Bridge structures face a critical threat from localized scour-induced damage, prompting urgent attention to civil infrastructure resilience. Prior research has primarily focused on the influence of pier shapes on scour patterns. However, the exploration of the combined effects of various debris shapes, each possessing distinct properties, on predictive scour depth models around the non-cylindrical pier has hitherto remained less researched. This study explored the complex dynamics governing local scour around bridge piers, focusing on the influence of surface and near-surface debris. This research shed light on changes in scour depth by investigating factors like pier geometries, debris arrangements, and submersion depths. The experiments and analysis revealed the effects of various pier shapes—cylindrical, square, rectangular, oblong, oval, and lenticular—on scour patterns. Different geometries influenced primary scour zones and affected areas, with square piers causing the deepest scour and lenticular ones showing shallower instances. Scour depths typically peaked upstream across geometries, but ogival and lenticular shapes exhibited unique patterns. The research also introduced a formula that integrated debris attributes into predictive scour depth modeling, validated with favorable accuracy. Ultimately, this predictive model advances scour prediction, particularly in debris-laden flows, offering valuable insights for engineering and management practices in understanding real-world scour mechanisms and hydraulic dynamics.