
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39300160
73089
10.1038/s41598-024-73089-1
Article
Analysis of vibration signals near ground surface during blasting excavation of a tunnel in fractured rock
Deng Zuhua 12
Meng Junyu 12
Deng Yongfeng 12
Ni Junjun nijunjun@seu.edu.cn

12
Ye Daicheng 3
1 https://ror.org/04ct4d772 grid.263826.b 0000 0004 1761 0489 Institute of Geotechnical Engineering, School of Transportation, Southeast University, Nanjing, 211189 China
2 https://ror.org/04ct4d772 grid.263826.b 0000 0004 1761 0489 Jiangsu Key Laboratory of Low Carbon and Sustainable Geotechnical Engineering, Southeast University, Nanjing, 211189 China
3 Xiamen R&B BAICHENG Co., Ltd, Xiamen, 361008 China
19 9 2024
19 9 2024
2024
14 2190915 7 2024
13 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
This study aims to analyze the vibration signals near the ground surface due to the underneath drilling and blasting activities in a fissured rock tunnel. Blasting induced vibration on the ground surface was continuously monitored in a fissured rock tunnel drilling and blasting excavation project in field. Wavelet packet analysis of the vibration signals using Matlab was carried out for signal denoising, differential blasting delay time interval identification, and three-way time-frequency energy analysis. The results show that within a 30 m range from the palm face, the dominant frequency bands of blasting-induced vibrations on the ground surface were concentrated in the range of 0–130 Hz. Two prominent peak frequency bands were identified at 31.25–39.063 Hz (low-frequency band) and 93.75–101.56 Hz (high-frequency band), accounting for 12% of the total energy. Among the three directions of ground surface vibrations, the energy decay was the most significant in the x-direction (tunnel excavation direction), which amounted to 54.29% of the overall energy decay with increasing distance. The energy decay within the 50–80 Hz range was the most pronounced (more than 90%), when the angle between the vibration propagation direction and the fissure or joint direction was 75°. The conclusions provide the insights in the attenuation of blast-induced vibrations in fissured rock and can potentially assist in the design of blasting vibration control.

Keywords

Wavelet analysis
Fractured rock tunnel
Blasting vibration
Frequency-energy distribution
Energy decay
Subject terms

Civil engineering
Seismology
http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China 52308342 U2340227 Ni Junjun issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Tunnel excavation using the drilling and blasting method is a popular construction technique due to its high applicability, cost-effectiveness, and efficiency1,2. However, this method generates seismic waves that propagate outward during the construction process, which can affect the surrounding environment and building facilities. Hence, it is of great importance to accurately predict and control the blasting vibration velocity3,4. In mountainous tunnels, the natural rock mass often contains faults, joints, and cracks, as well as other structural surfaces that cut the rock both longitudinally and horizontally. The complex reflection and transmission of seismic waves occurring at these nodal surfaces can alter the propagation of the blast stress wave at the joints. Therefore, it is of utmost significance to investigate the propagation laws of blast stress wave in the rock mass and monitor the surface vibration generated during the blasting process of the rock mass with joints and cracks.

In tunnel blasting, the propagation and attenuation of vibration waves exhibit differences between intact rock and fractured rock. In intact rock, vibration waves propagate more uniformly, with less attenuation, leading to clearer and more predictable signal characteristics5. The physical attenuation of waves in intact rock decreases with increasing confining pressure and then increases again as the pressure continues to rise. In contrast, in fractured rock, joints and fissures cause reflection, refraction, and scattering of vibration waves, leading to reduced wave velocity and rapid energy attenuation. The number, angle, and stress conditions of fractures significantly influence the propagation and attenuation characteristics of vibration waves. The presence of fractures also causes stress concentration, promoting the development of new cracks, thus altering stress distribution and wave propagation paths6. Additionally, vibration waves in fractured rocks cause greater dynamic stress concentration and more complex crack patterns, especially in multi-hole blasting scenarios, further enhancing crack initiation and propagation7,8.

The propagation of blasting vibration is the transmission and attenuation of vibration energy. The damage of blasting vibration to adjacent structures is a function of the strength of blasting seismic waves and the frequency9. The surface blast vibration wave measured in the field test is an extremely complex signal, which requires filtering, denoising, and characterization in terms of time-frequency and energy. In practice, several main methods were employed, including Fourier transform, Hilbert-Huang transform (HHT), wavelet analysis, and wavelet packet analysis10–12. Conventional Fourier transform has been used to analyze the spectrum of blasting vibration signal13–15. Based on the Fourier transform and spectrum analysis, the basting vibration spectrum variations with the distance and propagation path were obtained13. It should be noted that the Fourier transform is a kind of global transformation, which can describe the signal characteristics from the time domain or frequency domain only10. Moreover, HHT analysis was adopted to extract the main feature information of the time-history curve based on the original signal16,17.

The effectiveness of applying wavelet analysis techniques in analyzing blasting vibration signals, reconstructing signals, and identifying differential extension time has been demonstrated. They are more comprehensive analysis, which can describe the energy distribution of blasting vibration signals accurately. Many studies18,19 used wavelet analysis for the blasting vibration waves, which provided a theoretical basis to prevent lasting vibration destruction and a safety criterion for blasting vibration. However, wavelet analysis has the disadvantages of low frequency resolution and low time resolution. In order to improve the time-frequency, a wavelet packet was used to analyze the frequency and energy distribution of vibration signals during each blasting20,21. In the near zone of blasting, the vibration energy is concentrated in both high and low frequency bands. Wavelet packet transform was also used to decompose blasting signals in several layers to obtain the information of energy distribution22–24. In order to overcome the drawbacks of Fourier transform in analyzing non-periodic and non-stationary signals, Chen et al.25 developed a new calculation method for wavelet packet transform to accurately describe the frequency characteristics of blasting signals. Wavelet packet analysis can better capture the multi-major frequency distribution characteristics of energy distribution, with the dominant frequency band containing over 70% of the vibration signal’s energy. Hence, wavelet packet analysis can describe the frequency and energy distribution characteristics of blasting vibration signals more comprehensively10. However, the above studies have only focused on the distribution of blast energy in the frequency domain by examining the monitored blast signals. Most of the studies seldom involved the characterization of the geological conditions in the vicinity of the monitored sites, and the distribution of the blast vibration signal energy was relatively unstable in the various analyzed frequency bands.

This paper aims to investigate the propagation and attenuation characteristics of vibration signals on the ground surface due to blasting excavation of a fractured rock tunnel, specifically in the three-channel direction. Field measurement data was obtained from the Xiamen Dajianshan Tunnel blasting project. To interpret the results, wavelet packet analysis technique was adopted to examine the frequency-energy distribution characteristics of the blasting vibration signals. The ultimate goal was to gain insights into the laws governing the propagation and attenuation of blasting vibration in the fractured rock body near the ground surface. The frequency range that predominantly influenced the vibration of the surrounding environment was segmented for an analysis of the distribution and attenuation characteristics of energy within the blasting vibration signal on the surface of the fractured rock body in the frequency domain.

Field testing and monitoring

Overview of the field project

The Dajianshan Tunnel, which has a total length of 3183 m, was excavated using the drilling and blasting method. The tunnel consists of two holes, with the right hole spanning 3178 m and the left hole spanning 3188 m. The surrounding rock of the tunnel’s middle section mainly comprised medium-weathering tuff or granite, while the entrance and exit were fragmented bedrock areas, each covering a distance of approximately 400 ~ 600 m. The investigated tunnel area had two fracture zones and three zones of dense joints and fissures (fractured rock zones) that cut off the surrounding rocks of the tunnel longitudinally and horizontally. Joints and fissures near the rock tunnel were widely distributed, which can significantly affect the propagation and attenuation of blasting vibration of the surrounding rocks near the tunnel. According to the field investigation by Meng26, the main fissures were located above the palm surface, and the inclination angle of the joints or fissures with respect to the horizontal plane was about 15 ~ 20°.

The excavated tunnel was 5.0 m in height and 10.25 in width. On the upper left of the tunnel, there was a landfill site. The closest distance between the tunnel roof and the bottom of the landfill was 27.1 m. Meanwhile, there was a high-voltage tower right above the tunnel. In particular, pile number YK4 + 947.169 under the high-voltage pylon (Jiao Li I Road 021 220kv) in the right tunnel hole was situated at a depth of 27.7 m from the tunnel roof and approximately 23 m from the high-voltage pylon foundation base. It was highly susceptible to vibrations generated by tunnel blasting. In the tunnel blasting excavation, the unit price per cubic rock volume was about 20 RMB. The rock and soil mass from the surface to the tunnel roof were colluvial soil, soil-like strongly weathered tuff, and fragmented strongly weathered tuff. They were relatively fractured. Therefore, the test in this study was carried out on the surface near the tower.

Layout of measurement points

The measuring locations were arranged at 15 m intervals along the tunnel roof away from high voltage tower on the ground surface (Fig. 1). Speedometers were placed on the poured concrete platform on the surface (Fig. 2). The monitoring instrument used in this test was the TC-4850-type blasting vibration recorder produced by Chengdu Zhongke Measurement and Control Company Limited (Fig. 3). The testing instrument was characterized by its high intelligence and included an embedded computer module. It was capable of previewing parameters like maximum value, frequency, and waveform right after sampling, eliminating the necessity for external computer assistance. Additionally, it had an X, Y, Z three-dimensional integrated velocity transducer with a range from 0.001 cm/s to 35 cm/s, covering all the necessary ranges for blasting vibrations. Users had the flexibility to define their own sampling frequency and trigger recording threshold.

Fig. 1 Section profile of monitoring locations of blasting vibration.

Fig. 2 Installation of blasting vibration sensor in field.

Fig. 3 TC-4850 Blasting vibrometer system.

Characterization of engineering geological profile in field

As shown in Fig. 1, the stratigraphic conditions of the blasting vibration monitoring area near ground surface predominantly comprised of colluvial soil containing clay and gravel, overlaying a subsurface composed of tuff and its weathered layer. The specific layers can be delineated as follows: the uppermost layer comprised fragmented residual clayey soil, exhibiting a gray-yellow hue and was primarily composed of clay with approximately 10% sand content, displaying poor uniformity. Subsequent to this layer was gravelly soil, presenting light yellow and brownish-yellow stones, slightly moist, predominantly gravelly with intermixtures of clayey soil. Following this was residual sandy clayey soil, displaying shades of gray and gray-yellow, characterized by clayey powder particles with a coarse particle content ranging between 10 and 20%. Subsequently, there was a soil-like strongly weathered tuff layer, predominantly gray and gray-yellow, showcasing intense rock weathering, highly fractured with a bulk-like structure, featuring a sandy core prone to disintegration upon manual compression. This layer gradually became fragmented strongly weathered tuff, exhibiting dark gray, gray-yellow, and gray-white stones, indicative of severe rock weathering with a highly fragmented and fissured block structure, with a core composed of fragmented material prone to breakage. Finally, the lowest layer consisted of medium weathered tuff, primarily displaying greenish-gray and dark gray hues, with moderate weathering, significant fragmentation, mosaic fracture structures, block structures, and a core composed of compact blocks and short columns, representing a harder rock composition.

Stratigraphic integrity parameters in the blasting test area

Based on the ground investigation data, the SZK6 wave velocity test was conducted on the drilling holes in the blasting area. The stratigraphic integrity parameters of the blasting test area were obtained as shown in Table 1. The data in Table 1 was from the site investigation report, which was provided by Xiamen Municipal Highway Development Centre26. According to Table 1; Fig. 1, it can be found that the surrounding rock in the monitoring area was mainly composed of broken tuff, and only part of the tunnel passed through the moderately weathered tuff, while the overlying rock and soil bodies were all colluvial soil, soil-like strongly weathered tuff and fragmented strongly weathered tuff. This part of the rock and soil bodies had low integrity coefficients, slow propagation of longitudinal waves, and structural fragmentation, which seriously affected the attenuation of blasting vibration.

Table 1 Rock mass integrity parameters.

Stratigraphic name	Longitudinal wave speed/(m/s)	Integrity factor	Rock integrity parameters	
Colluvial Soil	/	/	/	
Soil-like strongly weathered tuff	/	/	/	
Fragmented strongly weathered tuff	1997	0.13	Extremely broken	
2262	0.16	Broken	
2028	0.13	Extremely broken	
2424	0.19	Broken	
Moderately weathered tuff	3935	0.49	Relatively broken	
4184	0.55	Relatively complete	
4158	0.54	Relatively broken	
4264	0.60	Relatively complete	
4141	0.54	Relatively broken	
4460	0.63	Relatively complete	
4963	0.78	Complete	

Blasting construction program

The surrounding rock of the tunnel body was classified as Grade V, Grade IV, Grade III, and Grade II. The blasting construction methods proposed included the bench method, the centre diaphragm method, and the full-section method. The explosives selected were No. 2 rock emulsion explosives, and the detonators chosen were non-electric millisecond delay detonating tube detonators and electronic detonators. The cords included detonating fuses and detonating tubes, and the detonation power sources were capacitive detonators and electronic detonator initiators. In the tunnel blasting parameter design, the blast hole diameter was taken as D = 38 ~ 42 mm. The designed penetration for Grade V surrounding rock was 0.8 m. Grade IV surrounding rock was 1.5 m, and Grade III surrounding rock was 3.0 m. During tunnel excavation, the blast holes were divided into cut holes, reliever holes, periphery holes, and bottom holes. When designing the blasting, the depth of the reliever holes and periphery holes should reach 1.1 times the boring penetration. The straight holes were used for the cut holes, and the cut holes were located in the low-middle part of the tunnel section excavation step. The depth of the cut holes should be 10 ~ 20 cm deeper than the reliever holes and periphery holes, depending on the depth of the blast holes. All blasting adopted millisecond-controlled blasting to increase the effect of the blasting interference and vibration reducing, ensuring that the initial support of the surrounding rock and nearby buildings (structures) were not damaged. The principle of the detonation sequence was that the previously detonated blast holes should create a free surface for the later detonated blast holes. The cut holes, reliever holes, and bottom holes all adopted continuous decoupling charge structure (as shown in Figs. 5 and 6), using 32 mm diameter emulsion explosives, with a decoupling charging coefficient of D = 0.042 m/0.032 m = 1.31.

The monitoring signal in the field experiment was the blasting signal during the step method of blasting construction. Figure 4 show the layout diagram of specific blasting excavation holes. hs-1, hs-3, hs-5, hs-7, hs-9, hs-11 represent the initiation blasting holes in sections 1, 3, 5, 7, 9, 11, respectively. In the blasting activity, electronic detonators were paralleled connected with the detonation network. According to the detonation sequence of the lasting construction method, the electronic detonators were set with delayed time one by one. After the delay time was set, the detonator buckles were sequentially connected to the detonation network parallelly.

Fig. 4 Schematic layout of the blasting holes during step excavation.

Data analysis methods

Wavelet domain denoising

Because wavelets only had values within a finite space of independent variables, it became feasible to focus on a small fraction of them for centralized fitting. Consequently, the coefficients taken for this purpose were inevitably larger than the wavelet coefficient values of the noise, whose energy was dispersed across many wavelet coefficients in the wavelet coefficient domain. This suggested that thresholding the wavelet coefficients eliminated noise below a fixed amplitude in the wavelet transform domain. In this study, MATLAB for wavelet noise reduction was employed and three methods were utilized, namely soft thresholding, hard thresholding, and fixed thresholding, to reduce the noise in one-dimensional blasting monitoring data. The performance of these techniques was evaluated by outputting the error signal-to-noise ratio (SNR), root mean square error (RMSE), and the noise image before and after noise reduction. The noise reduction process comprised three main steps: (i) wavelet transform processing on the noisy signal; (ii) removing noise from it by processing the transformed wavelet coefficients; (iii) wavelet inverse transform to obtain the denoised signal27.

Principle of determining differential extension time

In engineering blasting, it was often necessary to carry out differential blasting. The number of detonator segments for differential blasting depended on specific blasting conditions and purposes. Each detonator section contributed energy to the blasting system, and the detonation of each section led to a sudden change in energy within the system. To accurately determine the moment of sudden change in the vibration signal, the wavelet transform of the blasting waveform was monitored. By identifying the maximum value in the wavelet transform mode, the precise timing of each detonation during micro-differential blasting could be determined. This information was then used to calculate the actual millisecond blasting in the blasting process28.

Theory of wavelet packet transforms and energy methods

In this study, wavelet packet decomposition on a given signal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:x$$\end{document}(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document}) was performed to obtain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:j={2}^{i}$$\end{document} sub-bands in the i-th layer of decomposition. Assuming that the lowest frequency component of the original signal was 0 and the highest frequency component was \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\omega\:}_{m}$$\end{document}, the frequency width of each sub-band was \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\omega\:}_{m}/{2}^{i}$$\end{document}. Wavelet packet decomposition coefficients were reconstructed to extract the signal from the frequency range of each sub-band. Finally, the total signal was expressed as15:1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:x\left(t\right)=\sum\:_{k}{x}_{i,k}={x}_{i,0}+{x}_{i,1}+\dots\:+{x}_{i,j-1}$$\end{document}

In the context of this study, the reconstructed signal on the i-th decomposition node is represented by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{x}_{i,k}$$\end{document}, where k ranges from 0 to j−1.

The wavelet packet decomposition process was applied to the signal, taking into account the specific signal characteristics and the operating frequency of blasting vibration monitoring instrument used. The signal was decomposed into the i-th layer, and the corresponding energy for each sub-band was denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{n,j}$$\end{document}.2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{n,j}=\int\:{\left|{S}_{n,j}\right|}^{2}dt=\sum\:_{k=1}^{m}{\left|{x}_{j,k}\right|}^{2}$$\end{document}

The total energy of the analyzed signal, denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{0}$$\end{document}, was calculated as the sum of the energy contributions from each sub-band in the wavelet packet decomposition:3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{0}=\sum\:_{j=0}^{{2}^{n}}{E}_{n,j}$$\end{document}

To determine the energy distribution across different frequency bands, the percentage of energy for each sub-band, denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{j}$$\end{document}, was calculated as the ratio of the energy in that sub-band (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{n,j}$$\end{document}) to the total energy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{0}$$\end{document}), multiplied by 100%:4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{j}=\frac{{E}_{n,j}}{{E}_{0}}\times\:100\text{\%}$$\end{document}

This calculation allowed us to quantify the energy percentage distribution across different frequency bands in the signal after wavelet packet decomposition.

Wavelet analysis of vibration signals

Blast monitoring results

During the tunnel blasting, three-way Speedometer was installed. The x-direction represented the tunnel direction towards the explosive source, the y-direction was parallel to the ground surface and perpendicular to the tunnel direction, and the z-direction indicated vertical upward movement perpendicular to ground surface. After the measurements, four sets of typical blasting vibration data were obtained, as shown in Table 2. These four sets of data were typical of the vibration data collected from different blasts at the three measurement points.

Table 2 Typical blast vibration data.

Measurement point	Bursting center distance (m)	Vx (cm/s)	Vy (cm/s)	Vz (cm/s)	
A	9.7	300.9	192.3	248.4	
B	16.5	208	230.8	205.4	
C	24.2	165.4	245.4	108.6	
D	29.8	116.3	129.8	91.7	

Figure 5 shows the three-way velocity time profile at point A. It can be seen that the surface experienced triaxial vibrations resulting from the superposition of vibrations induced by individual sections of the blast, showing multiple vibration peaks. Along the x-direction, the vibration peak was the highest, followed by the y-direction, while the z-direction exhibited the smallest peak. Over a period of approximately 2.5 s, the monitored vibration velocities gradually decreased to zero in all three directions. The recovery of vibration velocity in the x and y directions was slower compared to the z-direction, which displayed a faster recovery rate. Additionally, the fluctuations in the vertical direction were also comparatively smaller.

Fig. 5 Three-way velocity time profile at point A.

Wavelet transform based denoising signal processing

In the analysis of blast vibration signals, denoising is a fundamental requirement due to the presence of noise signals in the collected data. The db8 wavelet basis, known for its smoothness, support, and approximate symmetry, has been successfully employed in blast vibration signal analysis. Therefore, in this study, wavelet decomposition using the db8 wavelet was applied for denoising the measured blast vibration signals by taking into account the characteristics of the recorded data. The primary objective of wavelet threshold denoising is to process the obtained wavelet coefficients, with a primary focus on the threshold value during this process. When decomposing the signal using wavelets, larger coefficients correspond to the signal, while smaller coefficients correspond to noise. By appropriately selecting a threshold, wavelet coefficients larger than the threshold are considered to be generated by the signal and are thus retained, while those smaller than the threshold are deemed to be produced by noise and are set to zero, thereby achieving denoising.

For signal analysis, a representative vibration data from a measurement point was selected, focusing on the x-direction vibration velocity. A total of 30,000 sampling points were chosen for waveform visualization using MATLAB. Thresholding denoising is normally used to distinguish noises from regular wavelet coefficients. Three denoising methods were commonly employed, including hard thresholding method, soft thresholding method and fixed thresholding method. Figure 6 illustrates the denoised waveform. In this context, wavelet coefficients are represented as ‘w’ and the threshold as ‘thr’. The concept of hard thresholding involves setting w = w for w > thr, and w = 0 for w < thr. On the other hand, soft thresholding is similar to hard thresholding but with slight modifications: for w > thr, w = w-thr, and for w < thr, w = 0. Additionally, fixed thresholding entails calculating the threshold using the formula \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:thr=\sqrt{2\times\:\text{ln}n}$$\end{document}, where ‘n’ represents the length of the signal. Upon visual inspection, it was observed that the original signal should have been a straight line in the initial section. However, the measured signal contained dense fluctuations. After applying the three denoising methods, the signal was flattened. However, it was difficult to visually evaluate the effect of the noise reduction for the three methods. To quantitatively evaluate the performance of the noise reduction, the signal-to-noise ratio and the root-mean-square error were employed as evaluation indices.

Fig. 6 Local comparison of three thresholding denoised signals.

The signal-to-noise ratio, denoted as SNR, refers to the ratio of the original signal energy to the noise energy. The larger the value, the smaller the noise content in the signal, indicating a better noise reduction effect. The root-mean-square error, denoted as RMSE, is the mean square error between the reconstructed signal and the original signal. It quantifies the difference between the original signal and the signal after noise reduction. The smaller the root-mean-square error, the better the noise reduction effect. The denoising effect for the three methods was calculated using MATLAB. By comparing the results presented in Table 3, it was observed that the application of the db8 wavelet basis for fixed denoising of the blasting signal yielded more reliable outcomes. Therefore, the fixed threshold approach was employed to denoise the vibration signal at each data point.

Table 3 Comparison of denoising effect.

Denoising methods	SNR (signal-to-noise ratio)	RMSE (rms error)	
Soft threshold denoising	43.4558	1.6519 × 10− 5	
Hard threshold denoising	32.9370	5.5454 × 10− 5	
Fixed threshold denoising	45.8296	1.2568 × 10− 5	

Differential burst time recognition

In the context of differential blasting, the vibration signal recorded at a measurement point was found to be the result of the superposition of segmented shock waves. As a consequence, the occurrence of each segment of the vibration wave signal inevitably caused a local mutation in the vibration signal. By utilizing the wavelet transform modulus maxima method, the location of these mutation points could be effectively identified. This enabled the determination of the precise timing of each segment of detonator-initiated micro-differential blasting and further facilitated the calculation of the actual micro-differential extension time during the blasting process. The continuous wavelet transform mode of the vibration signal in the Z direction at point B, with a scale of 16, is illustrated in Fig. 7.

Fig. 7 Continuous wavelet transform of the original burst signal.

Based on the analysis conducted in Fig. 6, it is evident that the continuous wavelet transform resulted in the identification of 10 mode extreme points. Figure 7 also depicts the differential blasting vibration signal resulting from the superposition of 10 blasting vibration waveforms. The 10 modal points aligning with the time coordinates represented the precise moments of detonation for each segment of the differential blasting detonator. These extreme points appeared at the following moments: 142.625ms, 434.375ms, 738.375ms, 1034.62ms, 13337.62ms, 1639.62ms, 1935ms, 2225.75ms, 2522ms, and 2812.12ms. Consequently, Table 4 was used to demonstrate the differential time between segments, which exhibited a close alignment with the design specification of 300ms. By comparing the original vibration signal graph, it is evident that although various vibration peaks were observable, the superimposed nature of the vibrations made it challenging to precisely isolate the explosive detonation time in each segment. This can be accurately discerned through the application of continuous wavelet transform. Furthermore, this approach validates the efficacy of the denoising method and the precision of the blasting program.

Table 4 Calculation of differential time intervals between segments.

Measurement point	Recognition moment (ms)	Delay interval (ms)	
B	142.625	291.75	
434.375	304	
738.375	296.245	
1034.62	303	
1337.62	302	
1639.62	295.38	
1935	290.75	
2225.75	296.25	
2522	290.12	
2812.12	\	

Energy analysis based on wavelet packet transform

In this study, blasting vibration data was acquired using the TC-4850 blasting vibrometer. The signal was recorded for duration of 4 s with an acquisition frequency of 8000 Hz, resulting in a Nyquist frequency of 4000 Hz. Wavelet packet decomposition was employed to decompose the data into 9 layers, with the lowest frequency band corresponding to 0–7.8125 Hz for the X-direction of the A point. Since the frequency of blast vibration signals is generally below 200 Hz, the energy distribution of each frequency band was obtained. Figure 8 shows the three-dimensional time-frequency plot in the x-direction at point A. Table 5 illustrates the energy distribution of each frequency band in the x-direction at point A.

Fig. 8 Three-dimensional time-frequency plot in x-direction at point A.

Table 5 Energy distribution of each frequency band in x-direction at point A.

Frequency (Hz)	Percentage (%)	
0	7.8125	8.63209	
7.8125	15.625	1.159237	
15.625	23.438	0.792822	
23.438	31.25	1.202172	
31.25	39.063	12.69616	
39.063	46.875	4.396958	
46.875	54.688	1.635168	
54.688	62.5	1.744923	
62.5	70.313	8.34552	
70.313	78.125	9.947057	
78.125	85.938	4.278447	
85.938	93.75	4.777205	
93.75	101.56	12.21577	
101.56	109.38	3.334123	
109.38	117.19	7.515426	
117.19	125	7.621179	
125	132.81	0.029907	
132.81	140.63	0.048733	
140.63	148.44	0.071315	
148.44	156.25	0.027127	
156.25	164.06	0.12588	
164.06	171.88	0.115071	
171.88	179.69	0.096861	
179.69	187.5	0.075357	
187.5	195.31	1.935471	
195.31	4000	3.388165	

Based on the observations from Fig. 8; Table 5, it is evident that the surface blasting vibration signal exhibited a relatively wide main seismic frequency band, primarily ranging from 0 to 100 Hz. Furthermore, this main seismic frequency band can be further categorized into multiple sub-seismic frequency bands. The response was characterized by multimodal and multishock patterns because the geotechnical body around the tunnel up to the surface was a system containing many substructures with different intrinsic properties. These substructures possessed diverse intrinsic properties, resulting in a response characterized by multi-modal and multi-vibratory behaviors under the geological conditions of blasting vibration signals.

The energy distribution analysis revealed that the energy was primarily concentrated in two frequency bands. The first frequency band spanned from 31.25 Hz to 39.063 Hz, while the second frequency band ranged from 93.75 Hz to 101.56 Hz. Remarkably, the energy contribution of these two bands accounted for approximately 12% of the total energy. The prominence of the low-frequency band can be attributed to the propagation process of blasting seismic waves. High-frequency signals encountered difficulties in traversing larger joints and cracks or experienced greater attenuation at these locations compared to low-frequency signals. Conversely, the concentration of energy in the high-frequency band was due to the absence of upper constraints on the surface of the rock and soil body. Consequently, vibrations experienced an increase in frequency and amplitude due to the whiplash effect induced by the seismic wave.

Variation of blasting vibration energy attenuation in fractured rock mass

Wavelet packet analysis was applied to determine the energy distribution percentage in various frequency bands along the X direction at four specific points. The results are illustrated in Fig. 9. The analysis of the results revealed that the blast vibration signal energy in the X direction (along the tunnel) was primarily concentrated below 130 Hz. The frequencies exceeding 200 Hz may include some denoised interference signals. Furthermore, as the distance increased, the high-frequency component experienced faster energy attenuation compared to the slower energy attenuation of the low-frequency component. Following wavelet packet analysis, the energy distribution across each sub-frequency band became increasingly intricate. In light of this complexity, vibration velocity control standards were proposed in blasting engineering safety protocols for various categories of protected entities. Given that different frequency ranges posed distinct risks, frequency-specific control standards were advocated to address these concerns. Notably, low-frequency vibrations were prone to resonance with adjacent building structures, necessitating a frequency-based approach to investigate energy attenuation patterns.

Fig. 9 Percentage of energy distribution of different frequency bands in X direction at four points.

The frequency bands are categorically divided into 0–10 Hz, 10–50 Hz, 50–100 Hz, and > 100 Hz. As depicted in Fig. 9c, vibration energy near the blasting site was predominantly concentrated in the 50–100 Hz range. Furthermore, it was observed that high-frequency energy experienced more rapid attenuation compared to low-frequency energy. Although high-frequency energy contributed significantly to rock fragmentation, its decay rate was accelerated. Conversely, while low-frequency energy constituted a smaller portion, its attenuation was slower, resulting in a greater propagation distance and potentially greater impact on the safety of surrounding structures.

Using the prescribed method, the energy at points A, B, C, and D were calculated, and the results are presented in Table 6. Figure 10 shows the variation of blast energy with outward distance. The burst center distance was employed as the horizontal coordinate. Based on the analysis of Table 6; Fig. 10, it was observed that as the burst center distance increased, the total energy of the signal exhibited a continuous decay. Specifically, the energy in the X and Z directions showed a gradual decrease, with similar rates of decay. Notably, the X direction consistently exhibited higher energy levels compared to the Z direction. On the other hand, the energy in the Y direction displayed slight fluctuations within the range of 0.2 m2/s2, indicating slower decay and carrying a relatively higher amount of energy. This sustained energy in the X and Y directions was considered the primary factor contributing to vibration damage, as they exhibited slower attenuation and carried more energy compared to the Z direction.

Table 6 Three-way vibration energy at points a, B, C and D.

Measurement point	Bursting center distance (m)	Ex(m2/s2)	Ey(m2/s2)	Ez(m2/s2)	E总(m2/s2)	
A	9.7	0.3427	0.2067	0.1965	0.7459	
B	16.5	0.3008	0.2205	0.1077	0.629	
C	24.2	0.1911	0.2695	0.0717	0.5323	
D	29.8	0.1227	0.116	0.0593	0.298	

Fig. 10 Variation of blast energy with distance.

After linear fitting, the fitted equations for the decay of energy with distance in three directions are:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{Total}=-0.02085x+0.96943$$\end{document}

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{x}=-0.01132x+0.46621$$\end{document}

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{y}=-0.00290x+0.26131$$\end{document}

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{z}=-0.00664x+0.24192$$\end{document}

The analysis of the results indicated that the decay of energy along the x-direction was the fastest, accounting for 54.29% of the total energy decay. The z-direction energy decay with distance was the second-fastest, accounting for 31.84% of the total energy decay. In contrast, the y-direction energy decay was the slowest, accounting for 13.91% of the total energy decay. This difference can be attributed to the surrounding rock constraints along the x-direction (parallel to the tunnel strike), the absence of constraints on the upper surface in the z-direction, and the influence of topography along the y-direction (perpendicular to the tunnel strike), which resembled a terrace shape. Moreover, the y-direction was affected by a step-like topography perpendicular to the tunnel strike.

Along the z-direction, which was perpendicular to the ground surface, the energy decay of blasting vibration signals with the frequency range of 50–80 Hz was the most significant, with only 2% left when reaching ground surface. According to the site monitoring layout, the angle between the line of detonation power source-monitoring location and the direction of fissures or joints was about 750. That means when the intersection angle between vibration wave propagation direction and fissure direction was 750, the wave energy decay was the most pronounced (larger than 90%) within the 50–80 Hz frequency range.

Conclusions

This study monitored and analyzed ground vibration signals generated by tunnel blasting in fractured rock. The parameters of the fissured rock body within the monitoring range were described. Energy analysis of the vibration signals was conducted, leading to the establishment of the energy attenuation characteristics within this particular rock structure. The main conclusions are as follows:The utilization of the fixed threshold denoising method with db8 wavelet base resulted in a significant enhancement in the denoising effect of the original blasting vibration signal. The signal-to-noise ratio was determined to be 45.8296 and the root mean square error was measured to be 1.2568 × 10− 5.

The application of wavelet continuous transform, specifically by selecting the mode with the largest value, allowed for a more accurate identification of differential blasting delay time intervals. The wavelet continuous transform approach provided improved precision in identifying differential blasting delay time intervals.

In the surrounding rock tunnels of fragmented strongly weathered and moderately weathered tuff, it was observed that the total energy of blasting vibration signal decreased as the core distance increased. The high-frequency component exhibited faster attenuation compared to the low-frequency component.

In terms of energy decay of vibration signals in each direction, it was observed that under the given geological condition, the x-direction exhibited the fastest rate of energy decay with distance, accounting for 54.29% of the total energy decay. The z-direction followed with the second fastest rate of energy decay, while the y-direction demonstrated the slowest rate of energy decay.

The inclination angle of main fissures or joints was 15°. When the blasting induced vibration waves had an intersection angle of 75° with respect to the directions of fissures or joints, the energy decay within the frequency range of 50–80 Hz was the most significant (more than 90%). In this study, vibration signals were only measured near the ground surface during the blasting activities in a fissure rock tunnel. In the future, vibration signals below ground surface at various depths should also be measured. Moreover, the 3D fissure distribution in the rock mass should be more accurately characterised for better interpretations of signal transmission in the fissured rock.

Acknowledgements

This study is financially supported by National Natural Science Foundation of China (52308342, U2340227), Fundamental Research Funds for the Central Universities (Grant No. RF1028623071, 2242024k30066) and the Department of Communication of Fujian Province, China (7921004060).

Author contributions

Zuhua Deng and Junyu Meng carried out the field test and drafted the initial version of this manuscript. Yongfeng Deng and Junjun Ni supervised the two research students and provided the fundings and suggestions during the research and paper drafting. Junjun Ni revised the manuscript several times. Daicheng Ye provided the funding and many suggestions during revision.

Data availability

Data available on request from the authors: the data that support the findings of this study are available from the corresponding author, Dr Junjun Ni, upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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