# Towards a Better Understanding of Concrete Arch Dam Behavior during the First Filling of the Reservoir

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## Abstract

**:**

## 1. Introduction

## 2. Analysis Considerations

#### 2.1. Behavior Model Selection

#### 2.2. Useful Features of the FEA Solvers

- Mesh updating at each construction stage;
- Formworks modelling;
- Spatial and temporal distribution of the structure temperature $T\left(x,y,z,t\right)$;
- Simulation of the evolution of the hydration reaction;
- Simulation of the artificial cooling;
- Properly modelling of joints in the dam and in the foundation mass;
- Simulation of the time-dependent response of concrete supported on appropriate creep laws;
- Use of restart files to continue an interrupted simulation;
- User-friendly interfaces to provide an effective communication between user and FEA.

#### 2.3. Meshing

#### 2.4. Thermal Analysis

#### 2.5. Nonlinear Structural Analysis

#### 2.5.1. Contraction Joints

#### 2.5.2. Dam–Foundation Interface

#### 2.5.3. Interface Elements

#### 2.6. Creep

#### 2.7. Effective Communication between User and FEA

## 3. Case Study

#### 3.1. General Description of the Project

^{3}for the full storage level (FSL) at an elevation of 665.40 m, and 1.5 hm

^{3}for the top water level (TWL) at an elevation of 667.00 m.

^{3}/s. The dam is also provided with a bottom outlet, located in the dam’s central zone, with a discharge capacity of 15 m

^{3}/s.

- Measurement of the main loads and structural responses;
- Periodic visual inspections to the dam, the surrounding rock mass, and the reservoir;
- Characterization of the rock mass and concrete properties;
- Development of models to simulate the dam/foundation behavior, in order to validate the monitoring data.

#### 3.2. Performance Assessment during the Initial Impoundment

#### 3.3. First Filling of the Reservoir

#### 3.4. Finite Element Model

#### 3.5. Thermal Analysis

#### 3.5.1. Thermal Properties

^{3}, with 55% of fly ash and a ratio w/c = 0.55. To consider the reduction in the total heat of hydration produced by the replacement of a portion of the Portland cement with fly ash, the results obtained in [33] were taken into account, which shows that for 50% fly ash, the decrease in the heat of hydration is of approximately one-third. Then, applying the approach presented in [16], the following parameters were determined [34]:$\text{}{\xi}_{\infty}$ = 0.77; ${k}_{\xi}/{\eta}_{\xi o}$ = 4 × 10

^{5}h

^{−1}; ${A}_{\xi o}/{k}_{\xi}$ = 1.04 × 10

^{−2}, and $\overline{\eta}$ = 5.59.

#### 3.5.2. Boundary Conditions

^{2}).

^{3}h °C). Taking into account that Expression (2) represents the average solar irradiance in the Serra da Estrela region, the influence of cloudiness was considered by using an equivalent concrete absorption coefficient varying between 0.45 and 0.65, that is, between dense cloud cover and clear sky, respectively. The increase and decrease in the concrete absorption coefficient, usually in the range of 0.5 to 0.6, was defined by calibrating the numerical model to obtain the temperatures measured by the thermometers installed in the dam.

^{3}h °C) was applied to the whole model, except in the surface insulated by the formwork. Due to the lack of information about the formwork characteristics, an empirical value of 0.10 times the concrete total heat transfer coefficient was adopted, resulting in ${h}_{t}$ = 9 kJ/(m

^{3}h 90 °C).

#### 3.5.3. Analysis and Results

#### 3.6. Mechanical Analysis

#### 3.6.1. Mechanical Properties

#### 3.6.2. Loads

#### 3.6.3. Analysis and Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Monthly average air temperature, reservoir levels, and comparison of predicted and monitored temperatures at thermometers T10 to T12.

**Figure 10.**Monthly average air temperature, reservoir levels, and comparison of predicted and monitored displacements.

**Figure 11.**Displacements contour plots calculated with the finite element model with contraction joints.

**Figure 12.**Monthly average air temperature, reservoir levels, and comparison of predicted stresses and values obtained from the strain-meter measurements.

Properties | Rock Mass Foundation | Concrete |
---|---|---|

Density, ρ [kg/m^{3}] | 2467 | 2380 |

Specific heat, c [kJ/(kg °C)] | 0.920 | 0.879 |

Thermal conductivity k [kJ/(m h °C)] | 8.4 | 8.4 |

Material | Properties | Values |
---|---|---|

Concrete | Double power law | |

E_{o} [GPa] | 35.00 | |

N | 0.12 | |

M | 0.51 | |

α | 0.043 | |

φ_{1} | 4.00 | |

Poisson’s ratio ν | 0.20 | |

Coefficient of thermal expansion α [1/°C] | 10^{−5} | |

Rock mass foundation | Young’s modulus E [GPa] | 20.00 |

Poisson’s ratio ν | 0.20 | |

Coefficient of thermal expansion α [1/°C] | 10^{−6} | |

Joints | k_{s} = k_{t} [GPa/m] | 833.00 |

k_{n} [GPa/m] | 2000.00 | |

f_{t} | 0.00 |

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**MDPI and ACS Style**

Leitão, N.S.; Castilho, E.; Farinha, M.L.B.
Towards a Better Understanding of Concrete Arch Dam Behavior during the First Filling of the Reservoir. *CivilEng* **2023**, *4*, 151-173.
https://doi.org/10.3390/civileng4010010

**AMA Style**

Leitão NS, Castilho E, Farinha MLB.
Towards a Better Understanding of Concrete Arch Dam Behavior during the First Filling of the Reservoir. *CivilEng*. 2023; 4(1):151-173.
https://doi.org/10.3390/civileng4010010

**Chicago/Turabian Style**

Leitão, Noemi Schclar, Eloísa Castilho, and M. Luísa Braga Farinha.
2023. "Towards a Better Understanding of Concrete Arch Dam Behavior during the First Filling of the Reservoir" *CivilEng* 4, no. 1: 151-173.
https://doi.org/10.3390/civileng4010010