International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243

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International Journal ofRock Mechanics & Mining Sciences

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Geomechanical model test for stability analysis of high arch dam basedon small blocks masonry technique

Y.R. Liu n, F.H. Guan, Q. Yang, R.Q. Yang, W.Y. ZhouState Key Laboratory of Hydroscience and Hydraulic Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o

Article history:Received 24 April 2012Received in revised form28 January 2013Accepted 1 March 2013Available online 9 April 2013

Keywords:Geomechanical model testArch damStabilityRock massBlock masonry

09/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.ijrmms.2013.03.003

esponding author. Tel.: þ86 10 62796954.ail address: liuyaoru@tsinghua.edu.cn (Y.R. Liu

a b s t r a c t

Rock mass deformation and strength property simulation plays a key role in the rupture tests of arch damgeomechanical model. Subject to the limit of geometry scale, usually the simulation of tectonicdiscontinuities, such as faults, disturbed belts, crush belts and weak interlayer were ignored as safetybuffer, which may yield overstated safety factors. In this paper, small block masonry technique and lowstrength binder invented make the simultaneous simulation of the rock mass and tectonic discontinuitiesavailable, which is more coincident with real engineering conditions. Based on the material test of blocksand binder, the small blocks masonry technique has been successfully applied in the rupture test ofXiluodu arch dam. With the assistance of high-accuracy monitoring and measuring system, the stress(strain) and displacement distribution of the dam, abutments and rock foundations are obtained. Byanalyzing these monitoring results, the failure process, mode and mechanism of the dam body andabutments are derived for further identification of weakness. At last, the comparative analysis with otherarch dam geomechanical rupture test results yields the evaluation of the dam's global stability andnecessary reinforcement measures.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Geomechanical model testing is mainly used for the failuremechanism analysis of foundation-superstructure system. The testfocused on the stability evaluation and failure process trackingafter the rock mass undergoing plastic flow post-yield, as wellas the stress and deformation distribution affected by tectonicdiscontinuities, such as faults, disturbed belts, crush belts andweak interlayer [1,2].

As pioneers, Fumagalli [3,4] have explored the technicalresearch of geomechanical model test in Institute of StructureModel Experiment and Simulation (ISMES) since the 1960s. Theirmodels included Almendra Dam (with height of 222 m), VajontDam (with height of 262 m), the Grancarevo arch dam and the Ca'Selva arch dam. The physical model of Ridracoli concrete arch-gravity dam had been finished at ISMES [5]. After that, subsequentresearch evolved in Portugal, the Soviet Union, Yugoslavia, France,Germany, the UK and Japan. Many physical models of arch damswere carried out at the Laborato'rio Nacional de Engenharia Civil(LNEC), in Lisboa, Portugal, such as Cambambe arch dam at scale1:200 [6,7], Alto Lindoso arch dam at scale 1:250 and Alqueva archdam at scale 1:250 [8]. Along with the fast paces of hydraulicproject construction since the 1970s, Chinese engineers endeavored

ll rights reserved.

).

in the study of analog materials [2,9–15], measurement techniques[16–21], loading methods [20], and testing systems [22].

Although the numerical approaches, especially finite elementmethod (FEM), were widely used in the simulation of geologicalstructures due to the rapid development of computer science inthe past decades, geomechanical model test is still an irreplaceablemethod in the stability and reinforcement analysis of dam [14,23–28],rock slopes [29–31], and underground caverns [12,32–35]. The advan-tages of geomechanical model tests are as follows [36]: (1) It is able tosimulate complex real structures; (2) The failure mechanism could bedirectly perceived through the loading process; (3) The testing resultcould support other researches and provide validation and calibrationfor numerical models [37]. With the rapid development of hydro-power stations in China, geomechanical models were widely andsuccessfully applied in stability and failure analysis of arch dams[14,15,21,38].

Xiluodu hydropower station is located on Jinsha River inSichuan Province, China, with a parabola double curvature archdam (285.5 m). The dam site is U shaped, embraced by steep sideslopes, as shown in Fig. 1. The gently rock stratum around the damabutment leaned to the left side of downstream, as shown in Fig. 2.

In this paper, physical model tests are conducted to investigatethe stability of the dam and the effect of the reinforcementmeasures. The geomechanical model is made up of small blocks,which accurately simulate the rock mass's behavior. Additionally,a three-dimensional overloading scenario is applied for bettersimulation of boundary conditions.

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2. Similitude theory of rupture test and simulation of rockmass materials

2.1. Principles of similitude

Geomechanical model is usually used for rupture tests that areconducted under nonlinear conditions. Physical models mustsatisfy a series of similarity requirements in terms of geometry.That is, some similarity coefficients, defined as the ratios ofprototype parameters to model parameters, must be constants.These prototype parameters are geometry, stress–strain relation-ship, friction and cohesion. Their similarity constants are definedas follows.

(1)

Geometric similarity: The geometric structure of the modelshould be similar with the prototype, as well as those tectonicdiscontinuities within it.

Fig. 1. Location of Xiluodu arch dam.

Fig. 2. Geological condition

(2)

s of X

Stress–strain relationship similarity: The deformation modu-lus, compressive and tensile strength of the model should besimilar with the prototype, as well as the stress–strainrelationship curve.

(3)

Shear strength similarity: The shear strength (f′ and c′) ofinterfaces between the dam, rocks and discontinuities of themodel should be similar with that of prototype.

According to dimensional analysis, similitude is presented asfollows:

CE ¼ CγCL ð1Þ

Cμ ¼ Cε ¼ Cf ¼ 1 ð2Þ

Cσ ¼ Cτ ¼ CC ¼ Cδ ¼ CE ð3Þwhere {CE ,Cγ ,CL,Cμ,Cε,Cf ,Cσ ,Cτ ,CC ,Cδ} represent similarity constantsfor Young's modulus, weight by volume, geometry size, Poisson'sratio, strain, friction coefficient, stress, shear strength, cohesionand displacement, respectively.

Cγ ¼ 1 is usually required in order to keep the test normal.Then:

CE ¼ CL ð4ÞIn the test, the geometry ratio is held as constant. The other

ratios could be obtained by solving Eqs. (2)–(4).Generally the tectonic discontinuity's connectivity rate of the

model should be the same as that of the prototype in order tomeet the similarity requirement. That could be achieved by specialmasonry and fabricating techniques, sometimes supported bydifferent size material blocks [1,23].

2.2. Experimental material

The appropriate experimental materials are crucial in thegeomechanical model test. If Cγ ¼ 1, the conversion of otherparameters could be straightforward. Additionally, the gravita-tional load could be well applied. According to Eqs. (3) and (4), the

iluodu arch dam.

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243 233

target experimental materials must be high density, low Young'smodulus, low strength [39]. Stimpson give a simple, qualitativeclassification of model materials for rock mechanics engineering[40]. There are several sample materials widely used in the testcurrently.

(1)

PbO or Pb3O4 as aggregate, ZnO as supplement [4,7]. Thematerial has high density. However, PbO or Pb3O4 is poisonousand ZnO is expensive. Some researcher used lithopone [14] asa substitute for ZnO, the result is satisfactory.

(2)

Mixture of epoxy resin, barite powder and glycerin [41]. Thismaterial has appropriate strength and Young's modulus. Thedisadvantage is that the material needs to be solidified by hightemperature, during which poisonous gas is generated as well.

(3)

Fluid wax as binder. These materials are mechanism propertystable, not sensitive to temperature or humidity changing.Besides, the pressed blocks need not to be dried. However, thefluid is expensive. Some researchers used engine oil as sub-stitute, the result is satisfactory [41,42].

(4)

Gypsum materials, sand or diatomite as supplement [8,10]. It isnot easy to handle with the water proportion and solidifyingtime for these materials.

(5)

High density metal materials, such as iron [9], lead [1], andcopper [43] powder as aggregates. The disadvantage isobvious: they are expensive. In addition, lead is poisonous,iron is constringent and rusty, and appropriate copper powderis not easily found.

(6)

NIOS [44] or IBSCM [45]. These materials perfectly meet thesimilarity requirement. The disadvantage is that the dryingprocess of NIOS is slow, while IBSCM is expensive by contain-ing the refined iron ore.

Fig. 3. Faults simulated in a geomechanical model.

Dam-Foundation model inside the steel frame

Fig. 4. The box-shape

(7)

d te

Temperature-analogue material [15]. These materials containfusible macromolecular, which could simulate the strengthreducing process.

This paper selects barite powder as aggregate, bentonite assupplement, and glue as binder. Barite has high density. Bentoniteis stable and inexpensive. Moreover, it could decrease the mix-ture's Young's modulus. Glue is useful for simulating the lowstrength of material. This analog material has several advantages.It satisfies all of the similitude's requirements, is inexpensive, andsuitable for simulation of brittle materials, such as concretes androcks. As a result, it well balanced the technical and economicconsiderations.

The Young's modulus E, internal friction coefficient angle φ andcohesion c of the analog material should be tested in order todetermine the mixture proportion ratios for different rock proper-ty's various requirements.

2.3. Model masonry technology

The existing techniques for constructing geomechanical modelsinclude pouring [3], tamping [19,20] and small block masonry[6,38]. Pouring method means to fill the liquid material into moldwithout binder. The model will not be available until drying out,and could not simulate the detailed tectonic discontinuities.Tamping method uses vibrating tamper to compact the materialsby layer paved in the testing frame preliminary. This process istime saving, and widely used in the underground carven modeltests. However, it is difficult to uniform the density of differentlayers [12] and simulate tectonic discontinuities. Small blockmasonry method constructs the model using the pre-pressedblocks one by one.

This paper developed a new small block masonry technique.The minimum size of the building blocks could be reduced to2 cm�2 cm�3 cm. The small blocks can be made with pressmachine. In the model, the small block simulates the deformationproperty of rock mass, while the binder works as strengthprovider. The scale of the model is usually between 1:100 and1:500, which required very low cohesive strength. The glue usedin this paper is newly invented, which could simulate f and c of therock mass at the same time. The glue is made of various propor-tional polyvinyl alcohol and water to simulate different level ofstrength, whose f and c will be further determined in a serial ofshear tests. The tensile strength of the glue is ignored in the testprocess thought it is nonzero. Additionally, the glue strength is notsignificantly affected by the temperature change within thenormal external environment (around 20 1C). As both the materialand model tests are performed in normal environment, theeffect of temperature change to glue's strength is not considered.

Used for support the displacement gauge, separated form model

Steel frame fixed with foundation

sting frame.

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243234

The rock joint plays a key role in the strength of the overall rockstructure. In order to simulate more accurately, the amount of glueused will be reduced proportionally according to the interfaceconnectivity rate (illustrated in Fig. 4) during the model masonrystage. No glue is applied in the connected area.

Usually the deformation property of the overall model is alsoemphasized other than the individual small blocks in order tocorrectly simulate the rocks of the prototype. Based on theprevious test's experiences, the Young's modulus of small blockmodel is 30–50% less than that of the continuous model [46]. Thatmeans the sizes of the small blocks could not be too small.

Table 1Similarity ratios.

Similarity ratio Value Similarity ratio Value

Cγ 1.0 CE 250CL 250 Cμ 1.0Cε 1.0 Cf 1.0Cσ 250 Cτ 250CC 250 Cδ 250

Table 2Mechanical parameters of the simulated rocks.

Type E/MPa μ c/MPa f

Prototype, 104 Model Prototype Model

Dam 2.40 96 0.167 2.5 0.01 1.60II 2.15 86 0.20 2.5 0.01 1.35III1

III1–1 1.49 59.6 0.25 2.2 0.0088 1.25III1–2 1.30 52 0.25 2.2 0.0088 1.25III1–3 1.20 48 0.25 2.2 0.0088 1.25III1–4 0.90 36 0.25 2.2 0.0088 1.25III1–5 1.00 40 0.25 2.2 0.0088 1.25

III2III2–1 0.60 24 0.28 1.4 0.0056 1.20III2–2 0.55 22 0.28 1.4 0.0056 1.20III2–3 0.50 20 0.28 1.4 0.0056 1.20

IV1 0.30 12 0.30 1.0 0.004 1.02

Table 3Mechanical parameters of the simulated interlayer disturbed belts.

Name Inclination Thick (cm) Altitude (

Prototype Model

Right bank C3 N241E, SE∠4–51 50 0.2 ▽345Lc5 N30–401E, SE∠8–101 60 0.24 ▽385Lc6 N30–401E, SE∠8–101 60 0.24 ▽423

C7 N30–351E, SE∠4–61 60 0.24 ▽479

C8 N381E, SE∠41 50 0.2 ▽536

C9 N361E, SE∠2–51 50 0.2 ▽562

Left bank C3 N18–231W, NE∠5–81 50 0.2 ▽339

Lc5 N20–301W, NE∠4–71 60 0.24 ▽380Lc6 N20–401W, NE∠8–111 60 0.24 ▽403C7 N25–351W, NE∠4–71 60 0.24 ▽479C8 N351W, NE∠51 50 0.2 ▽513

C9 N251W, NE∠41 50 0.2 ▽536

Riverbed C2 N25–301W, SW∠5–101 50 0.2 ▽302P2βn N25–301W, SW∠5–101 180 0.72 ▽240

a The range is the distance form surface of rock.

Fumagalli suggested that the sizes of blocks should be determinedbased on the mechanism test. The number of blocks should bemore than 100 [4].

2.4. The simulation of tectonic discontinuities (faults)

The mechanical property of tectonic discontinuities plays a keyrole in the stability of rock mass structure and reinforcementmeasures. Consequently it is crucial to simulate them accuratelywhen constructing the model. For the vital tectonic discontinu-ities, like faults, disturbed belts, overall model scale is unable toapply exactly due to the small size or low Young's modulus ofthem. At this moment, deformation similarity is held as constant,and the influence of side crush belts are also taken intoconsideration.

For the simulation of the friction coefficient f and cohesivestrength c, the previous tests adopted the technique by fillingvarnish mixed with grease and French chalk into the interfaces oflayers, which could provide large range of f (0.1–1.0). The dis-advantage is that its performance is unstable, sensitive to thetemperature changing and spraying technique, finally leadingdiscrete results [1]. Plastic films are also options in some tests,and the result is satisfactory. The analog materials used in thispaper are dehydrating gypsum (for deformation) and iridescentpaper (for strength). The material proportions depend on thethickness and mechanism of the interfaces.

Usually it is difficult to simulate cohesive strength c which isvery small after the similitude conversion, especially when f and chad already been determined by similarity requirements. Some-times c was ignored as safety buffer. This simplification will resultin lower safety factors. Fig. 3 shows the several faults constructedin a dam's geomechanical model.

3. Geomechanical model of Xiluodu arch dam

3.1. The masonry of the model

The simulated range of the model is determined by thesimilitude theory and prototype characteristics: 155 m of the

m) f C (MPa) Rangea (m)

Prototype Model Prototype�10−1 Model�10−4

0.5 0.5 1.7 70.55 0.55 2.5 100.43 0.43 0.8 3 o400.44 0.44 1.0 4 ≥400.43 0.43 0.8 3 o150.55 0.55 2.5 10 ≥150.43 0.43 0.8 3 o550.44 0.44 1.0 4 ≥550.35 0.35 0.5 2 o570.4 0.4 0.7 3 ≥570.43 0.43 0.8 3 o700.44 0.44 1.0 4 ≥700.55 0.55 2.5 100.44 0.44 1.0 40.55 0.55 2.5 100.35 0.35 0.5 2 o400.44 0.44 1.0 4 ≥400.35 0.35 0.5 2 o480.40 0.40 0.7 3 ≥480.35 0.35 0.5 20.35 0.35 0.5 2

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243 235

upstream (0.55 height of dam), 825 m of the down stream (2.9height of dam), 230 m depth under the riverbed (0.81 height ofdam), and 510 mwidth of two sides (1.8 height of dam). The modelis fabricated in a box-shaped testing frame (4.5 m�4.5 m�2.5 m)as presented in Fig. 4.

The model scale is set as 250:1 (CL¼250) according to thesimulated range and the size of the frame. By calculation of Eqs.(2)–(4), the similarity ratios are listed in Table 1.

Four interlayer disturbed belts are taken into consideration: C3,C7, C8 and C9, as well as another two internal interlayer belts (Lc5,Lc6). C2、P2β3 under riverbed are also included. For the basalt rockfracture sets which widely distributed among the dam site, twosteep representatives of them, N20–301W/SW(NE)∠75–821 andN60–801E/SE(NW)∠65–851 are simulated, too. Tables 2 and 3 list

Table 4Connectivity rate of the fracture cluster (%).

Rock type II III1 III2 IV1

Left bank 12 14 15 15Right bank 15 17 20 20

concrete replacof the foundati

Fig. 5. Layouts of the dam abutment

Dam Filling block

Fig. 6. Filling bloc

Load point

Cushion block Jack

Fig. 7. The hydraulic jacks. (a) Loading mode of

the mechanical parameters of the rock mass and discontinuities,and Table 4 shows the Connectivity rate (the real fracture propor-tion to the whole fracture surface) of the two fracture clusters.

The model also takes the proposed reinforcement measuresinto account: concrete replacement of the foundation, consolida-tion grouting, filling blocks etc. The layouts of the dam abutmentand filling block reinforcement measure are shown in Figs. 5 and 6.

3.2. Loading system

Water load could be simulated through hydraulic pressure,barometric pressure, and hydraulic pumps. Hydraulic pressureloads through latex bags [3] or rubber bags [21] filled with water,and high density fluid could be substitute in overloading scenarios.However, the high density solutions (unit weight 41.8, exceptmercury) is not stable, usually precipitating slowly. What worse is,the pressure is not high enough. Barometric pressure loadsthrough latex rubber bags filled with gas distributed by layersalong the dam side. The pressure could be adjusted by aircompressing engines. Hydraulic pump loads by jacks, with whichthe magnitude and direction of the loading pressure could beaccurately adjusted.

ement on

. (a) Upstream. (b) Downstream.

Dam

Filling block

k at riverbed.

Cushion block

the jack. (b) Layout of the hydraulic jacks.

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243236

Hydraulic jack is adopted in the test of this paper. In order tosimulate the water pressure better, steel-lining wood and gypsumblocks (worked as cushion layers) are fabricated between jacksand the dam model. Before that, the interfaces between the jacks,steel plates and dam are specially treated in order to perfectly fitwith each other as illustrated in Fig. 7(a). After that, the concen-trated force of jacks could be transferred to surface pressure whichcould be distributed evenly on the dam surface, like water load.

In the model test, sixty-one hydraulic jacks are placed by sevenlayers to simulate the different level water pressures, as shown inFig. 7(b). Step loading procedures are performed in overloadingprocess, whose incremental load is generally 0.2P0 (P0 is thenormal water pressure) by step. The same layer jacks are groupedwith one oil separator to synchronize the load step, and adjustedby nine precision pressure gauges. During the test process, theload is firstly applied on the bottom layers and then graduallyextended to the upper area. Multi times and stage loads wereapplied in elastic status, and then continuous loads followed untilfailure.

3.3. Data acquisition and monitoring system

There are three data acquisition systems installed in the modeltest:

(1)

Displacements of the dam and abutment rock surface δm,monitored by surface displacement gauges;

(2)

Relative displacement between disturbed belts Δδm, moni-tored by internal displacement gauges;

(3)

Strain of the dam, monitored by strain gauges.

Fig. 8. Layout of resistance cards and displacement gauges. (a

Twenty-two monitoring points are distributed on the down-stream surface of the dam, with forty-nine surface displacementgauges. Another forty-eight monitoring points are distributed onthe rock surface of dam abutments, with ninety-four surfacedisplacement gauges. Twenty internal displacement gauges areallocated in the interlayer disturbed belts of dam foundation.Additionally, 406 resistor chips are bended on the correspondingpoints of dam surfaces for stress and failure monitoring. There arefive resistor chips bended on the dam heel for fracture monitoring.The layouts of gauges and resistor chips are shown in Fig. 8.

These monitoring instruments are connected with UCAM-70A,a high-accuracy data acquisition system. The loading process couldbe accurately adjusted in response to feedbacks from monitoringsystem. Furthermore, three and five video systems are allocated inthe up and down stream sides, respectively, in order to monitorthe fracture development process. The measuring, monitoring andloading systems are coordinated with each other to form theentire model testing system.

3.4. Overloading process and safety evaluation for arch dam

Overload process is usually adopted in the geomechanical modeltest. There are two applying ways: higher water level or higherdensity of water. This paper use the later one, that is, keeps thewater level unchanged and adjusts the density of water. Overloadprocess can be identified by overload factor K and it is defined as

K ¼ P=P0 ð5Þwhere P the is current load on the dam, and P0 is the normalwater load.

) Upstream. (b) Downstream. (c) Downstream abutment.

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We can define three factors to evaluation the safety of archdam. They are overloading factors and similar with safety factorsobtained from numerical method [47]. They are given as follows:

(1)

Fig.(acr

K¼K1 represents the safety factor when crack initiation,generally on dam heel; That is, the crack occurred at damheel on K1P0 load.

(2)

K¼K2 represents the safety factor for large nonlinear deforma-tion. In this stage (K2P0), large area of the dam yielded and thedisplacement exhibited non-linear behavior.

(3)

K¼K3 represents the safety factor of ultimate load. The damfailed with large crack and could not burden load when K3P0.

4. Results and analysis

4.1. Displacement distribution of the dam

Fig. 9 shows the displacement and overloading factor (K)relationship curve for the downstream surface monitoring points,positive for along the river and to the right bank. It is noted thatthe displacement above 500 m of crown cantilever is much largerthan that of the lower position (Fig. 9(a) and (b)). As Fig. 9(a) shows, when the overloading factor K is larger than 7, thecantilever displacement is more than 2000. With K¼9, all of the

9. Dam displacement and overloading factor (K) relationship curves. (a) The crownoss the river). (c) Arch-side displacement (along the river, higher half). (d) Arch-sid

Fig. 10. Stress distribution on the up and downstream dam surfaces under norm

monitor points' displacement on the cantilever increase sharply,the dam fails.

According to Fig. 9(c) and (d), during the loading process, thedisplacement increment of left abutment is larger than that ofright side except for ▽420 m. The reason is that the strike angle ofthe disturbed belts has more negative impact on left side, and thereinforcement effect is less as well. At ▽420 m, the distances fromboth left and right abutments to Lc6 is close, and both sides havereinforcement measures. The displacement of the lower half of theabutment is comparatively larger, because there are several rockflow layers in the foundation, which weakens the rigidity.

4.2. Stress distribution of the dam

Fig. 10 is the stress distribution of dam surfaces under thenormal water pressure scenario. The maximum principal tensionstress is observed in the left dam heel area (1.57 MPa). Theprincipal stress on the downstream dam surface distributes alongthe arches. But the direction of principal stress changes near thefaults. The maximum principal compressive stress appears nearthe dam toe (7.85 MPa), which is comparatively low due to thefilling block reinforcement measure. Besides, there are tensionstress developed on both the upstream and downstream surfacesof dam, especially near the dam heel and faults. Cracks appeared inthese areas after final failure.

cantilever displacement (along the river). (b) The crown cantilever displacemente displacement (along the river, lower half)

al scenario (Unit 0.1 MPa). (a) Upstream surface. (b) Downstream surface.

Fig. 11. The abutment rock displacement and overloading factor (K) relationship curve. (a) Lc5 displacement on left bank (along the river). (b) Lc5 displacement on left bank(across the river). (c) Lc5 displacement on right bank (along the river). (d) Lc5 displacement on right bank(across the river). (e) Lc6 displacement on left bank(along the river).(f) Lc6 displacement on left bank(across the river).

0123456789

10

-20 0 20 40 60 80 100 120 140 160Δδm / mm

K /

Po

right bank upstream

left bank upstream

Fig. 12. The relative displacement of Lc6 vs K curve.

Fig. 13. The relative displacement of Lc5 vs K curve.

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243238

4.3. The displacement distribution of dam abutment rocks

Fig. 11 shows the displacement δm and overloading factor (K)relationship curve of abutment rocks (monitoring points areshown in Fig. 8(c)), positive for along the river and to the rightbank. The deformation direction of Lc5 near the abutment ismainly along the river, and changed to the crossing direction ofriver gradually away from dam. For deformation along the river ofLC6 under the normal scenario, the maximum displacement isobserved in monitoring point 9 (left bank). But during overloadingprocess, the displacement of points 10 and 11 is more than that ofpoint 9. The displacement across the river of point 9 does notchange much in the overloading, while that of point 11 has thelargest record (directs to riverbed).

The displacement distribution of abutment rocks is generally asfollows: the displacement of left side is larger than that of rightside, and lower elevation is larger than higher elevation. Thecomponents along the river are mainly to the downstream, whilethe components across the river mainly point to the bank andriverbed for right and left banks, respectively, which is unfavorablefor the stability of left dam abutment.

When K rose to 9, the displacement of the dam foundationincreased sharply, or even snapped back. That represents the damfailed eventually.

4.4. Relative displacement distribution of faults

Figs. 12 and 13 show the relative displacement of faults, Δδm,and overloading factor, K, relationship curves (positive for tensionand negative for compression). It is noted that no significant

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243 239

displacements occur under normal scenario. When K increases to2.0, there is sliding movement for the Lc6 on the upstream sides.As K increases to 2.5, the relative displacements of C3 in theupstream side and Lc5 (▽339–▽380 m) rise dramatically, as wellas monitoring point C9 on the right bank (▽560 m). The significantchanges of other monitoring points appear when K is more than 3.0.

4.5. Failure mode and mechanism

The failure process, mode and mechanism could be perceivedbased on the continuous monitoring and analysis of the distribu-tion of the displacement and stress (strain) of the dam, abutmentrocks and the faults.

(1)

Fig.final

Fig

The upstream surface of dam and dam heel: The failureprocess and final failure condition are shown in Fig. 14. Forthe right side dam heel, the crack initiates when K¼2.0(1.3 MPa of principal tension stress is observed as shown inFig. 14(a)), and then extends upward to Lc6. For the left sidedam heel, the crack initiates when K¼3.5, penetrated from theright side as shown in Fig. 14(b). The depth of the crack is notlarge but extends to left and right sides as the load increases.Large area failure occurs when K¼5.0, as shown in Fig. 14(c).When K increases to 2.5, the crack started near the right side

14. The failure mode of upstream surface of dam. (a) Failure process for upstream surfacfailure condition for upstream surface of the dam.

. 15. The failure mode of downstream surface of dam. (a) Failure process of downstrea

dam heel extends to Lc6, which results in the crack of the dambody. The reason is that Lc6 is the first tectonic discontinuityabove the filling block (▽392 m), and the tension stressconcentrates here. That could also be evidenced by theprincipal stress distribution shown in Fig. 10(a) where atension stress exits in this area. When K increases to 4.0–5.0,the left side dam body under Lc5 cracks, then extends to theinside of the dam as K continues to increase to 6.0–7.0. Othercracks on the upstream surface of the dam initiate whenK¼7.0–9.0.

(2)

The downstream surface of the dam and dam toe: The failureprocess and final failure condition is shown in Fig. 15. Thecrack initiates near left dam toe between Lc6 and Lc5 whenK¼2.5 since that the interspace between Lc6 and Lc5 isrelative smaller than that of other faults, and the position isjust above filling block (▽392 m). Then the crack extends bothupward and downward. When K increases to 3.5, the crackappears near Lc6 in the right side, after that extends upwardand downward to the inside of dam body, especially whenK46.0. The filling block splits away from downstream foun-dation when K¼6.5–7.0.When K¼2.5–3.0, the crack in left dam toe extends along thefilling block, and splits into two (one upward, another to left)when K¼6.0. For the right side, the dam crack initiates near

e of the dam. (b) The dam heel failure mode on left side when K¼3.5. (c) The

m surface of dam. (b) The final failure state for downstream surface of dam.

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243240

Lc6 when K¼3.5–4.0. Then the crack develops horizontally.As shown in Fig. 21(b), most of the cracks of downstream surfaceare horizontal (or close to) which occur at K¼7.5P0–9.0P0.The longest horizontal crack of downstream surface initiatesnear right side C8 when K¼5.0–7.0, and penetrates through as Kincreases to 8.0–9.0. It also could be evidenced by the model testresults of Agua de Toro dam in Argentina, from which the crackwas named as a separation crack. Fumagalli [3] believed that thisis caused by sharply increased tension stress of downstreamsurface of dam due to the water overloading while gravity ofdam is fixed (This type of condition in test has been consideredto satisfy the sudden accident). The location of the crack couldalso be derived through the distribution of principal tensionstress as shown in Fig. 10(b). The separation crack actuallyseparates the dam into upper and lower parts. The lower partbecomes an independent structure with higher flexibility tothe downstream side. That could be demonstrated in this test:the final downstream displacement of ▽500 m of the crowncantilever under the separation crack exceeds that of ▽610 m(as shown in Fig. 15(a)). The upper part works more like ahorizontal arch without the combination effect of the verticalcantilever beam. If the strength of the foundation rocks issufficient, the upper part could sustain. Otherwise this partdam body will fail immediately after the foundation sinks.Due to the low strength of left and upper foundation rock(mainly caused by C9), the crack initiated near dam abutmentextends, and finally leading the failure of overall upper part, asshown in Fig. 15(b). In addition, the failure modes of the

5.0~6.0

4.04.0

5.0~6.0

5.0~6.04.5

3.5~4.0

4.0~

3.0~2.0

4.0~3.5

5.0~4.0

Fig. 16. The failure mode of foun

upstream and downstream surface of the dam for the upperparts are similar (Fig. 14(a) and Fig. 15(a)), which could beevidences as above conclusion.

(3)

The failure of abutment: Fig. 16 shows the failure mode of thefoundation rocks. When K¼3.5–4.0, the crack firstly appearsnear the upstream side of right dam abutment. That is becausethe dam body distorts to the left side and stretches the rightabutment as the water load increases. The crack near the leftabutment initiates when K¼8.0–9.0, and extends downwardto downstream (where C9 and C8 locate) rapidly.

(4)

The crack in the downstream foundation: The cracks in thedownstream foundation mainly distribute around the faults inthe left side, especially between Lc5 and Lc6. When K increasesto 5.0, the displacement of monitoring point 1 (on Lc5, 5 mabove the dam toe) is close to 300 mm (as shown in Fig. 11(a)).At the same time, the displacement of monitoring point 9 (onLc6, 10 m above dam toe) increases to 180 mm (as shown inFig. 11(e)), and several cracks appear when K¼5–6. When Kincreases to 8, the crack in left side extends from ▽530 m to▽390 m sharply, as shown in Fig. 17(a).

The cracks developed in right side foundation are less than inleft side, and concentrate in dam toe area, as shown in Fig. 17(b).Also, the first crack initiates near Lc6 (K¼4.0). Several cracksappear when K increases to 6.0, but do not extend much. As aresult, the damage is less serious than that of the left sidefoundation.

5.0

6.05.0~6.0

3.0~4.0

8.0~9.0

8.0~9.0

9.0~10.0

9.0~10.0

4.0~5.0

8.0~9.0

8.0~9.0

3.5~4.0 4.0~5.05.0~6.0 7.0~8.0

8.0~9.0

8.0~9.0

dation rock.

Fig. 17. The failure state of abutment rock. (a) Left bank foundation. (b) Right bank foundation. (c) Dam toe.

Table 5The safety factors of arch dam geomechanical model tests in China.

Name Height (m) K1 K2 K3 State

Fengtan (hollow arch dam) 112.5 1.5 2.0 4.0 In serviceLongyangxia (gravity arch dam)a 177.0 1.2 1.8 3.25 In serviceJinshuitan 102.0 2.0 3.9 10.0 In serviceDongfeng (Thick scheme) 166.0 2.0 4.0 12.0 –

Dongfeng (Thin scheme) 166.0 2.0 3.8 8.0 In serviceLijixia 165.0 1.6 3.0 5.4 In serviceTongtou 75.0 1.5 1.5 4.0 In serviceJinping 305.0 2.0 4.0–5.0 6.0–7.0 In constructionXiaowan 292.0 1.5–2.0 3.0 7.0 In serviceErtan (Conhesion simulated) 245.0 2.0 4.0 11.0–12.0 In serviceErtan (Conhesion not simulated) 245.0 2.0 3.5 8.0 In serviceLaxiwa 250.0 2.0 3.5–4 7.0–8.0 In serviceXiluodu (This paper) 285.5 2.0–2.5 5.0–6.0 9.0–9.5 In construction

a Over load for water head was adopted in this test.

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243 241

When K¼4.0–5.0, uplift deformation and induced crack (5 mm,model dimension) is monitored near the joint between fillingblock and left foundation (compression-shearing [48]), so is inright foundation when K¼5.0–6.0 as shown in Fig. 17(c). Thecomparatively less serious and delayed dam toe crack is due to thefilling block reinforcement measure which enlarges the dam'sthickness.

5. Comparative analysis of global stability with other archdams

How to evaluate the testing result is the focus of engineering.The research team of this paper had completed most of thegeomechanical model tests for the high arch dams in constructionor design in China. The safety factors of thirteen testing arch damsin seventen experiments are listed in Table 5 for comparativeanalysis. The K1 and K2 result of Xiluodu dam model is the highest,and K3 ranks No.4 in all, which means that the global stability ofthe dam is comparatively high.

6. Conclusion

In this study, a geomechanical model of Xiluodu arch dam isconstructed using small block masonry and low strength bindertechnique, within which complex geological structures of damabutment rocks, tectonic discontinuities (faults), and reinforce-ment measures are accurately simulated. The stability of damabutments is evaluated after the overloading test. The conclusionsand engineering suggestions are as follows.

(1)

The right dam heel crack initiates when K¼2.0, and thenextends to Lc6 along the right bank, leading to the crack ofupstream dam surface. The dam heel crack penetrates whenK¼3.5, though the depth is low. When K¼2.5, the crackinitiates in the left side dam toe between Lc6 and Lc5. As Kincreases to 3.5, Lc6 in right bank cracks and then extendsupward and downward, as well as to the dam body. Severalhorizontal cracks appear on the downstream dam surface, andseparation crack develops. The left side abutment rocks nearC9 are not solid enough, results in the separation crack, whichinduces the overall failure of upper part of the dam.

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243242

(2)

The foundation crack firstly appears in the right and upstreamdam abutment when K¼3.5–4.0. While for left abutment, thecrack initiates when K¼8.0–9.0, and then extends to down-stream side rapidly, further to C9 and C8 downward. For thedownstream foundation, the cracks mainly distribute aroundthe faults in the left side when K¼5–6, especially between Lc5and Lc6. The cracks of right bank mainly locate near Lc6 whenK¼4.0, and are less than that of the left bank. Where there isfaults connection with dam toe, there are cracks generated, butnot seriously.

(3)

Compress-shear failure occur in left and right dam toes whenK¼4.0–5.0 and 5.0–6.0, respectively. The crack near the damtoe area is delayed due to the filling block reinforcement effect.

(4)

From the above monitoring result, it is necessary to arrangereinforcement measures between Lc5 and Lc6 in left bank, C9,and right bank Lc6, where the strength of the structures isrelative low.

(5)

The safety factors derived from Xiluodu dam geomechanicaltest is as follows: crack initiation factor K1¼2.0–2.5; nonlineardeformation factor K2¼5.0–6.0; ultimate load factor K3¼9.0–9.5. K1 and K2 are the largest, and K3 is high compared withother 13 dam model test's results. That means the globalstability of the dam is high.

(6)

Although the geomechanical model test plays an irreplaceablerole in the stability analysis of dam abutment, there are severalrestrictions still in place. The impact of construction phase orthe water penetration in crack propagation is not yet consid-ered due to technical reason or material property limitation,which distorted the model test effect and the final failurebehavior to a certain extent. There are still some disciplines forimprovement and enhancement in this area.

Acknowledgements

The work reported here was supported by State Key Laboratoryof Hydroscience and Engineering of Hydroscience with grant No.2013-KY-2 and China National Funds for Distinguished YoungScientists with grant No. 50925931.

References

[1] Du YJ. Research present situation and development trend of geomechanicsmodel test. NW Water Res Water Eng 1996;7(2):64–7 [in Chinese].

[2] Shen T. Development of geomechanic model experiment techniques. J YangtzeRiver Sci Res Inst 2001;18(5):32–6 [in Chinese].

[3] Fumagalli E. Stability of arch dam rock abutments. In: Proceedings of firstISRM Congress, Lisbon, Portugal; 1966. p. 503–508.

[4] Fumagalli E. Statical and geomechanical models. New York: Springer; 1973.[5] Oberti G, Fumagalli E. Static geomechanical model of the Ridracoli arch gravity

dam. In: Proceedings of fourth ISRM Congress, Montreux, Switzerland; 1979.p. 493–96.

[6] Lemos JV, Pina CAB, Costa CP, Gomes JP. Experimental study of an arch dam ona jointed foundation. In: Proceedings of the eighth ISRM Congress. Tokyo,Japan; 1995. p. 1263–1266.

[7] Lemos JV. Modelling of arch dams on jointed rock foundations. In: Proceedingsof ISRM international symposium—EUROCK 96. Turin, Italy; 1996. p. 519–26.

[8] Oliveira S, Faria R. Numerical simulation of collapse scenarios in reduced scaletests of arch dams. Eng Struct 2006;28:1430–9.

[9] Han BL, Zhang WC, Cunfen Yang. A new model material of geomechanics(MIB). J Wuhan Univ Hydraul Electron Eng 1983;1:11–7 [in Chinese].

[10] Gong SX, Guo CM, Gao DS. The experimental studies of the goemechanicalmodel material. J Yangtze River Sci Res Inst 1984;1:32–46 [in Chinese].

[11] Li CG, Ma YQ, Hu CQ. Experimental study on the geomechanical modelmaterials. J Chengdu Univ Sci Technol 1988;6:1–6þ14 [in Chinese].

[12] Li ZK, Liu H, Dai R, Su X. Application of numerical analysis principles and keytechnology for high fidelity simulation to 3-D physical model tests forunderground caverns. Tunnelling Underground Space Technol 2005;20:390–9.

[13] Wang HP, Li SC, Zhang QY, et al. Development of a new geomechanical similarmaterial. Chin J Rock Mech Eng 2006;25(9):1842–7 [in Chinese].

[14] Jiang XL, Chen J, Sun SW, et al. New material for rock foundation ofgeomechanical model of Jingping Project. J Yangtze River Sci Res Inst2009;26(6):40–3 [in Chinese].

[15] Fei WP, Zhang L, Zhang R. Experimental study on a geo-mechanical model of ahigh arch dam. Int J Rock Mech Min Sci 2010;47:299–306.

[16] Wang XQ, Ge H, Li Y. The application of white light speckle method to measuredeformation in modeling experiment of similar materials. J Chengdu Coll Geol1989;16(2):109–12 [in Chinese].

[17] Li BK, Sun ZH. Geomechanical model tests and the applications of speckletechniques. In: Sun Jun Lin Yunmei, editor. New developments in rock mechna-nics. Shengyang: Northeast University Press; 1989. p. 95–110 [in Chinese].

[18] Liu J, Feng XT, Ding XL, Zhang J, Yue DM. Stability assessment of the Three-Gorges Dam foundation, China, using physical and numerical modeling—PartI: Physical model tests. Int J Rock Mech Min Sci 2003;40:609–31.

[19] Li ZK, Wang AM. Application and consideration of using fiber-sensor measure-ment in a 3D geo-mechanical model test. Exp Technol Manage 2006;23(12):57–60 [in Chinese].

[20] Wang HP, Li SC, Zheng XF. Research progress of geomechanical model testwith new technology and its engineering application. Chin J Rock Mech Eng2009;28(supp.1):2765–71 [in Chinese].

[21] Dong WL, Zhang LD. Acoustic measurement in geomechanical modelingexperiment of arch dam abutment rockmass stability for ertan hydroelectric.J Eng Geol 1998;6(4):375–80 [in Chinese].

[22] Chen AM, Gu JC, Shen J, et al. Development and application of multifunctionalapparatus for geotechnical engineering model tests. Chin J Rock Mech Eng2004;23(3):372–8 [in Chinese].

[23] Zhou WY, Yang RQ, Liu YR, et al. Research on geomechanical model of rupturetests of arch dams for their stability. J Hydroelectric Eng 2005;24(1):53–58þ64 [in Chinese].

[24] Fei WP, Zhang L, Zhang R. Experimental study on a geo-mechanical model of ahigh arch dam. Int J Rock Mech Min Sci 2010;47:299–306.

[25] Chen GQ, Wu ZR, Cao M, et al. An investigation on stability of a gravity-archdam and its abutment by geomechanical model test. Chin J Geotech Eng1985;7(1):15–24 [in Chinese].

[26] Li TB. Geomechanical modeling study on stability of arch dam shoulder. Chin JRock Mech Eng 2004;23(6):1670–6.

[27] Ren QW, Yu TT, Ma LY. Numerical analysis and experiment study of stabilityfor Dam Section No. 3 of the Three Gorges Project. Eng Sci 1999;1(3):41–5 [inChinese].

[28] Zhuge YS, Chen XT. Experimental study of 3d geomechanical model on globalstability of an arch dam under complex geological condition. Hydrogeol EngGeol 2008;6:70–4 [in Chinese].

[29] Chen AM, Gu X, Gu LY, et al. Geomechanical model test research on stability ofreinforced wedge-shaped rock slope. Chi J Rock Mech Eng 2006;25(10):2092–101 [in Chinese].

[30] Li GR, She CX, Chen SH. Curved deformation damage test and FEM analysis ofslope with layered rockmass. Chin J Rock Mech Eng 1997;16(4):305–11 [inChinese].

[31] Xiao SR, Liu DF, Jiang FX, et al. Geomechanical model experiment onQianjiangping landslide in Three Gorges reservoir area. Chin J Rock MechEng 2010;29(5):1023–30 [in Chinese].

[32] Chen XT, Li L. Stability analysis of surrounding rock of large undergroundpowerhouse cavern group. Chin J Rock Mech Eng 2008;27(supp.1):2864–72[in Chinese].

[33] Chen XL, Han BL, Liang KD. Test research for the surrounding rock stability ofunderground openings. J Wuhan Univ Hydraul Electron Eng 1994;27(1):17–23[in Chinese].

[34] Zhu WS, LiY Li SC, Wang SG, Zhang QB. Quasi-three-dimensional physicalmodel tests on a cavern complex under high in-situ stresses. Int J Rock MechMin Sci 2011;48:199–209.

[35] Dai YH, Chen WZ, Yang CH, et al. A study of model test of Jintan rock salt gasstorage's operation. Rock Soil Mech 2009;30(12):3574–80 [in Chinese].

[36] Muller L, Reik G, Fecker E, Sharma B. Importance of model studies onGeomechanics. In: Proceedings of the international colloquium on geomecha-nical model. Bergamo, Italy: ISRM; 1979. p. 177–192.

[37] Alvarez MA. Mechanical models as compared with mathematics. In: Proceed-ings of the international colloquium on geomechanical model. Bergamo, Italy:ISRM; 1979. p. 149–151.

[38] Guan FH, Liu YR, Yang Q, et al. Research on anchorage of dam toe ofbaihetan high arch dam[J]. Chin J Rock Mech Eng 2010;29(7):1323–32 [inChinese].

[39] da Silveira AF, Azevedo MC, Esteves Ferreira MJ, Pereira da Costa CA. Highdensity and low strength materials for geomechanical models. In: Proceedingsof the international colloquium on geomechanical model. Bergamo, Italy:ISRM; 1979. p. 115–131.

[40] Stimpson B. Modelling materials for engineering rock mechanics. Int J RockMech Min Sci 1970;7:77–121.

[41] Shen T, Zou ZS. A study on geomechanical model materials and exploration ofsome experimental techniques. J Yangtze River Sci Res Inst 1988;4:12–23 [inChinese].

[42] Li CG, Ma YQ, Hu CQ. Experimental study on the geomechanical modelmaterials. J Chengdu Univ Sci Technol 1988;6:1–6þ14 [in Chinese].

[43] GU Zhaoqi, PENG Shouzhuo, LI Zhongkui. Underground chamber engineering.Beijing: Tsinghua University Press; 1994.

[44] Ma FP, Li ZK, Luo GF. NIOS model material and its use in geo-mechanicalsimilarity model test. J Hydraul Electr Eng 2004;23(1):48–51 [in Chinese].

Y.R. Liu et al. / International Journal of Rock Mechanics & Mining Sciences 61 (2013) 231–243 243

[45] Wang HP, Li SC, Zhang QY, et al. Development of a new geomechanical similarmaterial. Chin J Rock Mech Eng 2006;25(9):1842–7 [in Chinese].

[46] Zhou WY, Yang RQ. A research of rock block model in calculating the stabilityof dam abutments by means of finite element method and experiments.J Hydroelectric Eng 1982;1:53–65 [in Chinese].

[47] Jin F, Hu W, Pan JW, Yang J, Wang JT, Zhang CH. Comparative study procedurefor the safety evaluation of high arch dams. Comput Geotech 2011;38:306–17.

[48] Fishman YA. Features of shear failure of brittle materials and concretestructures on rock foundations. Int J Rock Mech Min Sci 2008;45(6):976–92.