In this study, relationship between peak pressure and rise time of the initial surge impact on a wall is systematically investigated after considering various experimental datasets with different scales. Since the coefficients of the relevant dimensional relationship demonstrate obvious variations among different experiments, it is difficult to obtain a universal power-law relationship. To address this limitation, normalization is considered to deduce a unified relationship between the normalized peak pressure and rise time with uniform coefficients among various experiments. Two normalization approaches employing the initial water head and the surge front velocity are developed, in which the normalization approach adopting the surge front velocity could characterize the power-law relationship for surge impact experiments without an initial water head. Statistical analysis reveals no clear differences in the initial water head-based relationship between the surge impact on vertical and inclined walls. In general, the normalization approach in terms of the initial water head performs better in establishing a unified peak pressure-rise time relationship. These findings provide valuable insights for comparison among cross-scaled surge impact data and offer practical dimensionless solutions adaptable to different experimental configurations.