This paper aims to propose a novel approach to assess the multi-crack behavior of layered fiber-polymer composites. The Compliance and R-curves generated from this novel approach were useful to understand the multiple delamination process, enabling to evaluate separately the strain energy release rate (SERR) related to each crack. A cohesive zone model was developed to simulate the failure process zone of three parallel cracks in web-flange junction (WFJ) specimens extracted from a pultruded bridge deck system subjected to transverse bending. The fracture parameters estimated based on the proposed approach led to a good agreement between the numerical model and the experiments in terms of load vs. displacement curves. Moreover, it was possible to observe that the formation of new cracks may lead to a significant drop on the R-curve, due to the closure of the former cracks.