# Experimental Study of the Effect of Axial Load on Stress Wave Characteristics of Rock Bolts Using a Non-Destructive Testing Method

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Work

#### 2.1. The Test Equipment

#### 2.2. The TEST Scheme

## 3. Analysis of Test Results

#### 3.1. Stress–Strain Analysis under Axial Load

#### 3.2. Filtering of Reflected Stress Wave Signal of Rock Bolt Excitation

_{k}is the IMF component; ∂

_{t}is the bias operation; ω

_{k}is the center frequency; σ is the unit pulse function; j is the imaginary unit; K is the number of modal decompositions; ⊗ is the convolution operation; and f(t) is the input signal.

_{k}are first obtained to build this model. Frequency mixing is performed to mix a central frequency for each logical modal signal, and then each modal range is transformed into the entire frequency band. Finally, the parametric number of the squared L

^{2}of the gradient of the demodulated signal is calculated to estimate the modal signal bandwidth [38].

#### 3.3. Time and Frequency Analysis of the Filtered Signal Based on Hilbert-Yellow

#### 3.4. Rock Bolt “Axial Load-Stress Wave Time-Domain Amplitude” Law Analysis

^{2}= 0.935 can be achieved.

## 4. Experimental Verification of Rock Bolt Axial Load Test Based on Time-Domain Amplitude of Reflected Stress Wave of Excitation

## 5. Conclusions

- (1)
- The collected excitation–emission stress wave signal can be successfully filtered by using VMD decomposition and FFT low-pass filter. The analysis of the time domain characteristic parameters showed that the decay rate of the first cycle of the stress waveform in the time domain changed with the increase in the axial load; the processing of the frequency domain data using the FFT low-pass filter showed that the peak amplitude and shape of the stress waveform in the frequency domain were also affected by the axial load.
- (2)
- For an intact and well-compacted rock bolt, the changes in axial load on the stress waveform signal characteristics of the rock bolt cannot be directly reflected from the time domain waveform and Fourier frequency domain and should be analyzed by combining multiple signal processing methods. The analysis results show that with the increase in axial load, the stress wave characteristics of the rock bolt change, and the time domain amplitude of the stress wave gradually decreases.
- (3)
- The axial load of the rock bolt was determined by a dynamometer test and compared with the load value of the tensile machine to verify the nondestructive testing method based on the stress wave method used in this paper. The error of the method used in this paper is much smaller than that of the traditional anchor load test method, and the test results are more stable and were further applied to determine the working load of anchor rods.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Time and frequency domain before and after filtering. (

**a**) Time domain waveform diagram. (

**b**) Frequency domain waveform diagram.

**Figure 6.**Time and frequency domain diagram of NDT signal. (

**a**) Time and frequency waveforms of 0 and 10 kN. (

**b**) Time and frequency waveforms of 25 and 45 kN. (

**c**) Time and frequency waveforms of 75 and 100 kN.

**Figure 10.**Time and frequency domain diagram of reconstructed signal for different loads. (

**a**) Reconstructed signal time domain diagram. (

**b**) Reconstructed signal frequency domain diagram.

Parameters | Values |
---|---|

Sampling rate f_{s}/MHz | 1 |

Sampling points N/K | 6 |

Amplification gain L/dB | 62 |

Emission energy E/J | 10 |

Trigger threshold ϕ/(kV/m) | 800 |

Axial Load (kN) | Root Mean Square | Variance |
---|---|---|

0 | 21.6373 | 468.24695 |

5 | 17.1906 | 295.5644 |

10 | 17.308 | 299.61435 |

25 | 18.984 | 360.45103 |

45 | 20.881 | 436.08582 |

75 | 23.1176 | 534.50895 |

100 | 22.9296 | 525.85211 |

Test Method | Measured Value (kN) | Measurement Error (Δ/20 kN) |
---|---|---|

Rock bolt pulling machine | 20 | 0% |

Rock bolt dynamometer | 18 | 10% |

Stress wave method | 19.917 | 0.185% |

Test Method | Measured Value (kN) | Measurement Error (Δ/40 kN) |
---|---|---|

Rock bolt pulling machine | 40 | 0% |

Rock bolt dynamometer | 37 | 7.5% |

Stress wave method | 40.035 | 0.193% |

Test Method | Measured Value (kN) | Measurement Error (Δ/60 kN) |
---|---|---|

Rock bolt pulling machine | 60 | 0% |

Rock bolt dynamometer | 58 | 3.33% |

Stress wave method | 60.056 | 0.197% |

Test Method | Measured Value (kN) | Measurement Error (Δ/80 kN) |
---|---|---|

Rock bolt pulling machine | 80 | 0% |

Rock bolt dynamometer | 77 | 3.75% |

Stress wave method | 80.074 | 0.186% |

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## Share and Cite

**MDPI and ACS Style**

Li, C.; Xia, X.; Feng, R.; Gao, X.; Chen, X.; Lei, G.; Bai, J.; Nie, B.; Zhang, Z.; Zhang, B.
Experimental Study of the Effect of Axial Load on Stress Wave Characteristics of Rock Bolts Using a Non-Destructive Testing Method. *Sustainability* **2022**, *14*, 9773.
https://doi.org/10.3390/su14159773

**AMA Style**

Li C, Xia X, Feng R, Gao X, Chen X, Lei G, Bai J, Nie B, Zhang Z, Zhang B.
Experimental Study of the Effect of Axial Load on Stress Wave Characteristics of Rock Bolts Using a Non-Destructive Testing Method. *Sustainability*. 2022; 14(15):9773.
https://doi.org/10.3390/su14159773

**Chicago/Turabian Style**

Li, Chuanming, Xin Xia, Ruimin Feng, Xiang Gao, Xiao Chen, Gang Lei, Jiankui Bai, Bochao Nie, Zhengrong Zhang, and Baoyou Zhang.
2022. "Experimental Study of the Effect of Axial Load on Stress Wave Characteristics of Rock Bolts Using a Non-Destructive Testing Method" *Sustainability* 14, no. 15: 9773.
https://doi.org/10.3390/su14159773