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Article

Study on Analysis Method and Control Index for Deformation of Super-High Arch Dam Suffering Alkali-Aggregate Reaction

1
China Institute of Water Resources and Hydropower Research, Beijing 100038, China
2
State Key Laboratory of Simulations and Regulations of Water Cycles in River Basins, Beijing 100038, China
3
POWERCHINA Chengdu Engineering Corporation Limited, Chengdu 610072, China
*
Author to whom correspondence should be addressed.
Water 2023, 15(7), 1399; https://doi.org/10.3390/w15071399
Submission received: 27 February 2023 / Revised: 21 March 2023 / Accepted: 1 April 2023 / Published: 4 April 2023
(This article belongs to the Section Hydraulics and Hydrodynamics)

Abstract

:
Alkali-aggregate reaction can not only cause uneven expansion of concrete but also lead to cracking and even destruction and consequently affect the working behavior and long-term safety of hydraulic concrete structures. Present researches on alkali-aggregate reaction focus on improving the composition ratio of concrete materials through experimental study to inhibit the reaction, whereas there is a lack of quantitative calculation and analysis. In the present study, the problem of alkali-aggregate reaction in the super-high arch dam of Jinping I Hydropower Station was taken as an example. The expansion of concrete suffering the alkali-aggregate reaction was simulated by means of the overall temperature rise in the dam. Similarly, the yield zone, the expansion process, and the deformation change law with the development of concrete expansive deformation under various load combinations were analyzed by using the elastic–plastic finite element method. Finally, a control index of allowable alkali-aggregate expansion of dam concrete under various load combinations was put forward. The research results demonstrated that the control index was 400~800 με. Since the arch dam has a low safety reserve when operating at a low water level, the lowest reservoir level should be raised as much as possible in dam operation to reduce its drawdown rate, thus restraining the adverse impact of alkali-aggregate reaction in concrete on the dam.

1. Introduction

Alkali-aggregate reaction (AAR) refers to the chemical reaction between alkaline substances in concrete and active components in the aggregate, which causes uneven expansion of concrete, cracking, and even destruction and adversely affects the durability of concrete [1]. In 1940, AAR was first found in the United States [2]. Subsequently, large-scale concrete project failures caused by AAR were successively reported in Canada, Japan, Britain, South Africa, Norway, and many other countries [3]. AAR often occurs inside the concrete and is continuous, which makes the repair and reinforcement of the dam hard. What’s worse, the reconstruction may be required one day. For more than half a century, the damage caused by AAR has resulted in great losses around the world. Especially, hydraulic concrete structures have a humid environment and long service life, which provides excellent environmental conditions and enough time for AAR to develop; thus, it is more dangerous when AAR occurs in hydraulic concrete than in ordinary concrete [4]. Based on the survey in Canada, 30% of the 480 dams belonging to the Quebec Water Conservancy Bureau were damaged by AAR [5]. Fontana Dam and Hiwassee Dam in the United States, Moxoto Dam in Brazil, Shambon Dam in France, and Beauharnois Dam in Canada are the typical ones [6]. In China, there are also some projects that have micro or macro cracks caused by AAR in the concrete on the overflow surface of the dam after a long-term operation, such as in the Daheiting Reservoir Dam [7].
Fortunately, the serious consequences caused by AAR have been increasingly studied. In recent years, more and more attention has been paid to the problem of AAR in many water conservancy projects. In many projects, the alkali activity test for aggregates is carried out before construction; thus, people can take active measures to prevent it. However, dam concrete is inevitably contacted with water, so at present, the main suppression measures reduce the alkali content of concrete, using inactive aggregates and mineral admixtures or additives [8,9,10,11,12]. The first method is the most direct and effective [13]. At the end of the 20th century, Japan, Britain, New Zealand, and other countries tried to reduce the alkali content of cement, and the alkali content of cement was reduced to 0.60% when active aggregates were used [14]. Using inactive aggregate, such as water-quenched slag as fine aggregate [15] and basaltic pumice aggregate [16], is the safest and most reliable measure to prevent AAR. Some scholars have even studied the possibility of making artificial lightweight aggregate from broken clay bricks, fly ash, glass waste, and other materials to inhibit AAR [17,18,19,20]. Adding mineral admixtures to concrete is also an important way to inhibit AAR. When geopolymers and mineral admixtures are used in an appropriate percentage, they can not only reduce AAR but also significantly improve the mechanical properties of concrete [21]. Commonly used mineral admixtures include fly ash [22,23,24], slag [25,26,27], volcanic ash [28,29,30], and flint powder [31]. Moreover, the use of chemical additives (lithium salt, calcium salt, etc.) is also effective [32,33,34,35]. Studies have shown that adding fiber materials into concrete materials can effectively delay concrete cracking and inhibit the expansive deformation caused by AAR [36,37,38,39,40].
Previous research concentrated on the composition ratio of concrete materials and achieved the inhabitation of AAR through engineering measures, which only verified the safety of concrete specimens in a short time under the test environment, but the long-term effectiveness of actual projects needs to be demonstrated. An advanced numerical simulation model is an important means to analyze the influence of AAR on a concrete dam structure [41]. The classical model widely used worldwide is the Charlwood model [42], but it is an empirical model with inaccurate deformation history. Starting from the governing micromechanisms of ASR expansion, Franz-Josef et al. developed a chemoelastic model that accounts for ASR kinetics and the swelling pressure exerted by the ASR reaction products on the skeleton [43]. Fairbairn et al. presented an alkali–silica reaction (ASR) thermo–chemo–mechanical expansion model, which considers the influence of temperature and humidity in the development of ASR [44]. Saouma et al. presented a new constitutive model for alkali-aggregate reaction (AAR) expansion. This thermo–chemo–mechanical model is rooted in the chemistry, physics, and mechanics of concrete, and the major premises of the model are the assumption of a volumetric expansion of the gel and redistribution on the basis of weights related to the stress tensor [45]. Comi et al. proposed a chemo–thermo-damage model to simulate the swelling and the deterioration of local stiffness and strength in concrete due to the alkali-aggregate reaction (AAR) [46]. AAR model for the long-term operation of concrete dams constructed by Pan et al. considers the coupling effect of alkali-aggregate chemical reaction and mechanics, and the influence of temperature, uneven distribution of relative humidity, and stress state is considered in alkali-aggregate chemical reaction kinetics. The mechanical behavior of concrete includes elastic–plastic damage and long-term creep effect [47]. However, these models are mainly used to simulate the alkali-aggregate expansion of concrete members, and there are few studies on numerical simulation of the alkali-aggregate expansion process in arch dams and its influence.
Jinping I Hydropower Station is located in Yanyuan County and Muli County, Liangshan Yi Autonomous Prefecture, Sichuan Province. It is a controlled reservoir on a cascade hydropower station in the lower reaches of the Yalong River. The arch dam has a crest elevation of 1885 m, a dam bottom elevation of 1580 m, and a maximum height of 305 m. The dam concrete usually has a large construction quantity. Limited by environmental and economic factors, the sand and gravel materials used in engineering construction can only be obtained from local materials, and marble and Silicarenite aggregates in the nearby stock ground are used. Silicarenite is a kind of alkali-active rock, which may lead to AAR in dam concrete with a potential threat. Jinping I Hydropower Station has been operating for about a decade. For this project, measures, such as using combined aggregate and 35% Grade I fly ash and controlling the total alkali content of concrete to be less than 1.5 kg/m3, were taken to inhibit AAR. Therefore, it is urgent to make a scientific evaluation of the long-term inhibition effectiveness of AAR in dam concrete. Dong et al. studied the long-term effectiveness of the measures to inhibit the alkali activity of the aggregate by means of petrographic analysis, micro-morphology, product analysis, accelerated curing, and elastic wave test for the dam concrete core samples that have been in operation for 10 years [48]. However, it is difficult to evaluate the long-term safety of dam concrete because the experimental conditions and theoretical assumptions adopted by different researchers are quite different from the actual situation of dam concrete.
The present paper aims to solve the problem of AAR in the super-high arch dam of Jinping I Hydropower Station. The possible expansion value equivalent to the corresponding temperature rise was predicted to simulate the expansive deformation of arch dam concrete by means of the overall temperature rise of the dam. All load combinations that can be encountered were considered. By adopting the elastic–plastic finite element method, not only was the working behavior of the arch dam suffering AAR under different load combinations calculated but also the expansion process of the arch dam yield zone and the change law of the arch dam deformation with further expansion under different load combinations were analyzed. The breakthrough of the yield zone and the inflection point of the relationship curve between displacement and expansive deformation were taken as the judging criteria. Then we obtained a control index for allowable alkali-aggregate expansion in dam concrete, which provided a basis for the long-term safe operation and control of the structure.

2. Calculation Model and Load Calculation

2.1. Computational Model

A three-dimensional finite element model of arch dam-foundation was established according to the actual shape, joints, detailed structure, material partition, and engineering geological conditions of Jinping level I super high concrete arch dam. In the finite element model, X-axis is the direction perpendicular to the river direction, pointing to the right bank; Y-axis is the direction along the river, pointing downstream; Z-axis is the vertical direction, pointing upward. There are 724,195 elements and 733,235 nodes in the grid, including 139,860 dam units and 152,581 nodes. The units are generally hexahedral units, and some parts use pyramid, prism, and tetrahedron units. The overall finite element model of the dam body foundation is shown in Figure 1 and the finite element model of the arch dam is shown in Figure 2.

2.2. Calculating Loads

The alkali-aggregate reaction can cause the expansive deformation of concrete, which is equivalent to the expansion caused by the overall temperature rise in the arch dam. Therefore, the latter was used in simulating the AAR expansion of arch dam concrete, and the possible expansion of concrete was equivalent to the corresponding temperature rise, which was applied to the arch dam in the form of temperature load, and then the working behavior of arch dam under the influence of AAR under different load combinations was calculated.
The concrete proportioning of the Jinping I Dam is shown in Table 1. The thermodynamic parameter experiment results of dam concrete are shown in Table 2.
The possible expansion value caused by AAR in the arch dam concrete was predicted, and the values ε v 1 , ε v 2 , , ε v i , , ε v n were converted into the corresponding temperature rise parameters Δ T 1 , Δ T 2 , , Δ T i , , Δ T n ; the possible expansion of concrete divided by the linear expansion coefficient of concrete, which can be expressed as
Δ T i = ε v i α , i = 1 , 2 , , n
where α is the linear expansion coefficient of concrete.
The linear expansion coefficient of arch dam concrete in Jinping I Hydropower Station was 8.5 × 10−6/°C [51,52], and the temperature load increment corresponding to the possible expansion value caused by AAR in concrete was calculated according to Equation (1), and the calculation results are shown in Table 3.
The load combinations that may be encountered during the operation of arch dams are the following:
  • Basic combination I: normal upstream water level + corresponding downstream water level + sediment pressure + dam self-weight + temperature drop + possible alkali-aggregate expansion;
  • Basic combination II: upstream dead water level + corresponding downstream water level + sediment pressure + dam self-weight + temperature drop + possible alkali-aggregate expansion;
  • Basic combination III: normal upstream water level + corresponding downstream water level + sediment pressure + dam self-weight + temperature rise + possible alkali-aggregate expansion;
  • Basic combination IV: upstream dead water level + corresponding downstream water level + sediment pressure + dam self-weight + temperature rise + possible alkali-aggregate expansion;
  • Accidental combination V: upstream exceptional flood level + corresponding downstream water level + sediment pressure + dam self-weight + temperature rise + possible alkali-aggregate expansion.

3. Calculation Principles and Methods

In this paper, the elastic–plastic finite element method was used to calculate and analyze the yield zone of the arch dam and the expansion process and deformation change law with the development of expansive deformation under various load combinations. The material nonlinearity of dam concrete and foundation rock mass was simulated by the DP yield criterion in the calculation and analysis.
The elastic–plastic constitutive relation can be written as [53]
{ σ } = [ D e p ] { ε }
where { σ } and { ε } are the stress and strain arrays of materials, respectively; [ D e p ] is the elastic–plastic matrix.
The iterative formula of the finite element equilibrium equation is
[ K 0 ] { δ 1 } = { F } + { R } ( i = 1 ) [ K 0 ] { Δ δ i } = { F } e v e [ B ] T [ D e p i 1 ] ( { ε i } { ε 0 } ) [ δ i ] = { δ i 1 } + { Δ δ i } ( i = 2 , 3 , 4 , )
where { R } is an unbalanced force.
In the Drucker–Prager yield criterion with maximum tensile stress, when the material is damaged by tension, the maximum tensile stress criterion is adopted, namely,
F = σ 1 R t = 0
When shear failure occurs, Drucker–Prager yield criterion is adopted, namely, [54]
F = α I 1 + J 2 k = 0
In Equation (5), I 1 is the first invariant of stress tensor; J 2 is the second invariant of deviatoric stress tensor; α and k are the material parameters, which are related to the friction angle φ and cohesion c of the material. The values of α and k were determined according to the following formula so that the Drucker–Prager yield surface is close to the Mohr–Coulomb yield surface.
α = 2 sin φ 3 3 sin φ , k = 6 c cos φ 3 3 sin φ
The yield condition of the Mohr–Coulomb yield criterion is
J 2 cos θ σ sin θ σ 3 sin φ + 1 3 I 1 sin φ c cos φ = 0
where I 1 is the first invariant of stress tensor; J 2 is the second invariant of deviatoric stress tensor; θ σ is the Lode angle of stress; c and φ are the cohesion and internal friction angle, respectively.

4. Influence Law of Alkali-Aggregate Reaction on Arch Dam Stress

The alkali-aggregate reaction can make the dam expand and deform, which further affects the dam’s stress. As shown in Figure 3 and Figure 4 (In the figures, the blue arrow indicates the tensile stress increment, and the red arrow indicates the compressive stress increment.), the tensile stress increment was generated at the cheeks at the middle-upper part of the upstream surface and on both sides of the downstream surface of the arch dam, and compressive stress increment was generated at the arch end of the upstream surface and the lower-middle part of the downstream surface of the arch dam; the stress increment of most parts caused by expansive deformation can offset the water pressure, and the compressive stress increment at the lower-middle part of the downstream surface caused by expansion can be superimposed with the water pressure load. Under the condition of low water level, large expansive deformation occurred is the most unfavorable to the dam.

5. Deformation Control Index Based on Elastic–Plastic Finite Element Method

5.1. Yield State of Arch Dam under Different Alkali-Aggregate Deformation

Figure 5 and Figure 6 show the distribution of the yield zone of the arch dam under different expansion values in basic load combination I (‘0’ means unyielding; ‘1’ represents the tensile yield; ‘2’ is the compression–shear yield). It demonstrated that the yield zones at the upstream and downstream arch ends gradually expanded with the deformation of the arch dam. When the deformation value reached 200 με, the downstream dam surface near the left and right abutments yielded at the upper elevation. Then, with the further development of expansive deformation, the yield zone continuously extended and was partly connected at the high elevation of the right bank foundation surface along the upstream and downstream surfaces when the deformation value reached 800 με.
Figure 7 and Figure 8 show the distribution of the yield zone of the arch dam under different expansion values in basic load combination II. It demonstrated that the yield zones at the upstream and downstream arch ends gradually expanded with the deformation of the arch dam. When the deformation value reached 100 με, the downstream dam surface near the left and right abutments yielded at the upper elevation. Then, with the further development of expansive deformation, the yield zone continuously extended and was partly connected at the high elevation of the right bank foundation surface along the upstream and downstream surfaces when the deformation value reached 800 με.
Figure 9 and Figure 10 show the distribution of the yield zone of the arch dam under different expansion values in basic load combination III. It demonstrated that the yield zones at the upstream and downstream arch ends gradually expanded with the deformation of the arch dam. When the deformation value reached 300 με, the downstream dam surface near the left and right abutments yielded at the upper elevation. Then, with the further development of expansive deformation, the yield zone continuously extended and was partly connected at the high elevation of the right bank foundation surface along the upstream and downstream surfaces when the deformation value reached 800 με.
Figure 11 and Figure 12 show the distribution of the yield zone of the arch dam under different expansion values in basic load combination IV. It demonstrated that the yield zones at the upstream and downstream arch ends gradually expanded with the deformation of the arch dam. When the deformation value reached 150 με, the downstream dam surface near the left and right abutments yielded at the upper elevation. Then, with the further development of expansive deformation, the yield zone continuously extended and was partly connected at the high elevation of the right bank foundation surface along the upstream and downstream surfaces when the deformation value reached 800 με.
Figure 13 and Figure 14 show the distribution of the yield zone of the arch dam under different expansion values in accidental combination I. It demonstrated that the yield zones at the upstream and downstream arch ends gradually expanded with the deformation of the arch dam. When the deformation value reached 300 με, the downstream dam surface near the left and right abutment yielded at the upper elevation. Then, with the further development of expansive deformation, the yield zone continuously extended and was partly connected at the high elevation of the right bank foundation surface along the upstream and downstream surfaces when the deformation value reached 800 με.

5.2. Displacement of Arch Dam under Different Alkali-Aggregate Reaction Deformation

Figure 15 shows the change process of dam crest displacement along the river under different expansion values in basic combination I. Under the normal water level + temperature rise condition, the deformation of the crown cantilever along the river gradually changed upstream with further expansion, whereas that at the dam abutment varied downstream. However, the deformation did not change suddenly, indicating that the overall dam body was in a linear elastic state when the expansion value was lower than 800 με, and no instability and failure occurred on the whole.
Figure 16 shows the change process of dam crest displacement along the river under different expansion values in basic combination II. Under the condition of dead water level + temperature rise, the deformation of the dam crest along the river gradually changed upstream with further expansion, and the inflection point appeared when the expansion value reached 400 με, indicating that the overall stiffness of the arch dam was obviously reduced.
Figure 17 shows the change process of dam crest displacement along the river under different expansion values in basic combination III. Under the normal water level + temperature rise condition, the deformation of the crown cantilever along the river gradually changed upstream with further expansion, whereas that at the dam abutment varied downstream. However, the deformation did not change suddenly, indicating that the overall dam body was in a linear elastic state when the expansion value was lower than 800 με, and no instability and failure occurred on the whole.
Figure 18 shows the change process of dam crest displacement along the river under different expansion values in basic combination IV. Under the condition of dead water level + temperature rise, the deformation of the dam crest along the river gradually changed upstream with further expansion, and the inflection point appeared when the expansion value reached 400 με, indicating that the overall stiffness of the arch dam was obviously reduced.
Figure 19 shows the change process of dam crest displacement along the river under different expansion values in accidental combination I. Under the normal water level + temperature rise condition, the deformation of the crown cantilever along the river gradually changed upstream with further expansion, whereas that at the dam abutment varied downstream. However, the deformation did not change suddenly, indicating that the overall dam body was in a linear elastic state when the expansion value was lower than 800 με, and no instability and failure occurred on the whole.

5.3. Control of Alkali Active Inflation

According to the degree of dam damage and the relationship curve between dam deformation and alkali-aggregate reaction expansion deformation, the dam safety risk grade under alkali-aggregate reaction in concrete is divided into three levels:
  • Normal: the dam body has no yield zone, and the slope of the relationship curve between dam deformation and expansive deformation is a constant;
  • Abnormal: the dam surface partly yields and the slope of the relationship curve between dam deformation and expansive deformation is a constant;
  • Danger: the yield zone of the dam extends along the dam thickness and is connected, and the slope of the relationship curve between dam deformation and expansive deformation suddenly increases.
According to the above calculation and analysis results and safety risk level criteria, the control threshold of alkali-aggregate expansion at different risk levels under various load combinations is shown in Table 4.
The construction of the Jinping I Arch Dam began in October 2009 and was capped in December 2013. During the dam pouring construction, continuous monitoring of the alkali activity of sandstone aggregate was conducted by drilling for the core. The monitoring results are shown in Table 5.
It can be seen from the table that the actual alkali-aggregate expansion rate of concrete for Jinping I Arch Dam does not exceed 180 με after various measures are taken, which is far less than its control index of 400 με and will not affect dam safety.

6. Conclusions

In the present study, an analysis method that took into account the influence of concrete expansion suffering alkali-aggregate reaction on the long-term safety of arch dam was established to solve the problem of AAR in the concrete of Jinping level I super-high concrete arch dam. With this method, the possible expansion value equivalent to the corresponding temperature rise was predicted to simulate the expansive deformation of arch dam concrete by means of the overall temperature rise of the dam. All load combinations that can be encountered were considered. By adopting the elastic–plastic finite element method, the working behavior of the arch dam suffering AAR under different load combinations was calculated and analyzed, and the conclusions are as follows:
  • Through the analysis of the yield state of the arch dam under different alkali-aggregate deformation, it is found that the dam surface partly yielded when the deformation value reached 100~300 με, and the yield zone was partly connected at the high elevation of the right bank foundation surface along the upstream and downstream surfaces when the deformation value reached 800 με. At this time, the dam is in a dangerous state, and the risk of dam failure increases;
  • Through the analysis of the displacement of the arch dam under different alkali-aggregate reaction deformation, it is found that the overall stiffness of the arch dam was obviously reduced when the expansion value reached 400 με under certain load combinations;
  • The expansion process of the arch dam yield zone and the change law of the arch dam deformation with further expansion under different load combinations were analyzed. The breakthrough of the yield zone and the inflection point of the relationship curve between displacement and expansive deformation were taken as the judging criteria, and the control index for deformation of the arch dam suffering alkali-aggregate deformation of 400–800 με was obtained;
  • According to the given control threshold of alkali-aggregate expansion in dam concrete, the arch dam has a low safety reserve when operating at a low water level; thus, the lowest reservoir level should be raised as much as possible in dam operation to reduce its drawdown rate, thus restraining the adverse impact of alkali-aggregate reaction in concrete on the dam. The analysis method and control index research method for deformation of super-high arch dam suffering alkali-aggregate reaction proposed in this paper has achieved a technical breakthrough in the combination of the subject of concrete alkali-aggregate reaction and arch dam structural design and put forward targeted engineering measures that can be taken to restrain concrete alkali-aggregate reaction in the actual operation of dams. For other arch dams, the same method can be used for nonlinear analysis based on the shape of arch dams and the characteristics of dam concrete materials to evaluate the safety status of the dam.

Author Contributions

Conceptualization, H.C., Y.L. and J.Z.; methodology, Y.L. and J.Z.; software, Y.W.; validation, H.C., Y.W. and Q.Z.; formal analysis, Y.W.; investigation, B.Y.; resources, H.C.; data curation, B.Y.; writing—original draft preparation, Y.W.; writing—review and editing, H.C., Y.L., Q.Z., J.Z. and B.Y.; visualization, B.Y. and Q.Z.; supervision, H.C.; project administration, Y.W.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Key Technologies Research and Development Program(2021YFC3090102) and the China Three Gorges Corporation Research Project (No. 412002002, XLD/2114).

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare that they have no conflict of interest.

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Figure 1. Overall finite element model of dam body foundation.
Figure 1. Overall finite element model of dam body foundation.
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Figure 2. Finite element model of dam body.
Figure 2. Finite element model of dam body.
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Figure 3. Vector diagram of tensile stress increment under arch dam expansion. (a) Upstream face. (b) Downstream surface.
Figure 3. Vector diagram of tensile stress increment under arch dam expansion. (a) Upstream face. (b) Downstream surface.
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Figure 4. Vector diagram of compressive stress increment under arch dam expansion. (a) Upstream face. (b) Downstream surface.
Figure 4. Vector diagram of compressive stress increment under arch dam expansion. (a) Upstream face. (b) Downstream surface.
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Figure 5. Yield zone of arch dam with expansion of 200 με (basic combination I). (a) Upstream face. (b) Downstream surface.
Figure 5. Yield zone of arch dam with expansion of 200 με (basic combination I). (a) Upstream face. (b) Downstream surface.
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Figure 6. Yield zone of arch dam with expansion of 800 με (basic combination I). (a) Upstream face. (b) Downstream surface.
Figure 6. Yield zone of arch dam with expansion of 800 με (basic combination I). (a) Upstream face. (b) Downstream surface.
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Figure 7. Yield zone of arch dam with expansion of 100 με (basic combination II). (a) Upstream face. (b) Downstream surface.
Figure 7. Yield zone of arch dam with expansion of 100 με (basic combination II). (a) Upstream face. (b) Downstream surface.
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Figure 8. Yield zone of arch dam with expansion of 800 με (basic combination II). (a) Upstream face. (b) Downstream surface.
Figure 8. Yield zone of arch dam with expansion of 800 με (basic combination II). (a) Upstream face. (b) Downstream surface.
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Figure 9. Yield zone of arch dam with expansion of 300 με (basic combination III). (a) Upstream face. (b) Downstream surface.
Figure 9. Yield zone of arch dam with expansion of 300 με (basic combination III). (a) Upstream face. (b) Downstream surface.
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Figure 10. Yield zone of arch dam with expansion of 800 με (basic combination III). (a) Upstream face. (b) Downstream surface.
Figure 10. Yield zone of arch dam with expansion of 800 με (basic combination III). (a) Upstream face. (b) Downstream surface.
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Figure 11. Yield zone of arch dam with expansion of 150 με (basic combination IV). (a) Upstream face. (b) Downstream surface.
Figure 11. Yield zone of arch dam with expansion of 150 με (basic combination IV). (a) Upstream face. (b) Downstream surface.
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Figure 12. Yield zone of arch dam with expansion of 800 με (basic combination IV). (a) Upstream face. (b) Downstream surface.
Figure 12. Yield zone of arch dam with expansion of 800 με (basic combination IV). (a) Upstream face. (b) Downstream surface.
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Figure 13. Yield zone of arch dam with expansion of 300 με (accidental combination I). (a) Upstream face. (b) Downstream surface.
Figure 13. Yield zone of arch dam with expansion of 300 με (accidental combination I). (a) Upstream face. (b) Downstream surface.
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Figure 14. Yield zone of arch dam with expansion of 800 με (accidental combination I). (a) Upstream face. (b) Downstream surface.
Figure 14. Yield zone of arch dam with expansion of 800 με (accidental combination I). (a) Upstream face. (b) Downstream surface.
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Figure 15. Variation process of dam crest displacement along the river under different expansions (basic combination I).
Figure 15. Variation process of dam crest displacement along the river under different expansions (basic combination I).
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Figure 16. Variation process of dam crest displacement along the river under different expansions (basic combination II).
Figure 16. Variation process of dam crest displacement along the river under different expansions (basic combination II).
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Figure 17. Variation process of dam crest displacement along the river under different expansions (basic combination III).
Figure 17. Variation process of dam crest displacement along the river under different expansions (basic combination III).
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Figure 18. Variation process of dam crest displacement along the river under different expansions (basic combination IV).
Figure 18. Variation process of dam crest displacement along the river under different expansions (basic combination IV).
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Figure 19. Variation process of dam crest displacement along the river under different expansions (accidental combination I).
Figure 19. Variation process of dam crest displacement along the river under different expansions (accidental combination I).
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Table 1. Concrete proportions of each dam area [49].
Table 1. Concrete proportions of each dam area [49].
Dam AreaStrength GradeWater-to-Binder RatioSand-Aggregate/%Concrete Material Consumption/(kg·m−3)Slumps/cmAir Content/%
WaterCementFly AshSandStone
AC180400.392282136.773.647717183.53.8
BC180350.432382124.066.750317103.54.0
CC180300.472481112.060.353017033.24.2
Table 2. Experiment results of thermodynamic parameters of dam concrete [50,51,52].
Table 2. Experiment results of thermodynamic parameters of dam concrete [50,51,52].
Dam AreaDam Area ADam Area BDam Area C
thermal diffusivity (m2/h)0.00330.00330.0033
heat conductivity (kJ/m·h·°C)8.418.688.59
specific heat (kJ/kg·°C)1.0121.051.04
unit weight (kg/m3)247524752475
Poisson’s ratio0.170.170.17
linear expansion coefficient (10−6/°C)8.508.508.50
Table 3. Temperature load increment corresponding to different expansion values.
Table 3. Temperature load increment corresponding to different expansion values.
Expansion Value (×10−6)050100150200250300350400800
Temperature load increase (°C)05.911.817.623.529.435.341.247.194.1
Table 4. Control threshold of alkali-aggregate expansion in dam concrete.
Table 4. Control threshold of alkali-aggregate expansion in dam concrete.
Load CombinationsRisk LevelControl Threshold of Alkali-Aggregate Expansion
Basic
combination I
normalεv < 200 με
abnormal200 με ≤ εv < 800 με
dangerεv ≥ 800 με
Basic
combination II
normalεv < 100 με
abnormal100 με ≤ εv < 400 με
dangerεv ≥ 400 με
Basic
combination III
normalεv < 300 με
abnormal300 με ≤ εv < 800 με
dangerεv ≥ 800 με
Basic
combination IV
normalεv < 150 με
abnormal150 με ≤ εv < 400 με
dangerεv ≥ 400 με
Accidental
combination I
normalεv < 300 με
abnormal300 με ≤ εv < 800 με
dangerεv ≥ 800 με
Table 5. Monitoring results of expansion rate of core samples [48].
Table 5. Monitoring results of expansion rate of core samples [48].
Sampling DateExpansion Rate of Concrete Core at Different Ages/%
28 d126 d182 d364 d712 d
2010-01 0.0040.0110.0120.0150.018
2011-030.0050.0080.0080.0110.015
2012-020.0070.0120.0130.0120.015
2013-010.0050.0120.0120.0150.018
2013-070.0060.0110.0110.0120.015
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Cheng, H.; Wang, Y.; Liu, Y.; Zhou, Q.; Zhang, J.; Yang, B. Study on Analysis Method and Control Index for Deformation of Super-High Arch Dam Suffering Alkali-Aggregate Reaction. Water 2023, 15, 1399. https://doi.org/10.3390/w15071399

AMA Style

Cheng H, Wang Y, Liu Y, Zhou Q, Zhang J, Yang B. Study on Analysis Method and Control Index for Deformation of Super-High Arch Dam Suffering Alkali-Aggregate Reaction. Water. 2023; 15(7):1399. https://doi.org/10.3390/w15071399

Chicago/Turabian Style

Cheng, Heng, Yan Wang, Yi Liu, Qiujing Zhou, Jing Zhang, and Bo Yang. 2023. "Study on Analysis Method and Control Index for Deformation of Super-High Arch Dam Suffering Alkali-Aggregate Reaction" Water 15, no. 7: 1399. https://doi.org/10.3390/w15071399

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