Survivability is mission-critical for elastic optical networks (EONs) as they are expected to carry an enormous amount of data. In this paper, we consider the problem of designing shared backup path protection (SBPP) based EON that facilitates the minimum quality-of-transmission (QoT) assured allocation against physical layer impairments (PLIs) under any single link/shared risk link group (SRLG) failure for static and dynamic traffic scenarios. In general, the effect of PLIs on lightpath varies based on the location of failure of a link as it introduces different active working and backup paths. To address these issues in the design of SBPP EON, we formulate a mixed integer linear programming (MILP) based robust optimization framework for static traffic with the objective of minimizing overall fragmentation. In this process, we use the efficient robust bitloading technique for spectrum allocation where each frequency slot of a request is assigned with different modulation format. In addition, we propose novel SBPP-impairment aware (SBPP-IA) algorithm considering the limitations of MILP for larger networks. For this purpose, we introduce a novel sorting technique named most congested working-least congested backup first (MCW-LCBF) to sort the given set of requests. Next, we employ our SBPP-IA algorithm for dynamic traffic scenario and compare it with existing algorithms in terms of different QoT parameters. Further, we guarantee the QoT of existing requests while allocating each new request without reserving any margin. We demonstrated through simulations that our study provides 33.94-41.02% more QoT guaranteed requests compared to existing ones at 70 Tbps traffic load.