failure analysis of high-concrete gravity dam based on

Available online at www.sciencedirect.com

www.elsevier.com/locate/compgeo

Computers and Geotechnics 35 (2008) 627–636

Technical Communication

Failure analysis of high-concrete gravity dam based on strengthreserve factor method

Zhou Wei *, Chang Xiaolin, Zhou Chuangbing, Liu Xinghong

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, Hubei 430072, China

Received 3 July 2007; received in revised form 8 October 2007; accepted 16 October 2007Available online 4 December 2007

Abstract

Maintaining stability against the sliding of a high-concrete gravity dam built on a rock mass of complex geology is a key problem. Inthis paper an anisotropic laminar layer element with thickness is used to simulate mechanical deformation properties of weak-bed inter-calations at a dam’s foundation as well as a contact friction interface element without thickness to simulate joints and fissures of the rockmass at the dam’s foundation. Nonlinear finite element method (FEM) analysis was used to calculate the resistance to sliding of a high-concrete gravity dam at the dam’s foundation. The strength reserve factor (SRF) method was adopted to simulate progressive failure andpossible unstable modes of the dam’s foundation system, and the method for determining the ultimate bearing resistance of this system.The strength analysis method of the connection of the plastic yield zone was used to obtain the ultimate bearing resistance of the dam’sfoundation while it was undergoing failure. Finally, nonlinear finite element analysis was performed to find a solution for the sliding ofthis dam, the high-concrete gravity dam of Xiangjiaba Hydropower Station on Jinshajiang River in Yunnan Province, China, while itwas under construction. The calculation shows that the failure of the dam is related to the strength (or weakness) of the silt-laden layer atthe dam’s foundation, and the strength reserve factor of final failure was 2.6.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Failure analysis; FEM; Concrete gravity dam; Strength reserve factor method

1. Introduction

The stability and safety of a gravity dam to guardagainst shallow sliding along the base interface, and deepsliding along the foundation, are key factors that must beaddressed in the design of gravity dams. Experience provesthat, as long as the strength and rigidity of the foundationis ensured, overall stability is achieved. Thus the loss of onegravity dam designed and built on the basis of modern the-ory and technology seldom occurs, and the only require-ment is to make sure that the design accounts forstability along the base interface. However, because a per-fect foundation does not usually exist, the foundation of anatural dam usually has intercalations of weak beds of siltor clay unfavorable for its stability. This condition is the

0266-352X/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compgeo.2007.10.005

* Corresponding author. Tel.: +86 27 68773778; fax: +86 27 68775112.E-mail address: [email protected] (Z. Wei).

one key factor that affects the safety of the dam, which isthe lack of deep stability that would otherwise preventthe sliding of a gravity dam in the research domain ofhydraulic structure. According to incomplete statistics,among large- and medium-size gravity dams in Chinaalready built, under construction, or in the design phase,82 have intercalations of weak beds in their foundations.Among these 82 dams, over 30 have had their designsaltered, their heights reduced, and the application ofincreased engineering measures or later-stage reinforce-ment. In comparison with remedies for shallow sliding,remedies for deep sliding are more complex, mainlybecause of the difficulty of assessing weak-bed intercala-tions and the complexity of determining shear parameters.Owing to these uncertain factors, no clearly definedmethod of analysis and no general safety coefficient fordeep anti-sliding measures have been established. In thespecifications for gravity dams in China, each project must

mailto:[email protected]

Fig. 1. Yield curves on p plane for different a,k.

628 Z. Wei et al. / Computers and Geotechnics 35 (2008) 627–636

be considered individually, and experience with similarprojects would help in making better decisions. Generallyspeaking, analysis methods for deep stability by preventinggravity-dam slippage should include the rigid-body limitingequilibrium method (LEM), the numerical method, and themodel test method, among others. The safety standards fordeep stability adopted usually refer to the requirements forsafety along the base interface.

The gravity method, based on rigid-body equilibriumand the beam theory, is normally adopted before consider-ing linear or nonlinear finite element models. FERC [1,2],CDA [3], USACE [4], ANCOLD [5], USBR [6], and Legeret al. [7] present guidelines for dam-safety assessment basedon the gravity method. Compared with the rigid-body lim-iting equilibrium method, the FEM used in the calculationof deep anti-sliding measures does not require the assump-tion of any slide plane. The computation model meets boththe equilibrium equation of force and the stress–strain rela-tionship of the base rock, which makes the calculationresults more reliable. Moreover, the finite element methodcan be used to analyze the foundations of various complexgeologic structures as well as to reflect the effect of founda-tion-reinforcement measures.

In this paper the nonlinear finite element analysis of thestress and the deformation condition of the dam and therock mass at the dam’s foundation of the XiangjiabaHydropower Station in the lower reach of the Jinsha Riverin China was calculated. The effect of the dislocation andthe intercalations of weak beds at the dam’s foundationwere studied, and the SRF method was used to simulateprogressive failure and possible unstable modes of thedam’s foundation system. Therefore, the ultimate bearingresistance of the dam’s foundation system was obtained,and the dam’s stability and the safety measures to preventthe dam from sliding were evaluated.

2. Constitutive model and yield criterion

2.1. Constitutive model and yield criterion of rock mass of

dam foundation

The isotropic, elastoplastic model with linear softeningcharacteristics was used for the constitutive relationshipof the rock-mass material of the dam’s foundation. Themost typical Drucker–Prager (D–P) criterion in geotechni-cal engineering is used for the yield criterion:

F ¼ aI1 þffiffiffiffiffiJ 2

p� k ¼ 0 ð1Þ

where, I1 and J2 are the first invariant of stress tensor andthe second invariant of stress partial tensor, respectively.Both a and k are positive constants, and the relation be-tween them and c,/ depends on the correlation betweenthe Mises conical surface and the Mohr–Coulomb hex-pyr-amid surface. Different yield criterions can be realized in fi-nite element calculations through changing the expressionsof a and k. Different circles ( Fig. 1) have different a and k

values.

When circumscribing the cone,

a ¼ 2 sin /ffiffiffi3pð3� sin /Þ

; k ¼ 6c cos /ffiffiffi3pð3� sin /Þ

ð2Þ

when inscribing the cone,

a ¼ 2 sin /ffiffiffi3pð3þ sin /Þ

; k ¼ 6c cos /ffiffiffi3pð3þ sin /Þ

ð3Þ

when having equal area to the cone,

a ¼ 2 �ffiffiffi3p

sin /ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffiffiffi3p

pð9� sin2 /Þq ; k ¼ 6

ffiffiffi3p

c cos /ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffiffiffi3p

pð9� sin2 /Þq : ð4Þ

Because the safety coefficient obtained by the finite ele-ment strength reserve factor is closely related to the yieldcriterion used, the results calculated with different formsof D–P criteria differ greatly from one another. The spireand edge angle of the yield surface of the Mohr–Coulombcriterion make numerical calculation difficult. The numeri-cal calculation shows that the application of the Mohr–Coulomb yield criterion in calculating the equivalent-areacircle cannot only meet the general expression of the D–Pcriterion to make the finite element numerical calculationeasier, but it also makes the calculation results closer tothose of the traditional Mohr–Coulomb yield criterion.Therefore, the D–P criterion of equivalent-area cones isused in this paper.

2.2. Constitutive model and yield criterion of weak

intercalations of dam foundation

The isotropic elastoplastic model with linear softeningcharacteristics was used for the weak intercalations at thedam’s foundation along the joint layer, and the incom-pressible rigid-body model was used for those along thenormal intercalation line. The D–P criterion of equiva-lent-area cones was still used for the yield criterion.

2.3. Selection of elements

For the rock mass at the dam’s foundation, the two-dimensional, four-joint isoparametric element was used.

Fig. 2. Stress-deformation relation on contact surface.

Z. Wei et al. / Computers and Geotechnics 35 (2008) 627–636 629

For the weak intercalation, the laminar layer Desai ele-ment with thickness [8] was used. This element can simulatethe interaction at the interface of two materials with greatlydifferent properties as well as the phenomenon that shearslippage within a laminar layer near the interface maycause material damage.

Because the joint in the rock mass has no thickness, theGoodman element model without thickness [9] was usuallyadopted. In a normal direction, the Goodman element takesa larger elastic rigidity to reflect the deformation of the inter-face in the normal direction. However, in the application, theelements on both sides may be embedded together, owing topressure, which can be resolved by adjusting the value ofnormal rigidity, and the great randomness of the value ofnormal rigidity results in a wave of normal stress. In thispaper the contact element based on the extended Lagrangemethod is used to simulate the joint, without thickness.The extended Lagrange method is a mathematical program-ming method developed to overcome shortages of the typicalpenalty function method and the Lagrange method. Simoand Laursen [10] used this method to solve the frictionalcontact problem. The extended Lagrange method can beused, with initial penalty and through extended Lagrangemultiplier iteration, to obtain contact force meeting accu-racy specification. In the whole process the unknown num-bers in the general equation do not increase, and therequirement for the penalty selection is greatly reducedthrough iteration. Meanwhile, the numerical implementa-tion is easier, and the constraint to the interface and consti-tutive relation are fully considered. Therefore, for resolvingproblems on contact friction, the extended Lagrange methodis superior to the traditional Goodman element.

While resolving the problems of contact friction with theextended Lagrange method as to three kinds of contactstates – separation, bonding, and sliding – the followingprecautions should be taken into account:

Separation: When the normal stress of the contact inter-faces is more than zero (it is generally agreed that notensile energy exits between rock fill and concrete wall),the contact interfaces separate.Bonding: When the normal stress rn is less than zero(the stress between contact interfaces is compressivestress) and tangential shear stress is less than allowableshear stress specified by the Mohr–Coulomb rule, con-tact interfaces are in the state of bonding (Fig. 2). Theformula of tangential shear stress of contact interfacesis:

s ¼ ks � du 6 f 0 � jrnj ð5Þ

du refers to relative displacement of contact surfaces, ks

to shear modulus, and f 0 Coulomb friction coefficient.Sliding: when the normal stress is compressive stress,and the tangential shear stress obtained by the Coulombfriction formula is more than allowable shear stress asspecified by the Mohr–Coulomb rule, contact surfacesare in the state of sliding:

s ¼ ks � du > f 0 � jrnj: ð6ÞUnbearable stress while contact surfaces separate, andthen part beyond shear strength while contact surfacesare in the state of sliding, will be transferred and distrib-uted to surrounding elements through incremental itera-tion of the extended Lagrange multiplier.

3. Failure analysis of gravity dam

3.1. Simulating method of progressive failure

The overload method and the SRF method are usuallyadopted in finite element calculation to study the ultimatebearing resistance of a dam’s body and foundation system.The overload method mainly concerns the uncertainty ofan applied load so as to study the bearing capability of astructure. This relatively visual method is suitable for struc-tural physical-model experiments in which numericalsimulation and physical simulation corroborate each other.The ultimate state of the loss of stability of the entire struc-ture requires a big overload coefficient, and such a state isactually impossible. Therefore, the overload coefficientobtained by this method is only a token index of structuralsafety. As for the SRF method, it emphasizes the uncer-tainty and possible weakening effect of material strengthso as to study the strength reserve degree of a structure.Natural rocks have obvious inhomogeneity owing to for-mation and tectonization, and rock joints and fissures havecomplex distribution, so it is hard to grasp relevant physi-cal mechanical properties accurately within the range ofconstruction. Thus great disparities among different mate-rial parameters are highly possible. Therefore, this methodis more suitable in the sense that it can, comparatively,truly reflect substantial structural failure and possibleunstable modes, by which progressive failure and degreeof stability of the dam’s foundation and the rock massare studied in this paper. Let K stand for the strengthreserve factor (K > 1.0), and f 0 and c 0 for actual shear-strength parameters. Then strength reduction can be calcu-lated by using f 0/K, c 0/K to replace f 0 and c 0. With anincrease in the value of K, the progression from localfailure to total failure of the dam can be gained. Sincethe system’s stability is studied by gradually decreasingthe strength until an ultimate state of failure is reached,


the stability factor and the actual glide mode can beobtained at the same time.

3.2. Strength-analysis method of research on ultimate

bearing resistance

While utilizing the strength reserve factor method todecrease material strength step by step for nonlinear itera-tion, it is necessary to judge whether the structure hasreached its ultimate bearing resistance. When elementstress exceeds yield stress, plastic strain will occur, fromwhich local failure will also occur. But that is not equalto the failed bearing capability of the dam’s body and foun-dation system. With progressive reduction of materialstrength, plastic yield of more elements will happen. Andwhen the plastic zone in the dam’s foundation forms a glidechannel, the dam’s body and foundation system may beconsidered to have reached the ultimate bearing resistance.This method is called the strength judgment method of ulti-mate bearing resistance.

As in this paper, the isotropic softening D–P materialmodel is adopted, for the finite element method used instress space, tangent elastic modulus at the initial stage ofstrain softening is negative and the stiffness matrix isnon-positive definite, which make the calculation of con-vergence difficult. So the following practical and approxi-mate method is adopted in concrete calculation:

(1) Adopt a very small positive value for the elastic mod-ulus at the softening stage while calculating stiffnessmatrix.

(2) Take a practical value for the elastic modulus at thesoftening stage in the later calculation of stressincrease.

(3) To have better convergence, the norm tolerance ofunbalanced force at the softening stage can be prop-erly increased.

The strength analysis method for research on ultimatebearing resistance is a visual method, for the analysis of

Fig. 3. Xiangjiaba Hydrop

progressive failure is easy to understand. Different consti-tutive models, the failure criterion, and human factors willimpact the accuracy of results, but as long as proper consti-tutive models and the failure criterion are prudentlyselected, this method is still a very good choice.

4. Analysis of stability against deep sliding of the Xiangjiaba

project

4.1. Brief introduction to the project

Xiangjiaba Hydropower Station is the last cascade ofthe cascade hydropower stations of the Jinshajiang Riverin China, which is located in the Xiangjiaba gorge outletwhere Yiben County of Sichuan Province borders ShuifuCounty of Yunnan Province. The hydropower station hasa gravity dam with a maximum height of 161 m. Fig. 3shows a design impression of the dam.

The dam’s foundation is situated at a level of complexgeology. The main geological structure comprises anticlines(see rock layers T 2�3

3 , T 2�43 , T 2�5

3 , and T 2�63 of Fig. 4) that

form an oblique crossing of the river bed. Next, the nonlin-ear finite element method was used to analyze, calculate,and evaluate the possible unstable modes and ultimatebearing resistance of the dam’s body and base rock of thispower station.

4.2. Finite element model

For the simulation of anticlinal rocks, a quality classifi-cation of the rock mass was considered, i.e. I, II, III1 andIII2, and the rock stratification of T 2�3

3 and T 2�53 and silt-

laden layers JC2-5–JC2-8. The typical 12# overflow damwas selected for the dam model.

For the 12# dam section, the number of nodes of finiteelement mesh is 10,040, and the number of elements, 9902.The analysis range of the foundation is as follows: Theupstream side (from the dam heel to upstream) is 2 timeshigher than the dam, the downstream side (from the damheel to downstream) is 3 times higher, and the level below

ower Station in China.

Fig. 4. The geological structure of Xiangjiaba Hydropower Station.


the base interface is 1.5 times higher. The contact elementand the laminar layer element were adopted for jointsand weak intercalations, respectively. See Figs. 5 and 6for the finite element mesh of the dam’s body andfoundation.

Table 1–3 gives the shear-strength parameters and elas-tic parameters of dam, foundation rock, geological struc-tures in foundation and interface between concrete androck. From the tables, we can see that the silt-laden layers

Fig. 5. The FEM grid of Xiang

Fig. 6. The FEM grid of Xiangjiaba Hydropow

JC2-5–JC2-8 and Pn are typical weak structural surfacewith lower Shear-strength values, and so those geologicaldefects will be main contributions to the failure of the grav-ity dam to a great extent.

In the calculation the load condition was considerednormal operating condition. The main loads are waterpressure acting on the upstream and downstream faces ofthe dam, uplift pressure, seepage body force, silt pressure,and the deadweight of the dam.

jiaba Hydropower Station.

er Station (local grid near dam foundation).

Table 1Shear-strength parameters of rock and interface between concrete androck

Rocktype

Longitudinalwave velocity(m/s)

Shear-strength ofrock

Shear-strength ofinterface betweenconcrete and rock

Frictionalcoefficient

Cohesion(MPa)

Frictionalcoefficient

Cohesion(MPa)

I >5000 1.40 1.80 1.30 1.30II 4000–5000 1.20 1.40 1.20 1.10III1 3500–4000 0.93–1.05 0.90–1.10 1.00–1.10 0.90–1.10III2 3000–3500 0.8–0.93 0.70–0.90 0.90–1.00 0.70–0.90IV 2000–3000 0.55–0.75 0.30–0.60 0.70–0.80 0.50–0.60V <2000 0.40–0.50 0.05–0.30 – –

Table 2Shear-strength parameters of geological structures in foundation

Geological structure typein foundation

T 2�53 T 2�3

3 JC2-5 JC2-6 JC2-7 JC2-8 Pn

Frictional coefficient 0.45 0.45 0.44 0.41 0.41 0.43 0.35Cohesion (MPa) 0.17 0.17 0.15 0.13 0.13 0.15 0.10

Table 3Elastic parameters of dam and geological structures in foundation

Type Density(kN/m3)

Elastic modulus(GPa)

Poisson’sratio

Dam concrete 24.0 22.0 0.167Dam foundation I 26.0 24.0 0.18

II 26.0 20.0 0.22III1 26.0 10.5–13.0 0.25III2 26.0 8.0–10.5 0.28IV 26.0 3.0–5.0 0.30V 26.0 1.28 0.40JC2-5–JC2-8 23.0 0.72 0.40Pn 23.0 0.72 0.40


4.3. Progressive failure and unstable modes of the dam and

foundation

See Figs. 7–11, which show the change in the plasticstrain zone for progressive failure of the dam’s foundationunder the condition of equal proportional reduction of

Fig. 7. The equivalent plastic strain zone distr

strength. The legends with the digital data for the grayzones in Figs. 7–11 have no units because the plastic strainof foundation rock and silt-laden layers is dimensionless.

From Figs. 7–11, we learned that when the materialstrength began to decrease, tensile-shear failure firstoccurred in the dam’s heel area because of the concentra-tion of tensile stress. Then the failure extended to theupstream area in which the yield region appears in the shal-low layer of the silt-laden layer T 2�5

3 and part of the deepbottom surfaces of rock layers T 2�3

3 and T 2�53 . Along with

the reduction of material strength, a zone of compres-sion–shear failure occurs at the toe of the dam, and theplastic failure zone of the dam heel kept increasing. After-wards, the plastic failure zone of layer T 2�5

3 expanded fromthe deep bottom to the upper area, and the yield region atthe base interface also developed from the dam heel and toeto the middle area. Finally, the yield regions of rock layerT 2�5

3 completely connected, and at this moment the entiresystem had basically reached its ultimate bearing resis-tance, while the yield region of the base interface had notbeen completely formed. Under the condition of equal pro-portional reduction of strength, the ultimate bearing resis-tance of the system was controlled by the strength of thesilt-laden layers. We should notice that the legends in Figs.7–11 have many different colors, which the red expresseslarger plastic strain and the blue smaller one. The largerplastic zone is mainly concentrated on the long-narrowsilt-laden layers JC2-5–JC2-8 and Pn, while the plasticdeformation of other zones is relative smaller, so in the fig-ures a majority of zone show the blue color, namely smallerplastic strain zone.In addition, there are plastic zones nearthe bottom line of the figure frame in Figs. 7–11, that is notnumerical errors, and because normal constraint is adoptedon the bottom line of the FEM model and the silt-ladenlayer Pn occurs the relative sliding deformation to producethe plastic strain.

While judging the ultimate bearing resistance of the dambody and foundation system on the basis of the thoroughconnection of the plastic yield zone, the strength reservecoefficient of the system was 2.6 when the parameters con-cerning the equal proportional reduction of materialstrength were f 0 and c 0. We need notice although the blue

ibution when strength reserve factor is 1.0.

Fig. 8. The equivalent plastic strain zone distribution when strength reserve factor is 1.5.




zone in Fig. 11 is not completely connected for the scale offigure, the plastic strain zone are actually thorough con-nected by real computation results.

5. Discussion

5.1. Discussion on the standard for judging ultimate bearing

resistance of the foundation of the gravity dam

The ultimate bearing resistance mentioned in this paperrefers to the strength reserve coefficient of the gravity dam

foundation when the dam-foundation system reaches theunstable state in the process of strength reduction. Forjudging whether the gravity dam system reaches the unsta-ble state, the following methods are available: displacementmutation method, calculation non-convergence methodand plastic yield zone connection method. Displacementmutation method means that the displacement of somepoint of the dam or the foundation increases sharply dur-ing strength reduction, and the inflection point of displace-ment-strength reserve coefficient curve is regarded as thatthe dam-foundation system reaches the unstable state and



the corresponding strength reserve coefficient is the ulti-mate bearing resistance of the foundation system. Calcula-tion non-convergence method refers to that, duringstrength reduction, when the calculation of nonlinear finiteelement reaches some time step, the strength reduction ofrock mass of the dam foundation results in that the gravitydam cannot continue to bear water pressure of upper reser-voir, and thus finite element program presents the informa-tion of calculation non-convergence. Then, the previoustime step of calculation non-convergence is regarded asthat the dam-foundation system reaches the unstable state.The method of plastic yield zone connection refers to that,during strength reduction, for the element of the dam foun-dation where plastic failure occurs, the glide path of thedam-foundation system has been formed, and along thisglide path the translation and rotation of the rigid bodyof the foundation system will occur and then the stabilityis lost. Then, the moment of plastic yield zone connectionis regarded as that the dam-foundation system reachesthe unstable state.

Due to the complexity of deep sliding stability of thegravity dam, the adoption of different judgment methodsof the unstable state may bring about different strengthreserve coefficients. The abovementioned three methodsfor judging the unstable state of the gravity dam have their

Fig. 12. The two key point’s dist

own advantages and shortages. The strength reserve coeffi-cient of the dam foundation acquired with displacementmutation method usually is smaller than the actual value.The reason is that, during nonlinear finite element calcula-tion, failure process of the dam foundation is progressive,and the time for different parts of the foundation to reachplastic yield is different, for instance, displacement muta-tion of the heel of the gravity dam is earlier than that ofresistance body of the dam toe. Generally, in nonlinearfinite element analysis of the gravity dam, the number ofthe elements is more than 1000, and thus, for the analysis,it will be quite difficult to find the last element, the defor-mation of which abruptly changes. Therefore, the strengthreserve coefficient acquired through using displacementmutation usually is smaller than the actual value. As forthe sliding stability problem of the gravity dam of Xiangji-aba Hydropower Station, the inflection point of displace-ment-strength reserve coefficient curve of the point 1 (seeFig. 12) at weak intercalation T 2�3

3 is 1.5 (Fig. 13), and thatthe point 2 of the dam toe is 2.0 (Fig. 14). According to thecalculation result above, the strength reserve coefficient ofthe dam-foundation system acquired with the method ofplastic yield zone connection is 2.6. Thereby, it is obviousthat, in the analysis on sliding stability of the gravitydam, if the displacement mutation method is used, a

ribution of dam foundation.

0

2

4

6

8

10

12

14

1 1 5 2 2 5 3Strength reserve coefficient

Ange

ntia

l rel

ativ

ede

form

atio

n(un

it:m

m)

Fig. 13. Developing process of tangential relative deformation of the Point 1.

— 7

—2

3

8

1 1 5 2 2 5 3Strength reserve coefficient

Verti

cal d

efor

mat

ion

(Uni

t:mm

)

Fig. 14. Developing process of vertical deformation of the Point 2.


strength reserve coefficient smaller than the actual valuewill be obtained.

In theory, it is feasible to use calculation non-conver-gence method to judge the unstable state of the gravitydam, because calculation non-convergence means that thedam foundation after strength reduction cannot continueto bear water pressure of upper reservoir of the dam. How-ever, the precondition for using calculation non-conver-gence method is that the finite element program usedmust be provided with quite high convergence, and the rea-son is that the analysis for the sliding stability of the gravitydam is a kind of typical nonlinear calculation and variousfactors like element type, element form, yield criterion,constitutive model, convergence precision and equationsolver may affect the convergence of the program, particu-larly convergence precision and equation solver have largeeffect on the convergence. Nevertheless, up to now, there isno finite element program that can absolutely ensure thatsuch a complex problem, the calculation of deep slidingstability of the gravity dam, is provided with good conver-gence (including commercial FEM software). As forXiangjiaba Hydropower Station, the strength reserve coef-ficient of the dam-foundation system acquired throughusing non-convergence criterion in commercial softwareABAQUS (the unbalance force of finite element equilib-rium equation is less than 10�6) to judge the unstable state

is 2.9. Thereby, it can be seen that there is a big deviationbetween the real ultimate bearing resistance of the dam andthe strength reserve coefficient acquired through using cal-culation non-convergence method.

Compared with the other two methods, the method ofplastic yield zone connection may be used to relatively visu-ally judge the scope of the plastic yield zone in the damfoundation. When the plastic yield zone in the foundationgradually expands until a glide mode is formed, it can bedetermined that the dam-foundation system has reachedthe unstable state. Therefore, in this paper, this method ismainly used to judge the unstable state of the gravitydam of Xiangjiaba Hydropower Station. With respect tothe current analysis level, the method of plastic yield zoneconnection is relative rational and feasible for judgingwhether the gravity dam reaches the unstable state.

5.2. Effect of different yield criterions on strength reserve

coefficient of the gravity dam

Several different Drucker–Prager criterions introducedin Section 2.1 of this paper are obtained through usingthe circles with different diameters to fit scalene hexagonof Mohr–Coulomb Criterion in p plane, and thus theresults obtained through nonlinear analysis with differentDrucker–Prager criterions are differential, which is mainly

Table 4Strength reserve factors from yield criterions

Yield Criterion Strength reservescoefficients

Mohr–Coulomb criterion 2.5D–P criterion of equivalent-area circle 2.6DP criterion of inscribed circle 1.9D–P criterion of exterior angle circumscribed to circle 2.9


reflected in the size of plastic yield zone. As for the slidingstability of the gravity dam of Xiangjiaba Hydropower Sta-tion, strength reserve coefficients obtained with differentyield criterions are as shown in Table 4. Seen from Table4, the strength reserve coefficient acquired with Mohr–Coulomb criterion is 2.5, and that acquired with DP crite-rion of equivalent-area circle is 2.6, therefore the differenceof the two criterions relatively is smaller. While the strengthreserve coefficients acquired with DP criterion of inscribedcircle and D–P criterion of exterior angle circumscribed tocircle have great differences from 2.5. Therefore, this papersuggests that, for analyzing the deep sliding stability of thegravity dam, Mohr–Coulomb Criterion or DP criterion ofequivalent-area circle should be adopted with priority.

6. Conclusion

(1) Owing to the complexity of deep anti-sliding and toseveral intercalations of weak geological layers, cor-responding constitutive model and element typeswere adopted for simulation. For the weak intercala-tions, the anisotropic constitutive elastoplastic modelcharacterized by linear softening, the D–P criterion ofequivalent-area circle, and the laminar layer elementwere adopted for simulation. For the rock-massjoints the contact element was adopted. This fail-ure-analysis method was applicable.

(2) Application of the strength method for judging theultimate bearing resistance under the conditions ofthe failed-dam foundation system is feasible.

(3) The three-dimensional nonlinear finite element analy-sis for the deep sliding of the gravity dam of Xiangji-aba Hydropower Station under construction wascarried out, and the calculation results show thatthe ultimate bearing resistance is controlled by the

strength of a silt-laden layer, given an equal propor-tional reduction of strength. When the local shallowglide surface turned to a plastic state, the strengthreserve coefficient was 1.3, and the ultimate strengthreserve coefficient was 2.6. According to comprehen-sive judgment, it is necessary to carry out further rein-forcement measures to improve the stability.

Acknowledgement

Special thanks are due to the National Science Fund forDistinguished Young Scholars (No. 50725931) and the Na-tional Natural Science Foundation of China (No.50579055) for supporting the present work.

References

[1] FERC (Federal Energy Regulatory Commission). Engineering guide-lines for evaluation of hydropower projects – Draft Chapter IIIGravity Dams. Federal Energy Regulatory Commission, Office ofEnergy Projects, Division of Dam Safety and Inspections, Washing-ton DC, USA; 2000.

[2] FERC (Federal Energy Regulatory Commission). Engineering guide-lines for evaluation of hydropower projects – Chapter III GravityDams. Federal Energy Regulatory Commission, Office of Hydro-power Licensing, Report No. FERC 0119-2, Washington DC, USA;1991.

[3] Canadian Dam Association (CDA). Dam safety guidelines. Edmon-ton, Alberta; 1999.

[4] USACE (US Army Corps of Engineers). Engineering and design:Gravity dam design. Report EM 1110-2-2000, Washington, DC;1995.

[5] ANCOLD. Guidelines on design criteria for concrete gravity dams.Australian National Committee for Large Dams; 1991.

[6] USBR (United States Bureau of Reclamation). Design of small dams.Denver, Colorado; 1987.

[7] Le’ger P, Larivie‘re R, Palavicini F, Tinawi R. Performance of gatedspillways during the 1996 Saguenay flood (Que’bec, Canada) andevolution of related design criteria. In: Proceeding of ICOLD 20thCongress Beijing, China, Q.79–R.26; 2000. p. 417–38.

[8] Desai CS, Drumm EC, Zaman MM. Cyclic testing and modeling ofinterfaces [J]. J Geotech Eng ASCE 1985;116(6):793–815.

[9] Goodman R E, Taylor R L, Brekke TL. A model for themechanics of jointed rock [J]. J Soil Mech Found ASCE 1968;99(3):637–60.

[10] Simo JC, Taylor RL. Quasi incompressible finite elasticity in principalstretches: continuum basis and numerical algorithms [J]. ComputMeth Appl Mech Eng 1991;85:273–310.

failure analysis of high-concrete gravity dam based on

Documents