In recent years, energy-efficient design of optical WDM networks has become increasingly important as efforts to reduce the operational expenditure (Opex) and the carbon footprint of the internet are prioritized. In this paper we focus on energy- efficient survivable network design where backup resources are shared for efficient capacity consumption. However there is a trade-off between energy-efficiency and survivability. Survivable network design strategies lead to lightly loaded links in order to minimize the risk in case of a failure and to increase the shareability of backup resources. On the contrary, energy-efficient network design strategies tend to increase the load in a set of links as a consequence of concentrating the traffic in order to be able to switch off as much network resources as possible. In this study, we present a novel method to simultaneously minimize Capex and Opex while providing an energy-efficient, shared backup protected network, under the assumption of backup capacity in sleep mode. For the first time we propose an ILP formulation for the energy-efficient shared backup protection problem. By exploiting the sleep mode for the backup resources, we observe that the ILP solution of our mathematical model brings up to 40% gain in energy efficiency in comparison to energy-unaware shared backup protection approach.