The study and application of soil arching theory in geosynthetic-reinforced pile-supported (GRPS) embankments have gained increasing attention, as accurate arching estimation significantly influences load-deflection behavior of structures. While most existing models rely on Rankine's earth pressure theory, which applies primarily to granular soils and neglects cohesion effects. This paper employs three-dimensional numerical simulations to examine the impact of soil cohesion on soil arching mechanisms in pile-supported embankments. Results indicate that cohesion enhances load transfer to piles, with arching efficacy increasing nonlinearly before stabilizing at higher cohesion values. Building on these findings, the ground reaction curve (GRC) model is proposed to predict arching behavior in both cohesive and non-cohesive embankments at various deformation stages. By integrating critical state soil mechanics with the concentric arch model, the transition between maximum and critical arching states is captured through changes in the mobilized friction angle with relative displacement. Model validation against two well-instrumented case studies demonstrates its accuracy, particularly in accounting for soil cohesion. Moreover, the maximum arching model better predicts GRPS embankments under small deformations (relative displacement <4 %), while the critical arching model is more suitable for large deformations (relative displacement >6 %). The proposed model effectively captures arching behavior improvements in both cohesive and non-cohesive soils.