Effects of outlets on cracking risk and integral stability of super-high arch dams

Research ArticleEffects of Outlets on Cracking Risk and Integral Stability ofSuper-High Arch Dams

Peng Lin1 Hongyuan Liu2 Qingbin Li1 and Hang Hu1

1 State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China2 School of Engineering The University of Tasmania Hobart Australia

Correspondence should be addressed to Peng Lin celinpetsinghuaeducn

Received 27 March 2014 Accepted 8 April 2014 Published 23 July 2014

Academic Editor Ting-Hua Yi

Copyright copy 2014 Peng Lin et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper case study on outlet cracking is first conducted for the Goupitan and Xiaowan arch dams A nonlinear FEMmethodis then implemented to study effects of the outlets on integral stability of the Xiluodu arch dam under two loading conditionsie normal loading and overloading conditions On the basis of the case study and the numerical modelling the outlet crackingmechanism risk and corresponding reinforcement measures are discussed Furthermore the numerical simulation reveals that(1) under the normal loading conditions the optimal distribution of the outlets will contribute to the tensile stress release in thelocal zone of the dam stream surface and decrease the outlet cracking risk during the operation period (2) Under the overloadingconditions the cracks initiate around the outlets then propagate along the horizontal direction and finally coalesce with thosein adjacent outlets where the yield zone of the dam has a shape of butterfly Throughout this study a dam outlet cracking riskcontrol and reinforcement principle is proposed to optimize the outlet design select the appropriate concrete material strengthenthe temperature control during construction period design reasonable impounding scheme and repair the cracks according totheir classification

1 Introduction

Arch dam has been constructed for water storage reservoirsince early times such as the Kurit dam constructed in Iranin the 13th century the Elche dam in Spain in the 17thcentury and the Pontalto dam in Italy in the 17th century[1 2] Since the middle of the 19th century the number ofarch dams has greatly increased [1] Nowadays the arch damhas attracted extensive researches in structural engineeringhealth monitoring [3ndash5] intelligent cracking control [6ndash8]and computer simulation [9] Design and optimization ofthe arch dam and health monitoring of the dam structuralperformance and behaviour under extreme loadings arejust being unfolded throughout these researches China isabundant in hydraulic resource which is estimated to be680 million kilowatt theoretically and 370 million kilowattavailable to be exploited Both of them rank the first in theworld For sustainable development of clean energy a series ofsuper-high arch dams have been constructed in southwesternChina including the Xiaowan Xiluodu Jinping I and Laxiwa

arch dams with heights of 2945m 2855m 305m and251m respectively [10 11] Nowadays the techniques forconstructing the general arch dam with a height less than200m may become mature but the construction of thesuper-high arch dam with a height of around 300m suchas the Xiaowan Xiluodu and Jinping I dams still facesmany challenges for example the cracking risk and integralstability of the dam body and the reinforcement measureand mechanical behaviour of the complex dam foundationsconsisting of jointed or altered rock mass and atypical faultsDuring the construction and service of the arch dams cracksmay develop in the dam body due to internal and externaltemperature variation concrete shrinkage differential abut-ment foundation deformation previous earthquake or otherreasons [11ndash16] Although these cracks may only propagate toa limited depth in the dam body theymay weaken the overallloading capacity of the arch dams

Moreover the super-high arch dams tend to layout moreancillary structures such as outlets for various purposes forexample flood discharging sediment removal silt scouring

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 312827 19 pageshttpdxdoiorg1011552014312827

2 The Scientific World Journal

123456789101112131415161718192021222324252627

Number1 empty bottom outlet

Number 2 empty bottom outlet

Bottom outlets

Middle outlets

Upper outlets

(a) Vertical profile of the Goupitan arch dam in the downstream side


(b) Snapshot of the Goupitan arch dam

Figure 1 Distribution of the outlets of the Goupitan arch dam

and reservoir emptying which are usually distributed in arelatively high density in the dam body as shown in Figure 1During the service of the super-high arch dams stresses mayconcentrate around the outlets causing cracking of the dambody [15 16] which poses further potential threats to theintegral stability of the arch dams In the past designersmainly focused on the dam body [17 18] but paid lessattention to the effects of the outlets on the integral stabilityof the dams [19ndash25] Although there are studies proving thatcracks around outlets have little effect on the integral stressstatus and loading condition of the dam [11 15 23 25] in the

long-term conditions the pore water pressure may stimulatethe cracks around the outlets to propagate and coalesce withthose caused by other factors mentioned above which mayresult in greater risk to the integral stability of the super-higharch dam

Three kinds of theoretical analysis are adopted in liter-atures to analyze effects of outlet cracking on the integralstability of the super-high arch dams (1) Plane stress analysisif the outlet opening is relatively small compared with thewhole dam body and the minimum distance between thecentre of the outlet and the dam foundation is not less

The Scientific World Journal 3

than three times of the width of the outlet only local stressdistributions of the dam will be affected by the outlet Thusappropriate two-dimensional (2D) section of the outlet maybe selected for plane stress analysis (2) Linear elastic analysisin the area where tensile stress exceeds the strength ofconcrete it is assumed that the concrete completely cracksand reinforcement bar bears all the tensile stress Linearelastic analysis is usually suggested for the preliminary designof the concrete dam and its components and usually leadsto a large safety factor in design [17 18] which cannotoften guarantee construction quality and economic benefit(3) Nonlinear analysis when induced tensile stress reachesthe tensile capacity of concrete cracks appear in the damconcrete which causes part of the excess stress to be releasedand the others are gradually shifted to the reinforcement barIn this case the stress near the crack tip remains below thetensile capacity of concrete As the load increases the existingcrack may further open and propagate At the same timesecondary and tertiary cracks may appear due to the bondingeffect between the reinforcement bars and the concrete whenstress in adjacent area reaches the tensile capacity of concrete[26ndash32] Three-dimensional (3D) numerical simulation isprobably the most popular nonlinear analysis method whichhas now been applied widely to analyze the integrity andstability of the high arch dams [11 12 22 25] and theassociated underground water transmission tunnels [28] (4)TheSaint-Venant principle submodelmethod can be adoptedto analyze the dam outlets according to the Saint-Venantprinciple that is when the actual load is replaced by anequivalent load stress and strain only changes in the loadingarea The specific steps are as follows (a) analyze the integralmodel of the super-high arch dam using finite elementmethod with coarser mesh (b) cut out a submodel with theoutlets from the integral model to establish a submodel withfiner mesh (c) calculate the displacements of all points onthe boundary of the submodel by interpolating the resultsfrom the step (a) and use the calculated displacements as theinitial boundary conditions of the submodel for the analysisin the next step and (d) analyze the submodel using thefinite element method analysis according to the boundaryconditions calculated from the step (c)

However most of the analyses available in literatures areconducted for the dams without sufficient considerationsof outlets which lead to a large gap between the obtainedand actual stresses andor displacements for the dams andmay adversely affect the dam design construction andoptimization processes In sum the effect of the outlets onworking condition of the super-high arch dam is still a blankarea worthy of further studies

In this study the status reason and consequence of theoutlet cracking in the Goupitan and Xiaowan super-higharch dams are first discussed The effects of the outlets onthe deformation stress cracking risk and overall stabilityof the Xiluodu super-high dam are then analyzed using afinite element method Finally a dam outlet cracking riskcontrolmethod is proposed on the basis of the outlet crackingmechanism identified above to ensure the safety and stabilityof the super-high arch dams

2 Case Studies on Dam Outlet Cracking

21 Outlet Cracking at the Goupitan Arch Dam

211 Introduction to the Outlets in the Goupitan Arch DamThe Goupitan high arch dam (Figure 1) is constructed ontheWujiang River in Guizhou Province southwestern ChinaThe dam is a double curvature concrete archwith amaximumheight of 2305m a ratio between thickness and height of0216 and a crest length of 55255m There are 6 flood dis-charging upper outlets 7 flood discharging middle outlets 2reservoir empting bottom outlets and 4 temporary diversionbottom outlets as shown in Figure 1 The elevation level (EL)of the upper outlets is 617m above the sea level and the sizeof each outlet is 12m times 13m (width times height) The size ofthe middle outlets is 7m times 6m The numbers 1 3 5 and7 middle outlets have plat bottom and their entrances areat EL 550m The numbers 2 and 6 middle outlets hold anexit jet angle of 25 degree and its entrance is at EL 543mThe number 4 middle outlet holds an exit jet angle of 10degree and its entrance is at EL 546mThe size of the controlsection in the reservoir empting bottom outlets is 38m times

6m and that in the temporary diversion bottom outlets is65m times 8m The entrance of the bottom outlets are at EL490m The upper surface of the outlets is built with C35abrasion-resistant concrete which extends from the surfaceto 1-metre-deep insideThe reservoir empting bottom outletsand diversion bottom outlets are built with C50 abrasion-resistant concrete and the transition zone of C50 and C18035is built with the C35 concrete C18035 is also used for theconstruction of the temporary diversion bottom outlets thereservoir empting bottom outlets and the flood releasingmiddle outlets of nonspillways in the numbers 11 to 17 dammonoliths

212 Outlet Cracking Status Three groups of defects werediscovered in the Goupitan concrete arch dam at the end ofMay 2008The first one was the peripheral fractures observednear the number 1 reservoir empting bottom outlets asshown in Figure 2 The second one was the cracks near thefoundation corridor in the number 19 dam monolith Thelast was the cracks near the lift platform of the number2 reservoir empting bottom outlets in the number 14 dammonolith as shown in Figure 3 Among them the peripheralfractures near the bottom outlets (Figures 2 and 3) havethe largest scale and most harm the integral stability of thedam Correspondingly these cracks are classified which aresummarized into Table 1 together with their characteristicsand subsequently adopted reinforcement measures

Furthermore the status of the peripheral fractures nearthe reservoir emptying bottom outlets is highlighted hereThe first series of cracks appeared at the end of November2006 in the surfaces of the number 13 dam monolith at EL491m for the number 1 reservoir emptying bottom outlet andthe number 14 dam monolith at EL 497m for the number2 bottom outlet as shown in Figure 2 and Table 2 Crack-limiting reinforced nets and chemical grouting pipe-systemare installed to control and repair these cracks Besides themthe other reinforcement method for the cracks mentioned


Flow direction

Roof

Floor

Roof

Leftwall

Rightwall

06m 06m06m17m16m

05m08m

07m

14m07m

11m 11m10m

11m

18m

09m

07m

07m

07m

08m

12m

(a) Crack propagation in the number 1 reservoir empting bottom outlet

Flow direction

Dam center lineEL 4970

3 crack series

11m 09m 07m

2 crack series

1 cracks seriesEL 4910

Depth lt 03m

Axis of 2 bottom diversion outlets

(b) Description of cracks in the number 1 reservoir empting bottom outlet

Red liquid representscracking penetration

(c) Photo of outlet cracking taken during site inspection

Figure 2 Schematic sketch and photo of outlet cracking in the number 1 reservoir empting bottom outlet of the Goupitan arch dam

hereafter includes filling in cracks using preshrinkagemortardrilling stress release hole and installing double-layer crack-limiting steel bar After the construction of the bottomoutlets but before the grouting of the transverse joint in thenumber 9 grouting zone (from EL 4790m to EL 4880m)all the bottom outlets are examined and new second seriesof cracks are found in the side walls and floors as shownin Figures 2 and 3(a) and Table 1 Then visual inspectionand water pressure test of transverse joints are carried onall the bottom outlets and the sonic wave test is adopted for

deep investigationThe third series of cracks are identified assummarized in Table 1

Moreover there are local cracks in the numbers 1 2 and4 diversion bottom outlets which coalesce with the transversejoints at a distance of about 10m from the upstream surfaceThese cracks are rather long but the width is about 02mmThe depth of the cracks in the floor and roof of the bottomoutlets is shallow and themajorities of them are less than 1mHowever the cracks in the side wall are somehow deeper andthe greatest depth is larger than 28m


Roof

Roof

Floor

Leftwall

Rightwall

06m

13m27m

14m14m

05m05m08m

08m07m

04m14m

14m15m16m

10m

06m

07m

07m

07m

07m12m13m

11m

Flow directionCrack 14

200

700

400

200

700


05m 05m 13m13m

Flow direction

Crack series number 1


Crack series number 303sim09m

(b) Description of original cracks of the number 2 reservoir empting bottom outlet

Figure 3 Schematic sketch of outlet cracking in the number 2 reservoir empting bottom outlet of the Goupitan arch dam

Table 1 Cracking characteristics and reinforcement measures of the numbers 1 and 2 reservoir emptying outlets in the Goupitan arch dam

Outlets Series number Cracking depth (m) Cracking description Reinforcement measuresMax Min

Number 1reservoiremptyingbottom outlet

Crack seriesnumber 1 03 03 Deck of the number 13 dam

monolith at EL 491mGroove in cracking surface

Fill in cracks usingpreshrinkage mortar

Embed grouting pipesystem

Drill stress release hole

Install double-layercrack-limiting steel bar

Crack seriesnumber 2

From EL 494m to EL 488malong the number 13 dammonolith


monolith at EL 497m



monolith at EL 497mCrack seriesnumber 2

From EL 494m to EL 488 alongthe number 13 dam monolith

Crack seriesnumber 3 17 03

Deck of the number 15 dammonolith at EL 490mDeck of the number 15 dammonolith at EL 494m

In sum the number of cracks in the different outletsranges from 13 to 21 and the majority of them is longitudinal(Figure 2(c)) according to the results from the crack inspec-tion

213 Reasons and Consequences of Outlet Cracking Fol-lowing the design requirements the reservoir emptyingand diversion bottom outlets are constructed with the C50concrete so as to improve their abrasion-resistance capacity


Table 2 Cracking characteristics and reinforcement measures of the middle outlets in the Xiaowan arch dam

Location Cracknumber

Depth of cracks (m) Cracking description Reinforcement measuresMax Min

Number 21dammonolith(number 1diversionoutlet)

21LF-1 12 03

Cracks are distributed at ring shape in thedam monolith from EL 1012msim1110mThere are 19 cracks with length less than3m in the left side wall of the number 1middle diversion outlet at thedownstream side and 1 microcrack withlength smaller than 23m in the rightsidewall

Crackings around the diversionmiddle outlets have beeninspected before August 2008 Atthat time these cracks did notcoalesce with the thermal crackscaused due to temperaturegradients which were notcompletely identified Thereinforcement measures werecracking filing and surfacepermeable-resistant coating

It was noted that cracks aroundthe diversion middle outlets havecoalesced with the thermalcracks due to temperaturegradients till May 2009 The mainreinforcement measures includechemical grouting crack fillingand surface permeable-resistantcoating which are detailed asfollows

(1) Cracks are grooved and filled

(2) Surface permeable-resistantcoating the surface of the dammonoliths is coated usingimpermeable polyurea with athickness of 4mm in 2m aroundthe cracks For the area with thedense fine cracks the 2m iscounted from the crack locatedin the boundary of the area

(3) Chemical grouting is appliedin the cracks which coalesce withthe thermal cracks due totemperature gradients

21LF-2 17 03

In April 2009 a crack with a length of29m along the flow direction was foundin the floor of the number 1 middlediversion outlet at the upstream sidewhich perpendicularly intersected withthermal cracks due to temperaturegradients No cracks were found in theroof and side walls

Number 22dammonolith(numberdiversionoutlet)

22LF-1 11 03

Cracks are distributed in the number 22dam monolith between ELs 1068m and1098m but above the floor of the number2 middle diversion outlet whose EL is1065m

22LF-222LF-3 1 02

Cracks coalesce with surface cracks in thenumber 2 middle diversion outlet Thecracks 22LF-2 are distributed in thenumber 22 dam monolith at ELs between1013msim1050m The cracks 22LF-3 aredistributed above 5msim7m below thecracks 22LF-2Large number of irregular microcrackswere observed to distribute in ring shapein the floor side walls and roof of thenumber 2 middle diversion outletbetween the thermal cracks 22LF-2 and22LF-3 in the second-round inspection ofthe outlets in February 2009

22LF-4 1 03

The cracks lie in the downstream side ofthe number 22 dam monolith betweenELs 972msim1012m which are expected tointersect with the surface of the dammonolith


23LF-1 17 05

The cracks are distributed in the number23 dam monolith between ELs1001msim1108m and extend through thenumber 3 middle diversion outlet

23LF-2 175 05

The cracks lie in the number 23 dammonolith between ELs 977msim1025mwhich extend till 1021m but have notreached the floor of the number 3 middlediversion outlet

As we know that the concrete has poor conductivity hightemperature gradients may be resulting in between theinterior and the surface of the concrete structural elementsor between parts of a concrete element during the sequentialpouring phases The temperature gradients may lead to ten-sile stresses whichmay result in the young concrete cracking

In the Goupitan arch dam the large amount of cementsthe high temperature of hydration and the hot weather inJuly during the construction of the bottom outlets lead tohigh temperatures inside the concrete As the temperatureof the concrete drops down sharply later stress due to thetemperature gradient of the concrete from inside to outside


creates several cracks As the time passes the temperature ofthe concrete decreases continually andmore andmore cracksare appeared In addition if the conservation measures arenot perfect for example the external concrete has not beensuppliedwith sufficientwater the concrete surfacewill shrinkgenerating further cracks Actually even if the upstreamwater level reaches EL 5900m the resultant stresses at thereservoir discharging bottom outlets in the Goupitan archdam are not more than the tensile or shear strengths of theC50 concreteThus it is not necessary to use the C50 concreteduring the construction of the abrasion-resistant layers of thebottom outlet from the point of view of the actual diversioncapacity of the bottom outlets in the Goupitan arch dam

In addition the C35 concrete is used to construct thedams in the transition zone from theC50 toC18035 concretesThe shrinkage coefficients of the concretes differ from eachother which further contribute to the outlet crackingThe 3Dfinite element method was conducted by the design instituteto analyze the stress and deformation of the Goupitan archdam during the operation phases with and without outletcracking It is found that the integral stability of the damis affected by the outlet cracking The analysis results showthat the existence of the cracks in the bottom outlets haslittle effects on the dam stress and displacement Duringthe operation phase compressive and shear stress of crackis small which indicates that the cracks will be closed andshearing slip will not occur Even if water pressures andexternal loads are applied the stress intensity factor at the tipof the cracks surrounding the outlets is still smaller than thefracture toughness 119870IC of the concrete illustrating that thecrack will not continue to propagate

22 Outlet Cracking at the Xiaowan Arch Dam

221 Introduction to the Outlet in the Xiaowan Arch DamThe Xiaowan arch dam (Figure 4) is constructed on theMeigong River in Nanjian County Yunnan Province south-western China which is a double curvature concrete archdam with a maximum height of 2945m and a dam crestlength of 905m The Xiaowan arch dam is the highest archdam in operation in the world As shown in Figure 4(a) threetypes of outlets that is the upper surface middle diversionand bottom exit outlets are constructed in the Xiaowanarch dam to meet the needs of construction diversion waterimpoundment and generation of the first generation setThe cross section of the two bottom outlets is rectangulareach of them has a size of 6m times 7m and their entranceELs are 1020m and 1050m respectively The three middlediversion outlets are located in the numbers 21 22 and 23dam monoliths and numbered using the numbers 1 2 and 3respectively from left to right in Figure 4(a) The maximumaverage diversion flow rate of single middle diversion outletis designed as 1884m3s The maximum average water flowspeed is 45ms but it is 38ms at the centre of the middlediversion outlet Taking the high speed and large amount ofthe diversion flow the middle diversion outlets should bereinforced with fiber concrete Below EL 1051m surfaces ofthe outlets are built with 06-metre-thick abrasion-resistantC2840W9010F90150 concrete

222 Outlet Cracking Status The outlet cracking mainlyoccurs in the middle diversion outlets in the Xiaowan archdam Correspondingly only the outlet cracking character-istics and reinforcement measures of the middle diversionoutlets are summarized into Table 2 Since most of the cracksin the middle diversion outlets coalesce with the thermalcracks induced due to temperature gradient in the dammonoliths these cracks are collected and classified accordingto the numbers of the dam monoliths in which the middlediversion outlets are located as shown in detail in Table 2Moreover the distributions of outlet cracking in the number22 dammonolith are depicted in Figure 4(b) while a snapshotof cracking near the number 2 middle diversion outlet isshown in Figure 4(c)

223 Reasons and Consequences of Outlet Cracking Becauseof the large displacement toward the upstream side of the archdamwhen thewater through the diversion outlets exceeds thedesigned amount the large tensile stress near the upstreamsurface may be the main cause of the outlet cracking in thearch dam

Cracks near the middle diversion outlets coalesce withthose thermal cracks due to temperature gradient whichbecome the main source of water leakage Our studies haveshown that if the pore water pressure in the crack reaches05MPa the crackmay propagateThe bigger the aspect ratiothe smaller the pore water pressure needed for the crack topropagate Currently the pore water pressure of 11MPa in thecracks has led to a large amount of water leakage through thenumbers 22 and 23 dam monoliths If appropriate measurescould not be taken timely to cut off the water source theirregular cracks in the side wall of the outlets may propagatecontinually under the repeated pressing of the pore water inthe cracks which may harm the overall instability of the archdamThe correspondingly crack reinforcement measures arelisted in Table 2

3 Effects of Outlets on Integral Stability ofthe Xiluodu Super-High Arch Dam

31 Introduction to the Xiluodu Super-High Arch Dam In thissection effects of outlets on the working status of a 300mhigh arch dam in theXiluodu hydropower station are studiedThe Xiluodu hydropower station is located on the JinshajiangRiver Leibo county Sichuan Province southwestern ChinaIt is the second largest power station in the world and canproduce 1386 million kW of power which is close to thecapacity of the largest power station that is theThree Gorgeshydroelectric power station The principal structures consistof a double-curvature arch dam with a height of 2855m anda crest length of 603m spillway underground powerhouseand logway The thickness of the dam is 14m at crest and60m at the lowest foundation There are 7 surface outlets 8deep outlets and 10 diversion bottom outlets placed in thenumbers 12sim19 dam monoliths The volume of the outletscounts for 2 of that of the whole dam

The rockmass strata in the reservoir basin are clastic rockcarbonate rock and basalt of Paleozoic a small amount of


Middle outlet number 2

Upper surface outlets

Bottom outlet

(a) Snapshot of the Xiaowan arch dam

Flow direction

Flow direction Flow direction

Flow directionFloor Roof

Left side wall Right side wall

21

2322

20

131

1

2

3

3

6

4

4

45

5

6

6

7

7

8

8

9

911

128

11

1010 18

1927

1617

15

14

12

Crack found in2008 year Crack found in

2008 year

Crack found in2008 year

39

37

38

35

33

36

34

2730

31 32

2928

24 25 26

1050m1050m

105824m105824m05 06 31

64 64

6464

1 06

085 17

46

07 05 060672499

265

499

265 499

499

11

12

0405 32

32 36171717

2

2

632 233

22LF-2 crack 22LF-3 crack

(b) Schematic sketch of new cracks in the number 22 dam monolith near the number 2 middle diversion outlet since 2009

Cracks

(c) A snapshot of the number 2 middle diver-sion outlet

Figure 4 Cracking near the middle diversion outlets of the Xiaowan arch dam

metamorphic rock of Presinian and dolomite of Sinian [3334]The depth of rockmass strongly unloaded due to the damconstruction is generally less than 10m No strong weatheredrock masses are founded in the reservoir generally exceptsome thinweathering sandwiches located in some fault zonesFresh rock and weak weathered rock mass is integral overallwhich can mainly be classified as the type II rock massTheserockmasses have an acoustic velocity of 4800ndash5500ms good

uniformity and weak permeability Surface water drainage isunobstructed groundwater level stays low and natural slopehas good stabilityThe foundation consists of several layers offine basalts (eg P21205731 and P21205732) with an average thicknessof about 25sim40m The main weak zones are the interstratabedding planes C9 C8 C7 C3 C2 and C1 and the intrastratarupture belts Lc6 and Lc5 [24 33]These weak zones are filledwith breccia embedded sharp-angled fragments coarse sand


and gravels which are about 25mm thick The foundation ofthe dam is divided into a number of riverbed monoliths (egfrom the numbers 14th to 19th monoliths) which are mainlycomposed of the type III1 rock masses with a few type III2rock masses at the elevations 3245m and 328m The typeIII1 rock mass is either unweathered or a slightly weatheredbasaltThe physical-mechanical properties of the rockmassesare listed in Table 5 The type III2 rock mass accounts forabout 10sim50 of the left and right steep slopes of the dammonoliths

32 Numerical Model and Methodology In this sectionthree-dimensional nonlinear finite element method is imple-mented to study the integral stability of the Xiluodu super-high arch dam with and without outlets under normal load-ing and overloading conditions Some preliminary resultsfrom these analyses were reported previously in a confer-ence paper ([35]) to exchange ideas with peers and collectfeedbacks However this paper will focus on the nonlinearfinite element analysis method and effects of the outlets onthe deformation stress and integral stability of the Xiluodusuper-high arch dam while the conference paper just brieflydiscussed the integral stability of the dam

321 Nonlinear Finite Element Analysis with Drucker-PragerYield Criterion The 3D finite element analysis adoptsDrucker-Prager (D-P) yield criterion which can be expressedin

119891 = 1205721198681+ 11986912

2minus 119867 = 0 (1)

where 1198681is the first invariant stress 119869

2is the second invariant

stress and 120572 and 119867 are material constants which can bedetermined according to

120572 =

3119905119892120593

radic9 + 121199051198922120593

119867 =

3119888

radic9 + 121199051198922120593

(2)

where 119888 is cohesion and 120593 is friction angle Equations (1)and (2) also show that the D-P criterion and the M-C (ieMohr-Coulomb) criterion have the same expressions for theplane strain problem In the 120587 plane the D-P circle has theintermediate values of circumstanced circle and inscribedcircle of the M-C hexagon Nonlinear elastoplastic finiteelement analysis can figure out conditions like plastic yieldsubcritical fracture and unstable extension and plot theunbalanced force and point safety factor contour in theupstream and downstream surface of the dam

The stress adjustment process in the nonlinear finiteelement analysis with the D-P criterion can be listed as inthe following stress and strain of the initial point is set to be1205900and 1205760and 119891(120590

0) le 0 For a given load step or iteration

the strain increment Δ120576 of the point can be obtained bydisplacement method and correspondingly the stress can becalculated using

1205901= 1205901

119894119895= D (120576

0+ Δ120576) (3)

where D is the elasticity tensor If 119891(1205901) gt 0 then the stress

needs adjustment If plastic strain increment of the loading

step or iteration is Δ120576119901 then the stress after adjusting can bewritten using

120590 = 120590119894119895= D (120576

0+ Δ120576 minus Δ120576

119901) = 1205901minusDΔ120576119901 (4)

Transform the AC flow rule to incremental form approx-imately which can be written into

Δ120576119901= Δ120582

120597119891

120597120590

(5)

Determine the representative value of 120597119891120597120590 by 1205901using

119891 (120590) = 0 120590 = 1205901minus Δ120582D 120597119891

120597120590

10038161003816100381610038161003816100381610038161003816120590=1205901

(6)

Then the stress after adjustment can be determined using

120590 = 120590119894119895= (1 minus 119899) 120590

1

119894119895+ 119901120575119894119895 (7)

where

119899 =

119908120583

radic1198692

119901 = minus119898119908 + 31198991198681

119898 = 120572 (3120582 + 2120583) 119908 =

119891

3120572119899 + 120583

(8)

where 1198692 1198681 and 119891 can all be determined by 120590 and 120582 and 120583

are Lame constants which can be expressed using

120582 =

119864](1 + ]) (1 minus 2])

120583 =

119864

2 (1 + ]) (9)

119864 and ] are Youngrsquos modulus and Poissonrsquos ratio respectivelyStress increment of each incremental step or iteration can bewritten in

Δ120590119901= 1205901minus 120590 = 119899120590

1

119894119895minus 119901120575119894119895 (10)

322 Numerical Model and Analysis Cases Figure 5 depictsthe numerical model for the Xiluodu arch dam whichconsists of the whole dam structural and the foundationsincluding faults and main weak zones such as the interstratabedding planes C9 C8 C7 C3 C2 and C1 and the intrastratarupture belts Lc6 and Lc5 The 3D finite element meshincludes a vast area of abutments and its size is 1500m times

1000m times 660m (length times width times height) The total numberof elements is 104785 with 6096 elements for dam body1890 elements for the surface outlets 420 elements for theside outlets and 1890 elements for the bottom outlets wherethe dam toe block in the downstream side is marked usingbrown colour as shown in Figure 5(a)Thenumericalmethodproposed in Section 321 was employed to perform the finiteelement analysis and study the outlet cracking and failurebehaviour

The 3D finite element nonlinear analysis was executed forthe Xiluodu arch dam in the following analysis cases

(1) Case A the whole dam under usual loads (ie thehydrostatic pressure silt pressure and gravity) andoverloads (ie the hydrostatic pressure silt pressuregravity and two to six times upstreamwater pressure)


Table 3 Physical-mechanical parameters of the rock masses and dam materials

Materials Bulk density (tm3) Deformation modulus (GPa) Poissonrsquos ratio Shear strength1198621015840 (MPa) 119865

1015840

Dam concrete 240 24 0167 50 170Concrete of bottom outlets 240 32 0167 50 170Rock of class II 285 165 020 25 135Rock of class III1 285 115 025 220 122Rock of class III2 275 55 028 14 12

Table 4 Dam displacement at the downstream side along the river direction under various analysis cases (unit mm)

Case Level position (m) 610 590 560 520 480 440 400 360 332

Case ALeft arch abutment 53 78 152 182 238 237 274 272 237

Arch crown 948 998 1039 1069 1005 893 722 488 253Right arch abutment 35 51 104 156 204 255 295 254 212

Case BLeft arch abutment 57 79 153 187 243 239 287 282 243


(a) Dam outlets and bottom block (analysis case A)

Bottom outlets

Middle outlets

Upper outlets

(b) Downstream snapshot of dam outlets

Figure 5 3D mesh model of dam and outlets

(2) Case B dam without outlets under usual loads andoverloads

It should be noted that in the analysis case A the existence ofsluice is not considered and there is no hydrostatic pressurein the area of the outlets Table 3 summarized physical-mechanical parameters adopted by the numerical simulationThe self-weights of the dam and abutments the normal waterloads at the upstream and downstream sides of the dam and

the temperature load are the main loads taken into accountduring these analysis cases The elevation height of the waterin the upstream side the silt and thewater in the downstreamside is 600m 490m and 378m respectively

33 Effects of Outlets on Dam Deformation For the analysiscases A and B the displacement distribution in the upstreamsides of the dam under normal loads is illustrated in Figures6(a) and 6(b) respectivelyMoreover the displacements at thecritical locations of the dam for the both analysis cases aresummarized in Table 4 Figure 7 depicts the variation of thedisplacement at the dam crown for both analysis cases undervarious overload conditions

It is known from the numerical results that (1) under thenormal loading conditions the maximum displacements ofthe dam crown decrease slightly when the outlets are takeninto account The maximum displacement decrease is about16mm as shown in Table 4Thus the outlets in the high archdam may help shift the arch thrust force to both abutmentsand increase the transverse deformation (2) The symmetryof the displacement distributions is good for both analysiscases A and B which indicates that the dam abutments havegood overall stiffness For the analysis case A the maximumdisplacements of the crown (Figure 7(a)) left arch abutmentand right arch abutment along the river flow direction were1069mm at EL 520m of the downstream surface 274mmat EL 400m of the downstream surface and 2957mm atEL 400m of the downstream surface respectively For theanalysis case B the maximum displacements of the crown(Figure 7(b)) left arch abutment and right arch abutmentalong the river flow direction were 1085mm at EL 520mof the downstream surface 287mm at EL 400m of thedownstream surface and 302mm at EL 400m of the down-stream surface respectively (3) In the analysis case B the dambody shoulders greater pressures from the water and silt atthe upstream side The carrying capacity of the arch fails toincrease relatively while that of beam becomes heavier These


UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03

(a) Upstream surface (case A)

UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03

(b) Upstream surface (case B)

Figure 6 Displacement contour along river direction under different analysis cases (normal loads)

0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750

1 time load2 times load3 times load4 times load

5 times load6 times load7 times load8 times load

Elev

atio

n (m

)

Displacement (mm)

(a) Under analysis case A

0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0

(b) Under analysis case B

Figure 7 Crown displacement along river direction under various analysis cases (overloading condition)

factors contribute to the increase of the displacement of thecrown compared with the analysis case A

34 Effect of Outlets onDam Stress Distribution In the designof the dam outlets it is vitally important to investigate clearlythe stress distributions in both dam and outlet especially inthe tensile zone at the roof floor and side walls of the outletsCorrespondingly the distributions of the major and minorprincipal stresses at the upstream and downstream surface ofthe dam are depicted in Figure 8 for the analysis cases Themaximum tensile and compressive stresses of the dam andoutlets are summarized in Table 5 for the analysis cases Aand B under normal loading conditions which include thehydrostatic pressure silt pressure and gravity

It can be seen from Figure 8 and Table 5 that (1) the valuesof characteristic stresses such as the maximum tensile stressand the maximum compressive stress from both analysiscases are nearly the same which indicates that though thedam body in the analysis case B carries more pressure fromthe water and silt in the upstream side because of ignoring theexistence of the outlets this small proportion of incrementalpressure does not make much difference The maximumcompressive stress at the downstream surface in the analysiscase B is 171MPa which is 02MPa bigger than that fromthe analysis case A (2) As for the maximum tensile stressat the upstream surface of the outlets it is found that theupstream surface of the outlets in the analysis case B is slightlycompressive while that in the analysis case A suffers fromsome high tensile stressThe surface outlet in the analysis case


S max principal(avg 75)

+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06

(a) The first principal stress at upstream surface


minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07

(b) The third principal stress at upstream surface


+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06

(c) The first principal stress at downstream surface


minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07

(d) The third principal stress at downstream surface

Figure 8 The principal stress distribution (analysis case A Unit pa ldquominusrdquo denotes compression stress and ldquo+rdquo denotes tension stress)

Table 5 Characteristic stresses at various key locations from both the analysis cases A and B (Unit MPa)

Location Content Case A Case B

Up stream surfaceMaximal tensile stress of dam heel 067 085Maximal tensile stress near left arch abutment 061 082Maximal tensile stress near right arch abutment 01 01

Down stream surfaceMaximal compression stress of dam toe 157 168Maximal compression stress near left arch abutment 169 171Maximal compression stress near right arch abutment 163 167

Upstream of bottom outletMaximal tensile stress of side wall minus1 mdashMaximal tensile stress of roof 0 mdashMaximal tensile stress of floor minus01 mdash

Downstream of bottom outletMaximal tensile stress of side wall 07 mdashMaximal tensile stress of roof 0 mdashMaximal tensile stress of floor 0 mdash

Surface outlets Maximum tensile stress in upstream surface 18 mdashMaximum tensile stress in downstream surface 19 mdash

Middle outlets Maximum tensile stress in upstream surface 15 mdashMaximum tensile stress in downstream surface 17 mdash

A is most likely to crack since the tensile stress there reaches18MPa (3) Under the normal loading condition the optimaldistribution of the outlets in the arch dam will contributeto the release of the tensile stress concentrated in the localzone of the upstream surface and decrease the cracking riskof the integral dam body during the operation period At thesame time stronger concrete and appropriate reinforcement

measures should be used in the area near the outlets (4) Theresults from the stress analysis and the displacement analysisare consistent with each other If the outlets are filled theelastic modulus of the filled outlets is increased or the elasticmodulus of the dam body is increased the load carryingcapacity of the arch dam improves significantly especially inthe part where the middle and bottom outlets are located


SIG1 (MPa)minus35 minus25 minus15 minus05 05 15 25

(a) The first principle stress distribution at upstream surface ofbottom outlet

SIG3 (MPa)minus26 minus22 minus18 minus14 minus10 minus6 minus2

(b) The third principle stress distribution at upstream surfaceof bottom outlet

(c)


(c) The first principle stress distribution at downstream surfaceof bottom outlet


(d) The third principle stress distribution at downstreamsurface of bottom outlet

Figure 9 The firstthird principle stress distribution of bottom outlets under analysis case A

However the tensile and compressive stresses at the left andright ends of the arch dam become larger

Figures 9 and 10 show the distribution of the major andminor principal stresses in various parts of the bottom outletsfrom the analysis case A It can be seen that the side walls andthe roof are mainly under compression during the operationperiod but the tension stresses concentrate in the area close tothe upstream side of the roof Compressive stresses dominatethe floor of the bottom outlets

35 Effect of Outlets on the Integral Stability of the Arch DamThe yield process of the arch dam at ultimate limit states ispredicted by applying overloads on the dam in the analysiscases A and B Figures 11(a) and 11(b) depict the yield zones inthe horizontal sections of themiddle outlets when the appliedload is 6 times normal water load in the analysis cases A andB respectively while the yield zones in the upstream anddownstream surfaces are shown in Figure 12 It can be seenthat the yield zones are located in the downstream surface ofthe dam and showed a ldquobutterflyrdquo symmetrical distribution(Figures 12(a) and 12(c)) Compared with the analysis case Athe analysis case B generates a more widely distributed yieldzone and a higher yield value Therefore filling the outletsdecreases the carrying capacity of the dam body

For the analysis case A under normal loads there is noyield zone occurring in either the upstream or downstreamsurfaces The factor of safety at various locations of theupstream surface is between 20 and 50 It is discoveredfrom the sequentially overloading process that when theapplied load is two times the normal load a small yieldzone appears in the heel of the upstream surface As for thedownstream surface the yield zone spreads quickly underoverload conditions and a large area becomes yield when theapplied load reaches 4 times the normal water load

For the analysis case B under normal loads there isagain no yield zone in either the upstream or downstreamsurfaces The factor of safety at various locations of theupstream surface is between 20 and 50 too The sequentialoverloading process in the analysis case B shows that whenthe applied load is two times the normal load a small yieldzone appears in the dam heel while some big yield zoneappears in the downstream surface As the times of theapplied overload increase the yield zone in the downstreamsurface spreads quickly When the applied load reaches 3 or 4times the normal water load large yield zone appears in thedownstream surface and the arch dam enters into nonlineardeformation stage which indicates the beginning of the damdestruction

It can be seen from the analysis cases A and B thatthe outlets are integral and help dam shoulder some loadalthough they relatively weaken the carrying capacity ofthe arch dam The initial cracking overload coefficient K1is 2 and the ultimate overload coefficient is 65sim7 It isobvious from above analyses that under the overloadingconditions the cracks initiate around the outlets propagatealong the horizontal direction and then coalesce in the areabetween the adjacent outlets The yield zone generated inthe dam under overloading conditions looks like a butter-fly

4 Outlet Cracking Mechanism andRisk Control

41 Outlet Cracking Mechanism Based on the case studieson the outlet cracking in the Goupitan arch dam and theXiaowan arch dam presented in Section 2 and the numericalsimulation on effect of outlets on overall stability of theXiluodu arch dam introduced in Section 3 it can be seen


DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20

(a) The first principle stress distribution at side wall of bottom outlet

Upstream

Roofdownstream

Side wall

Floordownstream

Side wallUpstreamSide wall

Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)

(b) The first principle stress distribution at roof and bottom floor of bottomoutlet


that the following factors contribute to dam outlet crackingdam structural design construction materials thermal con-trol maintenance processes and the impounding schemePotential reasons of the outlet cracking can be summarizedas follows

(1) ConcreteMaterials Outlets are always part of the hydraulicstructures which are usually built with stronger concreteso as to improve the abrasion-resistant ability Howeverthe stronger the concrete is the more the cement is usedwhich may generate the larger amount of hydration heatand the higher temperature All these factors set higherrequirements for the construction environment temperaturecontrol and maintenance measures Cracking may easilyoccur once the temperature in the construction environmentchanges sharply for example the drop of the temperature inthe late maintenance phase In addition if the concrete used

in the bottom outlets differs sharply from that used in thesurrounding dam body that is the shrinkage coefficients ofthe two kinds of concretes vary greatly the risk of crackingstill increase even if several different kinds of concretes areused in the transition zone

(2) Temperature Control and Maintenance Temperature con-trol and maintenance of the concretes used to construct theoutlets are relatively more complex than the other factorsIn addition to conventional measures of the temperaturecontrol the surface of the outlets has to be closed so asto prevent them from impact of low temperatures causedby cavern drafts flowing and water is kept to flow on thesurfaces of the dam body concrete If the measures of thetemperature control and maintenance are not carried outproperly thermal cracking may easily occur in the outletconcrete due to temperature gradients


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


Figure 11 Plane section of yield zone in middle outlets under various analysis cases (6 times overloading)

PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

(a) Downstream surface under analysis case A

PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

(b) Upstream surface under analysis case A

PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

(c) Downstream surface under analysis case B

PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

(d) Upstream surface under analysis case B

Figure 12 Yield zone in dam under various analysis cases (6 times overloading)

(3) Impounding Scheme During the construction phasethe water pressure in the reservoir influences the stressdistribution in the dam If the reservoir water is stored tooearly or toomuch large tensile stresses may be induced in theupstream surface heel and shoulder of the dam If the water

storage is delayed crackingmay easily be caused by the tensilestress in the upstream face of the crown cantilever which haslarge upstream-tend displacement Thus reasonable storagescheme should be figured out During the construction phaseof the arch dam the concrete structure above a certain


elevation belongs to a beam structure instead of an archbeam structure since the joints grouting of the arch dam onlyhappens after the temperature of the dam body drops to aspecified temperature

(4) Design Scheme Since the outlets may experience obviousdeformation and are prone to tensile stress reinforcementdesign is often required Because of the complex structure andthe big size difference from the dam body to the outlets andthe effects on the outlets caused by the dam weight waterpressure temperature gradient concrete creep behaviourand so on the accurate analysis of stresses on the outletsbecomes very difficult So the design scheme itself alonecould not reduce the cracking risk effectively

(5) Concrete Fracture Characteristics According to the exper-iment on fracture properties of full graded concrete usedin Xiluodu high arch dam the initial fracture toughness ofthe concrete with one month age is 03MPam12 in averagethe unstable fracture toughness is 1225MPam12 in averageand the cracking toughness is 448257Nm in average Thecorresponding values of the concrete with three months ofage are 0655MPam12 1387MPam12 and 470600Nmrespectively Because of the low cracking-resistance abilityof the early concrete and the complex conditions in theconstruction sites the concrete dam is prone to generateinitial microscopic cracks especially around stress concen-trated area like the outlets The analysis conducted aboveshows that the cracks around the outlets have little impacton the dam integral stress and displacement but these cracksmay propagate to coalesce with the interior temperaturecracks and traverse joints and become the main source ofthe water leakage The irregular cracks on the wall of theoutlet corridors may propagate under the high pore waterpressure in the cracks Once these cracks propagate intodeep depth or through the foundation and their directionis parallel to the axis of the dam the consequences maybe unbearable In this case these cracks may harm thedam structural integrity change the stress condition of theconcrete structure and damage some local dam structuresMoreover the durability of the concrete may be weakenedThus the effects of the superposition of the thermal andstructural stresses on the integral stability of the dam allow noignorance

(6) Outlet Cracking Risk Based on the case studies onoutlet cracking in the Goupitan and Xiaowan arch dams thediversion outlet is prone to local stress concentration andcrack initiation due to hydration heat associated with theexothermic chemical reactions in the fresh concrete Thusthe local reinforcement design is needed for the diversionoutlet which will be discussed in the next section Duringthe operation period the stress and deformation distributionaround the outlet generally satisfy the operation requirementof the dam under normal loading conditions The outletsmainly affect the overall stability of the dam under overloadconditions especially when the yield zones occur around theoutlets under the overloading conditions

42 Cracking Risk Control and Reinforcement

421 Experiences from Processing the Outlet Cracking inthe Goupitan Arch Dam Based on the case studies andthe numerical modelling crack reinforcement measures areproposed to repair the outlet cracks in the Goupitan archdam

As introduced in Section 21 the cracks inspected inthe Goupitan arch dam can be classified into four types asshown in Table 1 Depending on the types of the cracksthe cracking treatment measures include surface processingshallow processing and deep processing

(1) The surface processing is involved in brushing water-proof materials on the cracks which is suitable for the cracksthat have not gouged at the time of the inspection (2) Theshallow processing is involved in sealing and backfilling thecracks with preshrunk mortar and filling the grooved partof cracks with imperial materials during the inspection (3)The deep processing is used to repair deep cracks that is touse chemical grouting method to reinforce the crack Afterthe chemical grouting a site investigation should be doneto inspect the surfaces of the repaired cracks Moreoverthe grouting quality should be examined by core-sampledrilling and hydraulic pressure tests in 28 days after thechemical groutingThe samples from the core drilling shouldbe tested to obtain the compressive resistant capacity andsplitting resistant capacity besides the visual inspectionsThe testing results of the Goupitan arch dam show that thecompressive resistant capacity of the sample taken from thecore drilling after the chemical grouting is more than 40MPaand the splitting resistant capacity is more than 20MPaThe hydraulic pressure tests are conducted using the holesfrom the core drilling or those drilled alone and the pressureof the injected water during the inspection is 02MPa It isfound that the results from the hydraulic pressure tests satisfythe judgment standard which allows no more than 01 Lupermeation rate In addition the deep sonic wave tests arealso conducted after the grouting is completed whose resultsare compared with those from the visual inspection and thetests mentioned above so as to have a further examination ofthe grouting quality

422 Experiences from Processing the Outlet Cracking in theXiaowan Arch Dam Theoutlet cracking in the Xiaowan archdam has been reinforced in two times The reinforcementmeasure in the first time is intended to repair the cracksin the middle diversion outlets which happened beforeAugust 2008 At that time the cracks due to the temperaturegradients have not been observed and the cracks in themiddle diversion outlets have not coalesced with those dueto the temperature gradients yetThe reinforcementmeasuresinclude grooving the cracks and spraying impervious materi-als on the surfaces of the cracks

The reinforcements in the second time happened in May2009 when several cracks in themiddle diversion outlets hadbeen found to coalesce with the cracks due to the temper-ature gradients The main reinforcement measures includechemical grouting and grooving and spraying imperviousmaterials on the surface of the cracks which can be detailed as


follows (1) grooving and backfilling with preshrunk mortarimmediately (2) For the water leakage cracks a 4mm thickpolyurea coating is sprayed in the scope of 2 meters aroundthe cracks For the area with dense cracks the 2m scope isdetermined from the crack located in the edge of the area (3)Chemical grouting is applied in the cracks which coalescewith the thermal cracks due to the temperature gradientsinside the dam

423 Principles for Outlet Cracking Risk Control and Rein-forcement in the Super-High Arch Dam In this section areinforcement principle is proposed to control the outletcracking risk based on the reinforcement experiences of theoutlet cracking in the Goupitan and Xiaowan arch dams inSections 2 421 and 422 and the numerical studies on theeffect of the outlets on the integral stability of the Xiluoduarch dam in Section 3

(1) Selection of Appropriate Concrete Materials The damoutlets are a hydraulic structure for water diversion whichshould be designed using the concretes with appropriatestrengths according to their flow rate The concrete withhigh strengths should not be used blindly If the abrasion-resistant capacity of the concrete is only to be improved thefibre-reinforced concrete may be used which may reducethe use of the cement then lower down the hydration heatand alleviate the pressure from the temperature controlIf the outlet must be constructed using the high strengthconcrete whose expansion coefficient is much different fromthat of the concrete used to construct the dam body atransition area must be constructed between the outlets andthe dam body using various types of concretes and theexpansion coefficients of the adjacent concretes should notdiffer significantly

(2) Strengthening Temperature Control during ConstructionPeriod The routine temperature control measures shouldmake sure that the temperature of the concrete in eachprocedure satisfies the requirement including the concretemixing and pouring temperatures the highest temperatureinside the concrete and the temperature difference betweenthe inner and external surfaces of the concrete The concretemay be poured under low ambient temperatures such asnighttime Special temperature control measures may beadopted for the bottom diversion outlets (1) the concretestarted to pour from the outlets The surfaces of the outletsmay be closed using curtain-style closed doors to preventthe surface of the concrete from the wind blowing throughthem which may reduce the temperature of the concreteresult in too high temperature gradient and induce thermalcracking (2) When the mould at the sidewalls of the outletis dismantled thermal insulation quilt with 2 cm thicknessshould be installed to maintain the temperatures there (3)Canvas insulation frame is installed at the upstream anddownstream sides of the outlets to maintain the temperatureswhen the outlets are formed (4) When the construction ofthe floor of the bottom diversion outlet is finished waterflow is used to maintain the temperatures there which may

be replaced with watering in 1 or 2 days after the highesttemperature of the poured concrete appears

(3) Reasonable Impounding SchemeThe impounding schemeshould make sure that the reservoir is impounded with wateras early as possible when the stress state and the point factorof safety of the dam body and the outlets satisfy the designrequirements In this case the height of the cofferdam can bereduced as low as possible and the electricity can be generatedas early as possible

(4) Optimizing Outlet Design The outlets should be designedto reduce the size of the tensile stress which may appearnear the outlets and the area of the outlet which maybe under tension in order to reduce the reinforcement asfar as possible The potential engineering measures mayinclude changing the shape of the outlets grouting thetransverse joints filling and pressuring the transverse jointsand preloading and grouting aggregates Moreover physicalmodel testing and numerical modelling may be conducted tostudy the stress and strain characteristics of the outlets theprogressive development of the outlet crack initiation prop-agation and coalescence and the nonlinear reinforcementmethod for the outlets

(5) Outlet Cracking Classification and Reinforcement Basedon the case studies and numerical simulations conductedabove and the arch dam design code the outlet crackingcan be classified and reinforced according to the followingengineering procedure cracking investigation rarr causes ofcracking and cracking category analysis rarr hazard evaluationand classification rarr patching treatment rarr inspection andacceptance

5 Conclusions

This paper first conducts two case studies on the outletcracking in theGoupitan andXiaowan arch dams by focusingon the current statuses reasons and potential consequencesof the dam outlet cracking Then effect of outlets on theintegral stability of the Xiluodu super-high arch dam undernormal loading and overloading conditions is studied using3D nonlinear finite element method After that the outletcracking mechanism and risk control are discussed on thebasis of the two case studies andnumericalmodelling Finallya reinforcement principal is proposed to control the damoutlet cracking riskThe following conclusions can be drawn

(1) Special attention should be paid to the effects of theoutlets on the working conditions of the super-higharch dam It is found that the outlets decrease theupstream pressure of water and sandsilt and the damstress longitudinal displacement and transverse dis-placementThemaximumreduction ratio can be 35Thus the outlets may harm the structural continuityof the arch dam weaken the carrying capacity anddecrease the load pressing on the dam surface

(2) Under normal loading conditions the optimal dis-tribution of the outlets will contribute to the tensile


stress release in the local zone of the stream sur-face and decrease the cracking risk under operationperiod Under overloading conditions cracks initiatearound the outlet then propagate along horizontaldirection and finally coalesce with the adjacent outletcracks The yield zone of the dam has a shape of abutterfly The integral bearing capacity of the dammay increase about 20 if the elastic modulus of theconcrete used for the outlet increases

(3) The outlet cracking is caused by many factors includ-ing the concrete materials temperature control andmaintenance impounding scheme and dam designscheme

(4) A reinforcement principle is proposed to control theoutlet cracking risk through selecting the appropriateconcrete materials strengthening the temperaturecontrol during construction period designing rea-sonable impounding scheme optimizing the outletdesign and classifying the outlet cracking for variousreinforcement measures

Conflict of Interests

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

Acknowledgments

This research work was supported by the National NaturalScience Foundation of China (nos 11272178 and 51339003)the National Basic Research Program of China (973 Pro-gram) Grant nos 2011CB013503 and 2013CB035902 and theTsinghua University Initiative Scientific Research ProgramThe authors are very grateful to the China Three GorgesCorporation and HydroChina Chengdu Engineering Corpo-ration for supporting this study

References

[1] T Schudder ldquoThe future of large dams dealing with socialenvironmental institutional and political costsrdquo Earthscan pp1ndash30 2006

[2] D P James and H Chanson ldquoHistorical development of archdams from cut-stone arches tomodern concrete designsrdquo 2010httpbarragesorg

[3] T H Yi and H N Li ldquoMethodology developments in sen-sor placement for health monitoring of civil infrastructuresrdquoInternational Journal of Distributed Sensor Networks vol 2012Article ID 612726 11 pages 2012

[4] T Yi H Li and M Gu ldquoWavelet based multi-step filteringmethod for bridge healthmonitoring usingGPS and accelerom-eterrdquo Smart Structures and Systems vol 11 no 4 pp 331ndash3482013

[5] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures and Systems vol 12 no 3-4 pp 345ndash361 2013

[6] P Lin Q B Li and H Hu ldquoA flexible network structure fortemperature monitoring of a super high arch damrdquo Interna-tional Journal of Distributed Sensor Networks vol 2012 ArticleID 917849 10 pages 2012

[7] P Lin Q B Li S W Zhou and Y Hu ldquoIntelligent coolingcontrol method and system for mass concreterdquo Journal ofhydraulic engineering vol 44 no 8 pp 950ndash957 2013

[8] P Lin Q B Li and P Y Jia ldquoA real-time temperature datatransmission approach for intelligent cooling control of massconcreterdquo Mathematical Problems in Engineering vol 2014Article ID 514606 10 pages 2014

[9] A R Ingraffea ldquoCase studies of simulation of fracture inconcrete damsrdquo Engineering FractureMechanics vol 35 no 1ndash3pp 553ndash564 1990

[10] J Z Pan and S H Chen ldquoSome problems on the constructionof high arch damsrdquo Science and Technology Review vol 2 no17ndash19 1997

[11] P Lin R K Wang S Z Kang H C Zhang and W Y ZhouldquoStudy on key problems of foundation failure reinforcementand stability for superhigh arch damsrdquo Chinese Journal of RockMechanics and Engineering vol 30 no 10 pp 1945ndash1958 2011

[12] L M Feng O A Pekau and C H Zhang ldquoCracking analysisof arch dams by 3D boundary element methodrdquo Journal ofStructural Engineering vol 122 no 6 pp 691ndash699 1996

[13] E G Gaziev ldquoInclines of horizontal sections of Sayano-Shushenskaya arch-gravity damrdquo Power Technology and Engi-neering vol 46 no 3 pp 181ndash184 2012

[14] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012

[15] C Jin M Soltani and X An ldquoExperimental and numericalstudy of cracking behavior of openings in concrete damsrdquoComputers and Structures vol 83 no 8-9 pp 525ndash535 2005

[16] P Lin THMa Z Z Liang CA Tang andRKWang ldquoFailureand overall stability analysis on high arch dam based on DFPAcoderdquo Engineering Failure Analysis 2014

[17] The Professional Standards Compilation Group of PeoplersquosRepublic of China ldquoDesign criteria for concrete arch damrdquoTech Rep DLT5436ndash2006 National Development andReform Commission of the Peoplersquos Republic of China BeijingChina 2007

[18] United States Department of the Interior ldquoDesign criteria forconcrete arch and gravity damsrdquo US Government PrintingOffice Washington DC USA 1977

[19] J M de Araujo and A M Awruch ldquoCracking safety evaluationon gravity concrete dams during the construction phaserdquoComputers and Structures vol 66 no 1 pp 93ndash104 1998

[20] A Wang and X M Lu ldquoSummary and discussion on analysismethods of arch dam stabilityrdquo Journal of Western ExplorationEngineer vol 7 2005

[21] M T Ahmadi and S Razavi ldquoA three-dimensional jointopening analysis of an arch damrdquoComputers and Structures vol44 no 1-2 pp 187ndash192 1992

[22] S K Sharan ldquoEfficient finite element analysis of hydrodynamicpressure on damsrdquo Computers and Structures vol 42 no 5 pp713ndash723 1992

[23] P Lin W Y Zhou Q Yang and Y J Hu ldquoA new three-dimensional FEM model on arch dam cracking analysisrdquo KeyEngineering Materials vol 261ndash263 pp 1569ndash1574 2004


[24] P Lin S Z Kang Q B Li R Wang and Z Wang ldquoEvaluationof rock mass quality and stability analysis of Xiluodu archdam under construction phaserdquo Journal of Rock Mechanics andEngineering vol 31 no 10 pp 2042ndash2052 2012

[25] R Wang P Lin and W Zhou ldquoStudy on cracking and stabilityproblems of high arch dams on complicated foundationsrdquoChinese Journal of Rock Mechanics and Engineering vol 26 no10 pp 1951ndash1958 2007

[26] Y Che and Y P Song ldquoThree-dimensional nonlinear analysisof orifice of high arch damrdquo Journal of Dalian University ofTechnology vol 43 no 2 pp 218ndash222 2003

[27] X Li M P Romo O and J Aviles L ldquoFinite element analysis ofdam-reservoir systems using an exact far-boundary conditionrdquoComputers and Structures vol 60 no 5 pp 751ndash762 1996

[28] P Lin Y Zhou H Liu and C Wang ldquoReinforcement designand stability analysis for large-span tailrace bifurcated tunnelswith irregular geometryrdquo Tunnelling and Underground SpaceTechnology vol 38 pp 189ndash204 2013

[29] T T C Hsu ldquoNonlinear analysis of concrete membrane ele-mentsrdquo ACI Structural Journal vol 88 no 5 pp 552ndash561 1991

[30] F J Vecchio ldquoNonlinear finite element analysis of reinforcedconcrete membranesrdquo ACI Structural Journal vol 86 no 1 pp26ndash35 1989

[31] ABAQUS ABAQUS Users Manual vol 611 2011[32] S S Bhattacharjee and P Leger ldquoApplication of NLFM models

to predict cracking in concrete gravity damsrdquo Journal of Struc-tural Engineering vol 120 no 4 pp 1255ndash1271 1994

[33] P Lin X L Liu Y Hu W Xu and Q Li ldquoDeformation andstability analysis on xiluodu arch dam under stress and seepageconditionrdquo Journal of Rock Mechanics and Engineering vol 32no 6 pp 1137ndash1144 2013

[34] R KWang ldquoOverview on the main building design of Xiluoduhydropower station in JinSha Riverrdquo Construction of the ThreeGorge vol 6 pp 47ndash50 2005

[35] P Lin H Hu S Kang and C Wang ldquoThe effects of outletson integral stability of Xiluodu super-high arch damrdquo inProceedings of the 1st International Conference on Performance-based and Life-Cycle Structural Engineering J G Teng J G DaiS S Law Y Xia and S Y Zhu Eds pp 1676ndash1685 Hong Kong China December 2012


123456789101112131415161718192021222324252627

Number1 empty bottom outlet


Bottom outlets

Middle outlets

Upper outlets

(a) Vertical profile of the Goupitan arch dam in the downstream side


(b) Snapshot of the Goupitan arch dam

Figure 1 Distribution of the outlets of the Goupitan arch dam

and reservoir emptying which are usually distributed in arelatively high density in the dam body as shown in Figure 1During the service of the super-high arch dams stresses mayconcentrate around the outlets causing cracking of the dambody [15 16] which poses further potential threats to theintegral stability of the arch dams In the past designersmainly focused on the dam body [17 18] but paid lessattention to the effects of the outlets on the integral stabilityof the dams [19ndash25] Although there are studies proving thatcracks around outlets have little effect on the integral stressstatus and loading condition of the dam [11 15 23 25] in the

long-term conditions the pore water pressure may stimulatethe cracks around the outlets to propagate and coalesce withthose caused by other factors mentioned above which mayresult in greater risk to the integral stability of the super-higharch dam

Three kinds of theoretical analysis are adopted in liter-atures to analyze effects of outlet cracking on the integralstability of the super-high arch dams (1) Plane stress analysisif the outlet opening is relatively small compared with thewhole dam body and the minimum distance between thecentre of the outlet and the dam foundation is not less












Flow direction

Roof

Floor

Roof

Leftwall

Rightwall

06m 06m06m17m16m

05m08m

07m

14m07m

11m 11m10m

11m

18m

09m

07m

07m

07m

08m

12m


Flow direction


3 crack series

11m 09m 07m

2 crack series


Depth lt 03m










Roof

Roof

Floor

Leftwall

Rightwall

06m

13m27m

14m14m

05m05m08m

08m07m

04m14m

14m15m16m

10m

06m

07m

07m

07m

07m12m13m

11m


200

700

400

200

700


05m 05m 13m13m

Flow direction


















monolith at EL 497m














21LF-1 12 03







21LF-2 17 03



22LF-1 11 03


22LF-222LF-3 1 02


22LF-4 1 03



23LF-1 17 05


23LF-2 175 05


















Bottom outlet


Flow direction




21

2322

20

131

1

2

3

3

6

4

4

45

5

6

6

7

7

8

8

9

911

128

11

1010 18

1927

1617

15

14

12


2008 year


39

37

38

35

33

36

34

2730

31 32

2928

24 25 26

1050m1050m

105824m105824m05 06 31

64 64

6464

1 06

085 17

46

07 05 060672499

265

499

265 499

499

11

12

0405 32

32 36171717

2

2

632 233



Cracks









119891 = 1205721198681+ 11986912

2minus 119867 = 0 (1)




120572 =

3119905119892120593

radic9 + 121199051198922120593

119867 =

3119888

radic9 + 121199051198922120593

(2)





1205901= 1205901

119894119895= D (120576

0+ Δ120576) (3)




120590 = 120590119894119895= D (120576

0+ Δ120576 minus Δ120576

119901) = 1205901minusDΔ120576119901 (4)


Δ120576119901= Δ120582

120597119891

120597120590

(5)


119891 (120590) = 0 120590 = 1205901minus Δ120582D 120597119891

120597120590

10038161003816100381610038161003816100381610038161003816120590=1205901

(6)


120590 = 120590119894119895= (1 minus 119899) 120590

1

119894119895+ 119901120575119894119895 (7)

where

119899 =

119908120583

radic1198692

119901 = minus119898119908 + 31198991198681

119898 = 120572 (3120582 + 2120583) 119908 =

119891

3120572119899 + 120583

(8)



120582 =

119864](1 + ]) (1 minus 2])

120583 =

119864

2 (1 + ]) (9)


Δ120590119901= 1205901minus 120590 = 119899120590

1

119894119895minus 119901120575119894119895 (10)








1015840









Bottom outlets

Middle outlets

Upper outlets









UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References
















































Flow direction

Roof

Floor

Roof

Leftwall

Rightwall

06m 06m06m17m16m

05m08m

07m

14m07m

11m 11m10m

11m

18m

09m

07m

07m

07m

08m

12m


Flow direction


3 crack series

11m 09m 07m

2 crack series


Depth lt 03m










Roof

Roof

Floor

Leftwall

Rightwall

06m

13m27m

14m14m

05m05m08m

08m07m

04m14m

14m15m16m

10m

06m

07m

07m

07m

07m12m13m

11m


200

700

400

200

700


05m 05m 13m13m

Flow direction


















monolith at EL 497m














21LF-1 12 03







21LF-2 17 03



22LF-1 11 03


22LF-222LF-3 1 02


22LF-4 1 03



23LF-1 17 05


23LF-2 175 05


















Bottom outlet


Flow direction




21

2322

20

131

1

2

3

3

6

4

4

45

5

6

6

7

7

8

8

9

911

128

11

1010 18

1927

1617

15

14

12


2008 year


39

37

38

35

33

36

34

2730

31 32

2928

24 25 26

1050m1050m

105824m105824m05 06 31

64 64

6464

1 06

085 17

46

07 05 060672499

265

499

265 499

499

11

12

0405 32

32 36171717

2

2

632 233



Cracks









119891 = 1205721198681+ 11986912

2minus 119867 = 0 (1)




120572 =

3119905119892120593

radic9 + 121199051198922120593

119867 =

3119888

radic9 + 121199051198922120593

(2)





1205901= 1205901

119894119895= D (120576

0+ Δ120576) (3)




120590 = 120590119894119895= D (120576

0+ Δ120576 minus Δ120576

119901) = 1205901minusDΔ120576119901 (4)


Δ120576119901= Δ120582

120597119891

120597120590

(5)


119891 (120590) = 0 120590 = 1205901minus Δ120582D 120597119891

120597120590

10038161003816100381610038161003816100381610038161003816120590=1205901

(6)


120590 = 120590119894119895= (1 minus 119899) 120590

1

119894119895+ 119901120575119894119895 (7)

where

119899 =

119908120583

radic1198692

119901 = minus119898119908 + 31198991198681

119898 = 120572 (3120582 + 2120583) 119908 =

119891

3120572119899 + 120583

(8)



120582 =

119864](1 + ]) (1 minus 2])

120583 =

119864

2 (1 + ]) (9)


Δ120590119901= 1205901minus 120590 = 119899120590

1

119894119895minus 119901120575119894119895 (10)








1015840









Bottom outlets

Middle outlets

Upper outlets









UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References






































Roof

Roof

Floor

Leftwall

Rightwall

06m

13m27m

14m14m

05m05m08m

08m07m

04m14m

14m15m16m

10m

06m

07m

07m

07m

07m12m13m

11m


200

700

400

200

700


05m 05m 13m13m

Flow direction


















monolith at EL 497m














21LF-1 12 03







21LF-2 17 03



22LF-1 11 03


22LF-222LF-3 1 02


22LF-4 1 03



23LF-1 17 05


23LF-2 175 05


















Bottom outlet


Flow direction




21

2322

20

131

1

2

3

3

6

4

4

45

5

6

6

7

7

8

8

9

911

128

11

1010 18

1927

1617

15

14

12


2008 year


39

37

38

35

33

36

34

2730

31 32

2928

24 25 26

1050m1050m

105824m105824m05 06 31

64 64

6464

1 06

085 17

46

07 05 060672499

265

499

265 499

499

11

12

0405 32

32 36171717

2

2

632 233



Cracks









119891 = 1205721198681+ 11986912

2minus 119867 = 0 (1)




120572 =

3119905119892120593

radic9 + 121199051198922120593

119867 =

3119888

radic9 + 121199051198922120593

(2)





1205901= 1205901

119894119895= D (120576

0+ Δ120576) (3)




120590 = 120590119894119895= D (120576

0+ Δ120576 minus Δ120576

119901) = 1205901minusDΔ120576119901 (4)


Δ120576119901= Δ120582

120597119891

120597120590

(5)


119891 (120590) = 0 120590 = 1205901minus Δ120582D 120597119891

120597120590

10038161003816100381610038161003816100381610038161003816120590=1205901

(6)


120590 = 120590119894119895= (1 minus 119899) 120590

1

119894119895+ 119901120575119894119895 (7)

where

119899 =

119908120583

radic1198692

119901 = minus119898119908 + 31198991198681

119898 = 120572 (3120582 + 2120583) 119908 =

119891

3120572119899 + 120583

(8)



120582 =

119864](1 + ]) (1 minus 2])

120583 =

119864

2 (1 + ]) (9)


Δ120590119901= 1205901minus 120590 = 119899120590

1

119894119895minus 119901120575119894119895 (10)








1015840









Bottom outlets

Middle outlets

Upper outlets









UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References










































21LF-1 12 03







21LF-2 17 03



22LF-1 11 03


22LF-222LF-3 1 02


22LF-4 1 03



23LF-1 17 05


23LF-2 175 05


















Bottom outlet


Flow direction




21

2322

20

131

1

2

3

3

6

4

4

45

5

6

6

7

7

8

8

9

911

128

11

1010 18

1927

1617

15

14

12


2008 year


39

37

38

35

33

36

34

2730

31 32

2928

24 25 26

1050m1050m

105824m105824m05 06 31

64 64

6464

1 06

085 17

46

07 05 060672499

265

499

265 499

499

11

12

0405 32

32 36171717

2

2

632 233



Cracks









119891 = 1205721198681+ 11986912

2minus 119867 = 0 (1)




120572 =

3119905119892120593

radic9 + 121199051198922120593

119867 =

3119888

radic9 + 121199051198922120593

(2)





1205901= 1205901

119894119895= D (120576

0+ Δ120576) (3)




120590 = 120590119894119895= D (120576

0+ Δ120576 minus Δ120576

119901) = 1205901minusDΔ120576119901 (4)


Δ120576119901= Δ120582

120597119891

120597120590

(5)


119891 (120590) = 0 120590 = 1205901minus Δ120582D 120597119891

120597120590

10038161003816100381610038161003816100381610038161003816120590=1205901

(6)


120590 = 120590119894119895= (1 minus 119899) 120590

1

119894119895+ 119901120575119894119895 (7)

where

119899 =

119908120583

radic1198692

119901 = minus119898119908 + 31198991198681

119898 = 120572 (3120582 + 2120583) 119908 =

119891

3120572119899 + 120583

(8)



120582 =

119864](1 + ]) (1 minus 2])

120583 =

119864

2 (1 + ]) (9)


Δ120590119901= 1205901minus 120590 = 119899120590

1

119894119895minus 119901120575119894119895 (10)








1015840









Bottom outlets

Middle outlets

Upper outlets









UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References



















































Bottom outlet


Flow direction




21

2322

20

131

1

2

3

3

6

4

4

45

5

6

6

7

7

8

8

9

911

128

11

1010 18

1927

1617

15

14

12


2008 year


39

37

38

35

33

36

34

2730

31 32

2928

24 25 26

1050m1050m

105824m105824m05 06 31

64 64

6464

1 06

085 17

46

07 05 060672499

265

499

265 499

499

11

12

0405 32

32 36171717

2

2

632 233



Cracks









119891 = 1205721198681+ 11986912

2minus 119867 = 0 (1)




120572 =

3119905119892120593

radic9 + 121199051198922120593

119867 =

3119888

radic9 + 121199051198922120593

(2)





1205901= 1205901

119894119895= D (120576

0+ Δ120576) (3)




120590 = 120590119894119895= D (120576

0+ Δ120576 minus Δ120576

119901) = 1205901minusDΔ120576119901 (4)


Δ120576119901= Δ120582

120597119891

120597120590

(5)


119891 (120590) = 0 120590 = 1205901minus Δ120582D 120597119891

120597120590

10038161003816100381610038161003816100381610038161003816120590=1205901

(6)


120590 = 120590119894119895= (1 minus 119899) 120590

1

119894119895+ 119901120575119894119895 (7)

where

119899 =

119908120583

radic1198692

119901 = minus119898119908 + 31198991198681

119898 = 120572 (3120582 + 2120583) 119908 =

119891

3120572119899 + 120583

(8)



120582 =

119864](1 + ]) (1 minus 2])

120583 =

119864

2 (1 + ]) (9)


Δ120590119901= 1205901minus 120590 = 119899120590

1

119894119895minus 119901120575119894119895 (10)








1015840









Bottom outlets

Middle outlets

Upper outlets









UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References









































119891 = 1205721198681+ 11986912

2minus 119867 = 0 (1)




120572 =

3119905119892120593

radic9 + 121199051198922120593

119867 =

3119888

radic9 + 121199051198922120593

(2)





1205901= 1205901

119894119895= D (120576

0+ Δ120576) (3)




120590 = 120590119894119895= D (120576

0+ Δ120576 minus Δ120576

119901) = 1205901minusDΔ120576119901 (4)


Δ120576119901= Δ120582

120597119891

120597120590

(5)


119891 (120590) = 0 120590 = 1205901minus Δ120582D 120597119891

120597120590

10038161003816100381610038161003816100381610038161003816120590=1205901

(6)


120590 = 120590119894119895= (1 minus 119899) 120590

1

119894119895+ 119901120575119894119895 (7)

where

119899 =

119908120583

radic1198692

119901 = minus119898119908 + 31198991198681

119898 = 120572 (3120582 + 2120583) 119908 =

119891

3120572119899 + 120583

(8)



120582 =

119864](1 + ]) (1 minus 2])

120583 =

119864

2 (1 + ]) (9)


Δ120590119901= 1205901minus 120590 = 119899120590

1

119894119895minus 119901120575119894119895 (10)








1015840









Bottom outlets

Middle outlets

Upper outlets









UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References








































1015840









Bottom outlets

Middle outlets

Upper outlets









UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References






































UU2+107e minus 01

+982e minus 02

+894e minus 02

+807e minus 02

+720e minus 02

+632e minus 02

+545e minus 02

+458e minus 02

+370e minus 02

+283e minus 02

+196e minus 02

+108e minus 02

+207e minus 03


UU2+109e minus 01

+999e minus 02

+914e minus 02

+828e minus 02

+742e minus 02

+656e minus 02

+571e minus 02

+485e minus 02

+399e minus 02

+314e minus 02

+228e minus 02

+142e minus 02

+563e minus 03



0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

750



Elev

atio

n (m

)

Displacement (mm)


0 200 400 600 800 1000 1200300

350

400

450

500

550

600

650

700

75



Elev

atio

n (m

)

Displacement (mm)

0








+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References







































+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07



+667e + 06

+586e + 06

+506e + 06

+426e + 06

+345e + 06

+265e + 06

+184e + 06

+104e + 06

+231e + 05

minus573e + 05

minus138e + 06

minus218e + 06

minus299e + 06



minus812e + 04

minus149e + 06

minus289e + 06

minus429e + 06

minus570e + 06

minus710e + 06

minus851e + 06

minus991e + 06

minus113e + 07

minus127e + 07

minus141e + 07

minus155e + 07

minus169e + 07


















(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References










































(c)















DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References






































DownstreamUpstream

Roof

Floor

SIG1 (MPa)

minus35

minus25

minus20

minus30

minus15

minus05

minus10

050

15

10

25

20


Upstream

Roofdownstream

Side wall

Floordownstream


Side wall

SIG1

(MPa

)

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

minus35

minus25

minus15

minus05

minus10

minus20

minus30

05

00

15

25

20

10

SIG1

(MPa

)








PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References






































PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00



PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+803e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00


PEMAG(Avg 75)

+955e minus 03

+100e minus 03

+917e minus 04

+833e minus 04

+750e minus 04

+667e minus 04

+583e minus 04

+500e minus 04

+417e minus 04

+333e minus 04

+250e minus 04

+167e minus 04

+833e minus 05

+000e + 00

























5 Conclusions










Acknowledgments


References

























































5 Conclusions










Acknowledgments


References











































Acknowledgments


References





































Effects of outlets on cracking risk and integral stability of super-high arch dams

Documents

Transcript of Effects of outlets on cracking risk and integral stability of super-high arch dams