# Numerical and Field Investigations of Tremors Induced by Thick-Hard Strata Fracture
## 2 Numerical Simulation
### Results and Analysis  
#### 2.3.1 Static Stress Evolution  
Thick-Hard Roof Fracture  
The stress redistribution characteristics in different areas of overlying strata before and after goal formation are shown in Figure 2, in which the negative and positive values represent the compressive stress and the tensile stress, respectively. Obviously, due to the fall of the fractured strata above the goat, the stress distribution at different positions of the red bed had obvious differences. High compressive stress concentration easily occurred at both ends of the red bed, and shear failure easily appeared. The central part of the red bed had a high tensile stress concentration area, which was prone to tensile failure. Due to the strata fracture, the internal stress of the overlying roof was redistributed, resulting in plenty of elastic strain energy accumulated in the surrounding rock. Once the roof fractured, it generated strong tremors. Figure 3 shows the stress redistribution characteristics around the roadway before and after the goat formation. As seen in Figure 3, the horizontal tensile stress of the two sides was concentrated after the roadway excavation. With the formation of the goat and the increase in the lateral abutment pressure, the maximum horizontal tensile stress increased from 0.4 MPa to 10 MPa. Besides, the horizontal compressive stress in the roof was transferred to the deep, and the surface varied from compressive to tensile stress. Considering the tensile strength of the coal and rock was lower than its compressive strength, the roadway surface was the most prone to tensile failure under static load, resulting in a coal split. Meanwhile, the vertical stress distribution was similar to that of the horizontal stress. After the roadway excavation, the surface tensile stress was dominant, and the local compressive stress was concentrated at the corners. After that, the concentration degree and range of the tensile stress on the roadway surface gradually increased with the bend and subsidence of the red bed above the goat, while the compressive stress gradually decreased, and thus the stability of the roadway reduced. It can be indicated that the stress around the roadway was redistributed after the excavation of the roadway, and it was gradually close to the critical instability state. After that, when the overlying thick-hard strata broke and produced strong tremors, the roadway was likely to fail and experience instability under the strong dynamic load disturbance superimposed by high static stress. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Lithology**} & **Normal** & **Tangential** & \multirow{2}{*}{**Cohesion/MPa**} & \multirow{2}{*}{**Friction Angle/\({}^{\circ}\)**} & **Tensile** \\  & **Stiffness/(GPa/m)** & & & & **Strength/MPa** \\ \hline Siltstone 1 & 30 & 12 & 1.2 & 36 & 1.54 \\ Coal & 28 & 11.2 & 1.6 & 20 & 1.2 \\ Siltstone 2 & 25 & 12 & 1.6 & 10 & 1 \\ Medium sandstone & 40 & 21 & 1.6 & 10 & 1.2 \\ Mudstone & 36 & 18 & 1.6 & 10 & 1.2 \\ Fine sandstone & 76 & 30 & 8 & 60 & 5 \\ Clay & 20 & 8 & 1.3 & 25 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Micro-parameters of the interface. Influence of Tremors on Roadway  
The velocity propagation cloud diagrams after the occurrence of a strong mining-induced tremor in the thick-hard rock layers are shown in Figure 4.  
From Figure 4, the velocity diffused outward in an arc from the four corners of the rectangular source and gradually intersected into a circle with the increasing propagation distance, with a maximum velocity of 10 m/s. At 40 ms, the stress wave reached the roadway, resulting in the rapid increase in speed from 0 m/s to 2 m/s around the roadway. As shown in Figure 5, the kinetic energy rapidly reached the peak value of \(7.5\times 10^{6}\) J within 10 ms, and then begins to decrease gradually.