Temperature and Stress Fields in Hydropower House

Ding Lu-jun College of Water Resource and Hydropower, Sichuan University Sichuan college of architectural technology No 4, West Jialingjiang Road, Jingyang District, Deyang City, Sichuan Province, PR China. e-mail: [email protected]

Liu Yu-hong Sichuan college of architectural technology No 4, West Jialingjiang Road, Jingyang District, Deyang City, Sichuan Province, PR China. e-mail: [email protected]

ABSTRACT The concrete body of hydropower house is great and its structure is complex, so the temperature control simulation research has important practical application value. Considering concrete thermodynamics parameters along with the change of age, we have simulated the concrete dam construction process and adopted the three dimensional finite element method to calculate the temperature field and thermal stress. The result showed that for the site of pouring in cold season, the method of natural warehousing watering should be taken. whereas for the site of pouring in hot season, the method of control pouring temperature and the water cooling measures of the entire region should be taken. In this way the maximum temperature and the maximum thermal stress could meet requirements of the design specifications. The research results laid an essential basis for the powerhouse dam section of Hydropower Station design, construction and temperature control. KEYWORDS: powerhouse dam section; temperature field; thermal stress; three-dimensional finite element method; construction process

INTRODUCTION Mass concrete structures are widely used in water conservancy and hydropower projects, especially the construction of concrete dams. And the temperature control and temperature crack problem is perplexing the construction personnel for a long time. From 1930s to start [1], Many scholars established temperature crack control theory system, and has taken a series of measures of crack prevention, such as improving crack resistance of concrete, parting block, water pipe cooling, pre cooling aggregate, surface heat preservation, and so on. The temperature rise in the hydration heat of concrete can cause the temperature stress cracks in concrete, and then destroy the integrity of the structure, so that the durability of the concrete is decreased, and even endinger the safety of buildings. Therefore, need to take measures to solve the temperature control heat of water temperature inside concrete[2]. In this paper, the three-dimensional finite element method is used to simulate the construction process of the hydropower station.

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CALCULATION PRINCIPLES According to the theory of heat conduction, the three-dimensional unsteady temperature field should satisfy the following partial differential equations and the corresponding initial conditions and boundary conditions [3,4]. Universal equation is:

∂T ∂ 2T ∂ 2T ∂ 2T ∂θ = α( + + ) + (1) ∂τ ∂x 2 ∂y 2 ∂z 2 ∂τ where: ∂T —The change rate of temperature with time; ∂τ α —coefficient of temperature conductivity; θ —Adiabatic temperature rise of concrete. Initial condition is （ ， ， ） TT|τ =00= xyz (2)

boundary conditions are: first class boundary conditions: T= Tb (3) third kinds of boundary conditions: ∂T ∂T ∂T l l + l l + l l + β (T − T ) = 0 (4) ∂x x ∂y y ∂z z a adiabatic boundary condition: ∂T λ = 0 ∂n 5) where

lx ， ly ， lz —the direction cosine of the boundary normal; Tb —given boundary conditions; Ta —temperature; T（xyz， ， ） 0 —given initial temperature; λ —coefficient of heat conductivity; β ——surface heat coefficient. Strain increment of concrete under complex stress state includes the increment of elastic strain, creep strain increment, temperature strain increment, dry shrinkage strain increment and autogenous volume deformation increment. So there is: ∆e = ∆e e + ∆e c + ∆e T + ∆e s + ∆e 0 n n n n n n (6) where: ∆e e n —elastic strain increment; Vol. 21 [2016], Bund. 20 6733

∆ε c n —creep strain increment; ∆ε T n —temperature strain increment; ∆ε s n —dry shrinkage strain increment; ∆ε 0 n —autogenous volumetric strain increment . GENERAL ENGINEERING SITUATION A hydropower station project to generate electricity, installed capacity of 420mw, with the maximum dam height of 79.6m, crest elevation 1820.50m, crest length 346.4m. The total amount of concrete is 1164000m3. Powerhouse dam section of large volume, complicated structure form and consider alternatives to dam safety and temperature control measures, the temperature field and temperature should force simulation research, to provide a reference for engineering design and construction. CALCULATION PARAMETERS AND CALCULATION MODEL

Calculation Parameters The average temperature of the project is 22.68, the average minimum temperature is 7.47, the average annual temperature is 15.21. The dam area of the annual mean temperature is shown in table 1, the construction schedule is shown in table 2, thermodynamic parameters of concrete is shown in table 3. Table 1: The annual mean temperature of he dam area (unit: )

Month 1 2 3 4 5 6 7 8 9 10 11 ℃12 year

Temperature 7.47 8.83 11.43 14.43 18.98 21.35 22.68 21.8 20.5 16.15 10.93 8.05 15.21

Table 2: Plant dam upstream hydropower station construction progress Number Start construction time Initial height(m) Terminate height(m) 1 6/1/2015 1742.9 1744 2 6/20/2015 1744 1746.5 3 6/20/2015～7/20/2015 Consolidation grouting 4 7/20/2015～8/20/201 Cubital tunnel installation 5 9/10/2015 ～1/10/2016 1746.5 1763.0 6 1/30/2016 ～3/10/2016 1763.0 1772.0 7 3/10/2016～4/30/2016 Cone pipe installation and two stage concrete, spiral case 8 5/20/2016 1772.0 1774.4 9 6/10/2016 ～2/28/2017 1774.4 1820.5 Vol. 21 [2016], Bund. 20 6734

Note: the downstream unit section, the tail water platform section starting the construction period after 20 days.

Table 3: Thermodynamic parameters of dam concrete Linear Temperature Specific Thermal Hydration heat Concrete expansibility coefficient heat coefficient temperature (10-6 /℃) (m2/h) (kJ/kg· ) (kJ/m·h· ) rise )

Cushion 29.617(t0.907 − 0.46) T = 5.8 0.00313 0.9922℃ 7.28 ℃ ℃0.907 normal 0.40+t 32.05*τ Dam normal 5.75 0.00318 0.99035 7.395 T = 2.15 +τ

Computational Model and Coordinate System[5,6] The calculation model for dam transverse joints between the dam and the dam axis. The overall coordinate system origin of the dam left at the dam heel. Pointing to the right bank of the dam axis is the X axis direction is positive, downstream of the positive Y axis, vertical axis is Z positive. Calculate the model in the depth direction of the dam to take 100m, the upstream direction of 100m, the downstream direction is also taken 100 m. Temperature field calculation in boundary conditions is selected: foundation bottom surface and four side and monolith joint surface is adiabatic boundary, the dam downstream face above the water level for solid-gas boundaries, below the water table for solid-water boundary. Solid-gas boundary is treated by third kinds of boundary conditions. The selection of boundary conditions in the stress field calculation is: the foundation is treated by fixed bearing, and the foundation is treated with y in the upper and lower reaches. The other is the free boundary. Plant dam model is shown in Figure 1.

Figure 1: The calculation model of power building monolith

Calculation Scheme The power building monolith section of the dam foundation surface elevation for 1741.9m, crest elevation for 1820.5m, dam height 79.6m, dam length for 28.6m, dam width for 76.0m. The opening time of the test concrete was June 1, 2015, and the elevation of 1820.5m was reached by February 28, 2017. Downstream unit section, the end of the water platform to start construction period of 20 days. On 5~9 month casting parts adopt water cooling measures, pipe spacing 1.5*1.5m, water temperature Vol. 21 [2016], Bund. 20 6735 water temperature in the month, the watering time for 15 days, single cooling pipe length is 250m. The pouring temperature of each program is shown in Table 4. Table 4: The plant dam pouring temperature Pouring temperature Calculation scheme Restrained zones Non-Restrained zones 1 Tp=18°C Tp=20°C 2 Tp=20°C Tp=22°C 3 Tp=22 Tp=24

℃ ℃ ANALYSIS RESULT

Analysis of Temperature Control Standards and Temperature Field Calculation Results Temperature Control Standard During the construction of large volume concrete water cement of temperature increased control of concrete pouring temperature and the highest temperature inside is the key problem of temperature control and crack prevention of dam [7-8]. The power building monolith in different parts of the large volume concrete maximum allowable temperature is shown in Table 5.

Table 5: The maximum allowable temperature value in different parts of building monolith Control maximum temperature Position 11~3 month 4、10 month 5~9 month

1742.9～1763m 28~30 32~34 36 Building Normal concrete 1763～1774.4m 28~30 32~34 38 monolith >1774.4m 28~30 32~34 38

Analysis of Calculation Results of Unsteady Temperature Field The process of building concrete construction through simulation of hydropower station, the thermodynamic parameters of concrete varies with age, the simulation study on temperature field of dam, In order to analyze the variation of dam temperature field, it also draws the dam in different elevation typical point temperature curve, due to the very large amount of data, so only lists a program of 14 point temperature duration curve shown in Figure 2, the typical position shown in Figure 3. In the analysis of large amounts of data found in the highest temperature of different parts of concrete have appeared in May 2016, due to the number of data is very large, now only lists the Vol. 21 [2016], Bund. 20 6736 temperature peak in the temperature contour map of May 20, 2016, specifically shown in Figure 4 to Figure 6, the highest temperature in different regions are shown in table 6.

Figure 2: Scheme 1 Temperature duration curve of point 14

Figure 3: Location map of plant dam typical points

Figure 4: Scheme 1 contour map of temperature in May 20, 2016( )

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Figure 5: Scheme 2 contour map of temperature in May 20, 2016( )

℃

Figure 6: Scheme 3 contour map of temperature in May 20, 2016( )

℃ Table 6: The table of maximum temperature and allowable temperature of the different regional in different months of each scheme of building monolith Maximum temperature 1742.9～ Scheme 1763～1774.4m >1774.4m and allowable temperature 1763m 1 Maximum temperature 35.86 38.4 36.2

2 Maximum temperature 37.24 40.2 37.7

3 Maximum temperature 38.63 42.1 39.1

Permissible maximum temperature 36 38 38

From the calculation results can be seen that (1) In the range of 1742.9～1763.0m, the highest temperature is 35.86 in scheme 1 , which is less than the site allows temperature 36 , the highest temperature is 37.24 in scheme 2, the highest temperature is 38.63 in scheme3, they are greater than the maximum℃ allowable temperature . ℃ ℃ ℃ Vol. 21 [2016], Bund. 20 6738

(2) In the range of 1763.0m ~ 1774.4m, the highest temperature is 38.4 in scheme 1 , which is close to the site allows temperature 38.0 , the highest temperature is 40.2 in scheme 2, the highest temperature is 42.1 in scheme 3, they are greater than the maximum℃ allowable temperature. ℃ ℃ ( ) 3 In the range of 1774.4m~℃ 1820.5m, the highest temperature is 36.2 in scheme 1, the highest temperature is 37.7 in scheme 2, they are less than the maximum allowable temperature 38.0 ,the highest temperature is 39.1 in scheme 3, which is greater than℃ the site allows temperature. ℃ ℃ ℃ (4) The maximum temperature of the dam body is required to be a long process, and the temperature field calculation results show that the maximum temperature of the dam body is in the period of construction. Operation period, the dam body and the surrounding environment for heat exchange, the maximum temperature of the dam body is gradually reduced.Running about 30 years, the internal temperature of the dam is basically stable temperature field.

Analysis of Temperature Stress Calculation Results Due to the large amounts of data found in the low temperature of concrete tensile stress is larger, so the given contour corresponds to the maximum temperature stress diagram, the workshop section of each scheme stress contour of temperature in January 20, 2017, shown in Figure 7 to figure 9. The unit of stress in the figures is 0.1MPa. From the calculation results can be seen: the maximum stress of scheme 1 is 1.55Mpa, the maximum stress of scheme 2 is 2 1.71Mpa, the maximum stress of scheme 3 is 1.83Mpa. Concrete pouring temperature of scheme 1 is lower, and the maximum stress is also small.

Figure 7: Scheme 1 contour map of temperature stress in January 20, 2017 Vol. 21 [2016], Bund. 20 6739

Figure 8: Scheme 2 contour map of temperature stress in January 20, 2017

Figure 9: Scheme 3 contour map of temperature stress in January 20, 2017

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CONCLUSIONS The large volume and complex structure of hydropower station building, the paper uses the three- dimensional finite element method to simulate the construction process of temperature control simulation calculation. The results show: The maximum temperature and maximum stress of the scheme 1 meet the requirements. Therefore, for concrete in the range of 1742.9 m~1774.4m, the pouring temperature should be less than or equal to 18 ,for concrete in the range of 1774.4m ~1820.5m, the pouring temperature should be less than or equal to 20 ; at the same time the need for high temperature season casting parts adopt water cooling℃ measures, other months take natural pouring in.. The research results provided reference for the design, ℃construction and temperature control measures of the project. Through the above simulation, control of pouring temperature and in high temperature season whether for cooling, temperature field of concrete and influence of stress field is very large, so for the construction of large volume concrete dam, put forward the following suggestions: (1) the pouring temperature should be low; (2) high temperature should be avoided seasonal construction; (3) high temperature season if construction should be taken with water cooling measures of concrete temperature field of the peak, avoid excessive temperature difference caused by large tensile stress.

ACKNOWLEDGEMENTS The research described in this paper was financially supported by office of science and technology department of Sichuan province, China (2015JY0035) .

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Editor’s note. This paper may be referred to, in other articles, as: Ding Lu-jun and Liu Yu-Hong: “Temperature and Stress Fields in Hydropower House” Electronic Journal of Geotechnical Engineering, 2016 (21.20), pp 6731-6741. Available at ejge.com.