A fractal wave velocity evolution model of the water-bearing coal is constructed to explore the relationship between the complex pore and fissure structure parameters of the water-bearing coal mass and the ultrasonic P-wave velocity, based on the fractal theory and with consideration of the attenuation of ultrasonic waves propagating in the porous media of coal. In addition, experimental study and numerical analysis of the model are carried out, the following conclusions are reached. (1) The P-wave velocity increases with the increase of the coal sample length, the water content, the wave velocity in the coal matrix and the maximum pore radius, and decreases with the increase of the minimum pore radius. (2) The experimental results also show that the P-wave velocity increases with the increase of the water content and fractal dimension of the coal sample, indicating that the wave velocity prediction model has high accuracy. (3) The fractal dimension, water content, wave velocity in the coal matrix and coal sample length have great effects on the P-wave velocity of coal samples, while the minimum pore radius and the maximum pore radius have relatively little influences on the P-wave velocity.

基于分形理论，考虑以下因素，构建含水煤体分形波速演化模型，探讨含水煤体复杂孔隙和裂隙结构参数与超声纵波速度的关系超声波在煤的多孔介质中传播的衰减。此外，对该模型进行了实验研究和数值分析，得出以下结论。(1) 纵波速度随煤样长度、含水量、煤基质波速和最大孔隙半径的增加而增大，随最小孔隙半径的增大而减小。(2) 实验结果还表明，纵波速度随着煤样含水量和分形维数的增加而增加，说明该波速预测模型具有较高的精度。(3) 分形维数、含水量、煤基质中的波速和煤样长度对煤样的纵波速度影响较大，而最小孔隙半径和最大孔隙半径对P的影响相对较小- 波速。