The swift computation of geometric morphology and volume parameters of debris flow barrier dams is crucial for assessing dam stability and potential damage, aiming to reduce losses to life and property. In this study, the key parameters influencing river blockage by debris flow were integrated into six dimensionless factors. Through laboratory flume experiments and theoretical analysis, we examined the damming process and characteristics of debris flow barrier dams across various river blockage modes. The results revealed that: 1) Based on the characteristics of the river-blocking process by debris flows, the complete river-blocking mode is further refined into two types: the head-on collision mode and the continuous advancement mode. 2) The three-dimensional morphology of debris flow barrier dams differs under different river blocking modes. In the case of partial river-blocking mode, the horizontal projection of the dam body is fan-shaped, and the vertical profile is arch-shaped. For the head-on collision mode, the horizontal projection is trumpet-shaped or gourd-shaped, with the lowest point on the vertical profile being random. In the continuous advancement mode, the horizontal projection is trapezoidal or elongated, with the lowest point on the vertical profile located on the opposite bank. The cross-sectional shapes of the three river blocking modes conform to a Gaussian normal distribution. 3) Combining previous research with static equilibrium analysis and three-dimensional geometric analysis, we proposed a rapid prediction model for the geometric morphology and volume of debris flow barrier dams under different river blocking modes, which was successfully applied to the river-blocking event in Tianmo Gully on July 11, 2018, with a calculation error within 25%. The model in this study is based on the actual morphology of debris flow barrier dams, resulting in more accurate calculations.