# Study on Propagation Characteristics of Ground Penetrating Radar Wave in Dikes and Dams with Polymer Grouting Repair Using Finite-Difference Time-Domain with Perfectly Matched Layer Boundary Condition

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## Abstract

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## 1. Introduction

## 2. Basic Principles

#### 2.1. Ground-Penetrating Radar

**E**means the electric field strength,

**B**means the magnetic inductive intensity,

**H**means the magnetic field strength,

**D**means the electric displacement, ρ means the charge density, and

**J**means the electric current density.

#### 2.2. Finite Difference Time-Domain Method

## 3. Calculation Model

#### 3.1. Application Conditions

#### 3.2. The Model Parameters of Dikes and Dams

## 4. Forward Simulation

#### 4.1. Water-Filled Cave

#### 4.2. Air-Filled Cave

#### 4.3. Incompact Area

#### 4.3.1. Different Degrees of Repair

#### 4.3.2. Different Distance between Center Point of the Incompact Area to the Dam Surface

## 5. Conclusions

- (1)
- GPR can accurately identify shallow diseases such as water-filled caves, air-filled caves, and incompact areas. According to the reflection wave shape, amplitude, transmission time interval in the forward simulation profiles, and the reflection amplitude of single channel waveforms, the spatial distribution characteristics such as the water level position, the type, and depth of shallow diseases can be obtained.
- (2)
- The forward simulation profiles of dikes and dams with water-filled caves before and after polymer grouting repair present two clusters of hyperbolas. There were three clusters of hyperbolas with different amplitudes that were observed at 50% repair. The A-scan images of water-filled cave before and after repair showed two reflection waves, while the A-scan images of 50% of water-filled cave showed three reflection waves. When polymer grouting is used to repair the air-filled cave, the amplitude and reflection interval in the forward simulation profiles and the single channel waveforms before repair, 50% repair, and 100% repair are different. The air-filled cave repair can be evaluated by the amplitude of the forward simulation profile and the reflections the interval in the single channel waveform.
- (3)
- When detecting the incompact area, as the distance between center point of the incompact area to the dam surface gradually decreases, the top of the curve in the forward profile moves upward and the top amplitude of the curve becomes larger. When polymer grouting is used to repair the incompact area, the top amplitude of the forward simulation profiles and single channel waveforms before repair and 50% repair are significantly bigger than that of 100% repair. The incompact area can be evaluated by the amplitude of the forward simulation profile and single channel waveform.
- (4)
- The GPR propagation characteristics in dikes and dams with different shallow diseases using polymer grouting repair are analyzed. It provides theoretical basis for using the ground-penetrating radar to evaluate the effect of polymer grouting technology to repair dikes and dams with shallow diseases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Forward simulation profile of the water-filled cave at the different degrees of polymer grouting repair.

**Figure 6.**Forward simulation profile of the air-filled cave at the different degrees of polymer grouting repair.

**Figure 9.**Forward simulation profile of the incompact area at the different degrees of polymer grouting repair.

**Figure 11.**The different distance between the center point of the incompact area to the dam surface for the incompact area model.

**Figure 12.**Forward simulation profile of the incompact area at the different distance between the center point of the incompact area to the dam surface.

Parameter Type | Numerical Value |
---|---|

Forward model size/m | 5 × 3 |

Spatial grid step/m | 0.0025 × 0.0025 |

Time window/ns | 80 |

Initial transmit antenna coordinates/m | (0.4, 2.95) |

Initial receiving antenna coordinates/m | (0.5, 2.95) |

Antenna step distance/m | 0.05 |

Number of lines | 90 |

Excitation source frequency/MHz | 900 |

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**MDPI and ACS Style**

Dong, Z.; Xue, B.; Lei, J.; Zhao, X.; Gao, J.
Study on Propagation Characteristics of Ground Penetrating Radar Wave in Dikes and Dams with Polymer Grouting Repair Using Finite-Difference Time-Domain with Perfectly Matched Layer Boundary Condition. *Sustainability* **2022**, *14*, 10293.
https://doi.org/10.3390/su141610293

**AMA Style**

Dong Z, Xue B, Lei J, Zhao X, Gao J.
Study on Propagation Characteristics of Ground Penetrating Radar Wave in Dikes and Dams with Polymer Grouting Repair Using Finite-Difference Time-Domain with Perfectly Matched Layer Boundary Condition. *Sustainability*. 2022; 14(16):10293.
https://doi.org/10.3390/su141610293

**Chicago/Turabian Style**

Dong, Zhifeng, Binghan Xue, Jianwei Lei, Xiaohua Zhao, and Jianglin Gao.
2022. "Study on Propagation Characteristics of Ground Penetrating Radar Wave in Dikes and Dams with Polymer Grouting Repair Using Finite-Difference Time-Domain with Perfectly Matched Layer Boundary Condition" *Sustainability* 14, no. 16: 10293.
https://doi.org/10.3390/su141610293