# Thermal Simulation of Rolled Concrete Dams: Influence of the Hydration Model and the Environmental Actions on the Thermal Field

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Concrete Hydration Models

#### 2.2. Heat Fluxes

#### 2.3. Foundation Temperature

#### 2.4. Numerical Implementation

- First, $\alpha $ is updated with the values of ${\alpha}_{n}$ and ${\theta}_{n}$ by using Equation (9).
- Then, $\dot{Q}$ is computed with the updated values of $\alpha $ and ${\theta}_{n}$ by using Equation (7).

## 3. Case Study

## 4. Results and Discussion

#### 4.1. Influence of the Hydration Model over the Temperature Field

#### 4.2. Influence of the Weather Conditions on the Evolution of the Hydration Reaction and Concrete Temperature

#### 4.3. Effect of the Weather Conditions on the q-Peak and Time to Peak

#### 4.4. Influence of the Boundary Conditions over the Concrete Temperature

#### 4.5. Effect of the Construction Date on the Thermal Field

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AH | Adiabatic hydration |

NAH | Non-adiabatic hydration |

RCC | Roller-compacted concrete |

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**Figure 1.**Illustration of the case study and properties of the concrete. (

**a**) We simulate the thermal evolution of a roller-compacted concrete (RCC) dam during the construction phase. The boundaries of our numerical model are: (1) convection at the surfaces in contact with the air at the corresponding equivalent temperature, (2) no heat flow at the vertical boundaries of the foundation, and (3) imposed temperature at the bottom of the foundation. In the same figure, we also include the dimensions of our model. (

**b**) Here we plot the normalized heat generation function, $f\left(\alpha \right)$, against the degree of hydration, $\alpha $, of concrete.

**Figure 2.**Influence of the hydration model on the temperature field. The construction of the dam begins on 1 April 2014, and lasts 165 days. We simulate the evolution of the temperature field using a NAH model, and two AH models with $\beta $-parameters equal to $7.69\times {10}^{-6}$ s${}^{-1}$ and $1.21\times {10}^{-5}$ s${}^{-1}$, which correspond to placing temperatures of 16 ${}^{\circ}$C and 25 ${}^{\circ}$C respectively. We depict the temperature fields when the construction is at mid-height (50 m) (

**a**) for the NAH model, and (

**b**) for the AH model with $\beta =7.69\times {10}^{-6}$ s${}^{-1}$. We compare the temperature fields in a vertical profile located 10 m from the upstream face for the three simulations (

**c**). We repeat the three plots when the construction has finished in panels (

**d**)–(

**f**). The heat generation rate at mid-height time computed with the NAH model is included in the panel (

**g**), and the AH model with $\beta =7.69\times {10}^{-6}$ s${}^{-1}$ is in panel (

**h**). We also include a view of the last five lifts built in the insets.

**Figure 3.**Here we illustrate the influence of the weather conditions on the heat hydration. We have simulated the construction of an RCC dam starting at two different times: on 1 April 2014, (first row), and 1 October 2014, (second row). The construction processes last 165 days and take place in spring and autumn, respectively. The evolution of the concrete temperature is represented by the dashed lines, the heat generation rate by the solid lines, and the ambient temperature by the dotted line. Red lines represent the evolution of points situated at the top of the considered lift, and blue lines—those at the bottom. Panel (

**a**) includes the evolution of the points situated in the lift at 22.8 m height and built on 8 May 2014, at 8 a.m.—spring morning; and panel (

**b**) represents sparse points of the lift at 21.9 m height and built on 6 May 2014, at 8 p.m.—spring night. Similar results are presented for the dam construction starting on October, 2014; panel (

**c**) depicts the evolutions of the points in lift at 22.8 m height and built on 7 November 2014, at 8 a.m.—autumn morning. (

**d**) The points in the lift at 21.9 m height and built on 5 November 2014, at 8 p.m.—autumn night.

**Figure 4.**Effect of the weather conditions on the maximum heat generation rate, ${q}_{max}$, and timing of ${q}_{max}$, ${t}_{{q}_{max}}$. We have simulated the construction of two RCC dams whose building started in October, 2014—autumn—and April, 2014—spring. The hydration reaction is computed with the NAH model. (

**a**) Here we depict the schematic position of the analyzed points within the lift. (

**b**) We plot ${q}_{max}$ against ${t}_{{q}_{max}}$ for all the points within the dam body; i.e., points further than 1 m from the lateral dam faces. We set lifts at 8 a.m.; i.e., in the morning. The results of the dam built in spring are represented by triangles; red color depicts the point at the top of the lift, and blue the bottom. The results of the dam cast in autumn are plotted with circles; green color represents point at the top of the lift, and cyan the bottom. (

**c**) Here we depict ${q}_{max}$ against time for all points within the dam body and set lifts at 8 p.m.; i.e., at night.

**Figure 5.**Here we plot the difference between ${q}_{max}$ at the top part of the lift and at the bottom part, $\u2206{q}_{max}$, against the difference between ${t}_{{q}_{max}}$ at the top part of the lift and at the bottom part, $\u2206{t}_{{q}_{max}}$. We plot in panel (

**a**) the results of the lifts set in the morning, and in panel (

**b**) those set at night.

**Figure 6.**Here we illustrate the influence of the boundary conditions over the evolution of the concrete temperature. We have simulated the construction of a RCC dam starting on 1 April 2014, (first row), or 1 October 2014, (second row). The construction lasts 165 days and takes place in spring or autumn, respectively. The boundary conditions of our numerical models are computed through two approaches: (1) the methodology proposed in this paper, and (2) a simplified approach which only accounts for the convection between the dam surface and the air in contact with it. We compute the evolution of the concrete temperature through these two approaches: continuous lines plot the outputs of the models whose boundary conditions are computed with our methodology, and dashed lines with the simplified approach. Red lines represent the evolutions of points situated at the top of the considered lift, and blue lines the bottom. Panel (

**a**) includes the evolution of the points situated in the lift at 22.8 m height and cast on 8 May 2014, at 8 a.m.—spring morning, and panel (

**b**) represents sparse points of the lift at 21.9 m height and cast on 6 May 2014, at 8 p.m.—spring night. Similar results are presented for the dam construction starting in October; panel (

**c**) depicts the evolutions of the points in lift at 22.8 m height and cast on 7 November 2014, at 8 a.m.—autumn day, and panel (

**d**) the points in the lift at 21.9 m height and cast on 5 November 2014, at 8 p.m.—autumn night.

**Figure 7.**Here we illustrate the influences of the construction start date and the hydration model. We have simulated the construction of two RCC dams starting on April, 2014—spring, and October, 2014—autumn. The hydration reaction is computed with the NAH model. We plot the thermal field of the dam built in spring at mid-height in panel (

**a**) and that at the end of the construction in panel (

**b**). The thermal field of the dam built in autumn at mid-height is depicted in panel (

**c**) and that at the end of construction in panel (

**d**).

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**MDPI and ACS Style**

Ponce-Farfán, C.; Santillán, D.; Toledo, M.Á.
Thermal Simulation of Rolled Concrete Dams: Influence of the Hydration Model and the Environmental Actions on the Thermal Field. *Water* **2020**, *12*, 858.
https://doi.org/10.3390/w12030858

**AMA Style**

Ponce-Farfán C, Santillán D, Toledo MÁ.
Thermal Simulation of Rolled Concrete Dams: Influence of the Hydration Model and the Environmental Actions on the Thermal Field. *Water*. 2020; 12(3):858.
https://doi.org/10.3390/w12030858

**Chicago/Turabian Style**

Ponce-Farfán, Cristian, David Santillán, and Miguel Á. Toledo.
2020. "Thermal Simulation of Rolled Concrete Dams: Influence of the Hydration Model and the Environmental Actions on the Thermal Field" *Water* 12, no. 3: 858.
https://doi.org/10.3390/w12030858