## 1 Introduction  
In recent years, the escalating demand for traffic on transport networks, including the 5 th mobile communication technology, cloud computing, and the interconnection of data centers, has triggered a continuous increase in the requirement for data traffic in transmission networks [1]. Elastic optical networks (EONs) divide the wavelength into finer frequency slots (FSs). This greatly improves the spectrum utilization efficiency and enhances the transmission capacity of the network [2]. However, the existing transmission capacity of the network remains inadequate to satisfy the escalating traffic demand, hindered by the nonlinear Shannon limit of single-mode fibers (SSMF). Band division multiplexing (BDM) offers a promising mid-term solution by broadening the available spectrum range to tens of THz through the utilization of multiple bands within already deployed optical fibers. Furthermore, C+L-EONs have the potential to expand the transmission bands from the C band to the C+L bands on existing SSMF despite the need for novel network components such as transceivers and amplifiers to cater to the demands beyond the C band [3]. Consequently, this paper focuses on the scenario of C+L-EONs. The inter-channel stimulated Raman scattering (ISRS) effect, a nonlinear phenomenon, becomes increasingly significant, resulting in the transfer of power from higher to lower frequency components within the same optical spectrum [4]. Consequently, it is crucial to take into account the nonlinear impairments (NLI) experienced by the signal in C+L-EONs. Furthermore, the addition of a band dimension in the network necessitates the advancement of routing, modulation, and spectrum allocation considerations into a more comprehensive RBMSA problem. Furthermore, spectrum fragmentation poses a significant challenge in the resource allocation process of C+L-EONs [5]. When a request arrives in the network, it requires not only the selection of an appropriate path based on its source and destination nodes but also the allocation of a contiguous spectrum according to its bandwidth demand [6]. Three constraints must be met during spectrum allocation: spectrum continuity, adjacency, and non-overlap. Specifically, within the transmission optical path, consecutive FSs must be utilized on each link. However, the dynamic and random arrival and departure of requests cause optical paths to be established and released dynamically, leading to the emergence of unusable free FSs known as spectrum fragmentation in the links [7]. This fragmentation not only reduces spectrum utilization in the network but also elevates the network blocking rate. Therefore, it is crucial to consider spectrum fragmentation during the spectrum allocation process. On the other hand, in large-scale networks, there is the problem of a request interruption due to fiber failure [8]. In large-capacity networks, the failure of a single fiber can interrupt multiple established requests, resulting in huge economic losses. Therefore, it is necessary to study a survivability-based resource allocation algorithm for C+L-EONs. Common network survivability assurance methods are protection and recovery algorithms. Compared to recovery, protection takes less time and can efficiently ensure network survivability. This paper adopts the protection algorithm to ensure network survivability. Typical protection algorithms are dedicated path protection (DPP) and shared backup path protection (SBPP) [9]. DPP allocates a dedicated backup path for each primary path. While this protection mechanism offers faster fault recovery times, it consumes more network resources, potentially leading to lower resource utilization. For SBPP, the backup resource in the primary paths where the links do not intersect can be shared, which reduces resource redundancy [10]. Therefore, to optimize resource utilization and efficiency, SBPP is used to guarantee the network survivability in this paper.