This study investigates the survivable traffic grooming problem for elastic optical networks with flexible spectrum grid employing new transmission technologies. In such networks, instead of following the traditional fixed ITU-T wavelength grid, optical transponders are capable of properly tuning their rates, and consequently their spectrum occupation, by introducing the fine-granular spectrum unit, called a frequency slot. The number of contiguous frequency slots allocated to an optical path (i.e., lightpath) is adjusted to the current network flow. In this study, we propose a novel shared protection specific to elastic networks, namely, elastic separate-protection-at-connection (ESPAC). It not only provides traditional backup sharing, but also offers a new opportunity of spectrum sharing enabled by the elasticity of the transponders: 1) if the working paths of two connections are link disjoint physically, and 2) if their backup paths traverse two lightpaths which are adjacent on a fiber link, then the two backup lightpaths can share spectrum. The new opportunity of spectrum sharing is realized by using First-Fit to assign working traffic and Last-Fit to assign backup traffic, and allowing spectrum overlap between adjacent backup wavelengths. The elasticity of the transponder enables the expansion and contraction of the lightpaths, thus when a single failure occurs in the network, lightpaths carrying backup flows can be tuned to appropriate rates in such a way that the overlap spectrum is used by only one of the adjacent lightpaths. The results show ESPAC is very spectrum efficient in elastic network setting.