Abstract: During sustained debris flow impacts on water bodies, only a portion of debris particles governs the formation of maximum impulse wave amplitudes. Accurately determining the volume of these critical particles is of significant scientific and engineering value for disaster prevention and mitigation. This study utilizes a two-dimensional physical model to conduct simulation experiments on debris flow and impulse waves. By varying factors such as the debris flow slope gradient, movement path slope, water depth, debris flow initiation elevation, debris flow volume, and particle size, we investigate the mechanism of debris flow-wave interaction under multiple conditions and derive a prediction formula for the maximum first-wave amplitude based on effective wave-making volume. Key findings include: 1) In debris flow-impulse wave processes, the portion of debris that enters the water before the impulse wave propagates beyond the range of water body influenced by the debris flow constitutes the effective wave-making volume, which is the primary factor determining the amplitude of the first wave in the debris flow-wave process.     2) Experimental results demonstrate that the mobility of the debris flow significantly influences the proportion of the effective wave-making volume. When slope gradients are moderate to high inclination angle and is not less than the movement path slope, the debris flow exhibits high mobility, and the proportion of effective wave-making volume reaches 50% to 100%. Conversely, at low inclination angle and is less than the movement path slope, the debris flow mobility is lower, and the proportion of effective wave-making volume is only 20% to 38%. Notably, scenarios with smaller total volumes but higher effective proportions exhibit larger maximum first-wave amplitudes compared to scenarios with larger total debris volumes but lower effective proportions. 3) A dimensionless parameter k is proposed to characterize applicability, When the value of k is within the range of 0.10 to 2.59, the derived calculation formula for the effective wave-making volume and the wave amplitude prediction formula demonstrate strong applicability. These findings provide a theoretical foundation for understanding disaster mechanisms in debris flow-impulse wave hazard chains and for designing protective engineering measures.

Key words: debris flow, impulse wave, rigid body, effective wave-making volume