Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 528589, 12 pages

http://dx.doi.org/10.1155/2015/528589

## Sensitivity Analysis of Temperature Control Parameters and Study of the Simultaneous Cooling Zone during Dam Construction in High-Altitude Regions

^{1}Department of Structures and Materials, China Institute of Water Resources and Hydropower Research, Beijing 100038, China^{2}State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China^{3}Henan Yellow River Reconnaissance, Design and Research Institute Beijing Branch, Beijing 100073, China

Received 26 August 2014; Revised 18 December 2014; Accepted 2 January 2015

Academic Editor: Weizhong Dai

Copyright © 2015 Zhenhong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

There are unprecedented difficulties in building concrete gravity dams in the high altitude province Tibet with problems induced by lack of experience and technologies and unique weather conditions, as well as the adoption of construction materials that are disadvantageous to temperature control and crack prevention. Based on the understandings of the mentioned problems and leveraging the need of building gravity dam in Tibet, 3D finite element method is used to study the temperature control and crack prevention of the dam during construction. The calculation under recommend temperature control measures and standards shows that the height and number of simultaneous cooling zone have the more obvious influencers on concrete stress; therefore, it is suggested to increase the height of simultaneous cooling zone to decrease the stress caused by temperature gradient of adjoin layers so as to raise the safety level of the whole project. The research methods and ideas used on this project have significant values and can be taken as references in similar projects in high altitude regions.

#### 1. Introduction

Dams have been successfully built around the world, especially in low-altitude regions [1, 2]. In high-altitude regions, such as Tibet, however, the lack of experiences in dam-related technologies and systematic theories introduces challenges in building dams. A high altitude implies a complicated climate that features dry and thin air, strong sun radiation, and severe temperature difference between day and night [3, 4]. Compared with building dams in low-altitude regions that have warm and humid air and a small temperature difference between day and night, building dams in high-altitude regions requires specific, straightforward, and tailored measures and standards for temperature control and crack prevention.

Cracks in large volumes of concrete are always a challenge in the field of engineering. Many engineering cases involve cracks caused by temperature at different levels in large-volume concrete structures, such as dams, during and after construction. These cracks make structures appear weak, and they severely affect durability and safety [5–9]. Because temperature-induced cracking problems continue to be a major challenge in engineering, designers and builders also continue to study large-volume concrete projects and develop appropriate temperature control measures and standards to decrease temperature stress and avoid or reduce cracks. This study focuses on the Jiexu Dam, a gravity dam being built in Tibet. To analyze the sensitivities of conditions and parameters during the construction process in the region, the 3D finite element method [10–13] is used. The discussion concludes by presenting rules on the conditions and parameters that affect temperature stress in the dam. This study considers heat transfer and the hardening development process of concrete [14–17], the shrinkage deformation caused by temperature changes in concrete [18, 19], and the pipe cooling measures of concrete [20]. From the findings and information obtained from similar projects, a set of measures and standards suitable for dam construction in high-altitude regions are proposed to guide the safe construction of dams.

#### 2. Calculation Principles and Methods

##### 2.1. Differential Equation for Heat Conduction

Differential equation [21] (1) applies to the temperature field of even and isotropic homogeneous solid:

In the equation, stands for temperature (°C), , , and are the three coordinates of a point (m), stands for thermal diffusivity (m^{2}·h^{−1}), is the adiabatic temperature rise of concrete (°C), and stands for maturity (day).

The principle of minimum gravitational energy indicates that the differential equation for heat conduction (1) can be converted: temperature is set as the initial temperature when ; the heat conduction matrix , heat capacity matrix , and temperature load array are achieved when the extremum is given for each boundary and through spatial discretization and difference in the time domain. After integration, the partial differential of temperature at each nodal is determined:In the above equation, , , .

Equation (2) is a set of linear differential equations with as the independent variable. In the equation, is the heat capacity matrix, is the heat conduction matrix, is the temperature load column matrix, is the nodal temperature array, and is the derivative array of nodal temperature against time.

##### 2.2. Finite Element Method of the Stress Field

The strain increment of concrete under complex stress includes the elastic strain increment, creep strain increment, temperature strain increment, dry shrinkage strain increment, and autogenous volume strain increment [21]; thus,where is the elastic strain increment, is the creep strain increment, is the temperature strain increment, is the dry shrinkage strain increment, and is the autogenous volume strain increment.

We obtain a finite element governing equation of any time interval on the area from the physical equation, the geometric equation, and the equilibrium equation as follows:where is the displacement increment of all nodes in three directions in area and , , , , and are the equivalent nodal force increment caused by the external load, creep, temperature change, dry shrinkage, and autogenous volume deformation within , respectively.

##### 2.3. The 3D Finite Element Method Software SAPTIS

The Structure Analysis Program for Temperature and Induced Stress (SAPTIS) software package facilitates the FORTRAN language-programmed, large-scale multifield simulation, and nonlinear analysis. The software is used to simulate the calculation of temperature, stress, seepage, and deformation, among other factors, in the entire process of foundation excavation, pouring process, water storage process, and long-term operation of concrete dams. The main features of the program include the excavation and pouring simulation method, the hydration heat model, the water cooled model, the temperature boundary conditions, the elastic modulus model, the creep model, autogenous volume deformation, and MgO concrete characteristics in the entire simulation process of dams.

The program has a rich element library. 3D problems include 8–20 variable node hexahedron isoparametric elements, 6–15 variable node pentahedron isoparametric elements, and 8-node hexahedron isoparametric elements, as well as bar elements, joint elements, and contact elements, to name a few. SAPTIS has a variety of solvers. The direct solution method or the iterative solution method can be used to solve large linear equations. SAPTIS is characterized by its high speed and small memory capacity. It can use a computer to conduct simulation analysis, as well as general structural stress and deformation analysis of large concrete structures; it can also use a server for parallel computing. The software is successfully applied to more than 50 large and medium concrete dams of the Three Gorges, Ertan, Longtan, Xiaowan, Xiluodu, Jinping, Danjiangkou, and other dams, as well as for the simulation analysis of the temperature and stress fields of other structures. Favorable economic benefits are achieved as a result.

###### 2.3.1. Adiabatic Temperature Rise Model

Considerwhere is the adiabatic temperature rise of concrete (°C), is the final adiabatic temperature rise (°C), and are the law parameters of the adiabatic temperature rise, and is a constant.

###### 2.3.2. Elastic Modulus Model

where is the initial elastic modulus of concrete (GPa), is the final elastic modulus of concrete (GPa), is the age of concrete, and and are the variation coefficients of the elastic modulus of concrete.

###### 2.3.3. Creep Model

*Model 1*. Consider

*Model 2*. Considerwhere is the specific creep, 10^{−6}/MPa; , , and are the creep rate parameters; , , , , , , and are the specific creep parameters, 10^{−6}/MPa; is the time (day); and is the loading age (day).

###### 2.3.4. Autogenous Volume Model

Autogenous volume deformation is determined by the direct input of experimental data and the deformation values between the two experimental ages through spline function interpolation.

###### 2.3.5. Water Cooling Model

The contact surfaces of concrete with air, water, rocks, and other media transfer heat and have a cooling effect. With the pipe cooling effect considered, the problem is complex, such that it cannot be solved by theoretical methods; accurately solving it with the finite element method is also difficult. An approximate solution can be obtained only through consideration of the cooling water pipes as a negative heat source and of the function of the cooling water pipes, on average. If the initial temperature of concrete is set to , the intake water temperature is set to , the final adiabatic temperature rise of concrete is set to , and the time is set to ; the average temperature of concrete is calculated as follows:

Therefore, the equivalent thermal conductivity equation of concrete is as follows:where represents the pipe cooling effect and represents the adiabatic temperature rise effect. The details are discussed in [21].

The equation indicates that the problem can be simplified, and the common cooling effect of cooling water pipes can be approximately calculated with the existing finite element program and computational grid.

#### 3. Overview of the Gravity Dam

##### 3.1. Project Overview

Jiexu Hydropower Station is located at the boarder of Sangri County and Jiacha County in Shannan Region of the Tibet Autonomous Region. The station is a third-stage power plant in the gorge section from Sangri County to Jiacha County along midstream of Yarlung Tsangpo River. It is 7 km away from a planned Dagu Hydropower Plant in the upstream and 18 km away from the Zangmu Hydropower Plant currently being built in the downstream. Jiexu Hydropower Plant is primarily designed for power generation. In the up dam site, the catchment area is 157,407 km^{2}, and the average flow at the dam site is 1,010 m^{3}·s^{−1}. The standard impounded level of the dam is at 3,374 m, and the storage capacity is 47.48 million m^{3}, with an adjusted storage capacity of 9.85 million m^{3}. Four generators are installed with a total capacity of 560 MW and a firm capacity of 152 MW. The average power generation volume is 2,755.6 million kWh.

The Jiexu Hydropower Station river dam is a concrete gravity dam. From left to right are a left bank water-retaining dam section, diversion dam section, bottom outlet dam section, overflow dam section, and right bank water-retaining dam section. The dam crest is 340 m long, the crest elevation is 3,378.0 m, the maximum dam height is 117.0 m, the widest bottom of the dam is 99.8 m, and the total volume of dam concrete is around 1.64 million m^{3}. The largest dam section is 32.5 m wide. The project is constructed in 14 dam sections. The dam has five flood release orifices with a dimension of 14 m × 21.5 m, one bottom outlet for flood release with a dimension of 5 m × 8 m, and four power generation water inlets. The dam is a complicated structure, with its construction ongoing for a year now; it has a long construction cycle and involves complicated construction conditions.

##### 3.2. Engineering Difficulties

(1)Special geological conditions make temperature control challenging. The project is located in Tibet, a high-altitude region. Therefore, it is characterized by thin air, dry climate, strong solar radiation, severe temperature difference between day and night, and large monthly average temperature variance. Such a climate is disadvantageous in controlling temperature to prevent cracks on concrete.(2)The construction materials used in building the dam are not helpful for temperature control and crack prevention. The composition of concrete used for the project shows that within the same region and similar structure, the coefficient of thermal expansion of concrete is 9.0 × 10^{−6}, and the adiabatic temperature rise is 26.3°C, which is 1.22 times and 3°C higher than those of Zangmu, respectively. However, the modulus of elasticity and tensile strength in both stations are similar. The material parameters used for the Jiexu project are disadvantageous for crack prevention, and temperature control in Jiexu is also more difficult than that in Zangmu. Table 1 shows a comparison of the key temperature control parameters of Jiexu and Zangmu.