# Chemo-Thermo-Mechanical FEA as a Support Tool for Damage Diagnostic of a Cracked Concrete Arch Dam: A Case Study

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

The first and very important step of repairing damaged or deteriorated concrete is to correctly determine the cause of damage. Knowing what caused the damage, and reducing or eliminating that cause, will make the repair last longer. If no attempt is made to eliminate the original cause of damage, the repair may fail as the original concrete did, resulting in wasted effort and money (von Fay [7], p. 1–13).

## 2. Diagnosis Procedure

- The first stage, which usually lasts a few weeks, involves the following:
- a.
- Clinical history;
- b.
- Filed (dam) inspection;
- c.
- Initial cabinet works;
- d.
- First hypothesis.

- The second stage, which may take weeks to months, entails the following:
- a.
- Laboratory tests;
- b.
- Numerical modeling;
- c.
- Validation of the hypothesis;
- d.
- Prediction of future behavior.

## 3. Dam Description

^{3}/s. The reservoir’s normal level is 175 m. A concrete pad (called socle in Portugal) was added to the foundation to make the site symmetrical and to provide a better distribution of stresses on the foundation, as shown in Figure 1.

## 4. Clinical History and Field Inspections

#### 4.1. Dam Design

#### 4.2. Dam Construction and Initial Impoundment

#### 4.3. Cracking Evolution

## 5. Cabinet Works and Initial Diagnosis Hypothesis

## 6. Finite Element Model

A finite element model of a structure is an abstraction of the physical structure with a number of assumptions, generalizations, and idealizations. The abstraction process has two distinct steps: first, the abstraction from the structure to the mechanical model, and then the abstraction from the mechanical model to the finite element model. In the first step, assumptions and simplifications have to be made regarding to which extent and to which detail the structure has to be modeled, how the boundaries of the model are described, which loads on the structure are significant and how they are described, et cetera. The second step is to discretize the mechanical model into a finite element model, and attach the necessary attributes such as material models, boundary conditions, and loading to the finite element model (Hendrix et al. [26], p. 9).

#### 6.1. Finite Element Mesh

#### 6.2. Thermal Analysis

#### 6.2.1. Governing Equations

^{2}K). However, when $T$ and ${T}_{a}$ are close, which is the normal condition in civil engineering structures, it is possible to rewrite (6) in a quasi-linear form as follows:

#### 6.2.2. Chemo-Thermal Model

#### 6.2.3. Thermal Properties

^{3}], $t$ is the time in [h], $A$ = kJ/m

^{3}and $B$ = −65 h, as shown in Figure 9.

^{−1}; ${A}_{\xi o}/{k}_{\xi}$ = 1.34 × 10

^{−2}; and $\stackrel{-}{\eta}$ = 6.26.

#### 6.2.4. Boundary Conditions

^{2}).

^{2}K) for the whole model, with the exception of the formwork-insulated surfaces. Due to the lack of information about the formwork characteristics, an empirical value of 0.10 times the total heat transfer coefficient of the concrete was adopted, yielding ${h}_{t}$ = 2.4 W/(m

^{2}K). The concrete absorption coefficient was assumed as 0.5.

#### 6.2.5. Concrete Placement Schedule

#### 6.2.6. Analysis and Results

#### 6.3. Mechanical Analysis

… is not a simple, ideal, elastic body. Vertical contraction joints subdivide the dam in blocks. Even after grouting they will represent a discontinuity in as much as they cannot be grouted to the dam faces but only to the water-stops. Additionally, the grouting is seldom carried out in a completely satisfactory manner. Furthermore, the concrete is placed in layers and lifts making weakness planes possible at frequent elevations, and inhomogeneities and anisotropies – which can hardly be detected – are likely to exist in the concrete mass (Lombardi [38], p. 4).

#### 6.3.1. Mechanical Properties

#### 6.3.2. Loads

#### 6.3.3. Analysis and Results

## 7. Validation of the Diagnosis Hypothesis

## 8. Prediction of Future Behavior

In arch dams, potentially opened contraction joints and cracked lift lines may subdivide the monolithic arch structure into partially free cantilever blocks, capable of transmitting only compressive or frictional forces. In this situation, any failure mode of the arch structure would more likely involve sliding stability of the partially free cantilevers. For small and moderate joint openings, the partially free cantilever blocks, bounded by opened joints, may remain stable through interlocking (wedging) with adjacent blocks. The extent of interlocking depends on the depth and type of shear keys and the amount of joint opening (EM 1110-2-6053 [42], p. 2–9).

## 9. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Principal stress on the downstream face (on the left) and on the upstream face (on the right) obtained by model tests (adapted from [16]).

**Figure 7.**Monthly average air temperature, reservoir levels, and monitored crack openings between 2002 and 2016.

**Figure 10.**Concrete placement schedule: (

**a**) quarterly construction progress; (

**b**) comparison of the actual and simulated volume of concrete pouring per month; (

**c**) concrete placement schedule adopted for the simulation.

**Figure 11.**Monthly average air temperature, reservoir levels and comparison of predicted and monitored temperatures at thermometers in monoliths I–J at an elevation of 150 m.

**Figure 12.**Monthly average air temperature, reservoir levels and comparison of predicted and monitored radial displacements in monoliths I–J at elevations of 170 m, 150 m and 130 m.

**Figure 13.**Monthly average air temperature, reservoir levels and comparison of predicted and monitored vertical stresses in monoliths I–J at elevations of 118 m.

**Figure 14.**Distribution of principal stresses over the upstream surface for the empty reservoir with a water level of 137 m and 149 m.

**Figure 15.**Distribution of principal stresses over the upstream surface for water levels of 153 m, 155 m and 160 m.

**Figure 16.**Monthly average air temperature, reservoir levels and monitored radial displacement between 2002 and 2016.

**Figure 17.**Response of arch dams to major earthquakes (adapted from [42]).

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

Density ρ [kg/m^{3}] | 2657 | 2460 |

Specific heat c [J/(kg °C)] | 715 | 866 |

Thermal conductivity k [W/(m °C)]] | 4.91 | 2.65 |

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

Concrete | Double power law | |

${E}_{\mathrm{o}}$ [GPa] | 40.50 | |

n | 0.12 | |

m | 0.34 | |

α | 0.048 | |

${\phi}_{1}$ | 1.78 | |

Poisson’s ratio $\mathsf{\nu}$ | 0.20 | |

$\mathrm{Coefficient}\mathrm{of}\mathrm{thermal}\mathrm{expansion}\mathsf{\alpha}$ [1/°C] | 10^{−5} | |

Rock mass foundation | $\mathrm{Young}\u2019\mathrm{s}\mathrm{modulus}E$ [GPa] | 15.00, 5.00 or 1.80 |

$\mathrm{Poisson}\u2019\mathrm{s}\mathrm{ratio}\mathsf{\nu}$ | 0.20 | |

$\mathrm{Coefficient}\mathrm{of}\mathrm{thermal}\mathrm{expansion}\mathsf{\alpha}$ [1/°C] | 0.00 | |

Joints | ${k}_{s}={k}_{t}$ [GPa/m] | 2000.00 |

${k}_{n}$ [GPa/m] | 2000.00 | |

${f}_{t}$ | 0.00 |

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**MDPI and ACS Style**

Leitão, N.S.; Castilho, E.
Chemo-Thermo-Mechanical FEA as a Support Tool for Damage Diagnostic of a Cracked Concrete Arch Dam: A Case Study. *Eng* **2023**, *4*, 1265-1289.
https://doi.org/10.3390/eng4020074

**AMA Style**

Leitão NS, Castilho E.
Chemo-Thermo-Mechanical FEA as a Support Tool for Damage Diagnostic of a Cracked Concrete Arch Dam: A Case Study. *Eng*. 2023; 4(2):1265-1289.
https://doi.org/10.3390/eng4020074

**Chicago/Turabian Style**

Leitão, Noemi Schclar, and Eloísa Castilho.
2023. "Chemo-Thermo-Mechanical FEA as a Support Tool for Damage Diagnostic of a Cracked Concrete Arch Dam: A Case Study" *Eng* 4, no. 2: 1265-1289.
https://doi.org/10.3390/eng4020074