Rock pipe jacking in water-rich fractured strata presents considerable construction challenges due to significant disturbance of the surrounding rock. However, the variation in rock mechanical properties and frictional resistance prediction remains inadequately studied. This study employs a combined approach of model testing, theoretical analysis, and engineering practice to investigate the variation patterns of surrounding rock pressure and displacement across different rock classes influenced by groundwater. A simplified mechanical model is proposed to represent the pipe–slurry–residue contact frictional resistance, and its validity is analyzed using model test results and engineering measurements. The findings indicate the following. (1) The lower surrounding rock classes experience more pronounced displacement variations and stress release, with groundwater further amplifying these effects. (2) The unit frictional resistance increases linearly with the groundwater correction factor, distance from the groundwater level to the pipe, and friction angle between the pipe and residue zone, while it decreases with the elastic modulus, following a power function relationship. (3) The theoretical and model test values show consistent trends in frictional resistance variation, with an average error of 9.42% in unit frictional resistance, indicating strong agreement. These findings validate the applicability of the proposed model and provide a reliable prediction range for engineering conditions. The outcomes offer a theoretical foundation and practical data for frictional resistance prediction and construction optimization in rock pipe jacking projects within water-rich fractured strata.