Cracking Risk and Overall Stability Analysis of Xulong High Arch Dam: a Case Study

applied sciences

Article Cracking Risk and Overall Stability Analysis of Xulong High Arch Dam: A Case Study

Peng Lin 1,*, Pengcheng Wei 1, Weihao Wang 2 and Hongfei Huang 2

1 Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China; [email protected] 2 Changjiang Institute of Survey, Planning, Design and Research, Wuhan 430010, China; [email protected] (W.W.); [email protected] (H.H.) * Correspondence: [email protected]; Tel.: +86-139-1050-5719

Received: 31 October 2018; Accepted: 3 December 2018; Published: 10 December 2018

Featured Application: The cracking risk, the overall stability, and the reinforcement measures are directly related to the long-term stability of arch dams. The three safety factors and ﬁve stress zones have a great signiﬁcance for arch dam-foundation design of cracking control and overall stability evaluation.

Abstract: It is of great significance to study the cracking risk, the overall stability, and the reinforcement measures of arch dams for ensuring long-term safety. In this study, the cracking types and factors of arch dams are summarized. By employing a nonlinear constitutive model relating to the yielding region, a fine three-dimensional finite element simulation of the Xulong arch dam is conducted. The results show that the dam cracking risk is localized around the outlets, the dam heel, and the left abutment. Five dam stress zones are proposed to analysis dam cracking state base of numerical results. It is recommended to use a shearing-resistance wall in the fault f57, replace the biotite enrichment zone with concrete and perform consolidation grouting or anchoring on the excavated exposed weak structural zone. Three safety factors of the Xulong arch dam are obtained, K_1 = 2~2.5; K_2 = 5; K_3 = 8.5, and the overall stability of the Xulong arch dam is guaranteed. This study demonstrates the significance of the cracking control of similar high arch dams.

Keywords: the Xulong arch dam; yielding region; cracking risk; overall stability; dam stress zones

1. Introduction A series of super-high arch dams (height over 200 m) have been constructed or are being planned in China. Most of them are distributed in the mountainous areas in southwest China (Figure1), and therefore are subject to complex engineering challenges, such as high seismic intensity, high slope, huge water thrust, and so forth. The geological conditions are also very complex, for example, the deep-cutting valley, high ground stress, and some unfavorable geological conditions, such as atypical faults, dislocation interfaces, altered rock masses, and weak rock masses [1–3]. The complex geological conditions may lead to the crack of dam concrete or foundation, which eventually leads to dam failure [4]. Therefore, the construction of super-high arch dams still faces many challenges. Cracks may initiate in the outlets [5], heel [6], surface, and interior of dam concrete blocks [2], then propagate and coalescence along horizontal or vertical directions in concrete blocks. The main cracking factors include temperature variations, heat from concrete hydration, shrinkage and creep, dam foundation uncoordinated deformation, earthquake, and seepage effect [4]. Some research studies have been done related to the cracking mechanism on concrete blocks of dams experimentally and theoretically. Study on thermal mechanics of the concrete dam includes

Appl. Sci. 2018, 8, 2555; doi:10.3390/app8122555 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 2555 2 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 2 of 18 thetemperature temperature variation variation of of the the external external environment environment and and heat heat from from concrete concrete hydration. When When the the temperaturetemperature gradient changes changes dramatically dramatically inside inside the the dam, dam, the the thermal thermal stresses stresses will will concentrate concentrate and andcause cause the cracks the cracks to initiate to initiate under under cold coldwave wave conditions conditions [7], in [7 cold], in coldareas areas [8], under [8], under unfavorable unfavorable solar solarradiation radiation [9], and [9], in and dry, in hot dry, valley hot valley regions regions [10]. Temperature [10]. Temperature load is load the ismain the maincracking cracking factor factorof the ofKaraj the arch Karaj dam arch [11]. dam The [11 nonlinear]. The nonlinear analysis of analysis concrete of arch concrete dams archis necessary dams is to necessary check the to stability check theof cracks stability in high of cracks tensile in stress high tensileareas. Maken stress areas.et al. [12] Maken investigated et al. [12 ]the investigated mechanical the properties mechanical and propertiesshowed that and stress showed relaxation that stress is affected relaxation by the is affected concrete by temperature. the concrete They temperature. used a finite-element They used a ﬁnite-elementmodeling procedure modeling for procedure assessing for the assessing thermal the mechanical thermal mechanical behaviors behaviors of concrete of concrete dams, dams, and andsuccessfully successfully reproduced reproduced thethe oblique oblique cracks cracks present present on on the the downstream downstream face face of of Daniel Daniel Johnson Johnson dam. TheThe distributiondistribution ofof stressesstresses inin roller-compactedroller-compacted concreteconcrete damsdams isis greatlygreatly affectedaffected byby thethe startingstarting datedate ofof thethe roller-compactedroller-compacted concreteconcrete placementplacement scheduleschedule [[13].13]. Self-weightSelf-weight and weakweak foundation [[14,15],14,15], unevenuneven settlementsettlement ofof archarch damdam foundation,foundation, andand earthquakeearthquake [[16,17]16,17] cancan alsoalso leadlead toto thethe crackingcracking ofof archarch dams.dams. Hariri-ArdebiliHariri-Ardebili etet al.al. [[18]18] assessedassessed seismicseismic crackscracks inin threethree typestypes ofof concreteconcrete dams,dams, namelynamely gravity,gravity, buttress,buttress, and and arch,arch, usingusing anan improvedimproved 3D3D coaxialcoaxial rotatingrotating smearedsmeared crackcrack model.model. TheThe crackingcracking factorsfactors ofof archarch damsdams oftenoften interactinteract withwith eacheach otherother inin aa nonlinearnonlinear manner,manner, andand thereforetherefore cannotcannot bebe consideredconsidered separately.separately.

Northeast 1.79% North China northwest 1.82% 12.45% Beijing

Laxiwa 250.0m

Southwest 70.01% Yebatan Yangtze 217.0m River Xulong Daduhe River Daduhe 213.0m Minjiang River Eastern Dagangshan 210.0m China Jin ping I 4.44% 305.0m South Ertan Central China 9.48% 240.0m Xiaowan 294.5m

Wudongde 270.0m  Baihetan Xiluodu Goupitan The arch dams written in red are under construction; 289.0m 285.5m 232.5m  The arch dams written in black have been completed;  Xulong arch dam is planned to be built.

FigureFigure 1.1. Distribution of hydropower resourcesresources andand super-highsuper-high archarch damsdams inin China.China. The concrete dam cracking problems have been studied by different methods in the past 30 years The concrete dam cracking problems have been studied by different methods in the past 30 years as follows. (1) The finite element method (FEM) is widely used in the numerical simulation of as follows. (1) The finite element method (FEM) is widely used in the numerical simulation of dam dam cracking, including the FEM based on elastoplastic mechanics, the FEM based on fracture cracking, including the FEM based on elastoplastic mechanics, the FEM based on fracture mechanics mechanics [19,20], and the FEM based on damage mechanics [21,22]. Based on linear elastic crack [19,20], and the FEM based on damage mechanics [21,22]. Based on linear elastic crack mechanics and mechanics and three-dimensional boundary element modeling, Feng et al. [23] presented a procedure three-dimensional boundary element modeling, Feng et al. [23] presented a procedure to analyze the to analyze the cracks in arch dams. Chen et al. [24] introduced the existing constitutive model of cracks in arch dams. Chen et al. [24] introduced the existing constitutive model of large, light, large, light, reinforced concrete structures and the deficiency of the design procedure, and they also reinforced concrete structures and the deficiency of the design procedure, and they also presented a presented a three-dimensional nonlinear cracking response simulation procedure for outlet structures. three-dimensional nonlinear cracking response simulation procedure for outlet structures. The The overall stability of arch dams is analyzed by the three-dimensional numerical simulation [25]. overall stability of arch dams is analyzed by the three-dimensional numerical simulation [25]. Sato et Sato et al. [26] simulated the thermal stress of a concrete dam by three-dimensional linear elastic al. [26] simulated the thermal stress of a concrete dam by three-dimensional linear elastic FEM, and FEM, and the autogenous shrinkage strain was added to the thermal strain. (2) Dam geomechanical the autogenous shrinkage strain was added to the thermal strain. (2) Dam geomechanical model tests model tests were widely carried out in the United States, Switzerland, Yugoslavia, Russia, Germany, were widely carried out in the United States, Switzerland, Yugoslavia, Russia, Germany, Italy, Japan, Italy, Japan, and Sweden in the 1970s and 1980s [27]. The geomechanical model mainly refers to the and Sweden in the 1970s and 1980s [Error! Reference source not found.]. The geomechanical model model that reflects the specific engineering geological structure in a small range, such as the faults, mainly refers to the model that reflects the specific engineering geological structure in a small range, such as the faults, fractures, and weak zones in the dam foundation, and it follows the similarity theory [28]. Lin et al. [2] analyzed the cracking characteristics of the Xiaowan arch dam surfaces and Appl. Sci. 2018, 8, 2555 3 of 18

Appl.fractures, Sci. 2018 and, 8, x weak FOR PEER zones REVIEW in the dam foundation, and it follows the similarity theory [28]. Lin et 3al. of [ 182] analyzed the cracking characteristics of the Xiaowan arch dam surfaces and rock mass failure process rockof the mass abutments. failure process They of judged the abutments. the alteration They zones,judged weakthe alteration rock masses, zones, andweak other rock faultsmasses, in and the otherabutments faults that in causedthe abutments the arch thatdam causedto crack the and arch proposed dam the to crack method and of proposedfoundation the reinforcement. method of foundation(3) Many scholars reinforcement. also focus (3) onMany different scholars numerical also focus methods on different to simulate numerical dam methods cracking to processes, simulate damfor example, cracking processes, element-free for methodexample, [ 29element-free], interface method stress element[29], interface method, stress and element boundary method, element and boundarymethod [30 element]. Prototype method monitoring [30]. Prototype is also monitoringwidely used is in also arch widely dam cracking used in analysis.arch dam However, cracking analysis.there are However, still many there areas are for still improvement many areas in for the improvement analysis of cracking in the analysis of arch dams.of cracking Linear of finitearch dams.element Linear is not finite capable element of revealing is not capable the actual of revealing state of the the structure. actual state As of a popularthe structure. simulation As a popular method, simulationthe nonlinear method, numerical the nonlinear method has numerical no uniform method standard has no for uniform the selection standard of material for the constitutiveselection of materialmodels and constitutive parameters models and the and setting parameters of boundary and the conditions. setting of Although boundary the conditions. geomechanical Although model the of geomechanicalrupture test is straightforward, model of rupture the test loading is straightforward, control, boundary the condition loading simulation,control, boundary and error condition analysis simulation,of measurement and error data needanalysis to be of further measurement investigated. data need The cracking to be further theory investigated. of arch dams The has cracking not been theoryfully studied, of arch especiallydams has not for thebeen location fully studied, and propagation especially offor cracks. the location and propagation of cracks. ThisThis study study first first summarizes summarizes the the main main analysis analysis methods, methods, cracking cracking types, types, and and factors factors of of arch arch dams dams accordingaccording to thethe crackingcracking cases. cases. In In order order to to analyze analyze the the cracking cracking and and overall overall stability stability of the of Xulongthe Xulong high higharch dam, arch adam, nonlinear a nonlinear constitutive constitutive model and model overall and stability overall criterionstability arecriterion employed, are employed, and numerical and numericalsimulation simulation on the overall on stability,the overall cracking stability, analysis cracking of dam analysis outlets, of anddam arch outlets, abutments and arch are abutments performed. areThis performed. study aims atThis proposing study aims effective at proposing reinforcement effective methods reinforcement and prevention methods methods and for prevention arch dam methodscracking. for Through arch dam the cracking. analysis ofThrough the yielding the analysis region andof the stress yielding before region and after and thestress reinforcement, before and afterthe reinforcement the reinforcement, methods the ofreinforcement the Xulong arch methods dam areof the determined. Xulong arch Based dam on are the determined. analysis of the Based first onand the third analysis principal of the stresses first and and third yielding principal region stresses of the archand yielding dam, a method region of for the crack arch prevention dam, a method based foron fivecrack stress prevention zonesof based arch on dams five is stress proposed. zones of arch dams is proposed.

2.2. Summary Summary of of Cracking Cracking Types Types and Effect Factors of High Arch Dams

2.1.2.1. Cracking Cracking Types Types ConcreteConcrete arch arch dams dams are are generally constructed of of massive plain plain concrete concrete with with almost no no tensile resistance.resistance. Tensile Tensile stress stress can can occur occur due due to to concrete concrete shrinkage, temperature temperature variations, rigidity rigidity weakening due due to to seepage effects, and other factors like earthquake and and large large deformation of of the damdam abutments abutments due due to to a a weak foundation. The The tensile tensile stress stress often often leads leads to to cracking cracking of of arch arch dams, dams, which affects the safety and stable operation of arch dams. TableTable 11 summarizessummarizes thethe completedcompleted time,time, damdam height,height, crackingcracking position,position, andand crackingcracking reasonreason ofof thethe main main arch dams inin thethe world.world. TheThe crackcrack typestypes of of arch arch dams dams are are illustrated illustrated in in Figure Figure2 according 2 according to tothe the common common cracking cracking positions positions of of arch arch dams. dams.

Upstream Downstream Downstream

Cracking zone Cracking zone

(a) (b) (c)

Upstream

Downstream Cracking zone Cracking zone

(d) (e) (f)

FigureFigure 2. 2. CrackingCracking type type of of arch arch dam: dam: ( (aa)) dam dam heel heel crack; crack; ( (bb)) dam dam toe toe crack; crack; ( (cc)) transverse transverse joint joint open; open; ((d)) horizontal horizontal cracks cracks at at the the upstream upstream surface; surface; ( (ee)) cracks cracks at at the the downstream downstream surface; surface; ( (ff)) internal internal cracks. cracks.

Table 1. Summary of cracking types in high arch dams.

Dam Name Country Operation Year Height (m) Cracking Description Main Cracking Causes Appl. Sci. 2018, 8, 2555 4 of 18

Table 1. Summary of cracking types in high arch dams.

Dam Name Country Operation Year Height (m) Cracking Description Main Cracking Causes Vertical cracks at Temperature (extreme Buffalo Bill Arch Dam America 1910 107.0 downstream surface thermal gradients) Packard Sama Dam America 1928 113.0 Different settlement Earthquake Visible surface, mainly Alkali–silica reactions Stewart Mountain Dam [31] America 1930 64.6 upstream surface and expansions Transverse joints open at upstream Zeuzier Dam Switzerland 1956 156.0 Foundation Peripheral joints form downstream Horizontal cracks at Sardine Dam Italy 1957 115.0 Temperature upstream surface Leakage in dam Santa Maria Dam Switzerland 1968 117.0 Foundation foundation upstream Oblique cracks at Seasonal temperature Daniel Johnson Dam [12] Canada 1968 214.0 downstream surface Plunging cracks at the Geometric heel of the dam discontinuities Horizontal construction Kolnbrein Dam [6,14] Austria 1977 200.0 joints open Cracking at Foundation dam heel Horizontal cracks at Zillergrundl Dam [14] Austria 1985 186 heelVertical cracks in the Concrete hydration heat elevator shaft Vertical cracks in the Sayano-Shushenskaya Former Soviet Concrete hydration heat 1989 242.0 gallery Horizontal cracks Dam [14] Union and temperature at upstream surface Seven vertical cracks at Self-weight and weak Shuanghe Arch Dam [15] China 1991 82.3 downstream surface foundation Cracking at downstream Ertan Dam China 2000 240.0 Foundation Temperature surface Xiaowan Dam [2] China 2010 294.5 Internal cracking Temperature Cracking around the Concrete hydration heat Goupitan Dam China 2011 232.5 bottom outlets and temperature

2.2. Cracking Factors Many factors lead to the cracking of super-high arch dams, including different concrete materials, concrete temperature control measures, geological condition of dam foundation, seepage, geological exploration, arch dam proﬁle, and so forth. The cracking factors of arch dams are summarized as follows.

(1) Concrete materials. Different concrete materials have different properties such as hydration heat and tensile strength. High-strength concrete generally has a large content of cement, leading to high hydration heat. When the external temperature changes sharply or the temperature control measures are not appropriate, high-strength concrete can easily crack. Concrete materials should be selected according to different dam structures and high-strength concrete should not be used blindly. (2) Site selection of the arch dam. The complex geological conditions of the dam foundation directly affect the stress and deformation distribution of the arch dam. The uneven deformation of both abutments and different stiffness between arch dam and foundation can easily lead to arch dam cracking. Appropriate reinforcement methods are important for reducing the cracking risk of arch dams. (3) Temperature control and maintenance. Concrete temperature control measures are directly related to concrete thermal stress. The sharp increase or decrease of the external temperature has more inﬂuence on the dam abutment, heel, and outlets. The temperature control methods should be designed and implemented before the arch dam is built. For the special structures such as outlets, it is necessary to consider the cracking caused by the cavern drafts ﬂowing and the outlets should be closed. Appl. Sci. 2018, 8, 2555 5 of 18

(4) Dam profile design. Profile design needs to consider specific geological conditions. Arch dam profile is directly related to the stress distribution of the dam body. Outlets and dam heel should Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 18 be considered especially. The effects of different profiles on the stress, deformation, overall stability,be considered and cracking especially. of the The arch effects dam can of different be comprehensively profiles on the compared stress, deformation, by using the overall method of dividingstability, load and of cracking the arch of beam, the arch FEM, dam and can geomechanicalbe comprehensively model. compared by using the method of dividing load of the arch beam, FEM, and geomechanical model. 3. Numerical Modeling of the Xulong High Arch Dam 3. Numerical Modeling of the Xulong High Arch Dam 3.1. Numerical Method 3.1. Numerical Method Using a 3D nonlinear finite element analysis, the convergence of elastoplastic analysis solution shows theUsing stability a 3D ofnonlinear the structure. finite element The yieldinganalysis, the condition convergence of the of idealelastoplastic elastoplastic analysis model solution adopts Drucker–Pragershows the stability (D-P) yieldingof the structure. criterion The [5 yielding]. condition of the ideal elastoplastic model adopts Drucker–Prager (D-P) yielding criterion [5]. (1) Safety factors of the arch dam (1) Safety factors of the arch dam BothBoth in the in geomechanical the geomechanical model model experiment experiment and 3D and nonlinear 3D nonlinear numerical numerical simulation, simulation, overloading, strengthoverloading, reduction, strength and comprehensive reduction, and methodcomprehensive are main method methods are main to analyze methods the to ultimate analyze state the and safetyultimate factors state of archand safety dams factors [2,32 ],of asarch illustrated dams[2,32], in as Figure illustrated3. According in Figure 3. toAccording different to overloadingdifferent ways,overloading overloading ways, method overloading includes method increasing includes the increasing bulk density the bulk of the density upstream of the waterupstream and water upstream waterand level upstream (Figure water3a,b). level The (Figures comprehensive 3a,b). The comprehensive method combines method combines the overloading the overloading and strengthand reductionstrength method. reduction method.

(a) (b)

(c)

FigureFigure 3. Overloading 3. Overloading and and strength strength reduction reduction method. (a (a) )Increasing Increasing the the bulk bulk density density of the of upstream the upstream water;water; (b) increasing (b) increasing the the upstream upstream water water level; level; ((cc)) strength reduction reduction method. method. Appl. Sci. 2018, 8, 2555 6 of 18

The arch dam is a high-order statically indeterminate structure. In the process of overloading or strength reduction, the deformation of arch dams can be divided into three stages, namely the elastic deformation stage, plastic deformation stage, and total failure stage. Corresponding to three deformation stages, three safety factors, K1, K2, K3, are employed to evaluate the overall stability of the dam [2]. K1 represents the safety factor of crack initiation of the arch dam. A crack is generally initiated at the dam heel. As shown in Figure3a, K = γ1 ; in Figure3b, K = h1 . 1 γ0 1 h0 K2 represents the safety factor of structural nonlinear behavior initiation. The dam has a large displacement due to nonlinear deformation. Dam cracks rapidly propagate and coalesce with each other. As shown in Figure3a, K = γ2 ; in Figure3b, K = h2 . 2 γ0 2 h0 K3 represents the safety factor of the maximum loading of the dam–foundation system. The yielding regions connect. The dam foundation is totally destroyed and the undertaking capacity is lost. As shown in Figure3a, K = γ3 ; in Figure3b, K = h3 . 3 γ0 3 h0 (2) Evaluation of connection of yielding region Adopting to increase the bulk density of the upstream water (Figure3a), the yielding region of dam and foundation is simulated under overloading condition. The connection of the yielding region means that it connects piece by piece and forms movement mechanism so that the integrity stiffness of arch dam–foundation is weakened. The cracking or yielding caused by excessive local stress reduces the constraint to adjust the internal stress. If the yielding region is not fully connected, the structure can still provide support. This method can fully reﬂect the adjustment process of nonlinear stresses and exert the bearing capacity of the high-order statically indeterminate arch dam. Failure criterion can be deﬁned as Equation (1), that is, iteration does not converge.

∅(Ai) ≥ 0. (1) where ∅ is yielding surface. Ai is a mechanism composed of local yielding regions, that is, formed by the connection of the local yielding regions. Ai can be expressed as: Ai = ϕj ∪ ϕm ∪ ... ∪ ϕn. When any Ai is formed, the structure loses its integral stability. In addition, det[K] ≤ 0, where [K] is the integral stiffness matrix in FEM analysis.

3.2. Brief Introduction of Xulong Super-High Arch Dam The Xulong hydropower station is located on the main stream of Jinsha River, juncture of the Deqin county, Yunnan Province and Derong county, Sichuan Province. The total storage capacity of it is 829 million m3, and it has an installed capacity of 2220 MW. The principal structures consist of a double-curvature arch dam with a height of 213 m, underground powerhouse, diversion tunnel, and plunge pool. There are 3 upper outlets and 4 middle outlets placed in the numbers 9~12 dam monoliths. The entrances of the upper outlets are at elevation level (EL) 2286 m. The size of the middle outlets is 8 m × 6 m (height × width) at the entrances and 5 m × 7.2 m (height × width) at the exit. The entrances of the middle outlets are at EL 2222 m. The ratio of thickness and height of the arch dam is 0.217 and the length of the crest on the upper surface is 482.9 m. The dam site is deep canyon topography with an aspect ratio of 1.8. The Triassic Indosinian granite dike at the dam site slopes into the riverbed. The left bank is Mesoproterozoic Xiongsong Group plagioclase amphibole schist and the right bank is Mesoproterozoic Xiongsong Group migmatite. According to the double-hole acoustic testing results, the fresh granite, migmatite, and plagioclase amphibole schist have longitudinal wave velocities of 4300~5900 m/s, 4000~5600 m/s, and 3000~5800 m/s, respectively. The average longitudinal wave velocities of the fresh granite, migmatite, and plagioclase amphibole schist are 5100 m/s, 5000 m/s, and 4600 m/s, respectively, which can mainly be classiﬁed as the type II rock mass. The type II rock masses have an acoustic velocity of 4800~5500 m/s, weak permeability, and good uniformity. The width of strongly unloading zones due to the dam construction is generally less than 30 m. The strongly unloading rocks are only at the EL Appl. Sci. 2018, 8, 2555 7 of 18

Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18 2300 and 2308 m, which can be classiﬁed as the type IV rock mass. The width of weakly unloading zoneszonesAppl. is is between betweenSci. 2018, 8 , 15x FOR andm PEERand 35 REVIEW m35 withm with the the type type III1 III1 rock rock masses masses and III2and rockIII2 rock masses. masses. A total A oftotal 7 of 70 18 faultsof 70 faultsare found are found on the on surface the surface of the of dam the site,damof site, which of which the statistics the statistics are shown are shown in Figure in Figure4. Ten 4. of Ten them of zones is between 15 m and 35 m with the type III1 rock masses and III2 rock masses. A total of 70 themare low-angle are low-angle faults. faults. The widthThe width of the of faults the faults is 0.20~0.50 is 0.20 m~0.50 m, and m, the and length the oflength thefaults of the is faults usually is faults are found on the surface of the dam site, of which the statistics are shown in Figure 4. Ten of usually less than 100 m. The fault strikes can be divided into 4 groups: NE~NEE group, NWW group, less thanthem 100are m.low-angle The fault faults. strikes The canwidth be of divided the faults into is 40.20 groups: m~0.50 NE~NEE m, and the group, length NWW of the group,faults is NNE NNEgroup, usuallygroup, and NNW~NWless and than NNW~NW 100 group.m. The group. fault F1, f3,strikes F1, f10, f3, can f11, f10, be f26, dividedf11, f57, f26, f74, into f57, and 4 groups:f74, f75 and are NE~NEE relativelyf75 are group, relatively large NWW faults. large group, Figure faults. 5 FigureillustratesNNE 5 illustrates group, the bedrock and the NNW~NW bedrock distribution distribution group. of theF1, dam–foundationf3, of f10, the f11, dam–foundation f26, f57, interface. f74, and interface. f75 are relatively large faults. Figure 5 illustrates the bedrock distribution of the dam–foundation interface.

(a) (a) ( (bb)) (c) (c)

FigureFigureFigure 4. 4. SurfaceSurface 4. Surface fault fault fault statistics statistics statistics in in indam dam dam site site site area. area. area. ((aa)) Rose (a) Rose ofof thethe ofstrike; strike; the ( strike;b ()b rose) rose (ofb )dip;of rose dip; (c) of dip(c dip;) dipangle (anglec ) dip histogram.anglehistogram. histogram.

Right arch abutment Left arch abutment Right arch abutment Left arch abutment

FigureFigure 5. 5.Bedrock Bedrock distributiondistribution of of the the foundation foundation surface. surface. 3.3. Numerical3.3. Numerical Model Model and andFigure Analysis Analysis 5. Bedrock Cases Cases distribution of the foundation surface. FigureFigure6 illustrates 6 illustrates the the 3D 3D numerical numerical model model of ofthe the Xulong Xulong high higharch dam arch and dam foundation, and foundation, and 3.3. Numerical Model and Analysis Cases and thethe distribution of of main main faults faults including including F1, f3, F1, f10, f3, f11, f10, f26, f11, f57, f26, f74, f57, and f74, f75. and In this f75. 3D In model, this 3D the model, the simulationFiguresimulation 6 illustrates range range is is 840 the 840 m 3D m× 800 ×numerical 800m × 553 m × m model553 (length m of (length× thewidth Xulong × height).width high The× archheight). numerical dam Theand model numericalfoundation, adopts 8- model and theadopts distributionnode 8-node hexahedral hexahedralof main elements, faults elements, with including the withtotal F1, number the f3, total f10, of numberf11,129,241 f26, elements f57, of 129,241 f74, andand elements 147,331 f75. In nodes. this and 3D 147,331There model, are nodes. the 34,284 elements and 41,204 nodes for the dam. simulationThere are 34,284 range elementsis 840 m × and 800 41,204 m × 553 nodes m (length for the × dam. width × height). The numerical model adopts 8- Based on laboratory testing, the main physical–mechanical parameters of the rock masses and node hexahedral elements, with the total number of 129,241 elements and 147,331 nodes. There are damBased concrete on laboratory are listed testing,in Table the2. Considering main physical–mechanical the influence of temperature parameters and ofcomplex the rock geological masses and 34,284 elements and 41,204 nodes for the dam. damconditions concrete are on the listed cracking in Table of arch2. Considering dams, this study the inﬂuenceuses the overloading of temperature method and to judge complex the overall geological conditionsBasedstability on of laboratorythe the crackingarch dam testing, ofand arch foundation. the dams, main this Temperature physical–mechanical study uses load, the self-weights overloading parameters of methodthe damof the and to rock judge foundation, masses the overall and damstability concretewater of pressure, the are arch listed and dam insilt and Table pressure foundation. 2. Considering are considered Temperature the in influencethe ten load, analysis self-weightsof temperature cases as follows. of theand dam complex and foundation,geological conditionswater pressure,In on order the and cracking to silt compare pressure of arch the are dams, effect considered ofthis temperature study in theuses ten risethe analysis overloading and drop cases loading method as follows. on to the judge stress the and overall stabilitydisplacementIn orderof the to arch compare of dam the arch and the dam effectfoundation. during of temperature the Temperature construction rise and load, period drop self-weights after loading arch onclosure, of the the stress damtemperature andand displacement foundation, drop waterof theloading pressure, arch dam is applied and during silt in thepressure cases construction 1 and are 10, considered and period the other after in the loads arch ten closure,in analysis cases 1 temperature and cases 10 asare follows. the drop same. loading In order is appliedto in casesInobtain order 1 andthe three to 10, compare andsafety the factors other the to effect loads evaluate of in temperature casesthe dam 1 andoverall 10 rise stability, are and the cases same. drop 1–9 loading In correspond order on to obtain theto 1-9 stress times the three and of overloading, respectively, and the other loads in cases 1 and 9 are the same. displacementsafety factors of to the evaluate arch dam the dam during overall the stability,construction cases period 1–9 correspond after arch toclosure, 1–9 times temperature of overloading, drop The influence of temperature loading on cracking of the arch dam during operation period is loading is applied in cases 1 and 10, and the other loads in cases 1 and 10 are the same. In order to respectively,analyzed. and Under the other the long-term loads in external cases 1 and temperature 9 are the variation, same. the temperature loading can be obtain the three safety factors to evaluate the dam overall stability, cases 1–9 correspond to 1-9 times of overloading, respectively, and the other loads in cases 1 and 9 are the same. The influence of temperature loading on cracking of the arch dam during operation period is analyzed. Under the long-term external temperature variation, the temperature loading can be Appl. Sci. 2018, 8, 2555 8 of 18

The inﬂuence of temperature loading on cracking of the arch dam during operation period is Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 18 analyzed. Under the long-term external temperature variation, the temperature loading can be divided into meandivided and into linear mean temperatureand linear temperature difference. difference. The mean The mean and linearand linear temperature temperature difference difference under normalunder water normal level water is illustrated level is illustrated in Table in3. Table 3.

(a) (b)

FigureFigure 6. The 6. The 3D 3D numerical numerical model. model. ( a(a)) dam-foundation dam-foundation overall overall model; model; (b) ( mainb) main faults faults distribution. distribution.

TableTable 2. Physical–mechanical 2. Physical–mechanical parameters parameters of of the the rock rock masses masses and and dam dam materials. materials.

Shear ShearStrength Strength 3 3 Materials BulkBulk Density Density (t/m (t/m) )Deformation Deformation Modulus Modulus (GPa) (GPa) Poisson’s Ratio Materials Poisson’s Ratio 푪 0 푭 0 (MPa)C (MPa) F Dam concrete 2.40 25.0 0.167 5.0 1.7 Dam concrete 2.40 25.0 0.167 5.0 1.7 Rock of type Ⅱ 2.70 24.0 0.22 1.2 1.1 Rock of type II 2.70 24.0 0.22 1.2 1.1 Ⅲ Rock ofRock type of III1 type 1 2.602.60 17.517.5 0.24 0.24 1.05 1.051.0 1.0 Rock ofRock type of III2 type Ⅲ2 2.552.55 12.512.5 0.26 0.26 1.0 1.00.95 0.95 Rock ofRock type of IV type Ⅳ 2.502.50 6.06.0 0.30 0.30 0.65 0.650.60 0.60

Table 3. The mean and linear temperature difference under normal water level. Table 3. The mean and linear temperature difference under normal water level. Normal Water Level + Temperature Rise Normal Water Level + Temperature Drop NormalMean Temperature Water Level + TemperatureLinear Temperature Rise Mean Normal Temperature Water LevelLinear + Temperature Temperature Drop EL(m) Mean TemperatureDifference LinearDifference Temperature MeanDifference Temperature DifferenceLinear Temperature EL (m) 2308 Difference9.40 Difference0.00 Difference2.65 0.00Difference 23082302 9.407.67 0.003.09 3.22 2.65 −0.49 0.00 23022290 7.674.75 3.098.65 2.06 3.22 2.06 −0.49 22902270 4.752.42 8.6512.54 0.68 2.06 5.67 2.06 22702245 2.422.24 12.5414.18 0.92 0.68 7.99 5.67 22452220 2.242.79 14.1814.66 1.67 0.92 8.98 7.99 22202195 2.793.60 14.6614.85 2.62 1.67 9.29 8.98 2195 3.60 14.85 2.62 9.29 2170 3.58 14.72 2.65 9.45 2170 3.58 14.72 2.65 9.45 2145 1.43 9.96 0.83 6.53 2145 1.43 9.96 0.83 6.53 2120 2120 −0.97−0.97 4.744.74 −1.35−1.35 2.60 2.60 2095 2095 −1.88−1.88 2.662.66 −2.12−2.12 1.32 1.32

4. Cracking Analysis of the Xulong High Arch Dam 4. Cracking Analysis of the Xulong High Arch Dam 4.1. Effect of Temperature Load on Stress and Displacement of the Xulong Arch Dam 4.1. Effect of Temperature Load on Stress and Displacement of the Xulong Arch Dam For the analysis cases 1 and 10, the displacement and stress distribution of the dam (Figure 7), Forcharacteristic the analysis stresses cases (Table 1 and 4), 10,and the maximum displacement displacement and stress along distribution river direction of at the different dam (Figure key 7), characteristic stresses (Table4), and maximum displacement along river direction at different key Appl. Sci. 2018, 8, 2555 9 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 18 locations (Table(Table5 )5) are are obtained. obtained. The The maximum maximum displacement displacement along along river river direction direction is 32.9 is 32.9 mm mm near near the ELthe 2189–2226EL 2189–2226 m (case m (case 1) and 1) and 20.2 20.2 mm mm atthe at the dam dam crest crest (case (case 10). 10). The The dam dam tensile tensile stress stress of of case case 1 is1 slightlyis slightly greater greater than than that that of case of case 10. The10. The maximum maximum tensile tensile stress stress near thenear left the arch left abutment arch abutment is bigger is thanbigger that than of thethat right of the arch right abutment. arch abutment. This is relatedThis is torelated different to different geological geological conditions conditions on the left on andthe rightleft and bank right of thebank arch of the dam. arch dam. The sudden drop in temperature has a greater impact on the tensile stress and the displacement of the arch dam, which increases the possibility of dam cracking. This is why the temperature drop loads are applied toto thethe arch dam in cases 1 to 9. The insulation work of the arch dam should be done in February andand March, especiallyespecially atat thethe crestcrest andand outletsoutlets ofof thethe dam.dam.

(a) (b)

Figure 7. The firstfirst principal stress and the displacementdisplacement along the river direction distribution under analysis cases cases 1 1 & & 10. 10. (a) ( aThe) The first first principal principal stress stress distribution distribution under under analysis analysis case 1(Unit: case 1 Pa); (Unit: (b) Pa);the (displacementb) the displacement along the along river the distribution river distribution under underanalysis analysis case 1(Unit: case 1 mm); (Unit: ( mm);c) the (firstc) the principal first principal stress stressdistribution distribution under underanalysis analysis case 10(Unit: case 10 Pa); (Unit: (d) Pa); the (displacementd) the displacement along the along river the distribution river distribution under underanalysis analysis case 10(Unit: case 10 mm). (Unit: mm).

Table 4. Characteristic stresses at different key locations under analysis cases 1 & 10 (unit: MPa). Table 4. Characteristic stresses at different key locations under analysis cases 1 & 10 (unit: MPa). Location Content Case 1 Case 2 Location Content Case 1 Case 2 Maximum tensile tensile stress stress of dam of dam heel heel 0.90.9 0.890.89 Upstream surface Maximum tensile stress near left arch abutment 1.18 1.17 Upstream surface Maximum tensile tensile stress stress near near right left arch arch abutment abutment 0.971.18 0.941.17 Maximum tensile stress near right arch abutment 0.97 0.94 Maximum compression stress of dam toe 6.93 7.35 Downstream surface MaximumMaximum compression compression stress near stress left arch of dam abutment toe 8.766.93 8.887.35 Downstream surface MaximumMaximum compression compression stress stress near near right left arch arch abutment abutment 8.538.76 8.498.88 Maximum compression stress near right arch abutment 8.53 8.49 Table 5. Maximum displacement along river direction at different key locations under analysis cases 1 &Table 10. 5. Maximum displacement along river direction at different key locations under analysis cases 1 & 10. Case 1 Case 10 Left Arch Case 1 Right Arch Left Arch Case 10 Right Arch Arch Crown Arch Crown LeftAbutment Arch Abutment AbutmentLeft Arch AbutmentRight Arch Arch Crown Right Arch Abutment Arch Crown Maximum (mm)Abutment 6.55 32.9 5.04Abutment 8.29 20.2Abutment 5.98 MaximumEL (m) (mm) 6.55 2167.3 32.9 23085.04 2153 2167.38.29 226320.2 21535.98 EL (m) 2167.3 2308 2153 2167.3 2263 2153 Appl. Sci. 2018, 8, 2555 10 of 18

Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 18 4.2. Cracking Analysis of Dam Outlets 4.2. Cracking Analysis of Dam Outlets The outlets affect the stress continuity of the dam. The large tensile stress near the upstream The outlets affect the stress continuity of the dam. The large tensile stress near the upstream surfacesurface may may be be the the main main cause cause ofof thethe outletsoutlets cracking. The The maximum maximum tensile tensile stress stress of of the the upper upper and and middlemiddle outlets outlets is is about about 0.90.9 andand 0.480.48 MPa,MPa, respectively (Figures (Figure 88a,e).a,e). Therefore, the the upper upper outlets outlets shouldshould have have a a larger larger cracking cracking riskrisk thanthan thethe middle outlets. In In particular, particular, the the tensile tensile stress stress of ofthe the left left andand right right upper upper outlets outlets are are relatively relatively largelarge duedue to the pier. pier. Figure Figure 8c,d8c,d illustrates illustrates the the possible possible cracking cracking positionspositions of of the the outlets. outlets.

(a) (b)

(e) (f)

FigureFigure 8. 8.The The first first and and third third principalprincipal stressstress distributiondistribution and and possible possible cracking cracking positions positions of ofoutlets outlets underunder analysis analysis case case (Unit: (Unit: Pa).Pa). ((aa)) TheThe firstfirst principal stress stress distribution distribution of of upper upper outlets; outlets; (b ()b the) the third third principalprincipal stress stress distribution distribution ofof upperupper outlets;outlets; ( c)) possible possible crack crack positions positions of of the the middle middle upper upper outlet; outlet; (d()d possible) possible crack crack positions positions of of the the sideside upperupper outlet; ( (ee)) the the first first principal principal stress stress distribution distribution of ofmiddle middle outlets;outlets; (f ()f the) the third third principal principal stress stress distributiondistribution ofof middle outlets. outlets.

CracksCracks may may continue continue toto propagatepropagate if the pore water water pressure pressure in in the the crack crack reaches reaches 0.5 0.5 MPa MPa [5]. [ 5]. Therefore,Therefore, it it is is necessary necessary to to strictly strictly controlcontrol thethe cracks at the outlets, outlets, especially especially the the possible possible cracking cracking positionspositions predicted predicted inin FigureFigures8 c,d.8c,d. More attention attention should should be be paid paid to the to thereinforcement reinforcement bars barsof the of thepier pier and and outlets outlets to prevent to prevent tension tension cracks. cracks. Appropriate Appropriate concrete concretematerials materialswhich have which the abrasion- have the abrasion-resistanceresistance capacity capacity may be may used be usedaround around the outlets. the outlets. The The concrete concrete strength strength should should be be selected selected accordingaccording to to the the discharge discharge ﬂow flow and and velocity.velocity.

4.3.4.3. Cracking Cracking Analysis Analysis of of the the DamDam HeelHeel andand thethe Dam Abutments ThereThere are are always always stress stress concentrations concentrations near the upper dam dam heel. heel. The The maximum maximum tensile tensile stress stress of of thethe Xulong Xulong arch arch dam dam heel heel is is 0.9 0.9 MPaMPa underunder thethe analysisanalysis case case 1 1 (Figure (Figure 7).7). The The yielding yielding region region and and crackcrack usually usually ﬁrst first appear appear at at the the damdam heelheel andand abutments as as the the load load gradually gradually increases. increases. It Itis isrelated related toto the the discontinuous discontinuous geometric geometric shape shape andand stiffness.stiffness. The stress change law of the dam heel is analyzed without considering the seepage pressure. It The stress change law of the dam heel is analyzed without considering the seepage pressure. It is is assumed that the crack depth is 7.7 m, 15.4 m, and 23.1 m, respectively, that is, 1/6, 1/3, and 1/2 of assumed that the crack depth is 7.7 m, 15.4 m, and 23.1 m, respectively, that is, 1/6, 1/3, and 1/2 the dam bottom thickness. The maximum tensile stress of the dam heel is 0.875 MPa, 0.796 MPa, and Appl. Sci. 2018, 8, 2555 11 of 18

Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 18 of the dam bottom thickness. The maximum tensile stress of the dam heel is 0.875 MPa, 0.796 MPa, and0.874 0.874 MPa. MPa. With With the theincrease increase of crack of crack depth, depth, the the tensile tensile stress stress decreases decreases first ﬁrst due due to to the the increase increase of gravity stress at the crack and then increases duedue toto thethe increaseincrease ofof shearshear stress.stress. The geologicalgeological conditioncondition ofof both both abutments abutments are are complicated complicated (Figure (Figure9). 9). In particular,In particular, the faultthe fault f57 andf57 and xenolith xenolith of the of the left left abutment, abutment, the the fault fault f26 f26 and and biotite biotite enrichment enrichment zone zone of of the the right right bank bank have have a greata great inﬂuence influence on on the the stress stress distribution distribution of of the the arch arch dam dam abutments. abutments.

(a) (b)

Figure 9. Complex geological condition of the Xulong arch abutments. ( a) Left arch abutment of the model; (b) right arch abutment of the model; (c) left arch abutment of the site (the foundation face has not been excavated); (d)) rightright archarch abutmentabutment ofof thethe sitesite (the(the foundationfoundation faceface hashas notnot beenbeen excavated).excavated).

5. Overall Stability and Reinforcement Analysis of Xulong Arch Dam 5.1. Overall Stability Analysis 5.1. Overall Stability Analysis The overall stability analysis of the Xulong arch dam adopts the methods in Section 3.1 and obtains The overall stability analysis of the Xulong arch dam adopts the methods in Section 3.1 and three safety factors, K = 2~2.5; K = 5; K = 8.5. The capacity curve of the maximum displacement obtains three safety factors,1 퐾 =2 2~2.5;3 퐾 = 5; 퐾 = 8.5. The capacity curve of the maximum along river direction of the arch crown is illustrated in Figure 10. With 2 to 2.5 times overloading, displacement along river direction of the arch crown is illustrated in Figure 10. With 2 to 2.5 times cracks initiate at the dam heel. At the bottom of the dam to EL 2220 m, local yielding occurs on the overloading, cracks initiate at the dam heel. At the bottom of the dam to EL 2220 m, local yielding upstream of the left and right abutments. Therefore, the safety factor of crack initiation is estimated to occurs on the upstream of the left and right abutments. Therefore, the safety factor of crack initiation be 2~2.5. is estimated to be 2~2.5. When ﬁve times overloading, cracks initiate at the foundation surface and propagate from the When five times overloading, cracks initiate at the foundation surface and propagate from the upstream to the downstream between EL 2095 m and EL 2258 m. The maximum crack depth is about upstream to the downstream between EL 2095 m and EL 2258 m. The maximum crack depth is about 0.5 times the thickness of the dam. The local region of the dam toe and the outlets of the downstream 0.5 times the thickness of the dam. The local region of the dam toe and the outlets of the downstream begin to yield and gradually propagate to the surrounding region. The yield region of the foundation begin to yield and gradually propagate to the surrounding region. The yield region of the foundation surface between the dam heel and toe tends to coalesce and the capacity curve starts to be nonlinear surface between the dam heel and toe tends to coalesce and the capacity curve starts to be nonlinear at ﬁve times overloading (Figure 10). Therefore, the safety factor of structural nonlinear behavior at five times overloading (Figure 10). Therefore, the safety factor of structural nonlinear behavior initiation of the dam is judged as 5. initiation of the dam is judged as 5. When eight times overloading, the yielding region is not fully connected to form a movement mechanism, so the structure can still provide support (Figure 11a,b). When nine times overloading, the foundation surface forms two connected yielding regions and a movement mechanism (Figure Appl. Sci. 2018, 8, 2555 12 of 18

When eight times overloading, the yielding region is not fully connected to form a movement

Appl.mechanism, Sci.Appl. 2018 Sci., 8 2018, x FOR so, 8, thex PEER FOR structure PEER REVIEW REVIEW can still provide support (Figure 11a,b). When nine times overloading, 12 12 of of 18 18 the foundation surface forms two connected yielding regions and a movement mechanism 11c,d).(Figure11c,d). The 11 displacementThec,d). displacement The displacement along along river river alongdirection direction river of directiontheof the arch arch crown of crown the increases arch increases crown faster faster increases at at eight eight faster and and at ninenine eight timesand timesoverloading nine overloading times overloading (Figure (Figure 10). (Figure 10).The Theoverall 10 overall). The stability overallstability of stability archof arch dam–foundation of dam–foundation arch dam–foundation is is lost. lost. Therefore, isTherefore, lost. Therefore, thethe ultimatetheultimate ultimate undertaking undertaking undertaking coefficient coefficient coefﬁcient of the of thearch of the arch dam arch dam is dam judged is judged is judged as as8.5. 8.5. as 8.5.

10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 times Overloading Overloading times Overloading 1 1 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Displacement along the river direction (mm) Displacement along the river direction (mm) FigureFigure 10. 10.The The capacity capacity curve curve of of thethe maximummaximum displacement along along river river direction direction of of the the arch arch crown. crown. Figure 10. The capacity curve of the maximum displacement along river direction of the arch crown.

(a) (b) (a) (b)

FigureFigure 11. 11.The The(c yieldingyielding) region under under different different analysis analysis cases cases (PEMAG: (PEMAG: (plasticd) plastic strain strain magnitude). magnitude). (a) (a)Downstream Downstream surface surface under under case case 8; (b 8;) foundation (b) foundation surface surface under under case 8; case(c) downstream 8; (c) downstream surface under surface Figure 11. The yielding region under different analysis cases (PEMAG: plastic strain magnitude). (a) undercase case9; (d) 9; foundation (d) foundation surface surface under under case 9. case 9. Downstream surface under case 8; (b) foundation surface under case 8; (c) downstream surface under caseThe 9;The (d displacement) displacementfoundation surface distributions distributions under case of of the 9.the damdam are basically consistent consistent in in different different overloading overloading times times (Figure(Figure 12 ).12). The The maximum maximum displacement displacement along along the the river river direction direction of of the the arch arch crown crown is aroundis around the the dam crestThedam and displacement crest increases and increases with distributions the with increase the of increase the of overloading.dam of areoverloading. basically consistent in different overloading times (Figure 12). The maximum displacement along the river direction of the arch crown is around the dam crest and increases with the increase of overloading. Appl. Sci. 2018, 8, 2555 13 of 18 Appl.Appl. Sci. Sci. 2018 2018, ,8 8, ,x x FOR FOR PEER PEER REVIEW REVIEW 13 13 of of 18 18

2330 23302330 2330 2310 23102310 2310 2290 22902290 2290

22702270 22702270

22502250 22502250

22302230 22302230

22102210 22102210

21902190 21902190

21702170 21702170 Elevation (m) Elevation Elevation (m) Elevation 1 time load 1 1time time load load 21502150 1 time load 2150 Elevation (m) Elevation 2150

Elevation (m) Elevation 2 time load 2 2time time load load 2 time load 3 3time time load load 21302130 3 3time time load load 21302130 4 4time time load load 4 4time time load load 21102110 2110 5 5time time load load 5 5time time load load 2110 6 6time time load load 2090 2090 20902090 1 51 101 151 201 251 301 351 1 51 101 151 201 251 301 351 -10.5-10.5 -8.5 -8.5 -6.5 -6.5 -4.5 -4.5 -2.5 -2.5 -0.5 -0.5 Displacement (mm) Displacement (mm) DisplacementDisplacement (mm) (mm) ((aa)) ((bb))

FigureFigure 12.12. Crown Crown displacementdisplacement underunder variousvarious analysisanalysis casescases 11 toto 6.6.6. (a(a)) Crown CrownCrown displacement displacementdisplacement alongalong riverriver direction; direction; ( b(b))) crowncrown crown displacementdisplacement displacement crosscross cross riverriver river direction.direction. direction.

TheThe arch arch thrust thrust distribution distribution characteristics characteristics of of several several high high arch archarch dams damsdams are areare compared comparedcompared in inin Figure FigureFigure 13. 1313.. TheThe middlemiddle and and lowerlower elevationelevation archarch thruststhrusts of of thethe damdam are are huge huge and and the the upper upper elevation elevation arch arch thrust thrust isis small. small. The The Xulong Xulong and and other other archarch damsdams havehave the the same same thrust thrust distribution distribution characteristic.characteristic. characteristic. TheThe largelarge archarch thrustthrust regionregion isis consistent consistent withwith thethe largelarge yielding yielding region.region. region. TheThe distributiondistribution characteristicscharacteristics ofof thethe yieldingyielding region region andand and arch arch thrustthrust thrust cancan can bebe be usedused used asas as aa a validationvalidation validation ofof of thethe the ﬁvefive five stressstress stress zoneszones zones inin in SectionSection Section 5.2 5.2. 5.2..

320 Xiluodu arch dam 320 320 Xiluodu arch dam 320 XiluoduXiluodu arch arch dam dam Jinping Ⅰ Ⅰarch dam Jinping arch dam 300 JinpingJinping Ⅰ Ⅰarcharch dam dam 300300 Ertan arch dam 300 Ertan arch dam ErtanErtan arch arch dam dam Dagangshan arch dam 280280 Dagangshan arch dam 280280 DagangshanDagangshan arch arch dam dam FeasibilityFeasibility study study option option of of Wudongde Wudongde arch arch dam dam 260 FeasibilityFeasibility study study option option of of Wudongde Wudongde arch arch dam dam 260260 TheThe bidding bidding option option of of Wudongde Wudongde arch arch dam dam 260 TheThe bidding bidding option option of of Wudongde Wudongde arch arch dam dam FeasibilityFeasibility study study option option of of Xulong Xulong arch arch dam dam 240240 240240 FeasibilityFeasibility study study option option of of Xulong Xulong arch arch dam dam 220 220220

m) 220 m) ( ( 200200 200200 180180 180180 160160 160160 140140 140140 Dam height Dam Dam height (m) height Dam Dam height Dam Dam height (m) height Dam 120120 120120 100100 100100 8080 8080 60 6060 60 40 4040 40 20 2020 20 0 00 0 00 50 50 100 100 150 150 200 200 250 250 300 300 350 350 400 400 450 450 500 500 550 550 00 50 50 100 100 150 150 200 200 250 250 300 300 350 350 400 400 450 450 500 500 550 550 RightRight arch arch abutment abutment thrust thrust（（1010N/mN/m）） LeftLeft arch arch abutment abutment thrust thrust（（1010N/mN/m）） ((aa)) ((bb))

FigureFigure 13.13. TheThe distributiondistribution characteristicscharacteristics of of archarch thrustthrust ofof severalseveral highhigh archarch dams.dams.dams. ((aa) ) RightRight archarch abutmentabutment thrust; thrust; ( b(b)) left left archarch arch abutmentabutment abutment thrust.thrust. thrust. 5.2. Discussion on Dam Stress Zones 5.2.5.2. Discussion Discussion on on Dam Dam Stress Stress Zones Zones Based on past analytical experience and the analysis of the stress, displacement, and yielding BasedBased onon pastpast analyticalanalytical experienceexperience andand thethe analysisanalysis ofof thethe stress,stress, displacement,displacement, andand yieldingyielding region of the Xulong arch dam, five stress zones of the arch dam are proposed as follows. Figure 14 is a regionregion of of the the Xulong Xulong arch arch dam, dam, five five stress stress zones zones of of the the arch arch dam dam are are proposed proposed as as follows. follows. Figure Figure 14 14 schematic diagram of the five stress zones. The five stress zones can better guide the crack prevention isis a a schematic schematic diagram diagram of of thethe five five stress stress zones. zones. The The five five stress stress zones zones can can better better guide guide the the crack crack of the arch dam. preventionprevention of of the the arch arch dam. dam. Appl. Sci. 2018, 8, 2555 14 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 18

(a) (b)

FigureFigure 14. Five 14. F stressive stress zones zones of of high high arch arch dam. dam. ((aa)) Upstream surface; surface; (b () bDownstream) Downstream surface. surface. Note: Note: The numberThe number 1–5 1-5 represents represents compression compression zone zone of of upstream upstream surface, surface, tensile tensile and compressive and compressive zone of zone of upstreamupstream arch arch abutment, abutment, tensile stress stress zone zone of of upstream upstream dam dam heel, heel, compression compression stress stress zone zone of of downstream arch abutment, and tensile stress zone of downstream surface, respectively. downstream arch abutment, and tensile stress zone of downstream surface, respectively. (1) Three-way compression zone of upstream surface (1) Three-way compression zone of upstream surface This zone ranges from about 1/5 to 4/5 dam height, and the zone width is close to the height. The Thisstress zonestate in ranges this zone from indicates about the 1/5 structural to 4/5 dam state height,of the arch and dam the and zone it is width important is close to control to the the height. The stresscompression state in stress this zonein this indicates zone. In the general, structural the maximum state of the compression arch dam andstress it is around important the toarch control the compressioncrown beam at stress 1/3 elevation in this zone. of the In arch general, dam. theThe maximumcompression compression stress results stressof the isfinite around element the arch analysis are around 6.2~8.0 MPa. crown beam at 1/3 elevation of the arch dam. The compression stress results of the ﬁnite element analysis(2) Tensile are around and compressive 6.2~8.0 MPa. zone of upstream arch abutment (2) TensileThe and stress compressive state may zone be tensile of upstream stress in arch the abutmentdirection of both beam and arch or one of the directions is tensile stress. When upstream water pressure is considered, it is the state of double- Thetension stress single-compression state may be or tensile double-compression stress in the directionsingle-tension. of both Morebeam attention and should arch be or paid one to of the directionscontrol is the tensile tensile stress. stress When of this upstream area to prevent water cracking. pressure The is considered, calculation results it is the show state that of double-tensionthe tensile single-compressionstress of the left arch or double-compression abutment of the Xulong single-tension. dam reaches 1.18 More MPa of attention case 1. It shouldis suggested be paid to control to control the tensilethe tensile stress stress of thisof this area area to to prevent less than cracking. 1.5 MPa when The calculationthe FEM is adopted. results show that the tensile stress of the(3) left Tensile arch stress abutment zone of upstream the Xulong dam dam heel reaches 1.18 MPa of case 1. It is suggested to control the tensile stress of this area to less than 1.5 MPa when the FEM is adopted. Based on the analysis of several super-high arch dams in China, it is suggested that the tensile (3) Tensilestress should stress zonebe strictly of upstream controlled dam within heel 1.4 MPa if the tensile stress of arch dams is based on FEM simulation. The dam heel tensile stress of the Xulong arch dam is 0.9 MPa. Although the upstream Basedbottom onjoint the can analysis reduce ofthe several tensile stress super-high of the dam arch heel, dams attention in China, should it is be suggested paid to the that effect the of tensile stresshydraulic should befracturing. strictly The controlled upstream within bottom 1.4 joint MPa cannot if the affect tensile the construction stress of arch of the dams curtain is based grouting. on FEM simulation.The high The tensile dam stress heel is tensile related stress to the of discontinuous the Xulong archgeometric dam isshape 0.9 MPa.of the Althougharch dam heel. the upstream The bottomcracking joint of can the reduce dam heel the should tensile be paid stress more of theattention dam to. heel, attention should be paid to the effect of hydraulic(4) Compression fracturing. stress Thezone upstreamof downstream bottom arch jointabutment cannot affect the construction of the curtain grouting. The high tensile stress is related to the discontinuous geometric shape of the arch dam heel. This zone ranges from the bottom to the middle height of the dam. Normally, the largest The cracking of the dam heel should be paid more attention to. compression stress is in this zone and it is important to control it. The compression stress of the left (4) Compressionarch abutment stress of the zone Xulong of downstream dam reaches arch 8.88 abutment MPa of case 10. It is suggested to control the compression stress of this zone to less than 14 MPa when the FEM is adopted. This zone ranges from the bottom to the middle height of the dam. Normally, the largest compression(5) Tensile stress stress iszone in of this downstream zone and surface it is important to control it. The compression stress of the left arch abutmentThe arch dam’s of the downstream Xulong dam surface reaches between 8.88 the MPa upper of to case middle 10. Itelevation is suggested is a tensile to control zone, the compressionand the tensile stress stress of this is zonein the to direction less than of 14the MPa beam. when The tensile the FEM stress is adopted.may be large here due to the pier. When the upstream water level is low, this tensile stress zone will shift to the left and right arch (5) Tensileabutments. stress The zone results of downstream of the geomechanical surface model test also show that the cracking of the Thedownstream arch dam’s arch downstream abutment basically surface extends between to the the center upper of to the middle dam along elevation the normal is a tensile of the zone, foundation surface, which is the failure of the tension and shear [2]. and the tensile stress is in the direction of the beam. The tensile stress may be large here due to the pier. When the upstream water level is low, this tensile stress zone will shift to the left and right arch abutments. The results of the geomechanical model test also show that the cracking of the downstream Appl. Sci. 2018, 8, 2555 15 of 18 arch abutment basically extends to the center of the dam along the normal of the foundation surface, which is the failure of the tension and shear [2].

5.3. AbutmentAppl. Sci. 2018 Reinforcement, 8, x FOR PEER REVIEW Suggestion 15 of 18 Based5.3. Abutment on the Reinforcement analysis of Suggestion the overall stability, stress, and displacement of the arch dam, it is consideredBased that on the the fault analysis f57, xenolith, of the overall fault f26,stability, and biotitestress, enrichmentand displacement zone haveof the aarch great dam, effect it is on the stressconsidered distribution that of the the fault arch f57, abutments. xenolith, fault f26, and biotite enrichment zone have a great effect on Inthe order stress todistribution improve theof the stress arch stateabutments. of the dam abutments and decrease the cracking risk during long-termIn operation, order to improve it is recommended the stress state toof the use dam a shearing-resistance abutments and decrease wall the in thecracking fault risk f57, during to replace the biotitelong-term enrichment operation, zone it is with recommended concrete, to and use to a performshearing-resistance consolidation wall groutingin the fault or f57, anchoring to replace on the excavatedthe biotite exposed enrichment weak structuralzone with concrete, zone. Figure and to 15 perform illustrates consolidation the shearing-resistance grouting or anchoring tunnel on for the the excavated exposed weak structural zone. Figure 15 illustrates the shearing-resistance tunnel for left arch abutment and the concrete replacement for the right arch abutment. the left arch abutment and the concrete replacement for the right arch abutment.

(a)

(b)

FigureFigure 15. The 15. The abutments abutments reinforcement reinforcement method method of the Xulong Xulong arch arch dam. dam. (a) (a Shearing-resistance) Shearing-resistance tunneltunnel for the for leftthe abutment;left abutment; (b )(b concrete) concrete replacement replacement for the the right right abutment. abutment.

Through numerical simulation, the tensile stress and yielding zone changes of the arch abutments are obtained before and after reinforcement (Figures 16 and 17). The first principal stresses of the left and right arch abutments decrease by about 0.13 MPa and 0.17 MPa, respectively. The Appl. Sci. 2018, 8, 2555 16 of 18

Through numerical simulation, the tensile stress and yielding zone changes of the arch abutments Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 18 are obtainedAppl. Sci. 2018 before, 8, x FOR and PEER after REVIEW reinforcement (Figures 16 and 17). The ﬁrst principal stresses 16 of of the 18 left andreinforcement right arch abutments of the abutments decrease reduces by about the 0.13first andprincipal 0.17 MPa, stress respectively. and improves The the reinforcement stress state of ofthe the abutmentsarchreinforcement abutments, reduces ofthereby the the ﬁrst abutments reducing principal reduces the stress cracking the and first improves risk.principal The the stressreinforcement stress and state improves of method the the arch stressalso abutments, improvesstate of the thereby the reducingcomprehensivearch theabutments, cracking shear thereby risk. strength The reducing reinforcementof the theside-slip cracking methodsurface risk. and alsoThe ensures improvesreinforcement a certain the comprehensivemethod safety also margin improves shearfor the strengththe anti- ofsliding thecomprehensive side-slip of the surfacearch shear abutments. and strength ensures of the a certainside-slip safety surface margin and ensures for the a certain anti-sliding safety margin of the archfor the abutments. anti- sliding of the arch abutments.

(a()a ) (b(b) )

FigureFigureFigure 16. 16.The 16. The The ﬁrst first first principal principal principal stressstress stress atat at thethe the rightright arch abutment abutment fromfrom from EL EL EL 2264 2264 2264 m m to m to 2281 to2281 2281 m m(Unit: m(Unit: (Unit: Pa). Pa). Pa). (a)( Beforea) (Beforea) Before reinforcement; reinforcement; reinforcement; (b ()b (b after) )after after reinforcement. reinforcement. reinforcement.

(a) (b) (a) (b)

(c)

(d)

FigureFigure 17. The 17. The ﬁrst first principal principal stress stress and and yielding yielding ( regiond) distribution distribution of ofthe the left left abutment abutment (Stress (Stress unit: unit: Pa. PEMAG:Pa. PEMAG: plastic plastic strain strain magnitude). magnitude) (a) before. (a) concrete before concrete replacement; replacement; (b) after (b concrete) after concrete replacement; Figure 17. The first principal stress and yielding region distribution of the left abutment (Stress unit: (c) beforereplacement; concrete (c replacement;) before concrete (d replacement;) after concrete (d) after replacement. concrete replacement. Pa. PEMAG: plastic strain magnitude). (a) before concrete replacement; (b) after concrete replacement; (c) before concrete replacement; (d) after concrete replacement.

Appl. Sci. 2018, 8, 2555 17 of 18

6. Conclusions In this paper, the different cracking types and effect factors are summarized. The cracking risk, overall stability, and abutment reinforcement of the Xulong arch dam are analyzed through numerical simulation. The following conclusions can be drawn:

(1) A nonlinear constitutive model relating to the yielding region is proposed to evaluate dam cracking risk and overall stability. The temperature gradient change has a greater impact on the tensile stress and displacement of the arch dam, which increases dam cracking risk. In particular, the tensile stress of the left and right upper outlets are relatively large due to the pier.

(2) The three safety factors of the Xulong arch dam are obtained, K1 = 2~2.5; K2 = 5; K3 = 8.5, and the dam overall stability is guaranteed. (3) The ﬁve dam stress zones are proposed to analyze the dam cracking base of numerical results. It is recommended to use a shearing-resistance wall in the fault f57, replace the biotite enrichment zone with concrete, and perform consolidation grouting or anchoring on the excavated exposed weak structural zone. With optimal design of the dam structure according to the different stress characteristics of the ﬁve stress zones, the cracking risk and overall stability of the Xulong arch dam can be better controlled.

Author Contributions: P.L. and P.W. performed the numerical analysis on crack risk and overall stability evaluation; W.W. and H.H. provided original dam design parameters and scheme. Funding: This research was funded by Changjiang Institute of survey, planning, design and research, China. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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