Permeability estimate of underground long-wall goaf from P-wave velocity and attenuation by lab-scale experiment on crushed rock samples

In this study, forty-five crushed rock samples were formed from rock and coal particles of different sizes to simulate the crushed and fragmented condition of a goaf area in an underground coal mine. The porosity (φ) range of the crushed samples was based on field observations in actual goafs. The permeability (k) was measured by reducing the size of the fragments of the actual goaf to lab-scale particles. Ultrasonic wave velocity (V_PG) and attenuation (β) were measured for different porosities, particle sizes and frequencies. The ratio of the seismic wavelength and particle size was adjusted to match that of the parameters in the goaf. The results showed that the measured permeability conformed to the Kozney-Carman (K–C) equation with a percolation threshold porosity of 0.06. The permeability of the crushed rock was dependent on φ⁴. The variations of the seismic velocity (η) and attenuation (ξ) were defined based on the ratio of the seismic parameters of the crushed rock and intact rock. η showed a linear relationship with the square root of the tortuosity (τ) for τ = 5–10. ξ showed an approximately linear relationship with the porosity part of the K–C equation. An empirical equation is proposed based on the K–C equation, involving the seismic velocity, attenuation and particle size. The estimated permeability based on the modified K–C equation showed good agreement with the measured data. The permeability of the actual goaf was estimated as 1.0 × 10⁴–6.5 × 10⁵ d based on the rock properties in the goaf.