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Author: Admin | 2025-04-28
(e.g., heat, friction, etc.), and is usually 0 η ≤ 1.Assuming that the elastic strain energy density is uniformly distributed throughout the rupture process, i.e., U is approximated to be constant within the volume V, the total elastic strain energy can be simplified as: where V is the volume of the rupture region. Therefore, the microseismic energy Em can be expressed as:Combined with the definition of the strain energy density U, the above equation becomes: E m = η ( 1 2 K ( Δ V ) 2 + 1 2 G γ 2 ) ⋅ V (8) This equation states that the microseismic energy is related to the volume within the rupture region, the volumetric strain, the shear strain, the bulk and shear moduli of the material, and the conversion efficiency factor η.Microseismic signals are essentially caused by elastic wave propagation. The energy of an elastic wave is related to the velocity of the wave v, the density ρ, and the amplitude of the fluctuation A. For a one-dimensional elastic wave, the expression for the fluctuation energy is [31,32]: E w a v e = 1 2 ρ V v 2 A 2 (9) where: ρ is the density of the medium; ν is the propagation speed of the elastic wave; A is the amplitude; V and is the rupture volume.From the perspective of elastic fluctuation energy, the microseismic energy is a square function of the amplitude during elastic wave propagation and is positively correlated with the rupture volume, density, and wave velocity [30]. Combined with the derivation of the microseismic energy, assuming that most of the strain energy released during rupture propagates through the elastic wave, the microseismic energy can be approximated to be equivalent to the fluctuation energy expression, so as to establish a connection between the two in the framework of energy conservation [33,34,35].Through the above derivation, we obtain: E m = η 1 2 K Δ V 2 + 1 2 G γ 2 · V (10) This suggests that the microseismic energy Em is the energy released from the elastic strain energy within the ruptured volume V of the rock through the fluctuating form. The conversion efficiency coefficient η reflects the possible dissipation factors (e.g., heat, friction, plastic deformation, etc.) during the conversion of strain energy to microseismic energy [32]. This theoretical derivation shows that the elastic strain energy stored in rocks can serve as the primary source of microseismic energy. In the context of energy conservation, microseismic energy can be seen as the outcome of the release of this stored strain energy via the propagation of elastic waves.Based on the above principle that the elastic strain energy of rock is the main source of microseismic energy, the FISH language is compiled and applied to the simulation solution of FLAC3D for roadway mining to derive the elastic strain energy energy cloud. 4.5.2. Comparison and Verification of Simulation ResultsTo validate the reliability of the simulation results, the coordinates of the microseismic event gathering points from
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