Stability assesment of the Three Gorges foundation

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International Journal of Rock Mechanics & Mining Sciences 40 (2003) 609–631

Stability assessment of the Three-Gorges Dam foundation, China,using physical and numerical modeling—Part I: physical model tests

Jian Liu a,b, *, Xia-Ting Feng a , Xiu-Li Ding b , Jie Zhang b , Deng-Ming Yue ba Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Xiaohongshan, Wuhan, Hubei 430071, China

b Yangtze River Scientic Research Institute, Wuhan 430019, China

Accepted 31 March 2003

Abstract

Foundation stability is one of the most important factors inuencing the safety of a concrete dam and has been one of the keytechnical problems in the design of the Three-Gorges Project. The major difculties lie in two facts. The rst one is that the damfoundation consists of rock blocks, with joints and so-called ‘rock bridges’ and the gently dipping joints play a critical role in thefoundation stability against sliding. The second one is that, even in the regions where the gently dipping fractures are mostdeveloped, there are no through-going sliding paths in the rock mass due to the existence of the rock bridges; so the dam could slideonly if some of the rock bridges fail, so as to create at least one through-going sliding path. To date, due to unavoidableshortcomings in physical and numerical modeling techniques, there is not a single satisfactory method to solve the problemcompletely. For this reason, the integration of multiple methods was adopted in this study and proved to be an effective and reliableapproach.

This Part I paper describes work based on the results of geological investigations and mechanical tests, relating to the geologicaland geomechanical models of the Three-Gorges Dam, and then a systematic study procedure was developed to carry out thestability assessment project. Then, 2D and 3D physical model tests for some critical dam sections were performed. In the physicaltests, based on similarity theory, various testing materials were selected to simulate the rock, concrete, fracture and rock bridge. Theloading and boundary conditions were also modeled to meet the similarity requirements. The failure mechanism was derivedthrough a progressive overloading that simulated the upstream hydrostatic pressure applied to the dam, and the factor of safety wasdened as the ratio between the maximum external load inducing the start of sliding instability of the dam foundation and theupstream hydrostatic load. The experimental results indicated that the stability of the Three-Gorges Dam foundation satises thesafety requirements. Nevertheless, further discussions demonstrated that because of the incomplete denition of factor of safetyadopted in the physical model tests, it is also essential to study the stability of the Three-Gorges Dam foundation using numericalmodeling, which will be presented in the companion Part II paper.r 2003 Elsevier Ltd. All rights reserved.

Keywords: Dam foundation; Stability assessment; Physical model test; Gently dipping joint; Rock bridge; Three-Gorges Dam

1. Introduction

Foundation stability is one of the most importantfactors inuencing safety of a dam. Instability of a damgenerally results from pre-existing geological features inthe foundation, such as faults, joints, soft rocks andsolution channels, etc. Therefore, for a dam foundation,

stability analyses and assessment are essential and forma critical part of the safety assessment.

The Three-Gorges water conservancy complex lo-cated about half way along the Yangtze River is thelargest multipurpose water conservancy project everbuilt in China, indeed in the world ( Fig. 1 ). The Three-Gorges Dam is one of the three main parts of thisproject (the others are the power houses and navigationfacilities). It is a concrete gravity dam with a maximumheight of 185m and is designed to withstand a normalpool level of 175 m. According to the general layout of the dam ( Figs. 2–4 ), 23 spillway-dam sections are

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*Corresponding author. Institute of Rock and Soil Mechanics,Chinese Academy of Sciences, Wuhan, Hubei 430071, China.Tel.: +86-27-871-97913; fax: +86-27-871-97386.

E-mail address: [email protected] (J. Liu).

1365-1609/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S1365-1609(03)00055-8

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located in the middle of the riverbed with a total lengthof 483m, 26 powerhouse-dam sections are situated atthe two sides of the spillway dam and have a total lengthof 1228 m. Along the foundation line, the dam sectionsare built on different ground levels, low on the riverbottom and high on the riverbank. Detailed geologicalinvestigations show that although the dam foundation

mainly comprises plagioclase granite that is intact,homogeneous, of low permeability and high strength,there also exist weathered zones, faults and joints in therock mass. In particular, gently dipping joints are welldeveloped locally. When the project is nished and runsat the normal pool level, the resulting reservoir willextend nearly 600 km upstream and have a total storage

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Nomenclature

Lp geometrical parameter of the prototypes p stress of the prototypeep strain of the prototypedp displacement of the prototypeE p deformation modulus of the prototypenp Poisson’s ratio of the prototypeX p volume force of the prototyper p density of the prototype f p friction coefcient of the prototypecp cohesion of the prototypeRp compressive strength of the prototype% s p boundary stress of the prototypeLm geometrical parameter of the models m stress of the modelem strain of the modeldm displacement of the model

E m deformation modulus of the model

nm Poisson’s ratio of the modelX m volume force of the modelr m density of the model f m friction coefcient of the modelcm cohesion of the modelRm compressive strength of the model% s m boundary stress of the modelC L similarity constants for geometryC s similarity constants for stressC e similarity constants for strainC d similarity constants for displacementC E similarity constants for deformation modulusC n similarity constants for Poisson’s ratioC X similarity constants for volume forceC r similarity constants for densityC f similarity constants for friction coefcientC c similarity constants for cohesionC R similarity constants for compressive strength

C % s similarity constants for boundary stresses

l l o

w

Y e

R i v e r

Lanzhou

Lhasa

Kunming

R i v e r

Y a n g z t e

Chengdu

z t

e

Y a n g

Urumqi

R i

Guangzhou

Haikou

Nanni ng

Chengqing

Xi'an

Wuhan

Ye llow

v e r

R i

Nanjing

Taiwan

Shanghai

BeijingHohhot

v e r

Harbin

Shenyang

The Three Gorges Project

Fig. 1. Location of the Three-Gorges Project in China.

J. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 609–631610


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capacity of 39.3 billion cubic meters, which is of extremeimportance to the safety of the dam.

During the past decades, the Yangtze Water Re-sources Commission (CWRC), with the collaboration of the Chinese Academy of Science, the Ministry of

Geology, and a number of universities and institutesof China, carried out extensive geological investigations,eld and laboratory testing of the rock and soilproperties related to the Three-Gorges Dam. Thisresearch work has been thorough and systematic, and

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The numbered left powerhouse dam sections

S h i p l i f t

T e m p o r a r y s h i p l o c k

S p i l w

a y d a m

L e f t p

o w e r

p l a n t

R i g h

t p o w

e r p l a

n t

Assembla ge sectio n

1314 1211 10

89

4

76

5

23

1

Scale

Y a n g t z e R i v e r

P e r m a n e n t s h i p l o c k

N

1 km

Fig. 2. Layout of the Three-Gorges Project and the numbered left powerhouse-dam sections.

Fig. 3. Upstream view of the Three-Gorges Project under construction.

J. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 609–631 611


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sections for stability studies, using the knowledgefrom the geological investigation and conceptualiza-tion [12–14], is a critical process.

A systematic study procedure was established to carryout this stability assessment project. Based on the results

of geological investigations and mechanical tests of therock mass, the geological and geomechanical models of the Three-Gorges Dam foundation were rstly estab-lished and a study procedure for the stability assessmentwas provided. Then, using the same geomechanicalmodel, 2D and 3D physical model tests for some criticaldam sections were performed. In the physical modeltests, various testing materials were selected to simulatethe rock, concrete, fracture and rock bridge. Theprototype load and boundary conditions were alsomodeled according to similarity theory. During thetesting process, the displacements at some importantpositions of the dam structure and foundation weremonitored. The failure mechanism of the dam founda-tion was derived through a progressive overloading thatsimulated the upstream hydrostatic water pressure, andthe factor of safety was dened as the ratio between themaximum external load inducing the start of slidinginstability of the dam foundation and the upstreamhydrostatic load applied to the dam. The comparisonsbetween the results of 2D and 3D physical model testswere conducted.

This study mainly concerns the following aspects: (1)establishment of the geomechanical model of the damfoundation; (2) physical model tests; (3) numerical

modeling; (4) comprehensive stability assessments basedon modeling results; (5) additional treatment andreinforcement design. Part I of this paper describes thecharacterization and conceptualization of the geome-chanical conditions of the foundation, and physicalmodel tests. The Part II companion paper presents thenumerical modeling, comprehensive assessment, rein-forcement measures, and the overall conclusions.

2. Site geology and mechanical properties of the rockmass

2.1. Site geology

For identifying the geological setting at the dam site,various exploration techniques and methods wereadopted, including conventional techniques (such asgeological mapping, borehole drilling, adit, shaft ex-ploration, etc.), geophysical prospecting (such as acous-tic emission, remote sensing techniques, seismicreection, seismic refraction and electromagnetic wavetechniques), physical–chemical analysis and micro-structural analysis, etc. The investigations coveredbasically all the geologic aspects, including regional

geology, regional geomorphology, quaternary geologyand hydrogeology at the dam site [1,15]. This provides asound and adequate basis for the stability assessment.

The investigations show that the foundation rockmainly comprises plagioclase granite which is intact,homogeneous and of high strength. According to the

degree of weathering, the typical weathered prole maybe divided into four zones ( Figs. 5 and 6 ): completelyweathered, highly weathered, moderately weathered,and slightly weathered zones. The moderately weatheredzone can be further subdivided into an upper part and alower part. The total thickness of the rst threeweathered zones varies gradually from the ridge atriverbank (40–42m) to oodplain (17–20 m) and to low-water riverbed (11 m), while the thickness of the slightlyweathered zone is absent or very thin in the riverbed.The dam foundation is located on the lower part of themoderately weathered zone or on the top of the slightlyweathered zone.

Major faults and their dip angles at the dam site areillustrated in Fig. 7 . There are 886 faults identied withmostly steep dip angles. The statistical analysis demon-strates that 90% of them have lengths of less than 300 mand widths of less than 1 m. In accordance with theirstrike and persistence, these faults can be classied intofour groups.

* The rst group has trends NNW of 330–355 , withdip angles of 60–80 . They constitute 49% of thetotal fault population.

* The second group has NNE strikes of 5–30 with dip

angles of 55–75 , constituting 27% of the totalpopulation.

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Fig. 5. Borehole core of the granite rock in the dam site (core diameteris 800mm).


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constitute more than 90% of the total population of these two joint groups. Considering that the gentlydipping joints play an important role in the foundationstability, their distribution was divided into three kindsof regions with different densities along the verticaldirection in the boreholes. The statistical analysis

showed that, in the dam foundation, the average density

of short and long gently dipping joints is 0.24 and0.018 m 1 , respectively [15–17]. Fig. 9 depicts theseregions with the different densities. They are:

* relative developed region (I): long and short gentlydipping joints are both well developed, with linear

densities more than 0.024 and 0.31 m1

, respectively;* slightly developed region (II): either the density of longgently dipping joints is more than 0.024 m 1 , or, thedensity of short gently dipping joints is more than0.31 m 1;

* poor developed region (III): the densities of both longand short gently dipping joints are, respectively, lessthan 0.024 and 0.31 m 1 .

2.2. Mechanical properties of the rock mass

To dene the physical and mechanical properties of the rocks and fractures, both eld and laboratory testswere performed [18]. In addition, the deformationbehavior of the rock mass was acquired by means of plate bearing tests; the shear strengths of the rock andfractures were tested through in situ and laboratoryshear tests; the failure behavior of the rock mass wasobtained from triaxial tests [15–23]. The properties of

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Table 1Characteristics of the long gentle dipping joint sets in the Three-Gorges Dam foundation

Jointset

Dip direction Dip Developed level Characterist ics of joint surfaces

1 90–120 15–30 Relatively developed The joint surfaces are planar rough or undulating rough with jointllings of epidote

2 50–80 10–30 Slightly developed The joint surfaces are planar rough or undulating rough with jointllings of epidote or feldspathic minerals

3 170–190 10–30 Poorly developed The joint surfaces are undulating rough, without or with joint llingsof epidote

4 130–150 10–30 Poorly developed The joint surfaces are planar rough without joint llings

LEGEND 1 NptY

III II

27F

3 I

III

II

NptY

Right powerhouse dam

II

II

II

Spillway dam

4 II 5 III

F 7

6

0 80 160 240m

78 °

F 23

II

II

I I

I

Left powerhouse dam

II

III

7F

Dam axial line

1. Boundaries between plagiogranite and granite vein; 2. Faults and number ; 3. Relative developed regions of gently dipping joints;4. Slightly developed regions of gently dipping joints; 5. Poor developed regions of gently dipping joints;6. Boundaries of developed regions with different densities of gently dipping joints

N

Scale

Fig. 9. Plan of the developed regions of gently dipping joints (with different densities) in the Three-Gorges Dam foundation.

S

W E

N

0% ~ 3%

> 15 %

3% ~ 6%

6% ~ 9%

9% ~ 12 %

12% ~ 15 %

Dam axial line: NE 43.5 °

Fig. 8. Pole density contour plot of the gently dipping jointsinvestigated in the foundation of the left powerhouse-dam sectionsof the Three-Gorges Dam.


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plagioclase granites and structural planes are listed inTables 2 and 3 , respectively.

3. Model conceptualization and study procedure forstability analyses

Due to the complexity of the natural geologicalconditions and variability of mechanical properties of rock masses, it is difcult to accurately and fullysimulate the geological conditions and the mechanicalproperties of the rock mass—even with the costly andtime-consuming work of extensive in situ and laboratorycharacterization as carried out for the Three-GorgesProject. Hence, it is recognized that rational simplica-tion and conceptualization of both geological conditionsand mechanical properties of rock masses are necessaryfor physical model tests and numerical modeling[12–14].

The conceptualization process considered the follow-ing steps: (1) careful verication of the underlyinggeological conditions, such as rocks, discontinuities andtheir distributions; (2) determination of the mechanical

parameter values of rocks and discontinuities; (3) pre-analysis of possible sliding mechanisms and identica-tion of all the potential sliding paths; (4) on account of the discrepancies unavoidably occurred during the testperiod, a safety margin for errors has to be consideredand reserved; (5) based on all the above steps, choosingthe most important and representative dam sections tobe simulated. Meanwhile, to pre-analyze the potentialsliding paths and possible failure mechanisms, thefollowing aspects have been taken into account: (i)

spatial geometrical characteristics of each fractureexplored, such as inclination and dip angle; (ii)combinative spatial geometrical properties of fracturesystem (such as connectivity) by which potential slidingpaths could be formed; (iii) relative distance betweenfractures and the upper concrete structure; (iv) mechan-ical properties of the intact rock and fractures.

Based on the above rationalization, the geologicalconceptualization of the Three-Gorges Dam foundationwas carried out in the following sequence.

(1) Because the weak weathered zones would be mostlyexcavated and the foundation mainly consists of plagioclase granite that is intact, homogeneous andof high strength, the major factor inuencing thefoundation stability would come from the pre-existing discontinuities. However, among thesediscontinuities, the faults mostly have steep dipangles (as depicted in Fig. 7 ), thin thickness, andwell-cemented tectonite, so they would not playimportant roles in the foundation stability.

(2) Most of the joint sets have steep or moderatedipping angles as those of the fault groups, andwould also play a less important role in thefoundation stability.

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Table 2Geotechnical properties of the plagioclase granite in the Three-Gorges Dam foundation

Degree of weathering Structural types of rock mass

Compressivestrength (wet)(MPa)

Density(kN/m 3)

Deformationmodulus (GPa)

Poisson’sratio

Frictionangle

Cohesion(MPa)

Fresh Blocky 90–110 27.0 35–45 0.20 59.6 2.0–2.2

Slightly weathered Sub-blocky 85–100 27.0 30–40 0.22 56.3 1.6–1.8Inlaid structure 85–100 26.8 20–30 0.22 52.5 1.4–1.6

Moderately weathered(lower part)

Blocky 75–80 26.8 20–30 0.22 56.3 1.6–1.8

Sub-blocky 75–80 26.8 15–20 0.23 52.5 1.4Inlaid structure 70–75 26.5 10–15 0.25 50.3 1.0

Moderately weathered(upper part)

Blocky 40–70 26.8 5–20 0.25 50.3 1.0

Fractured 15–20 25.5 1–5 0.27 — —

Table 3Mechanical parameters of structural planes in the plagioclase granite

Types of structuralplanes

Friction angle Cohesion(MPa)

Planar smooth 31 0.13Planar rough 37 0.3Combination of theabove two types

35 0.2

Rough 42 0.5Extreme rough 45 0.6


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(3) The gently dipping joint sets that have low anglesand dip downstream would be the most importantfactor governing the foundation stability. Amongthem, the long gently dipping joints, especially thosethat dip downstream and have acute angles betweentheir strikes and the dam axial line, are the most

likely ones to create sliding paths [15–17]. There-fore, the potential sliding paths could be assumedaccording to the following reasons: (i) the assump-tion of sliding paths can be based on gently dipping joints, geological proles of the foundation anddam structures. (ii) the assumed potential slidingpath must consider the combined effects of longgently dipping joints, rock bridges and short gentlydipping joints, which are produced by projectingshort gently dipping joints on the assumed slidingpath. (iii) the assumed sliding paths could be linear,curved or stepped. The mechanical properties of thelong and short gently dipping joints are assumed tobe the same.

(4) Gently dipping joints are concentrated in thefoundation of no. 1–5 left powerhouse-dam sections

(as shown in Fig. 9 , for the locations of thesesections see Fig. 2 ), with the long gently dipping joints having a dominant strike of 28 , inclinationof 118 and dip angles of 25–27 . In addition, anexposed steep rock slope (with a temporary heightof 67.8 m and permanent height of 39.0 m) will be

excavated on the foundation behind the dam anddipping downstream. Its downstream free facewould lead to less resistance against potentialsliding. From the above reasoning, it is concludedthat the sliding-resistant capacities of no. 1–5 leftpowerhouse-dam sections are the poorest of thedam foundation. Our studies are therefore concen-trated on the stability of no. 1–5 left powerhouse-dam sections.

(5) Further detailed investigations showed that in thefoundation of the no. 3 left powerhouse-damsection, both the average linear fracture density(cf. Table 4 ) and the potential of the sliding pathformation ( Figs. 10 ) of the gently dipping joints arethe greatest. Figs. 11 and 12 show the section of geological sketch and Stereographic projection of

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Table 4Comparison of the average linear densities of long gentle dipping joints distributed in the foundations of no. 1–5 left powerhouse dam sections

No. 1 section No. 2 section No. 3 section No. 4 section No. 5 section

average linear densities (number/m) Less than 0.078 0.071 0.121 0.078 Less than 0.071

0

10

20

30

40

50

60

70

80

90

No. No1. No2. No3. No4. No5.

Number of no.1-5 dam sections

C o n n e c t

i v i t y o

f g e n t

l y d i p p

i n g

j o i n t s ( % )

The connectivity is defined as the percentage of the total length of the gently dipping joints in a potential sliding path.

Fig. 10. Connectivity distribution of the gently dipping joints of main potential sliding paths in the foundation of no. 1–5 powerhouse-dam sections.


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the joints in the foundation of no. 3 powerhouse-dam section. Therefore, the no. 3 left powerhouse-dam section is most likely the most unstable of theseve dam sections, and should be chosen as the basisof the model establishment.

The geological model of no. 3 powerhouse-damsection is illustrated in Fig. 13 . For investigating theconstraint effects on the stability of this section provided

by the foundations of the adjacent no. 2 and no. 4powerhouse-dam sections, the stability of all these threedam sections needs to be studied. The geological modelsof no. 2 and no. 4 sections are given in Figs. 14 and 15 ,respectively. The characteristics of the main assumed

sliding paths in the above three geological models are,respectively, listed in Tables 5–7 .As for the mechanical parameters of the rock and

fractures, statistic analysis, fuzzy selection and opti-mized rate of oblique method were applied [15–23]. Onthe basis of the results acquired by these methods, themechanical parameters were determined for the stabilityanalyses as listed in Table 8 .

Summarizing the process of conceptualization andparameterization as aforementioned, the study proce-dure for the stability assessment of the Three-GorgesDam foundation is given by the owchart shown inFig. 16 .

4. Physical model tests: similarity theory andexperimental method

Physical model tests are the laboratory simulation of natural processes at a proportionally reduced scale.When the processes to be studied are so complex that amathematical representation is not easy, physicalmodels are often necessary to identify the key mechan-isms, and are an instrument for validation and calibra-tion of numerical models [24,25].

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22.2m

1 1 0 ° / 2 5 °

1 1 0 ° / 2 5 °

1 0 0 ° / 3 6 °

9 5 ° / 3 0 °

1 4 5 ° / 4 0 ° 2 8

0 ° / 5

3 °

1 2 0 ° / 4 2 °

3 0 0

° / 7 0

°

1 1 0 ° / 2 5 °

1 2 0 ° / 3 6 °

9 0 ° / 4 0 °

9 0 ° / 2 0 °

9 0 ° / 2 7 °

1 2 5 ° / 3 1 °

1 1 8 ° / 3 0 ° 1 2 0 ° / 3 8 ° 1 0 0 ° / 3 8 °

1 2 0 ° / 1 6 °

1 4 0 ° / 1 9 °

1 1 0 ° / 2 3 ° 1 4 0 ° / 1 9 °

1 2 0 ° / 1 6 °

1 2 0 ° / 1 9 °

2 7 0

° / 5 5

°

1 2 5 ° / 2 8 ° 9 0 ° / 2 4 °

9 0 ° / 1 0 °

1 1 0 ° / 2 5 °

1 1 0 ° / 2 5 °

1 2 6 ° / 2 8 ° 9 5 ° / 3 0 °

1 1 6 ° / 3 0 ° 1 0 0 ° /

2 6 °

1 5 0 °

/ 6 0 °

1 2 0 ° / 3 3 °

1 3 0 ° / 3 3 °

1 4 9 ° / 2 6 °

2 4 5 ° / 1 5 ° 3 1 5

° / 6 5

°

1 7 8 ° / 2 5 °

1 4 9 ° / 4 8 °

1 6 4 ° / 4 2 °

1 3 0 ° / 2 5 ° 1 3 0 ° / 1 9 °

1 3 0 ° / 1 9 ° 1 5 0 ° / 2 2 °

1 2 6 ° / 4 4 °

1 3 0 ° / 2 5 °

9 0 ° / 2 2 °

9 0 ° / 3 4 ° 1 2 0 ° / 1 8 °

1 0 0 ° / 3 0 °

1 3 0 °

/ 5 8 °

1 0 0 ° / 2 8 °

1 0 0 ° / 3 0 °

1 3 5 ° / 2 5 °

2 8 0

° / 5 5

°

1 4 0 ° / 3 1 °

1 5 0 ° / 2 3 °

1 1 0 ° / 1 8 °

2 8 0

° / 5 5

°

2 8 0

° / 5 5

°

1 3 0 ° / 1 9 ° 2 1 5 ° / 1 8 °

1 7 0 ° / 4 3 °

9 1 ° / 4 9 °

2 3 0 ° / 6 2

°

1 0 2 ° / 1 4 °

8 4 ° / 1 6 °

1 0 6 ° / 2 7 °

1 8 8 ° / 3 1 ° 1 0 8 °

/ 5 8 °

1 3 0 ° / 2 0 °

8 5 ° / 3 8 °

2 7 0

° / 5 5 °

6 0 ° / 2 7 °

1 3 0 ° / 4 0 °

1 0 9 ° / 3 5 °

1 1 0 ° / 2 5 °

1 1 0

°

/ 3 1 °

Joints with their dipsand dip angles

Faults with their dipsand dip angles

65m

90m

81.7m

Legend:

Fig. 11. Geological section sketch of no. 2 powerhouse-dam section of the Three-Gorges Dam.

Azumith of dam axial line

N

Fig. 12. Stereographic projection of the joints in the foundation of no.3 powerhouse-dam section of the Three-Gorges Dam.


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Fig. 13. Geological model of no. 3 left powerhouse-dam section of the Three-Gorges Dam.

Fig. 14. Geological model of No. 2 left powerhouse-dam section of the Three-Gorges Dam.



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Fig. 15. Geological model of No. 4 left powerhouse-dam section of the Three-Gorges Dam.

Table 5Characteristics of the main potential sliding paths in the geological model of no. 3 left powerhouse dam section (Refer to Fig. 13 for paths)

Potentialsliding paths

Totallength (m)

Length of long joints (m)

Length of rockbridges (m)

Length of short joints in rockbridges (m)

Ratio of lengthof joints to thetotal length (%)

Sections Dipangles ( )

ABCDE 113.4 90 23.4 2.69 81.7 AB 41CDE 26

PBCDE 125.2 79.8 45.4 5.22 67.9 PBCDE 26

ABCDFGH 129.6 104.4 24.6 2.83 83.1 AB 41BCD 26DF 52FGH 32

Table 6Characteristics of the main potential sliding paths in the geological model of no. 2 left powerhouse dam section


Totallength (m)




Ratio of length of joints to the totallength (%)

Sections Dip angles

ABC 124.4 41.0 83.4 9.59 40.7 AB 36BC 21

EBC 129.4 37.0 92.4 10.63 36.8 EB 27BC 21


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Fumagalli systematically developed the theory andtechniques of statical and geomechanical model tests,which had been applied to the stability assessment of aseries of dams, such as Ridracoli, Itaipu, and Canelles,etc. [9,10,26] . M

.

uller and Rossenblad studied the

physical modeling methodologies of jointed rock mass[10,24]. Moreover, high-density and low-strength mod-eling materials for physical model test were alsoresearched [27,28].

In this study, two physical model tests for no. 3 andno. 2–4 powerhouse-dam sections have been carried out.One is a 2D test considering only the no. 3 dam sectionand another is a 3D model considering three damsections together, no. 2–4. The purpose of the latter is toexamine the constraint effects of no. 2 and no. 4 sectionson stability of no. 3 section. The similarity theory andexperimental methods are described below.

4.1. Similarity theory

Physical models must satisfy a series of similarityrequirements in terms of geometry, physical–mechanicalproperties, boundary conditions and initial states.According to elasto-plasticity theory and dimensionalanalyses, these similarity requirements can be deducedfrom force–equilibrium equations, geometry equations,Hooke’s law and boundary conditions [9,10,26] .

The theory requires that some similarity coefcients,dened as the ratios of prototype parameters to modelparameters, must be constants. These prototype para-

meters are geometry, stress, strain, displacement,deformation modulus, Poisson’s ratio, volume force,density, friction coefcient, cohesion force, compressstrength and boundary stress, respectively [9,10,26] .Their similarity constants are dened as

C L ¼ Lp =L m ; C s ¼ s p=s m ; C e ¼ ep =em ;C d ¼ dp =dm ; ð1a Þ

C E ¼ E p =E m ; C n ¼ np =nm ; C X ¼ X p =X m ;C r ¼ r p =r m ; ð1bÞ

C f ¼ f p = f m ; C c ¼ cp =cm ; C R ¼ Rp =Rm ;C % s ¼ % s p =% s m ; ð1cÞ

where C L ; C s ; C e; C d; C E ; C n; C X ; C r ; C f ; C c; C R ; C % srepresent the similarity constants for geometry, stress,strain, displacement, deformation modulus, Poisson’sratio, volume force, density, friction coefcient, cohe-sion force, compress strength and boundary stress,respectively. The symbols L; s ; e; d; E ; n; X ; r ; f ; c; R;% s denote the parameters of geometry, stress, strain,displacement, deformation modulus, Poisson’s ratio,volume force, density, friction coefcient, cohesionforce, compress strength and boundary stress. Thesubscript p denotes that the corresponding parameteris of prototype, while the subscript m indicates thatthe corresponding parameter is that of the physicalmodels.

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Table 7Characteristics of the main potential sliding paths in the geological model of no. 4 left powerhouse dam section


Totallength (m)




Ratio of length of joints to the totallength (%)

Sections Dip angles

ABCD 102.2 28 74.2 8.53 35.7 AC 23

BC 62CD 19

ABCE 109.4 28 81.4 9.36 34.2 AB 23BC 62CE 24

FGH 140.6 28 112.6 12.95 29.1 FGH 26.5

Table 8Mechanical parameters of the foundation rock and joint plane used in the stability studies

Type Compressivestrength (MPa)

Density (kN/m 3) Deformationmoduli (GPa)

Poisson’s ratio Friction angle Cohesion (MPa)

Plagioclase granite 100 27.0 35 0.20 59.6 2.0Joint planes — — — — 35 0.2Dam concrete 200 24.5 26 0.167 48 3.0Foundation surface — — — — 48 1.3


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The following similarity criteria must also be met inthe physical modeling:

C sC r C L

¼ 1; ð2Þ

C e ¼ C r ¼ 1; ð3Þ

C eC r

¼ 1; C d

C L¼ 1;

C cC s

¼ 1; C s

C R¼ 1;

C % sC s

¼ 1; ð4Þ

C f ¼ 1: ð5Þ

These criteria are the guiding parameters for choosingor manufacturing the modeling materials of the physicalmodel tests with specied mechanical properties, model

size and proportions, magnitudes of loading forces, andboundary conditions [9,10,26] .

4.2. Simulation of loads

Five kinds of loads were simulated in the physicalmodeling, including self-weight of dam and rockmass, water pressure, sediment pressure, and osmoticpressure acting on the grout curtain. From Eqs. (2)and (3), if C r equals 1 and C s equals C L ; the self-weight stress regime of the model can satisfy thesimilarity requirements. Thus, the simulations of self-weights can be done by choosing the model materialsthat have the same densities as those of the correspond-ing prototype materials [9,10,26] . The water pressure,

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Preliminary geological investigations

Comparison among the 15 candidate dam sites

Selection of the Sandouping dam site

Geological investigations Rock mechanics tests

Stability comparison and analysis of all the dam sections and selection of the

1st -5 th powerhouse dam sections for detailed analysis

Further study of the 3 rd powerhouse dam section as the

most unstable section

Establishing a geomechanical model for No.3 left powerhouse-dam section

Physical modeling Numerical modeling

Conclusion on the No. 3 section’s stability condition

according to the physical and numerical modeling

Foundation treatment and reinforcement design

End

Fig. 16. Flowchart of the stability study procedure for the Three-Gorges Dam foundation.




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sediment pressure and osmotic pressure acting on groutcurtain were simulated by use of the loading systemcombined with oil jack, jacking block and jack-carryingsteel frame (illustrated in Fig. 17 ) with their magnitudes

satisfying both Eqs. (2) and (4). The seepage pressure inthe dam foundation was not modeled in this study forthe following reasons. On the one hand, the Three-Gorges Dam foundation mainly comprises plagioclasegranite that is intact and of very low permeability;meanwhile, most of the joints in the foundation are notthrough-going and have a low connectivity with well-cemented tectonite, thus, the inuence of seepagepressure on the stability of the dam foundation wouldnot be so signicant. On the other hand, to date, thereare very few available data of the seepage pressuremonitored from the dam foundation; besides, there isconsiderable difculty in physical model tests to modelthe effects of seepage pressure [16,17,29,30] .

In order to understand the failure mechanisms of thedam foundation, a progressive overloading that simu-lated the upstream hydrostatic water pressure wasperformed. The factor of safety was dened as the ratiobetween the maximum external load inducing the startof sliding instability of the dam foundation and theupstream hydrostatic load applied to the dam. Themethod of the overloading test was the so-called triangleoverloading method through a progressive overloadingof the upstream water pressure, which is assumedequivalent to the increase of water density; meanwhile,

the self-weight of dam and rock mass remains un-changed. In the process of the modeling test, theupstream hydrostatic load was progressively appliedaccording to the same increment steps until the dam

fails. In each increment, 20% of the normal pool level(denoted as P 0) was applied.

4.3. Simulation of boundary conditions

The boundary conditions for both physical modelswere simulated in the same way: namely, the normalconstraint was applied to the upstream and downstreamboundaries (modeled by tight contacts between theseboundaries and the rigid plate xed in test frame), a xedconstraint to the bottom boundary (modeled by strongcontact between these boundaries and the rigid plate xedin test frame), and a free condition to the right and leftboundaries of the models. Nevertheless, it should benoted that boundary conditions of the right and leftboundaries of no. 3 dam section are different in these twophysical model tests—which are free in the physicalmodel of the single no. 3 section but are constrained bythe adjacent foundations of no. 2 and no. 4 sections in thephysical model of the integrated no. 2–4 sections.

4.4. Monitoring

In the physical modeling, the main objective of monitoring is to capture the displacements and their

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Damconcrete

Rock mass

Powerh ouse

Steel frame

Oil Jack Bearing block

Bearing block

Steel frame

Oil Jack

1 m0.5 m0 m

Steel supporting frame

Scale

Fig. 17. Loading apparatus for the physical model tests.




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development processes so that we can identify thestability state of the dam. The displacements monitoredin the models include absolute displacements (surfacedisplacement of dam and foundation) and relativedisplacements (internal displacement between the upperand lower sides of the fractures). The former weremeasured by inductive displacement sensors with aprecision of 0.001 mm, which was installed in a xedsteel frame made for this specic measuring objective.

The latter were monitored by internal displacementsensors (strain-gauged cantilevers) with the same preci-sion, which were buried in the lower side of the fracture,while a corresponding device was xed in the upper side(Fig. 18 ). For the positions of monitoring points of relative displacements, see Figs. 13–15 .

5. Physical modeling of no. 3 powerhouse-dam section

5.1. Similarity coefcients, simulation scope and model materials

Table 9 lists major similarity coefcients determinedfor this physical model tests. The dimensions of the damfoundation to be modeled are 150 m depth fromfoundation surface downward, 38.3 m of width (thesame as the dam body), 95 m in length directed upstreamfrom the dam heel and 345 m in length directeddownstream from the dam toe. Based on the geometrysimilarity coefcient of 150, the actual physical modelhas dimensions of 1.63 m height, 0.26 m width, 0.63 m(upstream direction) and 2.3 m (downstream direction)lengths. Fig. 19 shows a photograph of the physicalmodel of no. 3 powerhouse-dam section.

To nd out if the model materials met the similarityrequirements, different combinations of raw materials(including gypsum powder, barite powder, lithopone,cement, bentonite, machine oil, parafn oil, water, etc.)were rstly analyzed to obtain some tentative prescrip-tions. Then, different mixture ratios of these ingredientswere chosen for each specic prescription. The mixtureswere stirred sufciently and pressed in press moldingmachine to produce several sets of model materialspecimens, whose properties were tested in laboratory.Finally, based on the test results, two mixture ratios of gypsum powder, barite powder, lithopone, machine oiland water were selected for simulating the concrete androck. The joint surfaces were simulated by the ungluedinterfaces between model material blocks (which arenormally glued to construct the models). The shearstrength of this model interface was tested. Table 10 liststhe major properties of model materials, prototype

materials and joint surfaces, showing an acceptablesimilarity in material properties between the model andprototype.

5.2. Modeling results and analyses

Table 11 , Figs. 20 and 21 present the majordisplacement results and their development processesderived from the physical model test for the no. 3 damsection. The monitored displacements were convertedinto prototype displacement using the similarity coef-cients. According to these results, three different stagesof the displacement development can be identied,following the increases of the upstream hydrostaticloading.

A displacement development during the upstreamhydrostatic load increases from zero to 1 :8P 0 can beidentied as the rst stage. As shown in Fig. 21 , at thisstage all the load–relative displacement curves alongthe potential sliding planes remain as straight obliquelines. This indicates that during this loading process, thedam foundation behaves elastically without slidingalong any potential failure surfaces in the foundation.In addition, as shown in Table 11 , under normal loadingcombination (1.0 P 0), the magnitudes of the horizontal

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Table 9Similarity coefcients between prototype parameters and modelparameters used for the 2D physical model test of no. 3 leftpowerhouse dam section

C L C r C E C s C c C f C e

150 1.0 162 162 162 1 1

F i x e d e n

d

F i x e d e n

d

Strain gauges

Strain gauges

D

Strain gauges

C

B

A

Fig. 18. Internal displacement sensor for the relative displacement monitoring adopted in the physical model tests.


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displacements at both dam heel and toe are 2.10 mm,indicating that the shear strength along the foundationsurface is sufcient so that the horizontal displacementsalong this surface are small. Based on the aboveanalyses, it can be concluded that the dam foundationis stable until 1.8 P 0 ; and, the safety of the dam can beensured under normal loading combination.

A displacement development during the upstreamhydrostatic load increases from 1.8 P 0 to 3.5 P 0 can be

identied as the second stage. As shown in Fig. 21 , afterthe upstream hydrostatic load was applied up to 1.8 P 0;the slopes of the load–relative displacement curves atpoints 1, 2, 4 and 6 (see Fig. 13 for the locations of thesepoints) decreases gradually. Under the overloading of 1.8P 0; the rst turning points appear on these curves.This indicates that along the assumed slide planes of ABCD, IC and KNO (see Fig. 13 ), plastic sheardeformations occurs, with the result that at these

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Fig. 19. The physical model of no. 3 powerhouse-dam section of the Three-Gorges Dam.

Table 10Comparison of mechanical properties of 2D physical model materials and prototype materials of no. 3 left powerhouse dam section

Mechanicalproperties

Rock Dam concrete Joint Foundation surface

Prototype Model Prototype Model Prototype Model Prototype Model

Deformation

modulus (GPa)

35.0 0.210 26.0 0.160 — — — —

Density (kN/m 3)

27.0 25.0 24.5 22.7 — — — —

Friction angle 59.6 59.3 48 46 35 34.6 48 47.5Cohesion(MPa)

2.0 0.053 3.0 0.051 0.2 0.0 1.3 0.065

Table 11Displacements of key positions of no. 3 left powerhouse dam section under normal loading combination monitored from the 2D physical model test

Displacements of dam top (mm) Displacements of dam heel (mm) Displacements of dam toe (mm)

Horizontal Vertical Horizontal Vertical Horizontal Vertical

14.85 3.30 2.10 1.13 2.10 0.37


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monitoring points, the rate of increase of the displace-ments is larger than before. Nevertheless, the damremains stable at the second stage.

The third stage can be dened as the process from theloading of 3.5 P 0 until the dam failure. At this stage, theslopes of load–relative displacement curves at points 1,2, 4 and 6 decrease dramatically, with abrupt increase of displacements and occurrence of second turning pointson these curves. However, this situation does not occurat other monitoring points. The above results indicatethat after the load application of 3.5 P 0; the sliding alongthe paths of ABCD, ICD and KNO (see Fig. 13 ) occurssimultaneously, and may cause dam failure. On theother hand, fracture traces (shown in Fig. 22 ) can be

observed on the model surface along the above slidingpaths, and along aA and bA paths (cf. Figs. 13 and 22 )in the dam itself. This reveals that the concrete strengthof the dam plays an important role in sliding resistance.

Depending on the above analyses, a conclusion can bedrawn that the sliding starts under the overloading of

3.5P 0: Thereby, if the factor of safety is dened as theratio between the failure load and the normal hydro-static load [5], it should be 3.5.

6. Physical modeling for no. 2–4 powerhouse-damsections

6.1. Similarity coefcients, simulation scope and modeling materials

To study the constraint effects applied by thefoundations of no. 2 and no. 4 dam sections on thestability of no. 3 dam section between them, a 3Dphysical modeling of the combined no. 2–4 dam sectionswas conducted.

Table 12 lists major similarity coefcients designed forthis model. The dam foundation has the dimensions of 140 m depth, 114.9 m width (the same as the dambodies), and 74 m in length directing upstream from thedam heel and 250 m in length directing downstreamfrom the dam toe. According to a geometry similaritycoefcient of 120, the actual physical model has thedimensions of 1.96m height, 0.96m width, 0.62m(upstream direction) and 2.08 m (downstream direction)

lengths. The model material ingredients were the sameas those of the no. 3 dam section model, but differentmixture ratios of these ingredients were used forsimulating the rock and concrete for these two sections.The rock bridges and joints faces were simulated in thesame way as the 2D model simulating the no. 3 damsection. The major properties of all the model materialswere also tested and are listed in Table 13 . It should benoted that in this model, the left and right boundaries of no. 3 dam section are, respectively, connected with thefoundations of no. 2 and no. 4 sections, the latter wouldproduce constraint effects on the foundation of no. 3section. In addition, the left side of no. 2 section and theright side of no. 4 are treated as free surfaces.

6.2. Modeling results and analyses

Since the stability of the single no. 3 dam section hadbeen studied rst, for model tests of no. 2–4 damsections, only one monitoring point was selected for theresult analysis. This monitoring point positions at no. 1point is shown in Fig. 13 .

Similar to the model test of no. 3 dam section, threedifferent stages of the displacement development canalso be identied during the physical model test of the

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0.0

0.4

0.8

1.2

1.6

2.02.4

2.8

3.2

3.6

4.0

4.4

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

Horizontal displacements (mm)

L o a

d i n g r a

t i o s

( P / P o )

Dam top

Dam heel

Fig. 20. Load-horizontal displacement curves of monitoring points of the no. 3 powerhouse-dam section derived from the 2D physical modeltest.

0.00.40.81.21.62.02.42.83.23.64.04.4

-2 0 2 4 6 8 10 12 14 16 18 20 22

Relative displacements (mm)

L o a

d r a

t i o s

( P / P o )

1234567

Fig. 21. Load–relative displacement curves of monitoring points of theno. 3 powerhouse-dam section derived from the 2D physical modeltest.


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no. 2–4 dam sections (see Figs. 23–25 ). From zero to thenormal loading combination (1.0 P 0), all the load– relative displacement curves derived from this modelingappear to be straight oblique lines. This indicates that atthis stage, the dam foundations behave elastically andsliding does not occur. As shown in Table 14 , under thenormal loading combination, the magnitudes of thehorizontal displacements at both dam heel and toe of no. 3 dam section are less than 2.0 mm.

Fig. 23 reveals that under the load application of 4.0P 0; the nal turning point appears on the load– relative displacement curve at point 1. At this turningpoint, the slopes of this curve dramatically decreases andthe relative displacement increases abruptly. Thisdemonstrates that the sliding in the foundation of no. 3 dam section occurs at the overload of 4.0 P 0; whenno. 2 and no. 4 dam sections’ constraint effect was

considered and thereby, the factor of safety of this dam

section could be dened as 4.0.From Fig. 24 , we nd that the load–relative displace-

ment curves at no. 1, 2, 4, 6 and 7 have their respectivenal turning points under the overloading of 4.2 P 0;4.4P 0; 4.4P 0; 4.4P 0 and 4.8 P 0; respectively. These plotsshow that the sliding in the foundation of no. 2 damsection happens rst along the slide path of ABCD, andthen EBCD and FB (see Fig. 14 ). Simultaneously, thefracture traces (depicted in Fig. 26 ) along these slidepaths and aA path in the dam itself were observed onthe corresponding side faces of the model. Therefore, itfurther demonstrates that the shear strength of the damplays a helpful role in the sliding resistance, and the factorof safety of no. 2 dam section could be dened as 4.2.

As for no. 4 dam section, the load–relative displace-ment curves at monitoring points 1–5 have their nalturning points at the load of 4.2 P 0; 4.6P 0; 4.4P 0; 4.6P 0and 4.8 P 0 (as shown in Fig. 25 ), respectively. This is tosay that the sliding in the foundation of this sectionfollows along the paths of ABC, then CD, and nallyCE (see Fig. 15 ). This failure mechanism of no. 4 sectionalso was demonstrated by the observation of thefracture traces on the model surface (illustrated asFig. 27 ). Based on this failure mechanism, the factor of safety of no. 4 dam section can be dened as 4.2.

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Fig. 22. Sketch of fracture traces on the model surface of the no. 3 powerhouse-dam section observed from the 2D physical model test.

Table 12

Similarity coefcients between prototype parameters and modelparameters determined for the 3D physical model test of no. 2–4 leftpowerhouse dam sections

C L C r C E C s C c C f C e

120 1.0 120 120 120 1 1


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7. Comparisons and discussions

Comparing the horizontal displacements at the damtop and toe of no. 3 dam section derived from the two

physical model tests, it can be found that theirmagnitudes decrease from 14.85 (top) and 2.10 (toe) to11.74 (top) and 1.20 mm (toe) (cf. Table 11 and Table14), respectively. Consequently, the factor of safety of the no. 3 section increases from 3.5 (considering only no.3 section) to 4.0 (considering constraint effects of no. 2and no. 4 sections).

On the other hand, according to the results derivedfrom the second model test, the factor of safety of no. 3dam section, which is determined as 4.0, is lower thanthose of no. 2 and no. 4 section (both are 4.2). Thisagrees with the conclusion of the geological conceptua-lization that the foundation stability of no. 3 damsection is poorer than that of no. 2 and no. 4 damsection.

From this study, it has been found that physicalmodel tests have the following advantages. Firstly,since the rock bridges can be simulated directlyusing the same methods as that of the foundationrock, it is a more convenient and straightforwardapproach in this regard. Secondly, in the physicalmodel tests, the factor of safety is dened as theratio between the maximum external load inducingthe start of sliding instability of the dam foundation

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Table 13Comparison of mechanical properties of 3D physical model materials and prototype materials of no. 2–4 left powerhouse dam sections

Mechanical properties Rock Dam concrete Joint Foundation surface

Prototype Model Prototype Model Prototype Model Prototype Model

Deformation modulus (GPa) 35.0 0.305 26.0 0.21 — — — — Density (kN/m 3) 27.0 26.8 24.5 24.6 — — — — Friction angle 59.6 59.5 48 48 35 34.2 48 45Cohesion (MPa) 2.0 0.045 3.0 0.052 0.2 0.0 1.3 0.056

00.40.81.21.6

22.4

2.83.23.6

44.44.85.25.6

0 10 20 30 40 50 60


L o a

d r a t

i o s

( P / P o )

1

Fig. 23. Load–relative displacement curves of monitoring points of theno. 3 powerhouse-dam sections derived from the 3D physical modeltest.

0.40

0.81.21.6

22.42.83.23.6

44.44.85.25.6

-4 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56Relative displacements (mm)

L o a

d r a

t i o s

( P / P o )

1234567


0-4 0 4 8 12 16 20 24


L o a d r a

t i o s

( P / P o )

1

2

3

4

50.40.81.21.6

22.42.83.23.6

44.44.85.25.6



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and the upstream hydrostatic load applied to the dam.Therefore, it gives an indication of the foundationcapability to withstand external loads. Moreover, byusing the overload test, the physical modeling can revealthe most critical sliding mechanisms of potential damfailure.

In practice, the dam failure can be caused by otherfactors, namely the gradual decrease of the shearstrength of joints due to seepage, deformation anddamage, and geochemical reactions between waterand fracture surface minerals. To date, it is difcultfor the physical modeling techniques to consider sucheffects of the shear strength reduction of joints. Inaddition, in a case such as a dam, since the maximumhydrostatic loads are not particularly certain factors,the denition of factor of safety adopted in the phy-sical model tests may not be complete or fullyrepresentative [5].

8. Conclusions

The complexity of geological conditions and varia-bility of the rock mass properties resulted in difcultiesfor the stability study of the Three-Gorges Damfoundation. Therefore, the conceptualization of thegeomechanical conditions and determination of thestudy procedures was essential, and integration of multiple analysis methods were considered to be moreeffective and reliable approaches. In this paper, as Part Iof the study, the physical model tests and results wereused to study the foundation stability of some criticaldam sections in the Three-Gorges Dam. The followingconclusions can be drawn.

(1) Analyses and conceptualization of geomechanicalconditions of the Three-Gorges Dam foundationshows that the gently dipping joints are the most

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Table 14Displacements of key positions of no. 2–4 dam sections under normal loading combination monitored from the 3D physical model test

Dam sections Displacements of dam top (mm) Displacements of dam heel (mm) Displacements of dam toe (mm)

Horizontal Vertical Horizontal Vertical Horizontal Vertical

No. 2 section 11.42 2.67 1.96 1.02 1.08 1.44

No. 3 section 11.74 2.1 1.85 0.95 1.20 1.32No. 4 section 10.48 3.0 2.55 0.51 1.02 1.02



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important factors governing the foundation stabi-lity, and the foundation of no. 3 powerhouse-damsection is the most critical. This concept was veried

by the results of the physical model tests.(2) The results of the physical model tests show that

under normal load combination, the foundationstability of no. 3 dam section is sufcient. Thepotential sliding and failure of this dam sectioncould happen mainly along the potential slidingpath of ABCDFGH (see Fig. 22 ).

(3) The physical model tests of the associated no. 2–4dam sections demonstrated that the constrainteffects induced by the adjacent foundations play apositive role in the foundation stability of the mostcritical no. 3 dam section, with the increase of itsfactor of safety from 3.5 (without consideringconstraints of no. 2 and no. 4 sections) to 4.0(when their constraint effects were considered).

(4) Based on the Chinese Design Criterion for ConcreteGravity Dams (in which the factor of safety againstsliding of concrete gravity dam must be more than3.0), the experience from design and construction of many similar projects in China and the particularimportance of the Three-Gorges Project, the Tech-nical Committee of the Three-Gorges Projectdecided that the factor of safety against sliding of the Three-Gorges Dam must be more than 3.0[16,17,19,31] . Hence, the results of the physical

model tests indicate preliminarily that the stabilityof this dam section is ensured. Since the foundationof no. 3 powerhouse-dam section is the most critical

in terms of stability against sliding failure, it can betentatively deduced that the stability of the Three-Gorges Dam also satises the safety requirements.

Nevertheless, as stated previously in this paper,because of the incomplete denition of factor of safetyadopted in the physical model tests and the unavoidableerrors associated with the testing process, it is importantto study and assess the stability of the Three-GorgesDam foundation using other methods. For this reason,in Part II of this two part paper, numerical modeling,including FEM and LEM, are applied to analyze thestability of the Three-Gorges Dam foundation, based onthe same geological conceptualizations and materialproperties. The purpose is mainly to study the effects of gradual degradation of fracture shear strength undernormal loading combinations, which cannot be properlyand effectively investigated by physical model tests.

Acknowledgements

The paper has been nancial supported by the Three-Gorges Development Corporation, Changjiang WaterResources Commission, the Special Funds for Major

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State Basic Research Project under Grant no.2002CB412708, Pilot Project of Knowledge InnovationProgram of Chinese Academy of Sciences under Grantno. KGCX2-SW-302-02, and National Natural ScienceFoundation of China under Grant no. 59939190. Theinductive displacement sensors and model material

pressing apparatus used in this study were provided byISMES, Bergamo, Italy. The authors wish to thank alltheir colleagues in the Department of Structures andMaterials, Yangtze River Scientic Research Institute,for their valuable contributions to various parts of thework described in the paper, particularly Professor GongZhaoxiong, Han Shihao, Shen Tai and Chen Jin, andEngineers Ye Liu, Sun Shaowen and Huang Mingxiao.The authors are also grateful to Dr. Lanru Jing, RoyalInstitute of Technology, Stockholm, Sweden, and Prof.J.A. Hudson for helping in preparing this paper.

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Stability assesment of the Three Gorges foundation