Given that spillways adopt a hydraulic thin concrete plate structure, this structure is difficult to protect from cracks. The mechanism of the cracks in spillways shows that temperature stress is the major reason for cracks. Therefore, an effective way of preventing cracks is a timely and reasonable temperature-control program. Studies show that one effective prevention method is surface thermal insulation combined with internal pipe cooling. The major factors influencing temperature control effects are the time of performing thermal insulation and the ways of internal pipe cooling. To solve this problem, a spillway is taken as an example and a three-dimensional finite element program and pipe cooling calculation method are adopted to conduct simulation calculation and analysis on the temperature fields and stress fields of concretes subject to different temperature-control programs. The temperature-control effects are then compared. Optimization results show that timely and reasonable surface thermal insulation and water-flowing mode can ensure good temperature-control and anticrack effects. The method has reference value for similar projects.
With the increasing investment of China on their water conservancy projects, water resources of the southwest part have been gradually developed. Many major water conservancy projects have thus been established, including dams, spillways, and spillway tunnels, as well as other large-scale structures. As a consequence, the crack problem is subject to growing concern. High flow rate, large capacity, and high intensity of water put forward extremely high requirements for the comprehensive performances, construction technologies, and appearance quality of these concrete structures. Generally, spillways use high-grade impact and abrasion resistant concrete characterized by high cement content, high adiabatic temperature rise, quick temperature rise at early stage, and early strengthening. In addition, the spillways have thin floors, long partings along the rivers, and high basic constraint. These characteristics determine that temperature control is the key to ensuring project quality [
With the existing temperature control measures, cracks are difficult to avoid in impact and abrasion resistant concrete [
At any point within the computational domain
By adopting the variation principle, formula (
The water temperature increments along the pipe can be calculated according to the Fourier law of heat conduction and the thermal equilibrium conditions [
The strain increments of concrete under complex stress conditions include elastic strain increment, creep strain increment, temperature strain increment, drying shrinkage strain increment, and autogenous volume strain increment [
The FEM governing equation for the area
The special functions and features of spillways confirm that high-performance concrete with good strength, impact, and abrasion resistance is often used. However, high-performance concrete has various thermal properties such as small water-cement ratio, high cement content, high hydration heat, high adiabatic temperature rise, and an adiabatic temperature rise mainly concentrated at the early stage. It also has some mechanical properties such as large elasticity modulus, early strengthening, and large autogenous volume deformation. These properties make cracks difficult to control and become common and hard to prevent.
Unlike the concrete structure of a dam, spillways have thin structures with a thickness of 1-2 m. Unlike the aqueduct structure, spillways have very simple structures, without the deformation constraint between the floor and flank wall, side wall and floor, and main beam and floor. Unlike dams and aqueducts, spillways often have long partings along the river, and the entire structure of a spillway is under a strongly restrained zone. The structure is also subject to obvious restrain of the foundation, so cracks are easily generated. Once a crack appears, it is usually a penetrating crack that greatly affects the durability and security of the spillway structure.
In short, the characteristics of spillways with respect to material and structure confirm that they are sensitive to cracks. Spillways have more stringent anticrack requirements, and cracking is difficult to prevent. Minimizing harmful cracks during construction is of great importance for the future security of a project.
The hydropower station is located at the lower reach of Lantsang River at the junction of Simao District of Puer City and Lancang County, Yunan Province. It is at the fifth cascade in the eight-cascade planning for the middle-lower reach of Lantsang River. The open spillway of the hydropower station is arranged on the left bank of the dam and consists of the intake channel section, lock chamber section, chute section, deflecting bucket section, and the stilling pond section at the outlet. The spillway has an overall horizontal length of 1445.183 m, a width of 151.5 m, and a thickness of about 1 m. This spillway is China’s largest and the world’s second largest with the largest discharge power. This spillway adopts C18055W8F100 grade-II concrete. It is subject to year-round construction, and the temperature-control and crack-resistant tasks are complex and arduous. The concrete mix ratio is shown in Table
Mixing proportion of spillway concrete for the purpose of temperature-control test (unit: kg·m−3).
Intensity grade | Gradation | Sand ratio | Water-binder ratio | Fly ash replacement percentage | Water reducing agent | Air entraining agent | Amount of material per cubic meter of concrete | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Name | Dosage | Name | Dosage 1 × 10−4 | Water | Cement | Fly ash | Sand | Stone | |||||
C18055 | II | 36 | 0.37 | 20 | JM-PCA | 0.9 | JM-2000 | 0.8 | 116 | 251 | 63 | 699 | 1242 |
Thermal and mechanical parameters of spillway concrete.
Intensity grade | Thermal conductivity coefficient [kJ·(m·h·°C)−1] | Specific heat [kJ·(kg·°C)−1] | Linear expansion coefficient [(°C)−1] | Adiabatic temperature rise [°C] | Poisson’s ratio | Elastic modulus [GPa] | ||
---|---|---|---|---|---|---|---|---|
7 days | 28 days | 90 days | ||||||
C18055 | 9.83 | 0.985 | 8.3 × 10−6 | 48.67 × |
0.167 | 32.4 | 33.9 | 37.5 |
When calculating the temperature field, the bottom and the four sides of the foundation are taken as the adiabatic boundaries and the four sides and the top of the spillway are taken as category-3 boundary conditions. The ambient temperature adopts the average temperature over years. An equivalent algorithm is adopted for calculation once water cooling starts [
Simulation calculation grid.
The spillway uses high-performance concrete and is subject to year-round construction. Given the limited space, only a section of the spillway concrete constructed in summer is taken as an example to explain the temperature-control methods, such as surface thermal insulation and internal water pipe cooling. To achieve optimum temperature-control results, multiparameter and multicombination numerical simulation calculations are carried out. Temperature-control solutions in different combinations are shown in Table
Temperature-control program.
Program | Pouring temperature [°C] | Surface thermal insulation [kJ·(m2·h·°C)−1] | Target temperature [°C] | Water pipe cooling | ||
---|---|---|---|---|---|---|
Spacing [m × m] | Water temperature [°C] | Flow rate [m3·h−1] | ||||
Program 1 | 15 | — | — | 1.0 × 1.0 | — | — |
Program 2 | 15 | 20 | 28 | 1.0 × 1.0 | 13 | 2.0 |
Program 3 | 15 | The thermal insulation coefficient is 20 at early stage and 5 after October. | 28 | 1.0 × 1.0 | 13 | 2.0 |
Program 4 | 15 | Curing with flowing water is conducted at the early stage and the thermal insulation coefficient is 5 after October. | 28 | 1.0 × 1.0 | 13 | 2.0 |
The above programs are sequentially set; the next program is proposed based on the calculation results of the previous program and according to the problems existing in the construction conditions and the calculation results. Therefore, it is a gradual optimization process as a whole and the ultimate purpose is to provide the optimal temperature-control program.
The results of simulation calculation are shown in Table To understand the variation laws of temperature and stress, Program 1 is set to be the construction condition with no temperature-control measure. The calculation results show that the maximum temperature inside the spillway concrete can reach 41.75°C without any temperature-control measure. Without surface thermal insulation, the temperature decreases to 31.12°C on day 9, with a decreasing amplitude of 9.54°C and a cooling rate of 1.1°C·day−1. Considering that the construction is carried out on a hot weather, the concrete temperature changes with the ambient temperature; it continuously decreases and reaches the minimum value in the middle of next January. The concrete temperature decreases from its maximum temperature of 41.75°C to its minimum temperature of 16.62°C, with the decreasing amplitude above 25°C. Given that the structure is thin walled and is under a strong constraint condition, stress continuously increases and reaches its maximum value of 3.89 MPa at the age of 207 days (next January), exceeding the allowable tension stress of concrete and with a safety factor of only 1.15. Program 2 adopts temperature control measures on the basis of Program 1. The temperature-control measure is found to result in the following: surface thermal insulation coefficient of 20 kJ·(m2·h·°C)−1, water temperature of 13°C, flow rate of 2.0 m3·h, and target temperature of 28°C. Under these conditions, the maximum temperature of the concrete decreases from 41.75°C to 37.19°C. Considering surface thermal insulation, the temperature decreasing amplitude and the cooling rate of the concrete decrease. However, the maximum stress still exists in the next January when the air temperature is the lowest. The maximum along-the-flow stress of the concrete is 3.25 MPa and the safety factor of the concrete is only about 1.37. The improvement of stress is very limited. Program 3 adopts a different surface thermal insulation measure. In particular, the initial thermal insulation coefficient is 20 kJ·(m2·h·°C)−1. When the air temperature begins to significantly decrease (from October), 5 kJ·(m2·h·°C)−1 insulation materials are used. Calculation results show that this measure can greatly reduce the stress of the concrete. However, the safety factor is still about 1.6. Program 4 is proposed based on the above temperature-control measures. In Program 4, flowing water is used to further reduce the maximum temperature of the concrete at the early stage. When the air temperature significantly decreases (from October), the concrete is covered with thermal insulation material whose thermal insulation coefficient is 5 kJ·(m2·h·°C)−1 so as to reduce the impact of air temperature on the concrete. Calculation results show that, due to the water curing adopted at the early stage, the maximum temperature of the concrete decreases to about 35.7°C, the decreasing amplitude is obvious, and the initial safety factor is above 2.0. The maximum stress starts in the next January. The maximum stress of the concrete is only about 2.50 MPa because the thermal insulation material whose thermal insulation coefficient is 5 kJ·(m2·h·°C)−1 is used after October to significantly decrease the temperature fluctuation amplitude of the concrete. The safety factor is about 1.80 and the safety factor on the surface of the concrete is above 2.50.
Highest temperature and maximum stress of the spillway cast according to different programs in summer.
Program | Inside the concrete | Surface of the concrete | |||||
---|---|---|---|---|---|---|---|
Highest temperature [°C] | Maximum along-the-flow stress [MPa] | Age [day] | Safety factor | Maximum along-the-flow stress [MPa] | Age [day] | Safety factor | |
Program 1 | 41.75 | 3.89 | 207 | 1.15 | 3.37 | 201 | 1.33 |
Program 2 | 37.19 | 3.25 | 213 | 1.37 | 3.18 | 205 | 1.40 |
Program 3 | 37.60 | 2.87 | 225 | 1.56 | 2.73 | 219 | 1.64 |
Program 4 | 35.42 | 2.50 | 225 | 1.79 | 1.77 | 215 | 2.53 |
Thermograms of internal temperatures for various programs.
Thermograms of surface temperatures for various programs.
Internal stress hydrograph of various programs.
Surface stress hydrograph of various programs.
According to the results of the above multimode and multiparameter calculation and analysis, the recommended temperature control measures for pouring the impact and abrasion resistant spillway concrete in summertime are as follows:
The results of this work indicate the following. Spillways generally use high-grade impact and abrasion resistant concrete characterized by high cement content, high adiabatic temperature rise, quick temperature rise at early stage, and early strengthening. Spillways also have thin floors, long partings along the rivers, and high basic constraint. The structural characteristics of high-grade concrete determine temperature control and crack prevention which are more difficult to carry out during the construction period of a spillway. Surface thermal insulation and internal pipe cooling are the main methods of reducing this kind of cracks. Surface thermal insulation can help reduce the temperature difference between the interior and exterior of the structure, the impact of sudden ambient temperature change on the structure, and the temperature fluctuation of concrete, and this method is a major crack-prevention measure. Water cooling can prevent the concrete temperature from excessively increasing and can reduce the rate of temperature rise and temperature difference between the interior and exterior of the concrete. Combination of both has better temperature-control and crack-prevention effects. However, the thermal insulation coefficient and the cooling method will be reasonable and proper. Different temperature control measures have different temperature-control and crack-prevention effects. Each measure is required to be reasonable and proper; otherwise, no good temperature-control and crack-prevention effect can be achieved; sometimes, even adverse effect may be generated. Therefore, multiparameter and multimode simulation calculation and analysis are necessary to carry out to select suitable temperature-control and crack-prevention programs.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors acknowledge the support provided by the National Natural Science Foundation of China (Grant no. 51209235), the Governmental Public Industry Research Special Funds for Projects (Grant no. 201201050), the 973 Project (nos. 2013CB036406 and 2013CB035904), the Special Scientific Fund sponsored by IWHR for Department of Structures and Materials (nos. 1309, 1353, 1361, and 1169), and the Twelfth Five-Year Science and Technology Project (SQ2013BAJY4138B02).