# Numerical Simulation-Based Damage Identification in Concrete

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## Abstract

**:**

## 1. Introduction

## 2. An Overview of the Proposed Methodology

## 3. Simulation of Synthetic Concrete Mesostructures Subjected to Uniaxial Compressive Loads

## 4. Synthetic Coda Wave Generation

#### Simulation Set up and Time Series Dataset Acquisition Procedure

## 5. Damage Identification Using Supervised Machine Learning

#### 5.1. Data Processing

#### 5.2. CNN Damage Classifier

#### 5.3. Results

- Phase 1 damage: 85% of the signals corresponding to this phase were correctly identified. A total of 15% of the signals were wrongly identified as belonging to Phase 2 damage.
- Phase 2 damage: Only 58% of the signals corresponding to Phase 2 damage i.e., pre-peak microcracking were correctly identified. Indeed 33% of the signals belonging to the class of Phase 2 damage were incorrectly classified as Phase 1 and 9% were incorrectly identified as Phase 3.
- Phase 3 damage: 87% of the signals corresponding to this state were correctly identified. A total of 12% were misclassified as Phase 2 and 1% was wrongly classified as Phase 1.

## 6. Improvement of Accuracy Using Data Refinement

## 7. Conclusions

- The application of ultrasonic measurement in damage assessment of concrete structures is an active and yet challenging research field. The underlying challenge arises from complicated damage process in concrete and the high sensitivity of the coda wave especially to the environmental factors, which do not contribute to damage. Thus, computational approaches can assist experimental work in understanding the effect of damage processes on the characteristics of coda signals, while excluding the effect of the environmental factors.
- With a suitable feature analysis method, CNN can be used as a supplementary tool for ultrasonic-based damage identification in concrete.
- It has been demonstrated that data obtained from a damaged region has a negative effect on the performance of the CNN classifier. In practice, the damage location is generally not known a priori, thus, a filtering tool should be thoroughly formulated to enhance the robustness of the CNN classifier.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DEM | Discrete Element Method |

RSG | Rotated Stagger Grid |

CNN | Convolutional Neural Network |

CWI | Coda Wave Interferometry |

ML | Machine Learning |

CMG | Concrete Mesostructure Generator |

ANN | Artificial Neural Network |

ReLU | Rectified Linear Unit |

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**Figure 1.**Workflow of the simulation-based procedure to detect damage in concrete specimens subjected to uniaxial compressive loadings.

**Figure 2.**Voxelized concrete sample (

**left**) and the corresponding DEM sample (

**right**) (${D}_{min}=15$ mm, ${D}_{max}=30$ mm) considered in the uniaxial compression simulation.

**Figure 3.**Damage evolution of the concrete sample subjected to uniaxial compression. Legend: grey color—aggregate, blue color—undamaged mortar, red color—damaged mortar. Top right: normalized stress-strain curve obtained from the DEM simulation. The corresponding load levels at which the microstructure snapshots are extracted are highlighted by colored dots (see Table 2 for the strain levels of each damage snapshot).

**Figure 4.**(

**a**) Sender-Receiver configuration specified for the wave propagation simulation. (

**b**) zz-component of stress of source signal and (

**c**) frequency content of the source signal. (

**d**) signals recorded at 18 receiver locations specified in (

**b**).

**Figure 5.**CNN architecture. The input is presented in the form of an image. A total of 2592 input images are used for training the network. There are three convolution layers followed by flattening, dense, dropout and dense. SoftMax has been added in the end to convert the output in terms of probability.

**Figure 6.**

**Left**: Confusion matrix visualizing the performance of the classifier as the percentage of correct and incorrect classification of the damage phase (three phases of damage (Phase 1: Elastic deformation and microcrack initiation, Phase 2: pre-peak microcracking and Phase 3: Microcrack coalescence and post-peak crack localization)).

**Right**: Overall training and validation accuracy of the classifier for 200 epochs.

**Figure 7.**(

**a**–

**d**) Scatter plots of the average of the averaged envelope of the Coda signals as a function of increasing strain levels (from level 0 to 11) obtained for four locations of the sender (see Table 2 for the exact values of the strains corresponding to the strain levels). In each plot, three phases of damage (Phase 1: Elastic deformation and microcrack initiation, Phase 2: pre-peak microcracking and Phase 3: Microcrack coalescence and post-peak crack localization) of the concrete specimen are indicated.

**Figure 8.**

**Left**: Confusion matrix visualizing the performance of the classifier using the refined dataset. The matrix shows the percentage of correct and incorrect classification of the damage Phase (three phases of damage (Phase 1: Elastic deformation and microcrack initiation, Phase 2: pre-peak microcracking and Phase 3: Microcrack coalescence and post-peak crack localization)).

**Right**: Overall training and validation accuracy of the classifier for 200 epochs.

Elastic Parameters | Mortar | Aggregate | ||
---|---|---|---|---|

${K}_{n}$ | normal modulus | 8 | 16 | GPa |

${K}_{\tau}$ | tangential modulus | 1 | 2 | GPa |

Damage Law in Tension | ||||

${\epsilon}_{0}$ | limit elastic strain | $1\times {10}^{-4}$ | $1\times {10}^{-4}$ | |

$\frac{{\epsilon}_{f}}{{\epsilon}_{0}}$ | relative ductility | 50 | 50 | |

Elasto-Plasticity in Shear | ||||

${c}_{0}$ | initial cohesion | 1 | 2 | MPa |

$\mathrm{tan}\varphi $ | frictional angle | 0.57 | 0.57 |

Label | Snapshot ID | Strain Level [%] |
---|---|---|

Phase 1 damage | 0 | 0 |

1 | 0.031 | |

2 | 0.062 | |

3 | 0.093 | |

Phase 2 damage | 4 | 0.124 |

5 | 0.155 | |

6 | 0.186 | |

7 | 0.217 | |

Phase 3 damage | 8 | 0.233 |

9 | 0.248 | |

10 | 0.264 | |

11 | 0.279 |

Layer (Type) | Output Shape | Filter Size | Stride | No. of Parameters |
---|---|---|---|---|

Conv 2D | [98 × 98 × 8] | [5 × 5] | [2 × 2] | 208 |

Batch Normalization | [98 × 98 × 8] | - | - | 32 |

Conv 2D | [47 × 47 × 16] | [5 × 5] | [2 × 2] | 3216 |

Batch Normalization | [47 × 47 × 16] | - | - | 64 |

Conv 2D | [45 × 45 × 16] | [3 × 3] | [1 × 1] | 2320 |

Batch Normalization | [45 × 45 × 16] | - | - | 64 |

Flatten | [32,400] | - | - | 0 |

Dense | [16] | - | - | 518,416 |

Dropout | [16] | - | - | 0 |

Dense | [16] | - | - | 272 |

Batch Normalization | [16] | - | - | 64 |

Dense | [3] | - | - | 51 |

Total number of parameters: 524,707 |

**Table 4.**Performance evaluation of the classifier based on the Precision, Recall and F1 score metrics.

Precision | Recall | F1 score | |
---|---|---|---|

Phase 1 | 0.895 | 0.902 | 0.898 |

Phase 2 | 0.886 | 0.845 | 0.865 |

Phase 3 | 0.964 | 1 | 0.981 |

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## Share and Cite

**MDPI and ACS Style**

Vu, G.; Timothy, J.J.; Singh, D.S.; Saydak, L.A.; Saenger, E.H.; Meschke, G.
Numerical Simulation-Based Damage Identification in Concrete. *Modelling* **2021**, *2*, 355-369.
https://doi.org/10.3390/modelling2030019

**AMA Style**

Vu G, Timothy JJ, Singh DS, Saydak LA, Saenger EH, Meschke G.
Numerical Simulation-Based Damage Identification in Concrete. *Modelling*. 2021; 2(3):355-369.
https://doi.org/10.3390/modelling2030019

**Chicago/Turabian Style**

Vu, Giao, Jithender J. Timothy, Divya S. Singh, Leslie A. Saydak, Erik H. Saenger, and Günther Meschke.
2021. "Numerical Simulation-Based Damage Identification in Concrete" *Modelling* 2, no. 3: 355-369.
https://doi.org/10.3390/modelling2030019