In this paper, we demonstrate how to capture the robustness of a transportation network in the case of degradable links represented by decreasing capacities. In particular, with the use of Bureau of Public Roads user link travel cost functions, we propose two relative total cost indices to assess transportation network robustness in the case of travel behavior associated with either user optimization or system optimization. We derive upper bounds of the relative total cost index for transportation networks with special structure and congestion parameters under the user optimal flow pattern. We also derive an upper bound for the relative total cost index under the system optimal flow pattern for general transportation networks. Numerical examples are presented for illustration purposes. This research is the first to quantify transportation network robustness in the presence of degradable links and alternative travel behavior. This research has implications for transportation planning and management, for vulnerability analysis, as well as for security issues.