Current core networks are composed of high-end routers which are connected by high-speed fibers. These optical connections are commonly overprovisioned and in low utilization. Many of them are combined together to form bundle links or composite links and the component links are referred to as sublinks. These physical sublinks could be SONET connections, Ethernet circuits, wavelengths on a fiber, etc. And they could be shut down or brought up independently. Selectively shutting down sublinks during low traffic periods could save a large amount of energy while keeping the network topology unchanged. Based on this concept, we propose a local heuristical threshold- based method to explore the potential energy- savings in the backbone network by adjusting the number of active sublinks in bundle links. An experiment based on an Internet2 derived synthetic network was conducted to verify the performance of our method and the results show that 86% of energy consumed on ports of core routers could be saved when setting 90.0% as the link utilization threshold. The experiment also shows that setting 90.0% as threshold is safe enough to avoid data loss during extreme traffic increases in this case. Compared to previous proposed ILP (Integer linear programming) based global heuristic algorithms, our local heuristic algorithm can achieve energy-savings close to the optimum and greatly reduce the response time and the risk of data loss.