The potential failure in through-silicon vias (TSVs) still poses a challenge in trying to extend the useful life of a 3D integrated circuit (IC). A model is proposed to mitigate the communication problem in 3D integrated circuits caused by the breaks at the TSVs. We provide the details of a low-complexity network that takes advantages of redundant TSVs to make it possible to re-route around breaks and maintain effective communication between layers. Different configurations for the micronetwork are analyzed and discussed. We also present an evaluation of the micronetwork's performance, which turns out to be quite promising, based on several Monte Carlo simulations. Finally, we provide some directions for future research on the subject.