The major processes that occur when level ice interacts with sloping structures (especially wide structures) are the fracturing of ice and upcoming ice fragments accumulating around the structure. The cohesive zone method, which can simulate both fracture initiation and propagation, is a potential numerical method to simulate this process. In this paper, as one of the numerical methods based on the cohesive zone theory, the cohesive-element–based approach was used to simulate both the fracturing and upcoming fragmentation of level ice. However, simulating ice and sloping structure interactions with the cohesive element method poses several challenges. One often-highlighted challenge is its convergence issue. Numerous attempts by different researchers have been invested in this issue either to prove or improve its convergence. However, these researchers work in different fields (e.g., fracture of concrete, ceramic, or glass fiber) with different scales (e.g., from a ceramic ring to a concrete block). As an attempt to study the cohesive element method's application in the current ice-structure interaction context (i.e., an engineering scale up to hundreds of meters), the mesh dependency of the cohesive element method was alleviated by both creating a mesh with a crossed triangle pattern and utilizing a penalty method to obtain the initial stiffness for the intrinsic cohesive elements. Furthermore, two potential methods (i.e., introduction of a random ice field and bulk energy dissipation considerations) to alleviate the mesh dependency problem were evaluated and discussed. Based on a series of simulations with the different aforementioned methods and mesh sizes, the global ice load history is obtained. The horizontal load information is validated against the test results and previous simulation results. According to the comparison, the mesh objectivity alleviation with different approaches was discussed. As a preliminary demonstration, the results of one simulation are summarized, and the load contributions from different ice-structure interaction phases are illustrated and discussed.