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The measured temperature of a concrete pouring block depends strongly on the position of the buried thermometer. Only when the temperature measured by the thermometer accurately reflects the actual temperature of the concrete pouring block do reasonable temperature-control measures become possible. However, little research has been done on how to determine the proper position of thermometers buried in a concrete pouring block embedded with cooling pipes. To address this situation, we develop herein a method to determine the position of thermometers buried in a concrete pouring block. First, we assume that the design temperature-control process line characterizes the average-temperature history of the concrete pouring block. Under this assumption, we calculate the average-temperature history of the concrete pouring block by using the water-pipe-cooling FEM, following which the temperature history of an arbitrary point in the concrete pouring block is obtained by interpolating the shape function. Based on the average-temperature history of the concrete pouring block and the temperature history of the arbitrary point, we build a mathematical model to optimize the buried position of the thermometer and use the optimization algorithm to determine this position. By using this method, we establish finite-element models of concrete prisms with four typical water-pipe spacing cases for concrete-dam engineering and obtain the geometric position of the thermometers by using the optimization algorithm. By burying thermometers at these positions, the measured temperature should better characterize the average-temperature history of the concrete pouring block, which can provide useful information for regulating the temperature of concrete pouring blocks.

Numerous engineering practices have shown that massive concrete structures often have large tensile stresses due to variations in temperature during construction, which often cause cracks in the structure that may destroy the integrity of the structure, reduce the durability of the structure, and cause greater damage [

In the early 1930s, the US Bureau of Reclamation studied artificial cooling methods for concrete dams when designing the Hoover Gravity Arch Dam (the world's tallest concrete dam). In 1931, the US Bureau of Reclamation conducted a water-pipe-cooling field test at the Owyhee Dam, with the results showing that water-pipe cooling is very effective. Two years later, when construction began on Hoover Dam, water-pipe cooling was fully exploited with good results. Following this experience, the water-pipe cooling method has been widely used worldwide for temperature control of mass concrete during construction [

Since then, water-pipe cooling has been found to be a double-edged sword during actual engineering applications [

The analysis of the design temperature-control process line shows that this line actually represents the average-temperature history of the concrete pouring block. Thus, the thermometers must be buried in the concrete pouring block to properly monitor its temperature. However, because of the large size of the concrete pouring block and the limitations imposed by construction-site conditions and costs, only a small number of thermometers could be buried in each concrete pouring block. Previous experience with the temperature-control process has shown that, during the cooling period, the temperature field of the concrete pouring block is so complicated that the measured temperature is too low (high) when the thermometers are buried too close to (too far from) the water pipe. Therefore, we must determine the appropriate geometric position at which to bury the thermometers in the concrete pouring block so that the measured temperature properly reflects the average-temperature history of the concrete pouring block, which is crucial to obtain good monitoring results [

The optimal arrangement of the monitoring instruments should deliver the most reliable information possible with the minimum number of sensors. At present, significant literature exists on the dynamic monitoring system of bridges and frame structures and the optimal arrangement of high-dam sensors, but few reports are available on the optimal arrangement of temperature sensors for concrete pouring blocks [

In the construction of mass concrete, water-pipe cooling is an important temperature-control measure. However, simulating the temperature field generated by water-pipe cooling, in particular the temperature gradient near the water pipe, has always been difficult. In general, two types of calculation models are currently available for analyzing the cooling of a concrete dam embedded with cooling pipes: the water-pipe-cooling FEM and the water-pipe-cooling equivalent equation of heat conduction [

In engineering practice, obtaining the temperature field by using a densely divided mesh increases the workload and difficulty of the calculation. Therefore, simulating the water-pipe-cooling effect by using normal meshing is more popular in engineering practice. Although complicated pretreatment may be avoided by using the water-pipe-cooling equivalent equation of heat conduction, the temperature gradient near the water pipe is not properly considered. To obtain an accurate temperature distribution of a concrete pouring block embedded with cooling pipe, we thus use in this work the water-pipe-cooling FEM to calculate the temperature field because it is more in line with the actual situation [

Consider a section of the cooling-water pipe, as shown in Figure _{1} and W_{2} and during the time interval

Schematic diagram of cooling pipe in concrete.

Exchange faces of heat convection in pipe cooling.

The thermal energy transferred from concrete to water through the inner surface

The thermal energy of the water flowing through the inlet section W_{1} is

The thermal energy of the water flowing through the outlet section W_{2} is

The change in thermal energy in the water pipe between sections W_{1} and W_{2} is_{1} and W_{2.}

At thermal equilibrium, we have

Substituting Eqs. (_{1} and W_{2} may be expressed as

Considering that both the volume and the temperature increases of water are very small within

Assuming that the water temperature

Equation (

The finite element control equation for calculating the transient temperature field is available from the study by Zhu [

Assuming that the temperature-control process line represents the average-temperature history of the concrete pouring block, we adopt the following method to determine with the reasonable geometric position of the buried thermometers. First, we must obtain the average-temperature history of the concrete pouring block embedded with cooling pipes, and then we have to find the geometric position

^{3}] is the volume of the elemental Gauss point, ^{3}

The constrained optimization method, such as complex method, is used to solve Eq. (

As shown in Figure

Typical layout of cooling pipe.

Model of concrete embedded with cooling pipe.

To achieve uniform cooling, the flowing direction of the cooling water usually changes at regular intervals in the concrete model. By using the symmetry of the temperature field of the concrete model embedded with cooling pipes, we analyze the temperature field of the intermediate section of the concrete model. From the node temperature of the elements in the intermediate section, the temperature at an arbitrary point of the section is given by Eq. (

By using the average-temperature history calculated in Step

By using the optimization algorithm to solve the mathematical model for the position of the buried thermometers [Eq. (

According to previous engineering experience [^{3} per day based on engineering practices, the specific heat of water is

In practical concrete dam engineering, the cooling pipes embedded into concrete pouring blocks generally arrange in a serpentine layout. Zhu and Cai [

The finite-element simulation model is meshed using three-dimensional hexahedron 8-node isoparametric elements. When simulating the temperature field, we assume that the six surfaces of the concrete prism are adiabatic boundaries, and we set the initial temperature of the concrete and the inlet temperature of the cooling water both to 10°C. When using the water-pipe-cooling FEM to simulate the temperature field during the cooling period, the start time of water flow is day 1, the water flows for 10 days, and the time step is the 0.1 day. Figure

Average-temperature process line of concrete prisms for four water-pipe spacing cases.

To achieve uniform cooling, the flow direction of the cooling water changes at regular intervals in the concrete model. When assuming that the six surfaces of the concrete prism are adiabatic boundaries, the temperature of the intermediate section of the concrete prism does not depend substantially on the flow direction of the cooling water but only changes due to the cement hydration. According to the symmetry of the concrete prism, the temperature fields of the intermediate section of the concrete model are analyzed. Thus, we first obtain the temperature surface of the intermediate section of the concrete prism at a given time; in addition, the average temperature of the concrete prisms during the cooling period at a given time is called the “isothermal value,” and then we find the geometric position of the isotherm on the temperature surface. Specifically, we use the built-in function griddata of MATLAB (version R2014b) to obtain the temperature surface of the intermediate section at different times by biharmonic spline interpolation. Next, the average temperature

Temperature surfaces and isotherms for intermediate sections for four different water-pipe spacing cases at

Pipe spacing 1.0 m × 1.0 m

Pipe spacing 1.5 m × 1.5 m

Pipe spacing 1.0 m × 1.5 m

Pipe spacing 2.0 m × 1.5 m

Distribution of geometric position of average temperature of intermediate sections for four different water-pipe spacing cases.

Pipe spacing 1.0 m × 1.0 m

Pipe spacing 1.5 m × 1.5 m

Pipe spacing 1.0 m × 1.5 m

Pipe spacing 2.0 m × 1.5 m

Figures

(1) When the average temperature of the concrete pouring block is set as the isothermal value, the isotherms in the intermediate sections curve and the geometric position of the isotherms in the intermediate sections change with time over a certain range. With increasing cooling time, the geometric position of the isotherms gradually stabilizes until it remains constant.

(2) When the cross-sectional dimensions are 1.0 m × 1.0 m and 1.5 m × 1.5 m, the geometric positions of the isotherms in the intermediate sections change little and are approximately circular.

(3) When the cross-sectional dimensions are 1.0 m × 1.5 m and 2.0 m × 1.5 m, the geometric positions of the isotherms in the intermediate sections change significantly, although gradually, from the initial elliptical distribution to a parabolic distribution.

Figure

Meshing of intermediate sections for four different water-pipe spacing cases.

Pipe spacing 1.0 m × 1.0 m

Pipe spacing 1.5 m × 1.5 m

Pipe spacing 1.0 m × 1.5 m

Pipe spacing 2.0 m × 1.5 m

Quadrilateral 4-node element.

For an arbitrary point in the element of a quarter of the intermediate section, the temperature of this point can be calculated by the node temperature and shape function [

When these above possible elements are optimized one by one based on Eq. (^{−6} and 100, respectively. Since the objective function

By using the method of bisection, which is a one-dimensional search algorithm, to solve Eq. (_{i} and_{i} are the coordinates of node

In the above analysis, the optimal positions of the buried thermometer in a quarter of the intermediate sections are calculated. Once the optimized position of the buried thermometer is obtained for the quarter section, it may be obtained for the total intermediate section based on the symmetry. Figure

Optimized position of the buried thermometer for four different water-pipe spacing cases.

Pipe spacing 1.0 m × 1.0 m

Pipe spacing 1.5 m × 1.5 m

Pipe spacing 1.0 m × 1.5 m

Pipe spacing 2.0 m × 1.5 m

The geometric positions of the isotherms that correspond to the average temperature at different times (see Figure

(1) The analysis of four different water-pipe-spacing cases shows that the optimal position of the buried thermometer obtained from the mathematical model is similar to the geometric position of the isotherms based on the average temperature of the concrete pouring block at different times. The analysis result also shows that the mathematical model for determining the position of the buried thermometer adequately reflects the distribution of the average temperature in the intermediate section.

(2) For cross-sectional dimensions of 1.0 m × 1.0 m and 1.5 m × 1.5 m (i.e., equal distance between the horizontal and vertical water pipes), both the geometric position of the isotherms based on the average temperature of the concrete pouring block and the optimized position of the buried thermometer obtained from the mathematical model are approximately circular. For these two water-pipe spacing cases, the distances between the optimized geometric position of the buried thermometer and the center of the water pipe are both about 0.3 times the length of the side of the cross section.

(3) When the cross-sectional dimensions are 1.0 m × 1.5 m and 2.0 m × 1.5 m (i.e., unequal distance between the horizontal and vertical water pipes), both the geometric position of the isotherms based on the average temperature of the concrete pouring block and the optimized position of the buried thermometer obtained from the mathematical model are approximately parabolic. For these two water-pipe spacing cases, the distances between the optimized geometric position of the thermometer and the center of the water pipe are both about 0.25 times the length of the long side of the cross-section.

Figures

Temperature difference between average temperature and (a) the farthest point and (b) the nearest points.

Temperature difference at the farthest point

Temperature difference at the nearest point

Figure

To reduce the uncertainty in the position of the buried thermometer in a concrete pouring block, we develop a mathematical model to optimize the position. We use the optimization algorithm to obtain the geometric positions of thermometers buried in the concrete pouring block for four different water-pipe spacing cases. The results lead to the following conclusions:

(1) The temperature field of the concrete pouring block during the cooling period is so complicated that the measured temperature is too low (high) if the thermometer is positioned too close to (too far from) a water pipe. When the average temperature of the concrete pouring block is set as the isothermal value, the isotherms on the intermediate sections form curves, and the geometric positions of the isotherms in the intermediate sections change over time within a certain range. However, with increasing cooling time, the geometric position of the isotherms gradually stabilizes and becomes constant.

(2) Exploiting the symmetry of a concrete prism, we use the intermediate sections of the concrete prisms to calculate and analyze the temperature of an arbitrary point in the concrete pouring block. Since the temperature history at multiple locations in each possible element approaches the average-temperature history of the concrete pouring block, the possible elements are optimized one by one. Next, based on the average-temperature history of the concrete pouring block and the temperature history of the arbitrary point in the given element, we build a mathematical model to obtain the geometric position of the thermometer and use a one-dimensional search algorithm to solve the mathematical model. By analyzing different cases, we find this method to be feasible for determining the optimum position of a thermometer buried in a concrete pouring block.

(3) For equal distances between the horizontal and vertical water pipes, both the geometric position of the isotherms based on the average temperature of the concrete pouring block and the optimized position of the buried thermometer obtained from the mathematical model are approximately circular. For these two water-pipe spacing cases, the distances between the optimized geometric position of the thermometer and the center of the water pipe are both about 0.3 times the length of the side of the cross-section. For unequal distances between the horizontal and vertical water pipes, both the geometric position of the isotherms based on the average temperature of the concrete pouring block and the optimized position of the buried thermometer obtained from the mathematical model are approximately parabolic. For these two water-pipe spacing cases, the distances between the optimized geometric position of the thermometer and the center of the water pipe are both about 0.25 times the length of the long side of the cross-section.

The data in this article were calculated and analyzed by the authors. The data for Figures

The authors declare that they have no conflicts of interest.

This study was supported by the National Natural Science Foundation of China under grant no. 51779130.

Concise description for Figure

Concise description for Figure

Concise description for Figure