Measurement of the attenuation coefficient of acoustic signals generated by an operating roadheader in a coal mine

Introduction

Acoustic methods are widely used in mining to investigate rock-mass structure and properties, monitor various technological processes, and assess safety under the influence of various factors [1–3]. Among these methods, those used for operational prediction of gasogeodynamic phenomena (GGP) form a distinct group. This group, in turn, comprises two main subgroups. The first is based on recording acoustic emission from the near-face region of workings being driven [4–6]. The second relies on spectral analysis of acoustic signals generated either by operating mining equipment or by an impact source [7–9]. The impact source may be a sledgehammer or hammer¹, or a purpose-built drop-weight device in which a metal weight of known mass is dropped from a fixed height [10].

The main parameters used in acoustic investigations for regional, local, and operational GGP prediction are oscillation frequency and energy, wave propagation velocity, and attenuation in the monitored medium. These parameters must therefore be known for computer modeling of acoustic-wave propagation aimed at improving GGP prediction methods. In addition to the characteristics of the acoustic source, however, these parameters depend strongly on the structure, composition, physical and mechanical properties, and stress state of the specific part of the rock mass under investigation. These factors govern the generation, propagation, and attenuation of acoustic waves. Methods capable of rapidly determining these parameters experimentally are therefore required.

The operating frequency range is a key characteristic of acoustic signals. On the one hand, it determines the resolution of the method when monitoring rock-mass structure: the higher the frequency, the smaller the discontinuities that can be identified. On the other hand, the frequency range determines the acoustic attenuation coefficient and, consequently, the effective range of the monitoring method. The higher the frequency, the greater the acoustic attenuation coefficient and the shorter the effective monitoring range. For example, earthquakes are recorded at large source–receiver distances at very low frequencies of 0.001–16 Hz, whereas rockbursts within a mine field are recorded at frequencies ranging from a few hertz to several hundred hertz [11, 12]. Operational GGP prediction in coal mine workings using the method based on the parameters of an artificial acoustic signal employs a frequency range from a few hertz to 5 kHz when a piezoelectric transducer is used for signal acquisition [7–9]. In practice, however, strong signal attenuation at high frequencies and the operating characteristics of the acoustic receivers limit the usable range to 1.5–2.0 kHz. Thus, the acoustic attenuation coefficient depends on the type of acoustic receiver used, the rock-mass structure, its strength properties, and the stress state of the specific part of the coal–rock mass under investigation.

The objective of this study was to justify an algorithm for measuring the acoustic attenuation coefficient under mine conditions over the frequency range used for GGP prediction.

The following tasks were addressed:

1. Identify the factors and parameters governing the attenuation coefficient of acoustic signals generated by an operating roadheader in a coal–rock mass.
2. Synchronously record, using several sensors installed at different distances from the face of a development heading, the time history of acoustic signals generated by the roadheader cutting head.
3. Determine the spectrum of the recorded signals from the data obtained.
4. Analyze the results and propose an algorithm for determining the effective attenuation coefficient of the noise generated by an operating roadheader.

¹ Guidelines. Method for acoustic sounding of a rock mass using a hardware and software system. Moscow: Intersectoral Research and Engineering Laboratory for the Development, Manufacture, and Implementation of Automated Systems in the Mining Industry (MNTL RIVAS); 2016. 36 p. (In Russ.)

Parameters and factors governing acoustic-wave attenuation in a rock mass

The acoustic sources monitored using the above GGP prediction methods – cracks undergoing discontinuous growth and the noise generated by mining equipment cutting coal or rock – emit longitudinal and shear waves over a broad frequency range. These wave types differ in propagation velocity and attenuation coefficient, both of which depend strongly on the physical and mechanical properties, thermodynamic state, and structural characteristics of the rock mass [11–13]. Various sources report that the longitudinal-wave velocity is 1.5–2.5 times [14] or 1.7–1.9 times [15] the shear-wave velocity. The attenuation coefficient in solids and rock masses is approximately directly proportional to frequency [15–17] and inversely proportional to stress in the rock mass [18]. The attenuation coefficient of shear waves is generally lower than that of longitudinal waves [19]. For example, experiments have shown that “the shear-wave amplitude along the axis of the main lobe of its directivity pattern is generally 1.5–2 times that of the longitudinal wave in the same direction” [14].

The acoustic signal from a monitored source, as recorded by seismic receivers, is affected by numerous factors, including the layered structure of the rock mass, the presence of discontinuities and various heterogeneities, the stress state, the operational parameters of mining activities, and the simultaneous operation of other acoustic sources [20–22].

The layered structure of the coal–rock mass causes the coal seam to act as a waveguide. If the acoustic source is also located within the coal seam, most of the energy emitted by the source is concentrated in the seam rather than in the host rocks. Interference among longitudinal and shear waves and their reflections from interfaces between layers of contrasting acoustic impedance, together with possible mode conversion, gives rise to a channel wave in the coal seam [1].

The waveguide behavior of the coal seam also filters the full spectrum of the emitted signal, preferentially transmitting the harmonics with the lowest attenuation. Seam thickness determines the predominant frequency range recorded because it is an integer multiple of the half-wavelengths of the least attenuated harmonics. Accordingly, as seam thickness increases, the spectrum of harmonics filtered by the rock mass shifts toward lower frequencies. Conversely, as seam thickness decreases, the filtered harmonics shift toward higher frequencies.

Real acoustic sources, however, have relatively broad directivity patterns. Part of the acoustic energy is therefore refracted at the interfaces between the coal seam and the host rocks. These waves are subsequently reflected from interfaces between layers of contrasting acoustic impedance or from various heterogeneities and return to the coal seam. Because their propagation paths are longer than those of the direct longitudinal and shear waves, they arrive later. This time delay is evident when the signal source is impulsive. In particular, these additional oscillations in the tail of seismic signals generated by powerful impulsive sources such as earthquakes are known as coda waves [23].

With a continuous source and at short distances from the source, the longitudinal, shear, and coda waves cannot be resolved separately. Their harmonic components nevertheless interfere to form the resultant wavefield.

Because the resultant wavefield is produced by interference among these wave types, signal attenuation is evaluated in terms of an effective attenuation coefficient [1].

Acoustic-wave attenuation during propagation through a rock mass is caused primarily by energy absorption due to internal friction, energy scattering by heterogeneities in the medium, and geometrical spreading governed by the source radiation pattern [19]. Taking these factors into account, the signal amplitude at a given distance from the source can be expressed either as a function of the propagation time t to the receiver or as a function of the source–receiver distance r. In the first case, the amplitude of the resultant seismic wave A(f, t) at frequency f and time t can be written as follows [11]:

where S(f, t) is the source time function at frequency f and time t; γ is a dimensionless parameter characterizing geometrical spreading and is equal to 1.0, 0.5, or 0.75 for body, surface, and diffuse waves, respectively [11]; and Q(f) is the effective seismic quality factor. The function t^−γ is determined by the source radiation pattern and describes the geometrical spreading of radiated energy with time. At a fixed harmonic, the quality factor characterizes the relative loss of wave energy due to internal friction over one oscillation period. The quality factor increases as the relative energy loss decreases. The effective seismic quality factor characterizes this process for the entire wave packet.

In the second case, the amplitude of the resultant wave A(f, r) t distance r from the source can be written as follows [19]:

A(f, r) = A₀(f) ∙ R(r) ∙ exp [−α_eff(f)∙r], (2)

where A₀(f) is the resultant-wave amplitude at the source; R(r) is the geometrical-spreading function; α_eff(f) is the effective attenuation coefficient of the resultant wave produced by interference.

The exponential terms in square brackets in Eqs. (1) and (2) describe the same attenuation in the two representations of the resultant-wave amplitude and can therefore be equated. Substituting t = r/V, into the exponent in Eq. (1), where V is the effective velocity of the resultant wave, yields the following relationship between the effective attenuation coefficient and the effective seismic quality factor:

Modeling acoustic-wave attenuation with distance requires knowledge of the function R(r). For an acoustic source with a small radiating area located on the surface of a mine working, the radiation pattern at low frequencies can be approximated as spherical; that is, sound propagates in nearly all directions. In this case, R(r) = 1/r [19]. At high frequencies, the spreading function more closely approximates that of a plane wave [14], for which R(r) ≈ 1 [19]. Because the resultant wave generated by a crack undergoing discontinuous growth or by operating mining equipment contains a broad frequency spectrum, the spreading function may be represented as:

R(r) = r⁻ⁿ, (4)

where 0 < n < 1.

Based on experimental findings, cylindrical geometrical spreading, for which R(r) = 1/√r, was assumed in Refs. [1, 24]. Those studies, however, primarily examined ultrasonic waves. It may therefore be assumed that, in the frequency range of 0–1.5 kHz, a roadheader cutting head or drill rod generates a wave whose radiation pattern, depending on the harmonic frequency, is intermediate between spherical and cylindrical.

Eqs. (1) and (2) indicate that the resultant-wave amplitude decreases monotonically with increasing distance from the source. Experimental data reported in several studies, however, show departures from this relationship. In ultrasonic sounding of a rock mass, such departures are particularly pronounced at short source–receiver distances [14]. A nonmonotonic variation in wave amplitude with distance should produce a corresponding nonmonotonic variation in the effective attenuation coefficient. This behavior is demonstrated below using experimental results obtained over the frequency range employed for operational GGP prediction using the method based on artificial acoustic signal parameters.

Experimental determination of the attenuation coefficient

During operational GGP prediction at a Kuzbass mine using the method based on artificial acoustic signal parameters, a nonmonotonic variation in the amplitude of the noise generated by an operating roadheader was experimentally recorded over source–receiver distances ranging from 11 to 67.7 m. Roadheader noise was recorded using the Mikon-GEO hardware and software system and six seismic receivers (SRs) installed 11, 21, 31, 47.7, 57.7, and 67.7 m from the roadway face. The experimental conditions are described in Ref. [25].

The signal amplitude recorded by SR 6, the most distant receiver, was found to be comparable to the background acoustic noise level measured when the roadheader was not operating. Signals from this receiver were therefore excluded from further analysis. Fig.1 shows the initial signal spectra from the remaining five SRs before the subsequent averaging of harmonic amplitudes over the frequency and time windows considered below. The spectra were obtained using a fast Fourier transform with a frequency resolution of 1 Hz, and the amplitudes of the corresponding harmonics were averaged over 1-min time windows.

Fig. 1. Initial signal spectra recorded by SRs 1–5

The data also show that, under the experimental conditions, the signal amplitude at frequencies above 1200 Hz was comparable to the noise level recorded when the roadheader was not operating. Subsequent analysis was therefore restricted to the frequency range of 1–1200 Hz.

Fig. 1 shows, for example, that in the low-frequency range of 0–100 Hz, the harmonic amplitudes recorded by SR 2, which was farther from the source, were greater than those recorded by the closer SR 1. The amplitudes recorded by SR 5 also exceeded those recorded by SRs 3 and 4. As the frequency increased and the harmonic amplitudes recorded by all SRs decreased, the departure from a monotonic decrease in amplitude with increasing r became less pronounced.

When the distance dependence of the resultant-wave amplitude A(f, r) is expressed as in Eq. (2), the effective attenuation coefficient is calculated as follows [1]:

where α_i1 is the effective attenuation coefficient over the section between SR 1 and SR i, m⁻¹; А₁ and A_i are the harmonic amplitudes recorded by SRs 1 and i espectively, a.u.; r_i1 is the distance between SR i and SR 1, m

If the attenuation coefficient is determined from the spectrum shown in Fig. 1, it is negative at frequencies for which the amplitude recorded by a more distant SR exceeds that recorded by a closer SR. This contradicts the physical meaning of signal attenuation. To eliminate this paradoxical result, the harmonic amplitudes were averaged over frequency windows wider than 1 Hz.

Another source of variability in attenuation-coefficient estimates is the dependence of the signal spectrum on the position of the cutting head on the roadway face. Reference [25] showed that the spectra recorded during the first, third, and sixth minutes of roadheader operation differed substantially. To eliminate this effect, the spectral amplitudes were averaged over longer time windows. However, even averaging over a 9-min window did not eliminate the effect. The signal amplitude during the second 9-min interval was approximately twice that during the first interval (Fig. 2).

Fig. 2. Signal line spectra with harmonic amplitudes averaged within 20-Hz frequency windows and over 9-min time windows

The substantial difference between the signal spectra recorded during the first and second 9-min intervals was mainly attributable to changes in the distance between the acoustic source and receiver as the cutting head moved across the roadway face, variations in rock-mass fracturing as the cutting head penetrated deeper into the rock mass, possible variations in the force exerted by the cutting head on the rock mass, and the transition from cutting coal to cutting the host rock. These factors introduce variability into operational GGP prediction results. Their influence can be minimized by increasing the time over which the measured spectra are averaged. For a valid comparison of GGP prediction results obtained using geophysical and instrument-based methods, the averaging time should approximately correspond to the time required for the face to advance by the characteristic distance used in the instrument-based prediction method. This distance is 1 m—the length of the test-borehole interval used to measure the initial gas emission rate and/or drill-cuttings yield as the borehole is drilled in successive intervals. In practice, when prediction is performed using the method based on artificial acoustic signal parameters, a convenient averaging period is the duration of roadheader operation between successive roadway-support cycles, because the advance per cycle is close to 1 m. A roadheader generally requires approximately 30 min to advance the roadway by this distance.

To illustrate how the spectra change as the averaging time increases, Fig. 3 shows the spectrum of the same signal as in Fig. 2, but averaged over an 18-min interval.

Fig. 3. Signal line spectra with harmonic amplitudes averaged within 20-Hz frequency windows and over an 18-min time window

Fig. 3 shows that doubling the duration of the time-averaging window did not substantially change the distribution of harmonic amplitudes across frequency, but somewhat reduced the variability in spectral amplitudes caused by movement of the cutting head during roadheader operation between stoppages for roadway support installation. Nevertheless, the pattern persisted in the low-frequency portion of the spectrum: at some frequencies, the harmonic amplitudes recorded by more distant SRs exceeded those recorded by SRs closer to the source. Increasing the width of the frequency-averaging window from 1 Hz (Fig. 1) to 20 Hz (Figs. 2 and 3) made this pattern less pronounced but did not eliminate it. The frequency-averaging windows were therefore widened further. Fig. 4 shows the effect of this increase. The experimental points are plotted at the midpoint frequencies of the corresponding windows.

Fig. 4 shows that, with a 100-Hz averaging window, the sum of the harmonic amplitudes recorded by SR 2 in the 0–100 and 200–300 Hz windows exceeded the corresponding sums recorded by SR 1 (Fig. 4a). A similar pattern was observed for SR 3 relative to SR 1 in the 200–300 Hz window. When the averaging-window width was increased to 200 Hz (Fig. 4b), this pattern almost disappeared. It was completely eliminated when the frequency-averaging window was increased to 300 Hz (not shown).

Fig. 4. Harmonic amplitudes recorded by SRs 1–5 after averaging over 18 min and within frequency windows of (a) 100 Hz and (b) 200 Hz

By widening the frequency windows over which the harmonic amplitudes were averaged, the above nonmonotonic behavior of the roadheader-noise spectrum with distance from the source was eliminated. This made it possible to determine the effective signal attenuation coefficient for each section between SR 1 and SR i using Eq. (5). The results are shown in Fig. 5. As shown in the figure, the effective attenuation coefficient increases linearly with frequency over the range of 0–500 Hz.

Fig. 5. Frequency dependence of the effective attenuation coefficient of roadheader noise, α_{i1 ,} for the sections between SR 1 and SR i, and the corresponding mean value, α_avg

Fig. 6. Mean attenuation coefficient α_avg versus frequency f over 100–500 Hz (solid line) and the corresponding trend line extrapolated to 0–700 Hz (dashed line)

Fig. 6 shows the 100–500 Hz segment of the α_avg(f) curve presented in Fig. 5, together with the corresponding linear trend line extrapolated to 0–700 Hz (R²=0.997).

We previously proposed expressing the dependence of the attenuation coefficient on frequency and stress state as follows [8]:

where a_i  is the attenuation coefficient of the ith harmonic, m⁻¹; a₀ is the attenuation coefficient of the lowest-frequency harmonic within the geophone operating range in the absence of stress, m⁻¹; f_i and f₀ are the frequency of the ith harmonic and the lowest frequency within the operating range of the equipment, respectively, Hz; b is a parameter referred to here as the dynamic attenuation coefficient and determined by the properties of the rock mass, m⁻¹; s_lim and s_cur are the mean limiting and current stresses in the rock mass, respectively, Pa; M_min and M are the harmonic numbers corresponding to the lowest and highest frequencies within the geophone operating range, respectively.

The extrapolation equation obtained in Microsoft Excel and shown in Fig. 6 indicates that, in this case, α₀ = 0.0038 m⁻¹.

The dynamic attenuation coefficient β can be determined using the measured effective attenuation coefficients at the beginning and end of the linear segment of α_avg(f). Rearranging Eq. (6) gives:

According to the data in Fig. 6, α₀ ≈ 0.0038 m⁻¹ at a frequency close to f₀ = 1 Hz, whereas α₆₀₀ = 0.1238 m⁻¹ at a frequency close to f = 600 Hz, corresponding to the 500–700 Hz window. Substituting these values into Eq. (7) yields, for the experimental conditions,

The experiment was conducted in a section classified as nonhazardous using an instrument-based method for operational GGP prediction. Accordingly, the ratio σ_cur/σ_lim should also correspond to a nonhazardous stress state. Assuming that σ_cur/σ_lim = 0.6, substitution into Eq. (8) gives β = 0.00012 m⁻¹. For the seam section considered and the equipment used to record operating-equipment noise over the frequency range of 1–600 Hz, with f₀ = 1 Hz, Eq. (6) then takes the form:

α_i = 0.0038 + 0.00012f_i (σ_lim/σ_cur), m⁻¹; f₀ = 1 Hz; f_i ∈ [1, 600] Hz.                       (9)

It should be noted, however, that when Eq. (9) is used in algorithms for determining the GGP hazard indicator and criterion in prediction methods based on spectral analysis of operating-equipment noise, the harmonic amplitudes of the line spectrum should be averaged within frequency windows at least 200 Hz wide.

Conclusion

Acoustic signals generated by the roadheader cutting head and propagating through the near-face region of a mine working carry information about the stress state of the rock mass. The principal characteristics of these signals used to assess the rock-mass stress state are the operating frequency spectrum and the dependence of the attenuation coefficient on frequency and ground pressure.

The decrease in acoustic-signal amplitude with increasing distance from the cutting head is nonmonotonic and includes an oscillatory component. The signal spectrum also changes substantially as the cutting head moves across the roadway face and penetrates deeper into the rock mass. This reduces the reliability of attenuation-coefficient estimates. To overcome this limitation, it is proposed that the attenuation coefficient be determined from time-averaged data, with the harmonic amplitudes averaged within frequency windows.

The algorithm for determining the effective attenuation coefficient of noise generated by an operating roadheader comprises the following steps: installing several seismic receivers with identical specifications in the rib of the monitored roadway, 20–50 m from the face; simultaneously recording the acoustic signals generated by the cutting head; averaging the harmonic amplitudes over a time window corresponding to the duration of roadheader operation between successive stoppages for roadway rib support installation and within frequency windows 200–300 Hz wide; calculating the attenuation coefficient for the sections between the receiver closest to the face and each of the remaining receivers, followed by averaging the values obtained; and using these data to construct the frequency dependence of the mean attenuation coefficient and its linear extrapolation over the frequency range of 0–700 Hz, or over a wider range in which the attenuation coefficient increases with frequency. This extrapolation is then used to determine the parameters α₀ and β in Eq. (6), which describes the dependence of the effective attenuation coefficient on frequency and the stress state of the near-face region of the roadway.