

At present there are two main methods to study theoverall stability of dams three-dimensional geomechanicalmodel test and numerical simulation analysis [8ndash14]

HindawiAdvances in Civil EngineeringVolume 2021 Article ID 6641974 15 pageshttpsdoiorg10115520216641974

Among various numerical simulation methods the three-dimensional nonlinear finite element method is widely usedin the stability analysis of high arch dam using a three-dimensional nonlinear finite element method to calculatethe deformation and stress of the arch dam can well simulatethe constitutive relationship and load and boundary con-ditions of the complex rock and can better reflect thecomplexity of geological structure and the influence ofengineering measures on dam structure -erefore with thedevelopment of computer technology and the popularity ofgeneral finite element software finite element analysistechnology has been more and more widely used in solvingcomplex hydropower engineering problems and achievedgood engineering results For example Yang et al [15] triedto solve large finite element equations by an iterative methodin the three-dimensional finite element analysis of theGeheyan gravity arch dam in 1989 and obtained reasonablecalculation results Shen et al [16] solved the minimumsafety factor and the position of the corresponding potentialsliding surface during the excavation of Xiaolangdi highslope by using the three-dimensional finite element analysismethod and the results were confirmed by actual con-struction Chen et al [17] and Chen et al [18] respectivelycarried out a finite element analysis on the abutment rockmass stability and the dam heel cracking risk of the Xiaowanhigh arch dam Wang et al [19] simulated and analyzed thestress state of the Ertan arch dam during operationAccording to the results of numerical simulation and modeltest Zhang et al [20] analyzed the displacement and stressdistribution failure mechanism and overall stability of thearch dam the results are in good agreement Pei et al [21]simulated the construction process and impoundmentprocess of the Lizhou RCC arch dam and analyzed the stressdeformation behavior and development law of the dam bodyin the real working state during the impoundment process-ese applications show that the finite element numericalsimulation analysis has obvious advantages in studying thestress displacement and failure characteristics of high archdams and has become an effective way to study the damdesign reinforcement and stability evaluation of high archdams

-e accuracy of finite element analysis will be affected bythe selection of reasonable constitutive relations Arch damsare usually built into geologically complex mountains andvalleys and form an interactive system with dam foundationand dam abutments As the main engineering materialsrock and concrete are heterogeneous quasi-brittle materialswith complex mechanical properties -e researchers havemade in-depth discussions on their constitutive relationsfrom phenomenology and physical mechanisms includingstrength theory plastic constitutive theory damage con-stitutive theory and distributed fracture mechanics con-stitutive theory [22ndash26] It has been widely recognized thatthe fracture and failure process of rock or concrete is actuallythe whole process of microcracksrsquo generation and devel-opment until the formation of the transfixion zone underload In the past the constitutive relations of nonlinear finiteelements only grasped the ldquononlinearrdquo characteristics ofmaterial deformation from the macrolevel and participated

in the analysis and calculation as an elementrsquos attributewhich ignored the inhomogeneity of micromedium pa-rameters so there is no macromicro difference in the resultsIn fact due to the extreme heterogeneity of these materialstheir properties at the microlevel are very different from themacrolevel In order to fully consider the nonlinearity andheterogeneity during the fracture process of rock or con-crete Tang et al proposed a new numerical simulationmethod ldquoRFPA (Rock Failure Process Analysis) Methodrdquo[27ndash33] based on the basic theory of finite element to ex-plain the structural fracture process with statistical damagetheory and the basic principle of strength reduction method[34 35] was introduced to analyze the stability of geo-technical engineering [36] It is proved that the method canbe used to deal with geotechnical engineering under com-plex geological conditions effectively

In addition the number of grids affects the accuracy ofcalculation results and the size of the calculation scale Inorder to make the element size in numerical simulationreflect the basic microscopic properties of the medium theRFPA3D code is used to establish the superlarge model ofthe Xiluodu high arch dam with full hexahedron element (6632 192 elements 6893485 nodes more than 20 milliondegrees of freedom) -e large-scale parallel computingcluster [37] is used to realize the fine simulation of the damunder layered overall multiworking conditions and mul-tistress fields On the basis of fully reflecting the geologicalconditions after the actual excavation of the Xiluodu archdam the corresponding structural design and foundationtreatment measures the deformation and stress character-istics of the dam body and abutment rock mass underseveral different load combinations are studied -rough theapplication of overload the overload coefficient yield andcracking conditions of each failure stage are obtained toanalyze the overload capacity of the arch dam According tothe analysis results the overall stability and safety of the archdam under the structural design and foundation treatmentdesign scheme are demonstrated and the overall safety ofthe arch dam under the current implementation scheme iscomprehensively evaluated and the results provide a basisfor the structural design and foundation treatment design ofthe Xiluodu high arch dam

2 Engineering Background

-eXiluodu hydropower station is located in Xiluodu gorgewhich is adjacent to Leibo County in Sichuan Province andYongshan County in Yunnan Province -is is the thirdcascade in the development plan of the Jinsha River section-e double-curvature arch dam is selected as the dam type(the centerline of the arch dam is N 482degW) with a crestelevation of 6100m a foundation surface elevation of3320m and a maximum dam height of 2780m whichbears a huge water thrust of about 13 million tons requiringthe foundation to have the corresponding bearing capacity-e total amount of engineering concrete is 1296 millionm3 of which about 7millionm3 is dam concrete-e normalwater level of the reservoir is 60000m and the corre-sponding downstream water level is 37800m (38146m for

2 Advances in Civil Engineering

normal operation of 18 units) the dead water level is54000m and the corresponding downstream water level is37800m the total storage capacity is 1157 billion m3 andthe regulated storage capacity is 6416 billionm3-is projectis a giant hydropower station that mainly generates elec-tricity and has comprehensive utilization benefits such assand retaining flood control and improving downstreamshipping

-ere are abundant mountains on both sides of theXiluodu double-curvature arch dam with a steep valleyslope -e valley section is symmetrical ldquoUrdquo with the leftbank slope of 40deg～75deg and the right bank slope of 55deg～75deg-e rock property of the dam site area is single and thebedrock of the valley slope and the riverbed is the conti-nental basic volcanic rock flow with the intermittentlymultistage eruption of Emeishan basalt (P2β) which isdivided into 14 rock flow layers generally 25ndash40m thick-e representative lithology mainly includes porphyry basalt(1 6 layers) microcrystalline basalt (2 5 9ndash14 layers) andphenocryst basalt (3 4 7 8 layers) which are distributed inthe lower part of the flow layer basaltic breccia (agglom-erate) lava and a small amount of volcanic breccia andbasaltic tuff are distributed in the upper part of most flowlayers the lithology changes gradually from the top to thebottom

Compared with the design requirements and acceptancestandards the rock mass quality of the riverbed undernatural conditions is insufficient-erefore it is necessary tostrengthen consolidation grouting and adopt structuralforms expand the stress area of the foundation and improvethe homogeneity of rock mass and the stiffness of thefoundation so as to meet the requirements of damconstruction

3 Numerical Model Analysis

31 Introduction to theModel A three-dimensional model isadopted in this calculation Centered at the dam axis thecalculation range is as follows the upstream length is about 1times the height of the dam the downstream length is about25 times the height of the dam the banks are near twice theheight of the dam and the simulated depth of the damfoundation is almost the same as the height of the dam -emesh generation is carried out according to the drawingsprovided by the Chengdu Survey and Design Institute ofChina Hydropower Consulting Group and the total sim-ulation range is 1800times1000times 660m Eight-node hexahe-dron elements are adopted in the grid with a total number of6632192 elements a total number of 6893485 nodes and atotal number of 2692032 dam elements -e computationalgrid is shown in Figures 1 and 2

Combined with the current situation of the Xiluodufoundation rock mass the rock mass parameters are eval-uated by the method of layered segmented zoned andgraded benchmarking and on this basis various rockmasses dislocation zones C9 C8 C7 Lc6 Lc5 C3 and C2and weak interlayer P2βn are simulated and the distributioncharacteristics are shown in Table 1 and Figure 3 -efoundation concrete replacement and dam toe treatment are

shown in Figure 4 Concrete replacement the replacementand backfill treatment are carried out for the interlaminardislocation zone on the banks of the dam foundation at EL510ndash610m grade IV1 rock mass exposed above the EL560m grade IV 1 and class III2 exposed below the EL 560mthe staggered zone in the interlayer between the EL400ndash510m and the strongly weathered interlayer the gradeIV1 rock mass exposed on the foundation surface and thegrade III2 rock mass exposed at the middle elevation andlower elevation of the foundation surface Because thebroken rock mass and dislocation zone C3 are exposed at EL33000ndash35000m on the left bank of the dam foundation it isgrooved -e strongly weathered interlayer in the middledislocation zone of the P2βn layer is treated with a compositereplacement plug-e exposed IV 1 and III 2 rock masses onthe riverbed are treated by displacement excavation -eminimum excavation elevation is EL 3245m and the depthis about 7m -e depth of replacement excavation shall beadjusted locally according to the geological exposure of thesite

-e RFPA3D adopts the mesoelement elastic damagemodel [28] which considers the MohrndashCoulomb criterionof shear fracture and the maximum tensile failure criterionand assumes that the mechanical properties of the elementsatisfy Weibull distribution to consider its heterogeneity soas to reveal the macroscopic nonlinearity of quasi-brittlematerials such as rock or concrete from the simple elastic-brittle constitutive relation at the mesolevel -e elastic-brittle constitutive relation of primitive under uniaxial stressis shown in Figure 5

1800m

660m

1000m X

YZ

Figure 1 Computational grid diagram (Overall Diagram)

Figure 2 Computational grid diagram (Enlarged Partial Diagram)

Advances in Civil Engineering 3

For quasi-brittle materials such as rock especially in thecase of special mesoscale tensile damage mainly occurs inthe element -erefore if the mesoelement satisfies both theshear failure criterion and tensile failure criterion the tensilecriterion takes precedence

-e MohrndashCoulomb criterion with tensile failure cri-terion is expressed as follows

σ1 minus λσ3 ge σc

σ3 le minus σt1113896

σ1 gt σc minus λσt

σ1 le σc minus λσt(1)

where λ (1 + sinφ)(1 minus sinφ) tan2 θ θ is the angle ofrupture

Table 1 Characteristics of dislocation zone in the interlayer of the dam area

Place Weak zone EL (m) -ickness (m) AttitudeShear resistance Shearfprime cprime (MPa) f C (MPa)

Left bank

C9 536 05 N25degWNEang4deg 035 005 030 0040 007 034 0

C8 513 05 N35degWNEang5deg 035 005 030 0044 010 037 0

C7 479 06 N25sim35degWNEang4sim7deg 055 025 047 0Lc6 403 06 N20degsim40degWNEang8degsim11deg 044 010 037 0Lc5 380 06 N20degsim30degWNEang4degsim7deg 055 025 047 0

C3 339 05 N18degsim23degWNEang5degsim8deg 043 008 037 0044 010 037 0

Right bank

C9 562 05 N36degESEang2sim5deg 035 005 030 004 007 034 0

C8 536 05 N38degESEang4deg 043 008 037 0044 010 037 0

C7 497 06 N30sim35degESEang4sim6deg 043 008 037 0055 025 047 0

Lc6 424 06 N30degsim40degESEang8degsim10deg 043 008 037 0044 010 037 0

Lc5 385 06 N30degsim40degESEang8degsim10deg 055 025 047 0C3 345 05 N24degESEang4degsim5deg 050 017 042 0

River bed C2 302 05 N25-30degWSWang5ndash10deg 035 005 035 0P2βn 240 18 N25-30degWSWang5ndash10deg 035 005 035 0

Right bank Le bankXY Z

C9C8C7Lc6Lc5C3

C2P2βn

Figure 3 Relationship between the dislocation zone and the dambody in the interlayer

Dam toe

Concrete replacement


Figure 4 Relationship between foundation concrete replacementand dam toe (downstream)

fc0

fcrndashεt0

εc0

ndashft0

ndashεtundashftr

σ

Oε

Figure 5 Elastic-brittle constitutive relation of the element underuniaxial stress state


32 Material Parameters -e actual monitoring value ofdam deformation is usually very different from the originaldesign calculation value and the mechanical parameters ofthe rock foundation in the reservoir area also vary greatly-ese factors have a great influence on the deformation ofthe dam body and rock foundation-erefore it is necessaryto use measured data combined with numerical analysis andcalculation to carry out inverse analysis on the elasticmodulus Ec of the dam body the deformationmodulus Er ofthe dam bedrock foundation and the deformation modulusEb of the reservoir rock foundation and deduce the actualdeformation modulus by this method Table 2 shows themechanical parameters of Xiluodu materials

33 CalculationConditions In this paper the RFPA3D codeis used for finite element numerical calculation and only theself-weight stress field is considered for crustal stress As forwater load the upstream check flood level and corre-sponding downstream water level are 60700m and41461m and the upstream design flood level and corre-sponding downstream water level are 60070m and40978m -e upstream silt elevation is 49000m thefloating bulk density of the silt is 05 tm3 and the internalfriction angle of the silt is 0deg -e temperature load of thedam body is shown in Table 3 and the linear expansioncoefficient of dam concrete is 10times10ndash5degC -e calculationconsists of 16 calculation conditions as shown in Tables 4and 5

4 Dam Displacement and Stress Analysis

41 Dam Displacement Analysis In this paper the dis-placement characteristics of the dam body along the riverand transverse the river were analyzed the working con-ditions include basic load conditions 4ndash11 and special loadconditions 12ndash16 -e results show that the overall stiffnessof the dam foundation after reinforcement is good Figure 6shows the displacement distribution along the river ofXiluodu arch dam under conditions 4 and 6

Taking working condition 4 as an example the resultsshow that the maximum displacement of the crown alongthe river was 104356 mm located at EL 585 m -emaximum displacement of the left arch abutment alongthe river was 27612 mm at the downstream surface EL345m -e maximum displacement of the right archabutment along the river was 25617mm at the down-stream surface EL360m -e maximum displacement ofthe arch dam foundation is 25541 mm which is locatedat the right arch abutment EL 440m and the relativedisplacement of the disturbed belt is relatively small -etransverse displacement of the downstream dam surfacewas toward the mountains -e upstream surface variedfrom EL 480m to EL 440m and the displacement of theupper part points to the mountains and the displacementbelow EL 475m points to the dam in the transversedirection with the maximum displacement of 2203 mmFigure 6 shows the displacement characteristic curve

of the arch dam under a normal load condition (con-dition 4)

-e displacement characteristics under each conditioncalculated by RFPA3D code are as follows

(1) Along the river the maximum displacement of theXiluodu arch dam under various working conditionswas located at the downstream arch crown thedisplacement of the two arch abutments was equalthe displacement of the left abutment was slightlylarger than that of the right abutment and thedisplacement symmetry of dam body was goodUnder one to five times of normal water load therelationship between displacement and overloadcoefficient is basically linear which indicates that thedeformation of dam structure can still keep a certainlinear working state Figure 7 shows the displace-ment comparison of the dam abutments and archcrown under 1ndash5 times normal water load (otherloads are the same)

(2) Under different working conditions the displace-ment characteristics of the downstream surface ofthe dam body on the transverse direction of the riverwere similar and all of them were toward themountains so the dam body had good symmetryUnder the basic load combination transverse dis-placement of the upstream surface changed at EL400mndashEL 520m the upper abutments deformedtoward the mountains and the lower abutmentsdeformed toward the dam so it could be predictedthat the compressive stress was larger in this part

(3) -e temperature effect is shown in Figure 8 Underthe working condition of temperature rise the de-formation of the two arch abutments increased to-ward both the mountains and rivers while thetransverse deformation and deformation along theriver at the arch crown decreased which was ben-eficial to the stability of the arch crown and unfa-vorable to the stability of the arch abutments

It can be seen from the calculation results that under thebasic load combinations the dam surface was basically in arelatively uniform compression state With the increase ofload the tensile stress first occurred at the dam crest -emaximum tensile stress on the downstream surface was-1119MPa under working condition 4 and the maximumtensile stress under other working conditions did not exceed-05MPa -e compressive stress at the two arch abutmentsof the downstream surface was moderate and the maximumcompressive stress appeared at the arch abutments mainly atEL 350 mndashEL 380m -e compressive stress at the left archabutment and that at the right arch abutment were equiv-alent and the compressive stress at the left arch abutmentwas slightly larger -e characteristic stress values of archdams under different load combinations are shown in Ta-bles 6 and 7

As one of the main loads of arch dams temperature loadhas an important influence on the distribution of the stress


field and the change of dam body temperature is an importantreason for concrete cracks By comparing and analyzing thecharacteristic stress law of arch dam under eight workingconditions of 4 5 10 11 and 13ndash16 the results show that dueto the constraint of the abutment rock mass and foundation onthe dam body the temperature rise caused tension on theupstream surface of the arch dam which makes the upstreamsurface more prone to cracks and the downstream surface ofthe dam had a tendency of squeezing inward

42 Analysis of Stress Displacement and Point Safety of theFoundation

421 Displacement of Abutment Rock Mass -e defor-mation of the dam abutment rock mass can reflect thestiffness harmony between the rock mass on both banks andthe dam Excessive deformation of the dam abutment willlead to unreasonable stress distribution of the dam bodywhich will affect the overall stability of the dam body -ecalculation of the RFPA3D code shows that the displacementof the dam abutment rock mass along the river mainlyoccurred near the arch abutments and the maximum dis-placement occurred in the middle and lower parts of thedownstream arch abutments

Taking the displacement of the dam abutment rock massunder normal load condition (condition 4) as an examplethe displacement of the upstream dam abutments along theriver decreased gradually from the bottom elevation to thetop while the displacement of the downstream dam abut-ments decreased from middle elevation to the top and thebottom the displacement difference between the top andbottom elevation was small and the maximum displacementdifference was not greater than 125mm -e transversedisplacement of the two banks was basically symmetricalwhich was larger in the middle elevation and decreasedtoward the top and bottom gradually -e maximum dis-placement of the left bank was 10744mm located at EL565m and themaximum displacement of the right bank was-9835mm located at EL 525m (as shown in Figures 9 and10)

422 Foundation Stress -e following can be obtainedfrom the principal stress distribution of the foundationunder working conditions 4 to 16 (Figures 11 and 12 showthe principal stress distribution of the foundation undernormal working conditions)

(1) -e calculation results of the basic load combina-tions (working conditions 4 5 10 and 11) show that

Table 2 Material mechanical parameters of Xiluodu arch dam

Material Unit weight (tm3) Deformation modulus (GPa) Poissonrsquos ratioEffective shear

strengthCprime (MPa) Fprime

Dam concrete 240 24 0167 50 170Diversion bottom hole concrete 240 32 0167 50 170Class II rock 285 165 020 25 135III1 285 115 025 220 122III2 275 55 028 14 12IV1 26 30 030 10 102IV2 26 10 030 050 070V 22 05 035 005 035Left bank C9 24 05 03 007 04Right bank C9 24 05 03 006 04Left bank C8 24 08 03 01 044Right bank C8 24 09 03 01 044C8 24 3 03 025 055Left bank C7 24 17 03 02 055Right bank C7 24 13 03 02 05Left bank LC6 24 08 03 008 044Right bank LC6 24 09 03 008 044Left bank LC5 24 08 03 009 044Right bank LC5 24 08 03 008 044C3 24 08 03 017 05C2 24 05 03 005 035P2βn 24 15 03 005 035

Table 3 Temperature load of normal water level (degC)

Height (m)Item 6100 5900 5600 5200 4800 4400 4000 3600 3320

Designed temperature drop (degC) Tm 272 238 248 186 280 283 385 314 225Td 000 211 637 842 906 928 942 857 750

Designed temperature rise (degC) Tm 865 539 409 293 363 352 450 352 225Td 000 497 1140 1308 1323 1323 1311 1075 750


Tabl

e4

Basic

load

combinatio

ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

nGravity

Upstream

norm

alwater

level

Upstream

dead

water

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I

1radic

2radic

3radic

radic4

radicradic

radic（）

radicradic

5radic

radicradic（）

radicradic

6radic

radicradiclowast2（）

radicradic

7radic


radicradic

8radic


radicradic

9radic


radicradic

II10

radicradic

radic（）

radicradic

11radic

radicradic（）

radicradic


Tabl

e5

Specialloadcombinatio

ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

n

Gravity

Upstream

fullwater

level

Upstream

check

flood

level

Designed

flood

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I12

radicradic

radicradic

II13

radicradic

radic（）

radicradic

14radic

radicradic（）

radicradic

III

15radic

radicradic（）

radicradic

16radic

radicradic（）

radicradic

Noteldquoradic

rdquoindicatesthat

theload

isconsideredldquolowastrdquo

indicatesoverload

multip

le()indicatescorrespo

ndingdo

wnstream

water

levelcond

ition

s4and5areno

rmal

load

cond

ition

s


Le arch along the riverRight arch along riverArch crown transverse the river

Arch crown along the riverLe arch transverse to the riverRight arch transverse to the river

0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)

Figure 6 Displacement characteristic curve of the arch dam under normal load combination

Le arch Crown Right arch

Normal water load

2 times normal water load4 times normal water load 3 times normal water load

5 times normal water load

0100200300400500600700800

Disp

lace

men

t (m

m)

Figure 7 Comparison of the displacement of the arch dam along the river under different load combinations

4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002

Y displacement (mm) Step 2-(0)

(a)

ndash9835e + 000ndash7548e + 000ndash5262e + 000ndash2975e + 000ndash6888e + 0011598e + 0003884e + 0006171e + 0008457e + 0001074e + 001

X displacement (mm) Step 2-(0)

(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)

Figure 8 Comparison of the displacement distribution of the Xiluodu arch dam under conditions 4 and 5 Stress analysis of dam body(a) Downstream river direction (condition 4) (b) Downstream transverse direction (condition 4) (c) Downstream river direction(condition 5) (d) Downstream transverse direction (condition 5)


the foundation was basically in a compression statethe stress distribution on the two banks was basicallysymmetrical the additional stress caused by thethrust of the dam body was mainly distributed in thearea near the arch abutments and the stress far awayfrom the dam was controlled by the self-weight stressfield of rock mass only the dam heel of condition 5had tensile stress

(2) -e calculation results of the special load combi-nation (working conditions 12ndash16) show that thefoundation was basically under compression thestress distribution on the two banks is basically

symmetrical the additional stress generated by thethrust of the dam body was mainly distributed in thevicinity of the arch abutments and the stress faraway from the dam was controlled by the self-weightstress field of rock mass only the dam heel ofcondition 13 had tensile stress

423 Point Safety Analysis of Foundation Surface

(1) After consolidation grouting the average elasticmodulus of the dam foundation was 123GPa at0ndash5m and 133GPa at 5ndash20m Combined with the

Table 6 Characteristic stress value and position of the arch dam under basic load combination (unit MPa)

Condition

Upstream surface Downstream surface Dam toe

Maximumtensile stress

Maximumcompressive stress


Left abutmentmaximum compressive

stress

Right abutmentmaximum compressive

stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537

Condition10 0 2468 (410m) minus0438

(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183

Note ldquo-ldquo means tensile stress and ldquo+rdquo means compressive stress

Table 7 Characteristic stress value of arch dam under special load combination (unit MPa)

Working conditionUpstream surface Downstream surface Dam toe

Minimumstress

Maximumstress

Minimum stress ofdam surface

Left abutmentmaximum stress

Right abutmentmaximum stress Maximum stress

Condition 13 minus1635 (332m) 5234 (470m) 0062 (560m) 16626 (375m) 15865 (375m) 11281Condition 14 minus0053 (dam heel) 8862 (500m) minus0953 (480m) 14831 (380m) 14529 (380m) 10319Condition 15 0392 (dam heel) 8590 (500m) minus1092 (480m) 14962 (380m) 14689 (380m) 9993Condition 16 minus1539 (345m) 4894 (440m) 0 15741 (380m) 15419 (380m) 11031

ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002

1609e + 002Y displacement (mm) Step 2-(0)

Figure 9 Displacement of foundation along the river in working condition 4 (unit mm)


current situation of the foundation rock mass therock mass evaluation method of layered segmentedzoned and graded benchmarking proposed in thedesign reflected the characteristics of the foundationplane

(2) Under normal load conditions the KP of the riv-erbed was 12ndash35 the point safety degree was smallwhile the KP of both sides of the riverbed was15ndash50 With the overload increase the excess forceof the riverbed gradually shifts to the sides Over-loading to 3P0 the whole downstream surfaceKP 10ndash15 and the abutment rock mass yieldedlocally Overloading to 4P0 the whole downstreamsurface KP was 10ndash15 the riverbed part could stillbear large thrust and a load of dam abutmentsturned to the riverbed area with higher safetyoverloading to 5P0 KP 12

(3) Because the foundation of the banks is mainly onclass II rock the riverbed of both banks can stillmaintain a high degree of safety in the process ofoverload Until 35ndash4P0 both banks first yielded

43 Arch Dam Cracking Failure Analysis In this paper theRFPA3D code is used to analyze the cracking process ofthe dam under overload conditions to evaluate the safetyof the arch dam -e dam failure under four overloadconditions from working conditions 6 to 9 is mainlysimulated -e water load is 2 3 4 and 5 times of normalwater load respectively and other loads remain un-changed -e yield and cracking state of each elevation ofthe dam under overload conditions are shown in Table 8and Figure 13 From the calculation results the followingcan be seen

(1) Under normal load condition (1P0) the dam bodydid not yield and was in the normal elastic workingstate -e deformation and stress in the dam andabutment are basically symmetrical -e safety fac-tors of the rock mass near the abutments of theXiluodu arch dam were greater than 10 indicatingthat the abutments were in a stable state-e value ofthe stability safety factor of the rock mass near thedam abutments was the same and that on the surfacewas lower than the internal rock mass

ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001

1976e + 001X displacement (mm) Step 2-(0)

Figure 10 Transverse displacement of the foundation under working condition 4 (unit mm)

ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001

2450e + 001Max principal stress (MPa) Step 2-(0)

Figure 11 Maximum principal stress of foundation under working condition 4 (unit MPa)


(2) Under 2P0 the upstream surface of the dam heelyielded locally and the dam heel cracked -edownstream surface of the left dam abutment atEL 480m yielded and the failure zone increased-e dam surface at EL 560mndashEL 440m yieldedlocally

(3) Under 3P0 the cracks of the upstream dam heeldeveloped the cracks of the left dam abutment

extended to EL 420m and the downstream surfaceon the left abutment yielded at EL 480m resulting inmore failure zone -ere was a large surface yieldarea on the left dam surface and the dam foundationsystem entered the yield stage

(4) Under 4P0 the upstream dam heel continued tocrack to the two abutments to EL 450m -edownstream surface of the left dam abutment yielded

ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000

3606e + 000Min principal stress (MPa) Step 2-(0)

Figure 12 Minimum principal stress of foundation under working condition 4 (unit MPa)

Table 8 Yield and cracking state of each elevation of the dam under overload conditions

Position Load times1P0 2P0 3P0 4P0 5P0

EL 610mUpstream dam surface Compressive stress no yield

zoneNo yieldzone Yield Ba4 Transfixion

Downstream damsurface

Compressive stress no yieldzone

No yieldzone Yield Ba2 Transfixion


zone Yield Ba8 Yield Ba8



No yieldzone Local yield Cracking

Ba6Split Ba4

EL 52 0mUpstream dam surface Compressive stress no yield

zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone


Compressive stress no yieldzone Yield Ba8 Yield Ba4 Yield Ba5 Yield Ba3


zoneNo yieldzone



No yieldzone Yield Ba4 Yield Ba3


zoneNo yieldzone Yield Ba4 Yield Ba3



Bottom of arch crownbeam

Upstream dam heel Compressive stress no yieldzone

No yieldzone Split Ba15

Downstream dam toe Compressive stress no yieldzone

No yieldzone

Note ldquoBardquo refers to the thickness of the dam body


at EL 480m and resulted in the increase of the failurezone and tensile stress failure units -e upper andmiddle parts of the downstream surface yielded andexpanded

(5) Under 5P0 the yield zone at the bottom of the dambody gradually penetrated and extended to the up-per-middle elevation of the dam abutments and theyield range of the upper-middle dam body remainedunchanged with more failure zone and obvioustensile stress failure

(6) Under 75ndash8P0 the dam became unstable and thenatural arch was destroyed

(7) As shown in Table 9 and Figure 7 with the increaseof overload multiple the variation characteristicsof dam structure deformation and characteristic

stress are basically linear without obvious accel-eration or sudden change indicating that thestructure could still maintain certain stabilitybefore 5P0

Stress concentration zone

ndash1123e + 0019361e + 0002995e + 0015055e + 0017114e + 0019173e + 0011123e + 0021329e + 0021535e + 0021741e + 002

(a)


(b)ndash1645e + 0011369e + 0014383e + 0017397e + 0011041e + 0021342e + 0021644e + 0021945e + 0022246e + 0022548e + 002

(c)


(d)ndash2168e + 0011806e + 0015779e + 0019752e + 0011373e + 0021770e + 0022167e + 0022565e + 0022962e + 0022359e + 002

(e)


(f )ndash2690e + 0012239e + 0017169e + 0011210e + 0021703e + 0022196e + 0022689e + 0023181e + 0023674e + 0024167e + 002

(g)


(h)

Figure 13 Maximum principal stress distribution of Xiluodu arch dam under overload condition (black dot indicates failure zone unitMPa) (a) Upstream (2 times normal water load) (b) Downstream (2 times normal water load) (c) Upstream (3 times normal water load)(d) Downstream (3 times normal water load) (e) Upstream (4 times normal water load) (f ) Downstream (4 times normal water load) (g)Upstream (5 times normal water load (h) Downstream (5 times normal water load)

Table 9 Stress and displacement characteristics of the arch damunder overload condition

Overload multiple projects 2 3 4 5Maximum principal tensilestress (MPa) minus1123 minus1645 minus2168 minus2690

Maximum principalcompressive stress (MPa) 1741 2548 3359 4167

Maximum displacementalong the river (mm) 296713 439763 582714 725752


5 Conclusions

In this paper the RFPA3D code is used to establish thehexahedron elements of the Xiluodu superlarge modelwhich realizes the fine simulation of stress and deformationof the dam under layered overall multiworking conditionsand multistress fields Based on the calculation results thefollowing conclusions can be drawn

(1) Under various working conditions the displace-ment distribution of the arch dam body was uni-form and symmetrical the displacement along theriver of the arch abutments was equal and thedisplacement of the left abutment was slightly largerthan that of the right abutment which stated thatthe displacement symmetry of dam body was goodIn the transverse river direction the displacementcharacteristics of the downstream surface of thedam body have little difference and they were alltoward the mountains so the symmetry of the dambody was good It can be seen that the homoge-nization has performed well after the reinforcementtreatment of dam abutment rock mass and damfoundation surface -e maximum displacement ofthe dam foundation is about 276mm which isequivalent to Ertan and Jinping arch dam andsmaller than the Xiaowan project

(2) Under normal load the abutment rock mass wasbasically under compression without obvious con-centrated stress the dam body and dam foundationrock mass are in the linear elastic working state-ere is a tensile stress area at the upstream archabutment and the replaced rock mass at the EL400mndashEL 332m the maximum tensile stress is-11MPa (right arch abutment at EL 380m) and thetensile damage is very small which will not affect theoverall operation of the arch dam -e point safetyfactor of rock mass and dislocation zone along thebank is more than 12 and more than 15 in the deep

(3) Under the condition of temperature rise the de-formation of the abutments increased toward boththe mountain and river direction while the defor-mation of the arch crown decreased toward bothtransverse direction and the river direction which isbeneficial to the stability of the arch crown andadverse to the stability of the arch abutments -etension on the upstream surface made it easier toproduce cracks

(4) -e calculation results of various working conditionsshow that the foundation surface at the dam heel hadlocal yield and the dam heel cracked -e left damabutment of the downstream surface yielded at EL480m and the dam body at EL 560mndashEL 440myielded locally Besides with the increase of theoverload coefficient the tensile stress failure pointsincreased and the overall failure zone also increasedbut the failure range did not change greatly

(5) Under overload conditions the overall overloadcapacity of the dam abutment rock mass aftercomprehensive reinforcement was high -e rockmass quality had been improved in the interlayer Lc5and Lc6 at EL 400ndash380m on the left bank and in thedam area near EL 570ndash520m on the right bank

(6) -e overall overload safety degree of the Xiluoduarch dam is obtained as follows the overload factorof crack initiation K1 2P0 the nonlinear defor-mation overload factor K2 35ndash4P0 and the limitload factor K3 75ndash80P0 -e arch dam has a highdegree of overload safety and dam safety can besatisfied

(7) -e numerical simulation reasonably reflects thestress deformation and failure characteristics ofdam concrete structure foundation replacementconcrete dam foundation consolidation groutingand various rock masses (interlayer dislocation zoneweak structural plane geological defects) of damfoundation and comprehensively reflects the inter-action between arch dam and foundation -esimulation results verify the feasibility of concretereplacement and backfill engineering measures forthe Xiluodu arch dam -e stress-strain state andoverload capacity of the Xiluodu arch dam are goodwhich can meet the safety requirements of damconstruction -e RFPA3D is used to establish asuperlarge fine model to study the working state andoverload capacity of the arch dam proposed in thispaper which can be used as a reference for the designand research of super-high arch dam

Data Availability

-e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research work was supported by the National KeyResearch Development Plan (No 2018YFC1505301) and theChinese National Natural Science Foundation (Nos41941018 and 51627804)

References

[1] J P Zhou Z Y Yang and G F Chen ldquoPresent situation andchallenges of high dam construction in Chinardquo Journal ofHydraulic Engineering no 12 pp 1433ndash1438 2006

[2] X Q Zhou W Y Xu X Q Niu et al ldquo3D visualizationmodeling and stability analysis of arch dam and abutmentrdquoRock and Soil Mechanics vol 29 no S1 pp 118ndash122 2008

[3] H Zhong ldquoLarge-cale numerical simulation for damagepredictionof high arch dams subjected to earthquake shocksrdquoDalian University Of Technology PhD-esis Dalian China


[4] D Wang S Y Li andW Cao ldquoANSYS-based optimal designfor shape of arch damsrdquo Journal of Hydro-Science and En-gineering no 4 pp 51ndash55 2005

[5] Y Liu B Yang J Zhang et al ldquoPerformance simulation-based study on design of super-high arch dam and its ap-plication Part I development status and prospect of structuralanalysis method for arch dam in Chinardquo Water Conservancyand Hydropower Technology vol 51 no 10 pp 41ndash54 2020

[6] M Herzog and M Wang ldquoDiscussion on the damage phe-nomenon of 20 arch dams (I)rdquo Northwest Hydropower no 4pp 56ndash61 1991

[7] G D Zhang ldquoLessons from the failure of malpassit archdamrdquo Journal of Hydraoelectric Engineering no 4 pp 97ndash991998

[8] W Y Zhou X H Chen R Q Yang et al ldquoExperimentalstudy on geomechanical model of overall stability of high archdamrdquoWater Resources Planning and Design no 1 pp 50ndash572003

[9] X Yu Y F Zhou and S Z Peng ldquoStability analyses of damabutments by 3D elasto-plastic finite-element method a casestudy of Houhe gravity-arch dam in Chinardquo InternationalJournal of Rock Mechanics and Mining Sciences vol 42 no 3pp 415ndash430 2005

[10] L Zhang W P Fei G L Li et al ldquoExperimental study onglobal geomechanical model for stability analysis of high archdam foundation and abutmentrdquo Chinese Journal of RockMechanics and Engineering no 19 pp 67ndash71 2005

[11] X L Jiang J Chen S W Sun et al ldquoExperimental study onentire stability for high arch damrdquo Journal of Yangtze RiverScientific Research Institute vol 25 no 5 pp 88ndash93 2008

[12] W Y Zhou P Lin Q Yang et al ldquoExperimental research onstability of jinping high slope with three-dimensional geo-mechanical modelrdquo Chinese Journal of Rock Mechanics andEngineering vol 27 no 5 pp 893ndash901 2008

[13] Q W Ren ldquo-eory and methods of high arch damrsquos entirefailure under disaster conditionsrdquo Engineering Mechanicsvol 28 no S2 pp 85ndash96 2011

[14] XWang Y Liu Z TaoWWang and Q Yang ldquoStudy on thefailure process and nonlinear safety of high arch dam andfoundation based on geomechanical model testrdquo EngineeringFailure Analysis vol 116 Article ID 104704 2020

[15] J L Yang H Zheng and X R Ge ldquo-e analysis of -reedimensional FEM for interaction of the gravity-arch dam andcomplex ground at Geheyan Qingjiang Riverrdquo Rock and SoilMechanics no 4 pp 5ndash19 1989

[16] F S Shen C L Ji B Li et al ldquoStability analysis of south intakehigh slope of Xiaolangdi project during completion of con-structionrdquo Chinese Journal of Geotechnical Engineeringvol 20 no 2 pp 6ndash9 1998

[17] W Z Chen W S Zhu X B Qiu et al ldquoResearch on re-inforcement scheme for xiaowan abutmentrdquo Chinese Journalof RockMechanics and Engineering vol 21 no 3 pp 374ndash3782002

[18] S H Chen W M Wang M Y Xu et al ldquoFinite elementanalysis of the crack propagation in high arch dam heel ofXiaowan projectrdquo Journal of Hydraulic Engineering no 1pp 66ndash71 2003

[19] J T Wang J Yang J H Wang et al ldquoSimulation of stressdistribution and sensitivity analysis on material parametersfor high arch damrdquo Journal of Hydraulic Engineering vol 38no 7 pp 832ndash837 2007

[20] L Zhang Y R Liu Q Yang et al ldquoGlobal stability ofYangfanggou Arch Dam by 3D nonlinear FEM analysis and

geomechanical model testsrdquo Chinese Journal of GeotechnicalEngineering vol 35 no S1 pp 239ndash246 2013

[21] L Pei J S Zhu Y S Lu et al ldquoAnalysis on stress and de-formation behaviors of Lizhou RCC Arch Dam duringimpounding processrdquo Water Resources and HydropowerEngineering vol 46 no 10 pp 47ndash52 2015

[22] L S Chen and C C Li ldquoOn the constitutive relations ofrocksrdquo Advances in Mechanics no 02 pp 173ndash182 1992

[23] RWang and Y Q Yin ldquoElastic-plastic constitutive relation ofengineering rock mediumrdquo Chinese Journal of Mechanicsno 04 pp 317ndash325 1981

[24] F S Zhu ldquoStrength theory and constitutive relation of rockrdquoMechanics and Practice no 5 pp 9ndash15 1997

[25] C C Li L S Chen H Li et al ldquo-e constitutive relationshipof micro-damage for rock-like brittle materialrdquo Rock and SoilMechanics vol 10 no 2 pp 55ndash68 1989

[26] J Xu S C Li Y B Liu et al ldquoDamage constitutive model ofrock based on Drucker-Prager criterionrdquo Journal of SouthwestJiaotong University vol 42 no 3 pp 278ndash282 2007

[27] Z Z Liang -reeimensional failure process Analysis ofrockand associated numerical tests PhD -esis North-eastern University Boston MA USA 2005

[28] W C Zhu C A Tang T H Yang et al ldquoConstitutive re-lationship of Mesoscopic elements used inRFPA2D and itsvalidationsrdquo Chinese Journal of Rock Mechanics and Engi-neering vol 22 no 1 pp 24ndash29 2003

[29] C A Tang ldquoNumerical simulation of AE in rock failurerdquoJournal of Rock Mechanics and Engineering vol 16 no 4pp 75ndash81 1997

[30] M L Huang C A Tang and W C Zhu ldquoNumerical sim-ulation on failure process of rockrdquo Chinese Journal of RockMechanics and Engineering vol 19 no 4 pp 468ndash471 2000

[31] Z Z Liang C A Tang Y B Zhang et al ldquo3D numericalsimulation of failure process of rockrdquo Chinese Journal of RockMechanics and Engineering vol 25 no 5 pp 931ndash936 2006

[32] W C Zhu C A Tang Q L Zhao et al ldquoMechanical modeland numerical simulation of fracture process of concreterdquoAdvances in Mechanics vol 32 no 4 pp 579ndash598 2002

[33] C Tang ldquoNumerical simulation of progressive rock failureand associated seismicityrdquo International Journal of RockMechanics and Mining Sciences vol 34 no 2 p 249 1997

[34] Y R Zheng S Y Zhao and L Y Zhang ldquoSlope stabilityanalysis by strength reduction FEMrdquo Engineering Scienceno 10 pp 57ndash61 2002

[35] Z He S Y Zhao and Y K Song ldquoAdvances in theory studyand engineering application of wavelet finite elementrdquo Chi-nese Journal of Mechanical Engineering vol 41 no 3 pp 1ndash62005

[36] L C Li C A Tang Z Z Liang et al ldquoRFPAmethod for slopestability analysis and associated applicationrdquo Journal of BasicScience and Engineering no 4 pp 501ndash508 2007

[37] Y B Zhang ldquoe research on parallel compuatation method ofrock fracture process analysisrdquo PhD -esis NortheasternUniversity Boston MA USA 2007


Among various numerical simulation methods the three-dimensional nonlinear finite element method is widely usedin the stability analysis of high arch dam using a three-dimensional nonlinear finite element method to calculatethe deformation and stress of the arch dam can well simulatethe constitutive relationship and load and boundary con-ditions of the complex rock and can better reflect thecomplexity of geological structure and the influence ofengineering measures on dam structure -erefore with thedevelopment of computer technology and the popularity ofgeneral finite element software finite element analysistechnology has been more and more widely used in solvingcomplex hydropower engineering problems and achievedgood engineering results For example Yang et al [15] triedto solve large finite element equations by an iterative methodin the three-dimensional finite element analysis of theGeheyan gravity arch dam in 1989 and obtained reasonablecalculation results Shen et al [16] solved the minimumsafety factor and the position of the corresponding potentialsliding surface during the excavation of Xiaolangdi highslope by using the three-dimensional finite element analysismethod and the results were confirmed by actual con-struction Chen et al [17] and Chen et al [18] respectivelycarried out a finite element analysis on the abutment rockmass stability and the dam heel cracking risk of the Xiaowanhigh arch dam Wang et al [19] simulated and analyzed thestress state of the Ertan arch dam during operationAccording to the results of numerical simulation and modeltest Zhang et al [20] analyzed the displacement and stressdistribution failure mechanism and overall stability of thearch dam the results are in good agreement Pei et al [21]simulated the construction process and impoundmentprocess of the Lizhou RCC arch dam and analyzed the stressdeformation behavior and development law of the dam bodyin the real working state during the impoundment process-ese applications show that the finite element numericalsimulation analysis has obvious advantages in studying thestress displacement and failure characteristics of high archdams and has become an effective way to study the damdesign reinforcement and stability evaluation of high archdams

-e accuracy of finite element analysis will be affected bythe selection of reasonable constitutive relations Arch damsare usually built into geologically complex mountains andvalleys and form an interactive system with dam foundationand dam abutments As the main engineering materialsrock and concrete are heterogeneous quasi-brittle materialswith complex mechanical properties -e researchers havemade in-depth discussions on their constitutive relationsfrom phenomenology and physical mechanisms includingstrength theory plastic constitutive theory damage con-stitutive theory and distributed fracture mechanics con-stitutive theory [22ndash26] It has been widely recognized thatthe fracture and failure process of rock or concrete is actuallythe whole process of microcracksrsquo generation and devel-opment until the formation of the transfixion zone underload In the past the constitutive relations of nonlinear finiteelements only grasped the ldquononlinearrdquo characteristics ofmaterial deformation from the macrolevel and participated

in the analysis and calculation as an elementrsquos attributewhich ignored the inhomogeneity of micromedium pa-rameters so there is no macromicro difference in the resultsIn fact due to the extreme heterogeneity of these materialstheir properties at the microlevel are very different from themacrolevel In order to fully consider the nonlinearity andheterogeneity during the fracture process of rock or con-crete Tang et al proposed a new numerical simulationmethod ldquoRFPA (Rock Failure Process Analysis) Methodrdquo[27ndash33] based on the basic theory of finite element to ex-plain the structural fracture process with statistical damagetheory and the basic principle of strength reduction method[34 35] was introduced to analyze the stability of geo-technical engineering [36] It is proved that the method canbe used to deal with geotechnical engineering under com-plex geological conditions effectively

In addition the number of grids affects the accuracy ofcalculation results and the size of the calculation scale Inorder to make the element size in numerical simulationreflect the basic microscopic properties of the medium theRFPA3D code is used to establish the superlarge model ofthe Xiluodu high arch dam with full hexahedron element (6632 192 elements 6893485 nodes more than 20 milliondegrees of freedom) -e large-scale parallel computingcluster [37] is used to realize the fine simulation of the damunder layered overall multiworking conditions and mul-tistress fields On the basis of fully reflecting the geologicalconditions after the actual excavation of the Xiluodu archdam the corresponding structural design and foundationtreatment measures the deformation and stress character-istics of the dam body and abutment rock mass underseveral different load combinations are studied -rough theapplication of overload the overload coefficient yield andcracking conditions of each failure stage are obtained toanalyze the overload capacity of the arch dam According tothe analysis results the overall stability and safety of the archdam under the structural design and foundation treatmentdesign scheme are demonstrated and the overall safety ofthe arch dam under the current implementation scheme iscomprehensively evaluated and the results provide a basisfor the structural design and foundation treatment design ofthe Xiluodu high arch dam

2 Engineering Background

-eXiluodu hydropower station is located in Xiluodu gorgewhich is adjacent to Leibo County in Sichuan Province andYongshan County in Yunnan Province -is is the thirdcascade in the development plan of the Jinsha River section-e double-curvature arch dam is selected as the dam type(the centerline of the arch dam is N 482degW) with a crestelevation of 6100m a foundation surface elevation of3320m and a maximum dam height of 2780m whichbears a huge water thrust of about 13 million tons requiringthe foundation to have the corresponding bearing capacity-e total amount of engineering concrete is 1296 millionm3 of which about 7millionm3 is dam concrete-e normalwater level of the reservoir is 60000m and the corre-sponding downstream water level is 37800m (38146m for










1800m

660m

1000m X

YZ













Left bank

C9 536 05 N25degWNEang4deg 035 005 030 0040 007 034 0

C8 513 05 N35degWNEang5deg 035 005 030 0044 010 037 0



Right bank


C8 536 05 N38degESEang4deg 043 008 037 0044 010 037 0






C9C8C7Lc6Lc5C3

C2P2βn


Dam toe




fc0

fcrndashεt0

εc0

ndashft0

ndashεtundashftr

σ

Oε



























Height (m)Item 6100 5900 5600 5200 4800 4400 4000 3600 3320




Tabl

e4

Basic

load

combinatio

ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

nGravity

Upstream

norm

alwater

level

Upstream

dead

water

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I

1radic

2radic

3radic

radic4

radicradic

radic（）

radicradic

5radic

radicradic（）

radicradic

6radic


radicradic

7radic


radicradic

8radic


radicradic

9radic


radicradic

II10

radicradic

radic（）

radicradic

11radic

radicradic（）

radicradic


Tabl

e5


ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

n

Gravity

Upstream

fullwater

level

Upstream

check

flood

level

Designed

flood

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I12

radicradic

radicradic

II13

radicradic

radic（）

radicradic

14radic

radicradic（）

radicradic

III

15radic

radicradic（）

radicradic

16radic

radicradic（）

radicradic

Noteldquoradic

rdquoindicatesthat

theload


indicatesoverload

multip


ndingdo

wnstream

water

levelcond

ition

s4and5areno

rmal

load

cond

ition

s




0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)



Normal water load



0100200300400500600700800

Disp

lace

men

t (m

m)


4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002


(a)



(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)









Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References

















































1800m

660m

1000m X

YZ













Left bank

C9 536 05 N25degWNEang4deg 035 005 030 0040 007 034 0

C8 513 05 N35degWNEang5deg 035 005 030 0044 010 037 0



Right bank


C8 536 05 N38degESEang4deg 043 008 037 0044 010 037 0






C9C8C7Lc6Lc5C3

C2P2βn


Dam toe




fc0

fcrndashεt0

εc0

ndashft0

ndashεtundashftr

σ

Oε



























Height (m)Item 6100 5900 5600 5200 4800 4400 4000 3600 3320




Tabl

e4

Basic

load

combinatio

ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

nGravity

Upstream

norm

alwater

level

Upstream

dead

water

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I

1radic

2radic

3radic

radic4

radicradic

radic（）

radicradic

5radic

radicradic（）

radicradic

6radic


radicradic

7radic


radicradic

8radic


radicradic

9radic


radicradic

II10

radicradic

radic（）

radicradic

11radic

radicradic（）

radicradic


Tabl

e5


ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

n

Gravity

Upstream

fullwater

level

Upstream

check

flood

level

Designed

flood

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I12

radicradic

radicradic

II13

radicradic

radic（）

radicradic

14radic

radicradic（）

radicradic

III

15radic

radicradic（）

radicradic

16radic

radicradic（）

radicradic

Noteldquoradic

rdquoindicatesthat

theload


indicatesoverload

multip


ndingdo

wnstream

water

levelcond

ition

s4and5areno

rmal

load

cond

ition

s




0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)



Normal water load



0100200300400500600700800

Disp

lace

men

t (m

m)


4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002


(a)



(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)









Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References


















































Left bank

C9 536 05 N25degWNEang4deg 035 005 030 0040 007 034 0

C8 513 05 N35degWNEang5deg 035 005 030 0044 010 037 0



Right bank


C8 536 05 N38degESEang4deg 043 008 037 0044 010 037 0






C9C8C7Lc6Lc5C3

C2P2βn


Dam toe




fc0

fcrndashεt0

εc0

ndashft0

ndashεtundashftr

σ

Oε



























Height (m)Item 6100 5900 5600 5200 4800 4400 4000 3600 3320




Tabl

e4

Basic

load

combinatio

ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

nGravity

Upstream

norm

alwater

level

Upstream

dead

water

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I

1radic

2radic

3radic

radic4

radicradic

radic（）

radicradic

5radic

radicradic（）

radicradic

6radic


radicradic

7radic


radicradic

8radic


radicradic

9radic


radicradic

II10

radicradic

radic（）

radicradic

11radic

radicradic（）

radicradic


Tabl

e5


ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

n

Gravity

Upstream

fullwater

level

Upstream

check

flood

level

Designed

flood

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I12

radicradic

radicradic

II13

radicradic

radic（）

radicradic

14radic

radicradic（）

radicradic

III

15radic

radicradic（）

radicradic

16radic

radicradic（）

radicradic

Noteldquoradic

rdquoindicatesthat

theload


indicatesoverload

multip


ndingdo

wnstream

water

levelcond

ition

s4and5areno

rmal

load

cond

ition

s




0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)



Normal water load



0100200300400500600700800

Disp

lace

men

t (m

m)


4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002


(a)



(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)









Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References

































































Height (m)Item 6100 5900 5600 5200 4800 4400 4000 3600 3320




Tabl

e4

Basic

load

combinatio

ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

nGravity

Upstream

norm

alwater

level

Upstream

dead

water

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I

1radic

2radic

3radic

radic4

radicradic

radic（）

radicradic

5radic

radicradic（）

radicradic

6radic


radicradic

7radic


radicradic

8radic


radicradic

9radic


radicradic

II10

radicradic

radic（）

radicradic

11radic

radicradic（）

radicradic


Tabl

e5


ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

n

Gravity

Upstream

fullwater

level

Upstream

check

flood

level

Designed

flood

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I12

radicradic

radicradic

II13

radicradic

radic（）

radicradic

14radic

radicradic（）

radicradic

III

15radic

radicradic（）

radicradic

16radic

radicradic（）

radicradic

Noteldquoradic

rdquoindicatesthat

theload


indicatesoverload

multip


ndingdo

wnstream

water

levelcond

ition

s4and5areno

rmal

load

cond

ition

s




0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)



Normal water load



0100200300400500600700800

Disp

lace

men

t (m

m)


4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002


(a)



(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)









Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References









































Tabl

e4

Basic

load

combinatio

ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

nGravity

Upstream

norm

alwater

level

Upstream

dead

water

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I

1radic

2radic

3radic

radic4

radicradic

radic（）

radicradic

5radic

radicradic（）

radicradic

6radic


radicradic

7radic


radicradic

8radic


radicradic

9radic


radicradic

II10

radicradic

radic（）

radicradic

11radic

radicradic（）

radicradic


Tabl

e5


ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

n

Gravity

Upstream

fullwater

level

Upstream

check

flood

level

Designed

flood

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I12

radicradic

radicradic

II13

radicradic

radic（）

radicradic

14radic

radicradic（）

radicradic

III

15radic

radicradic（）

radicradic

16radic

radicradic（）

radicradic

Noteldquoradic

rdquoindicatesthat

theload


indicatesoverload

multip


ndingdo

wnstream

water

levelcond

ition

s4and5areno

rmal

load

cond

ition

s




0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)



Normal water load



0100200300400500600700800

Disp

lace

men

t (m

m)


4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002


(a)



(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)









Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References









































Tabl

e5


ncond

ition

s

Calculated

working

cond

ition

Load

combinatio

n

Gravity

Upstream

fullwater

level

Upstream

check

flood

level

Designed

flood

level

Sediment

Temperature

rise

Temperature

drop

Mou

ntains

Dam

I12

radicradic

radicradic

II13

radicradic

radic（）

radicradic

14radic

radicradic（）

radicradic

III

15radic

radicradic（）

radicradic

16radic

radicradic（）

radicradic

Noteldquoradic

rdquoindicatesthat

theload


indicatesoverload

multip


ndingdo

wnstream

water

levelcond

ition

s4and5areno

rmal

load

cond

ition

s




0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)



Normal water load



0100200300400500600700800

Disp

lace

men

t (m

m)


4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002


(a)



(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)









Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References











































0

20

40

60

80

100

120

Disp

lace

men

t alo

ng th

e riv

er(m

m)

350 400 450 500 550 600 650300Elevation (mm)

ndash20

ndash10

0

10

20

Tran

sver

se d

ispla

cem

ent

(mm

)



Normal water load



0100200300400500600700800

Disp

lace

men

t (m

m)


4810e + 0001587e + 0012693e + 0013799e + 0014905e + 0016011e + 0017117e + 0018223e + 0019330e + 0011044e + 002


(a)



(b)6374e + 0001562e + 0012488e + 0013413e + 0014338e + 0015263e + 0016188e + 0017113e + 0018038e + 0018963e + 001


(c)



(d)









Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References















































Condition






stress


stress


Condition4

minus0115(610m) 8426 (500m) minus1119

(475m) 14794 (375m) 14632 (375m) 9986

Condition5

minus0373(335m) 5317 (440m) 0 16025 (370m) 15941 (370m) 11537


(450m) 11895 (355m) 11560 (355m) 9268

Condition11

minus0168(610m) 5623 (410m) minus0269

(450m) 9893 (355m) 9658 (355m) 7183




Minimumstress

Maximumstress





ndash1799e + 001

1772e + 001

3563e + 001

5353e + 001

7143e + 001

8933e + 001

1072e + 002

1251e + 002

1430e + 002









ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References














































ndash1360e + 001

ndash9891e + 000

ndash6185e + 000

ndash2479e + 000

1228e + 000

4934e + 000

8640e + 000

1235e + 001

1605e + 001



ndash5240e + 000

ndash1935e + 000

1370e + 000

4675e + 000

7980e + 000

1128e + 001

1459e + 001

1789e + 001

2120e + 001








ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References













































ndash1168e + 002

ndash1035e + 002

ndash9007e + 001

ndash7669e + 001

ndash6331e + 001

ndash4992e + 001

ndash3654e + 001

ndash2316e + 001

ndash9777e + 000















Ba6Split Ba4


zoneNo yieldzone



No yieldzone

Surfaceyield

CrackingBa6

Split Ba3


zoneNo yieldzone




zoneNo yieldzone












No yieldzone










(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References
















































(a)



(c)



(e)



(g)


(h)







5 Conclusions









Data Availability




Acknowledgments


References









































5 Conclusions









Data Availability




Acknowledgments


References









































Overall Stability Analysis of Xiluodu High Arch Dam Based ...

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