Strong nonlinear effects, such as wave slamming, suction effects, and wave overtopping, may be induced during wave-bridge interaction. However, an accurate understanding of these nonlinear effects is still insufficient. This study comprehensively investigates the wave slamming and suction effects on pier-pile group foundations of sea-crossing bridges in a 1:50 scale laboratory experiment. Random and regular waves with different strengths are generated based on wave conditions at the bridge site. Five water depths with a 2 cm spacing are designed to simulate varying pile cap clearances. Various pile arrangements are also set up to explore the influence of piles. Results show that wave slamming is low-aeration and is triggered mainly on the cap bottom wall, whereas the wave action on the vertical wall of the pile cap is quasi-static. The suction effect is generally recorded in the quasi-static phase of pressures and depends on the water exit process and the wave crest height. Moreover, the pressure oscillation after the impact phase results from the flow separation and rotation at structure corners. The wave slamming enhances with the increasing wave frequency when the impact area is constant, otherwise, it depends on the impact area. On the cap bottom wall, the wave slamming on inter-pile areas is enhanced, but the suction effect is less affected by pile arrangements. The increase in pile cap clearances reduces vertical forces but has less effect on horizontal forces. Additionally, a sustained increase in the wave crest height may reduce the slamming force. An empirical method for predicting wave forces is finally proposed based on the water entry theory and experimental findings. This work enhances the physical understanding of nonlinear effects during wave-bridge interaction and aims to support the design of substructures for sea-crossing bridges.