Simulation Research on Energy Evolution and Supply Law of Rock–Coal System under the Influence of Stiffness

The energy supply effect caused by the stiffness difference between roofs and sidewalls is an important factor that induces strain coal bursts. In order to quantitatively reveal the energy supply mechanism of strain coal bursts, this paper first establishes a coal burst energy model of the rock–coal system and proposes the calculation formula of coal burst kinetic energy considering supply energy and the stiffness ratio of rock to coal. Then the whole energy evolution law of the rock–coal system with different stiffness ratios is researched by using the numerical simulation method, and the whole process is divided into three stages. With the decrease in the stiffness ratio, the elastic strain energy of the coal changes little, while its kinetic energy is negatively correlated with the stiffness ratio in a power function. Meanwhile, the elastic strain energy and kinetic energy of the rock have power function relations with the stiffness ratio, too. When the rock–coal system is fractured, the kinetic energy of the coal comes from the release of elastic strain energy from the coal and the energy supplied from the rock. The energy supply rate is between 22% and 35% when the stiffness ratio changes from 3.0 to 0.5, and they show a linear relationship, while the supplied energy has a negative power function relationship with the stiffness ratio.