Experimental Study on Pressure Wave Propagation in Mine Ventilation Disasters

Abstract

This study experimentally investigates the propagation characteristics of static pressure waves (S-waves) and dynamic pressure waves (D-waves) induced by coal and gas outbursts of varying intensities, utilizing a self-built 1:30 scaled laboratory mine ventilation model. Systematic measurements and quantitative analyses were conducted to determine waveform morphology, propagation velocities, attenuation laws, and frequency distributions. The results demonstrate that outburst-induced D-waves exhibit a distinct full-sinusoidal waveform, whereas S-waves present a half-sinusoidal profile. Notably, the wavelength of both wave types remains highly stable regardless of initial outburst intensity and propagation distance. Conversely, the wave amplitude is positively correlated with the outburst intensity and attenuates progressively with distance. Furthermore, D-waves demonstrate a significantly higher sensitivity to propagation distance than S-waves. Spectral analysis confirms that the primary energy of both pressure waves is concentrated in the ultra-low-frequency range below 1.0 Hz. The average propagation velocities of S-waves and D-waves were measured at 395.67 m/s and 280.27 m/s, respectively, indicating that S-waves propagate considerably faster. It should be noted that since these findings were derived under scaled laboratory conditions, direct extrapolation to full-scale, long-distance field roadways requires further validation. Ultimately, this work elucidates the fundamental propagation mechanisms of attenuated pressure waves within mine ventilation networks, providing critical waveform signatures for the remote identification and localization of underground disaster sources.

1. Introduction

Among coal mine disasters, coal and gas outbursts and gas explosions represent the most severe hazards. Improper or delayed emergency responses often exacerbate these accidents, leading to increased casualties and property losses. Pressure waves are elastic waves that propagate through fluids when there is a change in pressure. These waves can travel forward or backward along the direction of fluid flow. During events such as coal and gas outbursts, gas explosions, and air blasts in gob areas, powerful shock waves are generated. After traveling a certain distance, these shock waves gradually transition into pressure waves. These pressure waves propagate at the speed of sound. By studying the waveform characteristics of pressure wave propagation and using monitoring devices to detect pressure waves generated by coal mine disasters, it becomes possible to effectively identify and locate such incidents, thereby facilitating timely monitoring and management of disaster incidents. This is crucial for ensuring the safety of coal mine operations [1,2].

Extensive research has been conducted on shock waves induced by coal mine disasters. Wang K et al. [3] investigated the formation of shock waves during coal and gas outbursts through both experimental and numerical simulation approaches. They examined the causes behind the formation of outburst shock waves and established a relationship between these shock waves and coal seam gas pressure. Meanwhile, Miao F et al. [4] explored the formation mechanisms of outburst shock waves under different flow conditions, building on previous research on the motion parameters of coal–gas two-phase flow. Zhang et al. [5] conducted physical simulation experiments of coal and gas outbursts under varying permeability conditions using a self-developed multi-functional coal and gas outburst simulation test system. The results demonstrated that the shock waves generated during the migration of the outburst two-phase flow exhibit a staged evolution characteristic. Specifically, the maximum absolute value of the shock wave over-pressure trough in the negative pressure phase was found to be greater than the peak over-pressure in the positive pressure phase. Regarding shock wave propagation, Wei J et al. [6], guided by aerodynamic principles, investigated the propagation laws of outburst shock waves in both straight and curved roadways. Wang K et al. [7] employed a coal–gas surge experimental system to study shock waves under different airflow and resistance conditions. They determined the propagation laws of shock waves and airflow, as well as the effects of these shock waves on ventilation networks. To determine propagation velocities, Cao J et al. [8] investigated the propagation laws of outburst shock waves in roadways. They developed a mathematical model for the propagation of these shock waves and provided a formula for calculating shock wave velocity. Sun, D et al. [9] derived formulas for parameters such as pressure, density, and temperature before and after the outburst shock wave, based on shock wave theory. They also deduced an expression describing the relationship between the pressure of the outburst gas and the intensity of the outburst shock wave, and introduced the concept of equivalent sound velocity for gas flow. The generation of shock waves frequently releases immense energy, which can be harmful to underground ventilation systems and workers. As shock waves propagate through roadways, their energy gradually dissipates with increasing distance. Zhou A et al. [10] conducted a numerical simulation to investigate the propagation characteristics of sudden airflow and its impact on surge shock waves induced by rapid gas desorption. The findings reveal that the rapid release of gas compresses the air within the roadway, generating a high-speed burst shock wave. Over time, the intensity of this burst shock wave gradually diminishes. Additionally, the convective transport speed of the gas is slower than the propagation speed of the burst shock wave. Xue H et al. [11] used a self-developed device to simulate and measure the energy propagation and parameters of coal and gas outbursts, analyzing the energy dissipation patterns of these shock waves within complex ventilation networks. Qiu et al. [12] tested the effect of roadway bends on gas explosion shock wave attenuation using an 18 cm diameter pipe. Their findings revealed that pressure wave attenuation is mainly governed by the bending angle and the peak over-pressure before the bend. Sun H et al. [13] established a shock wave propagation model by examining the propagation laws of outburst shock waves. They determined the relationship between shock wave over-pressure and factors such as outburst strength, gas desorption rate, initial gas pressure, roadway cross-section, and distance. Additionally, they identified the key factors influencing shock wave energy dissipation. Existing scholarship on shock waves arising from coal mine disasters addresses four pivotal axes: formation mechanisms, elucidating the origins of gas–solid two-phase flows; propagation characteristics in complex roadway geometries; velocity modeling and formula derivation; and energy dissipation, identifying attenuation laws and critical determinants.

As the distance increases, the shock wave gradually attenuates into a pressure wave. Research on pressure waves in the coal mining industry is relatively limited, with most studies focusing on the pipeline transportation industry. These studies primarily examine the propagation patterns and propagation characteristics of pressure waves within pipelines. Gao L et al. [14] employed techniques such as wavelet transform, spectral analysis, Laplace transform, and singular value decomposition to extract waveform features of pressure waves in transportation pipelines and developed a method for identifying pressure wave events. Wang T et al. [15] used measured data and numerical simulation methods to conduct an in-depth study on the propagation and reflection of pressure waves in pipelines, as well as the variations in stress and deformation within the pipelines during pressure wave propagation. They also investigated the penetration and reflection coefficients of pressure waves at valves. Mei F et al. [16] investigated the propagation characteristics of pressure waves in pipelines and analyzed how factors such as propagation distance, density, temperature, and pressure affect the propagation speed of pressure waves. Chen E et al. [17] derived the propagation expression and velocity calculation formula for pressure waves in pipelines using transient dynamics, unsteady airflow theory, and other methods. Guo et al. [18] employed a specially designed experimental pipeline system and three-dimensional numerical simulations to investigate the pressure wave and flow field characteristics of transient flow generated by mechanical shock in a leaking pipeline. They also analyzed the generation and propagation processes of the pressure waves.

Despite the extensive foundational research on shock waves and pipeline pressure waves, several critical knowledge gaps remain in the context of coal mine safety monitoring. First, existing mine disaster studies predominantly focus on the extreme destructiveness and extreme destructiveness of shock waves. However, the immense energy of these near-field waves frequently destroys monitoring sensors, rendering continuous, close-range data acquisition practically unfeasible. Second, while the gradual attenuation of shock waves into pressure waves over long distances is a recognized physical phenomenon, the specific dynamic response characteristics and propagation laws of these disaster-induced pressure waves within complex mine ventilation networks remain largely unexplored. Most existing pressure wave research is confined to simple pipeline fluid transportation, which cannot accurately represent the aerodynamic complexities, rough wall boundary conditions, and scale effects inherent in underground mine disasters. Furthermore, existing numerical simulations often rely on idealized assumptions that fail to fully capture these physical intricacies.

To bridge these critical knowledge gaps and advance the field of disaster monitoring, this study shifts the research paradigm by utilizing similarity scaling laws to safely and accurately simulate disaster-induced pressure waves. This paper focuses on investigating the specific waveform characteristics of static pressure waves (S) and dynamic pressure waves (D) using a self-built 1:30 scaled laboratory mine ventilation network model. Based on the similarity ratio, the initial outburst pressure in the experimental conditions is significantly scaled down compared to actual underground outbursts. The main contributions of this study are twofold: (1) it overcomes the limitations of full-scale destructive testing by systematically capturing real waveform data of pressure waves under safely scaled outburst intensities; and (2) it elucidates the distinct propagation laws and waveform signatures of both S-waves and D-waves, which carry specific disaster-type information while being harmless to monitoring equipment. By establishing the correlation between outburst intensities and pressure wave characteristics under similar scaled conditions, this research provides a vital theoretical framework and robust empirical evidence for developing a pressure wave-based disaster identification and positioning system [19].

2. Theoretical Analysis

The propagation of pressure waves in underground ventilation systems is analogous to that in confined pipelines. In enclosed spaces like pipelines, pressure waves typically propagate rapidly and may be complicated by reflections, bends, or other forms of interference at the end of the pipeline. Pressure waves propagate in air primarily in two forms. The first is the compression wave (longitudinal wave), caused by alternating pressure in the direction of propagation. Compressive waves can be regarded as an equivalent to dynamic pressure; thus, in this paper, they are referred to as dynamic pressure waves (abbreviated as D-waves). The second type is the transverse wave, which represents the pressure component perpendicular to the direction of fluid flow. It can be considered equivalent to static pressure and is hence termed the static pressure wave (abbreviated as S-waves).

The propagation of pressure waves in mine roadways falls within the regime of subsonic compressible flow (Ma << 1), which ensures that the wave propagation mechanism is consistent with real underground conditions. Static pressure waves (S) represent the normal component of fluid pressure, which is less affected by viscous dissipation and maintains strong propagation stability. In contrast, dynamic pressure waves (D) represent strong transient compression fluctuations, which are accompanied by significant thermal dissipation and nonlinear effects, leading to faster energy attenuation. Such physical differences determine the distinct waveform patterns, propagation speeds, and attenuation laws between S-waves and D-waves observed in experiments.

The underground ventilation system is a closed system. In studying the propagation characteristics of pressure waves in roadways during underground disasters, the propagation velocity of pressure waves is a critical physical parameter. The propagation velocity of pressure waves in pipes [20] is calculated using Equation (1):

$${\mathrm{a}}_0={\displaystyle \frac{\sqrt{\raisebox{1ex}{$\mathrm{K}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\rho }$}\right.}}{\sqrt{1+\frac{\mathrm{K}\mathrm{D}}{\mathrm{\delta }\mathrm{E}}}}}=\sqrt{{\displaystyle \frac{\mathrm{K}}{\left(1+\frac{\mathrm{K}\mathrm{D}}{\mathrm{\delta }\mathrm{E}}\right)\mathrm{\rho }}}},$$

(1)

where $a_0$ is the velocity of pressure wave; $K$ is the volumetric elastic modulus of the media in the pipe; $D$ is the diameter of the pipe; $\delta$ is the thickness of the pipe wall; $E$ is the elastic modulus of the material for the pipe wall and $\rho$ is the fluid density.

If the above formula is applied to the mine ventilation roadway, the propagation medium is air, assuming isothermal conditions, and the volume elastic modulus of air is equal to the closed space atmospheric pressure. And the pipe diameter corresponds to the equivalent diameter of the roadway, and the wall thickness is assumed to be infinite. The elastic modulus of the pipe wall material is taken as the elastic modulus of the surrounding rock of the roadway. According to this formula and initial values, the propagation speed of pressure waves in roadways is theoretically about the propagation speed of sound waves under corresponding conditions. This theoretical framework is used to verify whether the experimentally measured wave velocities in Section 4.3 are reasonable and consistent with classical theoretical predictions.

3. Experimental Setup and Procedure

To simulate medium-intensity coal and gas outbursts in a mine ventilation system and acquire relevant data, an experimental model was established based on geometric, dynamic, and kinematic similarity criteria. The overall structure of the model includes a main intake airway, return airway, connecting crosscut, heading face, and mining face. The pipeline is constructed from acrylic with a uniform wall thickness of 5 mm. Based on the 1:30 geometric similarity ratio, the equivalent cross-section size of the main haulage way, haulage cross-cut, and return airway is 15 × 15 cm, while the size of other roadways (heading face, mining face, special return airway) is 13 × 13 cm. The experimental platform was established at a geometric similarity ratio of 1:30 relative to the actual mine roadway, ensuring consistent section shape and layout structure between the model and real roadways.

3.1. Experimental Platform

The experimental platform simulates the regional ventilation in a mining area, which consists of a main haulage way, a return airway, a haulage cross-cut, an intake air rise, a mining face, and a heading face, as shown in Figure 1. Five adjustable air doors and an outburst-proof door are also installed in the model. By adjusting these air doors, the ventilation mode of the working face can be converted to different modes, such as U-type ventilation, U + L-type ventilation, and partial Y-type ventilation. Additionally, the air volume at each location can be adjusted accordingly. The adjustable air doors can be controlled remotely through electrical means or manually, with an opening range of 0 to 90 degrees. The ventilation direction for the entire model uses extraction ventilation. The electric motor of the main fan is controlled by a frequency converter, which can adjust the air pressure within the range of 0 to 0.05 MPa.

The mine disaster ventilation experimental platform consists of a mine ventilation roadway simulation system, a monitoring data propagation system, and a data acquisition system. It is a comprehensive experimental platform for coal and gas outburst prediction and early warning that integrates information monitoring, data propagation, and storage. The mine ventilation roadway simulation system primarily includes simulated roadways, ventilation fan devices, and other components, enabling the simulation of mine ventilation systems. The monitoring data propagation system mainly consists of a mine safety monitoring system, a monitoring server, and other components, enabling mine safety monitoring. The data acquisition system of the experimental platform consists of pressure sensors, high-precision timing instruments, and disaster pressure wave data acquisition instruments. The pressure sensors use a self-developed, high-precision, high-speed atmospheric pressure collection device, which can dynamically monitor both static and dynamic pressures. Data transmission between the acquisition device and the sensors is achieved via the IIC interface, with a pressure resolution of 2.0 Pa and a sampling rate of 50 kHz. The data acquisition device communicates with the data acquisition terminal computer over a local area network (LAN), with a communication speed of up to 100 Mbps. The high-precision timing instrument has a timing accuracy of 10 μs. The timing device includes switches, GPS timing interfaces, sensor interfaces, and indicator lights. After the instrument is powered on, the GPS timing module is activated. Upon completion of timing calibration, the indicator light begins flashing. Subsequently, ensure temporal alignment across all sensors. Configured with an isolated power supply, it ensures the accuracy and stability of data acquisition and facilitates secondary data processing.

The experimental platform was constructed at a geometric similarity ratio of 1:30 relative to the actual mine roadway. To ensure the rationality of the scaled model, dynamic similarity was qualitatively analyzed based on Reynolds number and Mach number under typical outburst conditions. The Mach number in both the model and real roadways is much less than 1, indicating that the flow is subsonic and the compression wave propagation mechanism is consistent. The flow regime in the model is consistent with that in full-scale mine roadways, and the propagation mechanism of pressure waves remains unchanged under the scaled conditions.

It should be noted that the inner walls of the model roadway are relatively smooth, whereas actual mine roadways possess rough rock surfaces. While this discrepancy results in lower frictional resistance and slower energy attenuation within the laboratory model compared to field conditions, the experimental findings remain highly effective for revealing the fundamental propagation mechanisms and waveform evolution laws of pressure waves. Consequently, this study provides a robust theoretical reference for understanding pressure wave propagation in actual underground roadways.

3.2. Experimental Methods

This study focuses on the waveform characteristics of pressure waves induced by coal and gas outbursts of varying intensities. In the experiment, coal and gas outbursts of different intensities are simulated by adjusting the pressure of the high-pressure fan. To analyze the differences in pressure wave characteristics between outbursts of various intensities, five pressure levels are selected: 0.01 MPa, 0.015 MPa, 0.02 MPa, 0.025 MPa, and 0.03 MPa. The selection of these pressure levels is based on the Chinese national standard and the geometric similarity ratio of the experimental platform: the critical gas pressure for coal and gas outbursts specified in the national standard is 0.74 MPa, and the converted critical pressure in the scaled model (1:30 geometric similarity ratio) is approximately 0.0247 MPa, so 0.025 MPa is set as the critical intensity level. The other four pressure levels are set in a gradient to cover low to medium outburst intensities, ensuring measurable differences in pressure wave characteristics.

The pressure wave monitoring device must be capable of monitoring both static and dynamic pressure waves. In this experiment, the MS5611-01 atmospheric pressure sensor (TE Connectivity, Schaffhausen, Switzerland) and the SDP810-125 differential pressure sensor (Sensirion AG, Stäfa, Switzerland) were used. MS5611-01 features an accuracy of 150 Pa and a sampling frequency of 120–1800 Hz. SDP810-125 provides a high accuracy of 0.08 Pa with a sampling frequency up to 2000 Hz. Both types of sensors communicate through the I2C digital interface. Detailed performance parameters are listed in

Table 1. Sensor Performance Parameters.

Sensor Name	Accuracy	Resolution	Acquisition Frequency	Digital Interface
MS5611-01	150 Pa	1.2–6.5 Pa	120–1800 Hz	SPI, I2C
SDP810-125	0.08 Pa	0.004 Pa	2000 Hz	I2C

. Each sensor receives control commands and processes data via the I2C digital interface.

The entire experimental system is configured with three monitoring points: Point A, Point B, and Point C. Each of these points is configured with two types of sensors—an MS5611-01 atmospheric pressure sensor and an SDP810-125 differential pressure sensor—enabling synchronous measurement of static pressure and dynamic pressure. To monitor changes in static and dynamic pressure across different roadways, Point A is located at the heading face, Point B at the haulage crosscut, and Point C at the return airway. The distances from the outburst source to each monitoring point are 0.5 m, 3.5 m, and 8.0 m, respectively. The sensor arrangement is shown in

Table 2. Sensor Layout Location.

Monitoring Point Number	Sensor Type	Sensor Position	Distance from Outburst Source
A	MS5611-01	Heading face	0.5 m
	SDP810-125
B	MS5611-01	Haulage cross-cut	3.5 m
	SDP810-125
C	MS5611-01	Heading face	8.0 m
	SDP810-125

and a diagram of the sensor layout is provided in Figure 2.

4. Analysis of Experimental Results

To minimize environmental interference, all experiments were conducted under stable weather conditions. In order to reduce the error between the sensors, the initial errors of the sensors at monitoring points A, B, and C were eliminated through zero-calibration. The primary focus of this study is to investigate the influence of distance and outburst intensity on the propagation of pressure waves, without considering other influencing factors such as roadway shape or obstacles. A pipeline equipped with a valve was installed between the fan and the roadway. Initially, the fan pressure was set to 0.01 MPa and maintained stably for 30 s. The pipeline valve was then closed, allowing air pressure to accumulate within the pipeline. Three seconds later, the valve was opened to release the accumulated air pressure, simulating a coal and gas outburst and generating a pressure wave. After each experiment, the airflow was allowed to stabilize for 30 s before the fan was turned off. The experimental data were exported from the data acquisition device using a computer for subsequent data processing. The air pressure of the fan was sequentially set to 0.01 MPa, 0.015 MPa, 0.02 MPa, 0.025 MPa and 0.03 MPa to simulate outbursts of varying intensities. The collected data were analyzed to compare the pressure wave signal trends under different conditions and to summarize the impact of coal and gas outbursts of different intensities on the pressure waves in the ventilation system. The experimental results are analyzed as follows.

4.1. Analysis of Waveform Characteristics

To analyze the propagation dynamics of static pressure waves (S-waves) and dynamic pressure waves (D-waves), original pressure signal waveforms under various outburst intensities were plotted. For optimal clarity, the maximum outburst intensity of 0.030 MPa was selected for detailed analysis. Figure 3 illustrates the raw pressure signals at monitoring points A, B, and C over a 300 ms period. Given that Point A is located merely 0.5 m from the disaster source, the pressure wave reaches it first, followed sequentially by Points B and C.

As observed from the waveform curve diagram (shown in Figure 3), both static and dynamic pressures fluctuate around stable baselines prior to the outburst. Upon the event, both pressures rise abruptly to their peak values. The S-waves peaked at Point A at 100 ms with a maximum pressure of 96,094.91 Pa. Subsequently, it peaked at Point B at 112 ms (95,849.68 Pa) and at Point C at 120 ms (95,878.33 Pa), demonstrating a clear temporal delay. Conversely, the D-wave peaked at Point A earlier, at 88 ms, with a value of 12.06 Pa, followed by Point B at 122 ms (3.09 Pa) and Point C at 138 ms (1.70 Pa).

As shown in Figure 3, following the primary peak, the static pressure rapidly attenuates. Concurrently, the dynamic pressure experiences a sharp decay, dropping into negative values before returning to its initial baseline. Notably, the static pressure exhibits a secondary rise before eventually stabilizing. This phenomenon occurs because an outburst is not an instantaneous pulse but a continuous process; the initial violent burst generates the primary pressure wave, while subsequent weaker gas releases generate successive, attenuating waves. Consequently, the static pressure at each monitoring point rises twice before its fluctuations gradually dampen to a stable state.

To investigate the waveform characteristics and the effect of propagation distance on amplitude, the static (S-wave) and dynamic (D-wave) pressure signals across the three monitoring points were analyzed. For optimal clarity, the maximum outburst intensity of 0.030 MPa was selected for this comparison (Figure 4). As illustrated, upon the occurrence of an outburst, the dynamic pressure in the roadway surges to its peak, plummets significantly below the initial baseline, and subsequently recovers. This fluctuation profile closely resembles a complete sinusoidal wave, characterized by a distinct peak and valley. Concurrently, the static pressure also exhibits a sharp increase; however, post-peak, it decays only to a slightly lower plateau before eventually stabilizing, thereby exhibiting a half-sinusoidal profile.

To quantitatively substantiate these waveform characteristics, a detailed mathematical characterization and curve-fitting analysis were performed on the raw discrete pressure data using the 0.030 MPa outburst scenario. Initially, the absolute pressure readings were normalized to relative pressure fluctuations ($\Delta P$). Key quantitative parameters, including rise time ($t_r$), decay rate ($\lambda$), and shape factor ($K_f$), were then extracted. The rise time, defined as the duration required for the amplitude to increase from 10% to 90% of its peak, was calculated at monitoring Point A to be 24.00 ms for the D-waveand 32.00 ms for the S-wave. The decay rate ($\lambda$) serves as a crucial metric for evaluating energy dissipation during propagation. As shown in

Table 3. Quantitative waveform parameters at points A, B, and C under 0.030 MPa outburst intensity.

Monitoring Point	Wave Type	Rise Time ${\mathit{t}}_{\mathit{r}}$ (ms)	Decay Rate $\mathit{\lambda }$ (pa/ms)	Shape Factor  ${\mathit{K}}_{\mathit{f}}$	Curve Fitting  ${\mathit{R}}^2$
A	S-wave	32.00	19.4833	1.515	0.559
	D-wave	24.00	0.3344	1.416	0.692
B	S-wave	24.00	16.5745	1.641	0.474
	D-wave	22.00	0.0211	1.137	0.329
C	S-wave	22.00	4.5710	1.495	0.455
	D-wave	28.00	0.0082	1.369	0.385

, both wave types exhibit a pronounced attenuation trend with increasing distance from the source. Specifically, the S-wave decay rate decreases from 19.4843 Pa/ms at Point A to 4.5710 Pa/ms at Point C. Similarly, the D-wave decay rate plummets from 0.3344 Pa/ms at Point A to a mere 0.0082 Pa/ms at Point C. This drastic reduction quantitatively demonstrates that the pressure fluctuations lose intensity and the waveforms effectively “flatten” as they propagate deeper into the roadway, fully consistent with the energy dissipation induced by wall friction and aerodynamic resistance.

Furthermore, the shape factor ($K_f$), defined as the ratio of the root-mean-square amplitude to the average amplitude over a single wave cycle, was computed. For an ideal sinusoidal or half-sinusoidal wave, the theoretical $K_f$ is approximately 1.11. The calculated $K_f$ values ranged from 1.495 to 1.641 for the S-waves, and from 1.137 to 1.416 for the D-waves. Although these empirical values deviate slightly from ideal mathematical constants due to experimental noise and fluid-solid coupling effects, they remain fundamentally consistent with the characteristics of sinusoidal waveforms. The complete quantitative parameters for all monitoring points are summarized in Table 3. Finally, to mathematically verify the observed waveform patterns, standard curve fitting was applied to the normalized experimental data. The D-wave fluctuations were fitted using a damped sinusoidal model, whereas the S-wave data were fitted with a half-sine model. The curve fitting yielded reasonable coefficients of determination ($R^2$ ranging from 0.329 to 0.692). Ultimately, this mathematical characterization, grounded in raw temporal data, substantiates the previous qualitative observations while reflecting the complex dynamics of disaster propagation.

A quantitative comparison of the temporal wavelengths of pressure waves at the three points was conducted to verify their propagation characteristics. To accurately represent the temporal wavelength of the main pressure pulse and mitigate the interference of long-tail turbulence, the Full Width at Half Maximum (FWHM) was introduced as a robust statistical metric. For the static pressure waves (S-waves), the calculated temporal wavelengths at points A, B, and C were 40.0 ms, 32.0 ms, and 38.0 ms, respectively. Statistical error analysis revealed a mean temporal wavelength of 36.67 ms with a standard deviation of 3.40 ms. The coefficient of variation is exceptionally low at 9.27% (<10%), providing strong statistical evidence that the wavelength of S-waves does not change significantly with increasing propagation distance. Similarly, the temporal wavelengths of the dynamic pressure waves (D-waves) at points A and B are highly consistent (32.0 ms and 30.0 ms, respectively). Although the D-wave experiences wavelength broadening at the furthest point C (76.0 ms), due to dynamic energy dissipation, the overall wavelength scales remained structurally coherent.

Additionally, regarding the wave energy (shown in Figure 4), the maximum amplitude at point A was 96,930.23 Pa, at point B were 96,798.43 Pa, and at point C were 96,539.94 Pa, indicating that the amplitude of the static pressure wave (S) decreases with increasing distance. When comparing the dynamic pressure fluctuations at the three points, it can be observed that point A, which is closer to the outburst source, experienced drastic pressure oscillations, characterized by a precipitous rise followed by a rapid drop into negative pressure regimes. In contrast, the fluctuations at Points B and C were significantly dampened; nevertheless, dynamic pressure variations remained discernible, with the amplitude at Point C being notably lower than that at Point B. This attenuation trend is consistent with the results for static pressure waves.

Overall, it can be concluded that the temporal wavelength of pressure waves remains relatively constant as the propagation distance increases, whereas their amplitudes undergo progressive spatial attenuation with increasing distance.

To further investigate the relationship between pressure wave amplitude and initial outburst intensity, waveform profiles at various monitoring points were analyzed across a range of simulated intensities (Figure 5). The data illustrate that at the maximum tested outburst intensity of 0.030 MPa, the peak amplitudes of both static (S-waves) and dynamic (D-waves) pressure waves reached their absolute maxima across all monitoring points. Conversely, at the minimum simulated intensity of 0.010 MPa, the corresponding amplitudes recorded their lowest values. These findings conclusively demonstrate a strong positive correlation between the amplitude of the propagating pressure wave and the severity of the initial outburst.

4.2. Spectral Analysis of Coal and Gas Outburst Disasters

To systematically investigate the frequency components dominating pressure wave propagation across different monitoring points, Fourier transform analysis was applied to the acquired temporal signals. Specifically, experimental data corresponding to the maximum outburst intensity of 0.030 MPa were selected to extract frequency-domain amplitudes and construct the corresponding spectral profiles (Figure 6). The left and right panels of Figure 6 present the amplitude spectra for the static (S-wave) and dynamic (D-wave) pressure signals, respectively, across the three monitoring locations. The subsequent analysis primarily focuses on the spatial evolution of these frequency components as propagation distance increases.

The spectral curves clearly reveal that the energy of the pressure wave signals is predominantly concentrated in the low-frequency band. For the D-wave, the average amplitude peaked at 0.45 Pa at 0.20 Hz and dropped to 0.103 Pa at 0.40 Hz. Amplitudes at higher frequencies were uniformly below 0.1 Pa, essentially merging with the background noise. This prominent low-frequency peak rapidly decays toward zero as frequency increases, confirming that the signal’s energy is highly localized within the low-frequency spectrum.

In comparison, the S-wave spectrum exhibits a broadly similar low-frequency dominance but possesses significantly higher peak amplitudes, particularly at Point A (closest to the outburst source). This indicates that the S-wave retains substantially greater energy near the origin. When evaluating spatial attenuation, the D-wave amplitude at Point A is markedly higher than those at Points B and C, especially within the dominant low-frequency band. Conversely, the S-wave spectral curves across the three points nearly overlap, showing no significant spatial divergence. This observation confirms that propagation distance exerts a profound influence on the frequency-domain characteristics of D-waves, while its effect on S-waves is relatively marginal. This macroscopic difference is deeply rooted in their underlying physical mechanisms: D-wave attenuation is driven by strong nonlinear compression and severe thermal dissipation, which stems from the conversion of kinetic energy into heat via fluid viscosity, intense gas turbulence, and frictional resistance against the roadway walls during high-velocity propagation. These processes constitute typical high-order energy loss mechanisms. In contrast, S-waves are governed by weak linear viscous damping; consequently, they are significantly less susceptible to spatial decay, maintaining highly stable waveform and energy signatures over longer distances.

4.3. Analysis of Propagation Speed

When investigating the propagation dynamics of disaster-induced pressure waves in underground roadways, wave velocity serves as a critical physical parameter. To calculate the velocities of the static (S-waves) and dynamic (D-waves) pressure waves, the original pressure waveform profiles were plotted across the three monitoring points under various outburst intensities. To accurately determine these velocities, the peak arrival time was rigorously identified by extracting the time coordinate corresponding to the absolute maximum amplitude (${\left|\Delta P\right|}_{max}$) of the primary pressure pulse. Additionally, a standard moving average filter was applied to the raw discrete time-series data prior to peak extraction to prevent high-frequency experimental noise spikes from causing false identifications. Figure 7 illustrates the waveform characteristics of both waves at the three points under the 0.030 MPa outburst intensity. Notably, as detailed in the updated Table 2, monitoring Point C is located 8.0 m from the outburst source. Therefore, the effective propagation distance between Point A (located at 0.5 m from the source) and Point C is explicitly calculated as 8.0 m − 0.5 m = 7.50 m in the 1:30 scaled laboratory model.

According to Formula (1), the theoretical propagation speed of standard acoustic waves in the roadway is approximately 340 m/s. However, experimental calculations reveal specific behaviors for outburst waves. For the S-wave, the peak arrival time was 100 ms at Point A and 118 ms at Point C. Conversely, the D-wave peaked at 88 ms at Point A and 114 ms at Point C. Using these transit times over the 7.50 m calculated distance, the propagation velocities under this specific intensity were calculated to be 416.67 m/s for the S-wave and 288.46 m/s for the D-wave. This methodology was systematically applied across all experimental conditions.

Table 4. Time and wave velocity from point A to point C under different outburst intensities.

Intensity of Outburst	S-Wave		D-Wave
	Time	Wave Velocity	Time	Wave Velocity
0.030 MPa	18 ms	416.67 m/s	26 ms	288.46 m/s
0.025 MPa	18 ms	416.67 m/s	26 ms	288.46 m/s
0.020 MPa	19 ms	394.74 m/s	26 ms	288.46 m/s
0.015 MPa	20 ms	375 m/s	28 ms	267.85 m/s
0.010 MPa	20 ms	375 m/s	28 ms	267.85 m/s

summarizes the transit times and resulting velocities from Point A to Point C under varying outburst intensities. To establish a representative baseline for overall wave propagation behavior, the arithmetic mean of the velocities from the five distinct intensity levels was computed. The results demonstrate that the overall mean velocities of the S-waves and D-waves are 395.67 m/s and 280.27 m/s, respectively. Consequently, it is evident that the static pressure wave propagates significantly faster than the dynamic pressure wave.

It is noteworthy that the calculated velocities exhibit significant variation across different outburst intensities (S-wave velocities range from 375.00 m/s to 416.67 m/s). Given the high-frequency sampling rate of the data acquisition system, the maximum potential time-resolution error is minimal. The observed velocity variance of over 40 m/s drastically exceeds the boundaries of any measurement error, confirming that this variability is a statistically significant phenomenon driven by physical principles rather than random experimental fluctuation. According to gas dynamics, unlike an infinitesimal acoustic wave (340 m/s), an outburst pressure wave acts as a finite-amplitude compression wave. Higher outburst intensities generate more violent initial gas expansion and stronger compression effects on the roadway air. This intense compression increases the local gas density and temperature at the wave front, naturally resulting in a faster propagation velocity.

It should be emphasized that all results are obtained from a 1:30 scaled laboratory model with a limited monitoring distance of 7.50 m. Due to differences in geometric scale, wall roughness, and field boundary conditions, these velocity results reveal the propagation mechanism in the scaled model and cannot be directly extrapolated to long-distance propagation in actual mine roadways.

4.4. Discussion

In this study, we investigated the propagation characteristics of pressure waves under coal and gas outburst conditions, with particular focus on waveform features and propagation velocity. The results demonstrate that following an outburst, the pressure within the roadway increases dramatically, with both static and dynamic pressures rapidly reaching their peak values. Subsequently, the static pressure decreases to its initial state and then exhibits an alternating pattern of peaks and troughs before gradually stabilizing. In contrast, the dynamic pressure shows a sharp decline to negative pressure after reaching its initial peak, followed by similar oscillatory behavior before eventually stabilizing.

These findings show remarkable consistency with the physical simulation experiments conducted under different permeability conditions in reference [6], which investigated the spatiotemporal evolution characteristics of outburst shock waves in roadways. The experimental results revealed a consistent evolution pattern in the shock wave over-pressure curve: a rapid rise to peak pressure, followed by a sharp decline to negative phase pressure, then oscillatory behavior, and finally gradual stabilization. This trajectory aligns exceptionally well with the pressure waveform characteristics documented in our current study, thereby cross-validating our experimental approach.

Furthermore, the measured propagation velocities of S-waves (395.67 m/s) and D-waves (280.27 m/s) are both close to the speed of sound in air under similar environmental conditions, which is consistent with the classical theoretical prediction of pressure wave propagation in confined spaces. This consistency verifies the rationality and reliability of the experimental data. The pressure waves measured in this study are the attenuated form of outburst-induced shock waves, and their propagation laws can reasonably reflect the real mechanism of disaster-induced wave propagation in mine roadways.

5. Conclusions

This study systematically investigated the propagation characteristics of pressure waves induced by coal and gas outbursts using a 1:30 scaled laboratory mine ventilation network model. By applying similarity scaling laws to safely simulate outburst events with proportionally reduced initial pressures, this research provides a vital experimental basis for disaster monitoring. The main conclusions and contributions are summarized as follows:

(1)

Waveform Signatures and Attenuation: The static pressure wave exhibits a half-sinusoidal profile, while the dynamic pressure wave presents a complete sinusoidal pattern. Quantitative statistical analysis using the Full Width at Half Maximum (FWHM) confirms that the temporal wavelength of the S-waves remains highly consistent (CV < 10%) and is independent of propagation distance within the limited range of this experiment. Furthermore, wave amplitude is positively correlated with the initial outburst intensity and attenuates progressively as the distance from the source increases.

(2)

Frequency Domain Characteristics: Fourier transform analysis reveals that the primary energy of the pressure waves is concentrated in the ultra-low-frequency range (below 1.0 Hz). Furthermore, the propagation distance exerts a more significant morphological distortion effect on the D-waves compared to the S-waves.

(3)

Propagation Velocity and Gas Dynamics: Driven by the principles of gas dynamics, the outburst-induced pressure waves behave as finite-amplitude compression waves. Consequently, the propagation velocities vary with outburst intensity. The overall mean velocity of the S-waves (395.67 m/s) demonstrably exceeds the standard speed of sound in air due to localized gas compression effects at the wave front. In contrast, the D-waves propagate at a comparatively slower overall mean velocity (280.27 m/s).

Practical Implications: Studying full-scale destructive shock waves poses immense challenges for sensor survivability. By utilizing similarity ratios to proportionally reduce the outburst pressure, this study successfully captured the specific waveform signatures, propagation velocities, and attenuation laws of disaster-induced pressure waves in a non-destructive manner. These findings lay a solid foundation for developing an advanced, pressure wave-based early warning system to precisely locate and characterize underground disasters.

Limitations and Future Work: It should be emphasized that all experimental results were obtained from a 1:30 scaled model with a limited monitoring distance of 7.50 m. Specifically, the physical experimental roadway is constructed from acrylic material, resulting in relatively smooth inner walls. This constitutes a significant physical boundary difference compared to the highly rough, irregular, and frictional surfaces of actual underground mine roadways. Due to this lack of realistic wall friction, combined with the proportionally reduced outburst intensity based on the similarity ratio, direct extrapolation of these quantitative parameters to full-scale real mine roadways requires caution. Moving forward, future research will focus on integrating full-scale numerical modeling to systematically correct for these scale and wall-roughness effects. Additionally, subsequent studies will investigate the waveform evolution and propagation characteristics under more complex physical conditions, specifically examining the influence of typical underground obstacles (such as mine cars, roadway supports, and conveyor belts). Ultimately, by combining these comprehensive waveform databases with machine learning algorithms, this research aims to achieve intelligent, real-time disaster recognition in practical coal mine engineering.