## 1 Introduction  
Characterized with easy shaping, efficient fabrication and construction, concrete material structures are widely used for most civilian and military infrastructure, e.g., nuclear power plants, liquefied natural gas storage tanks and civil air defence, which are designed to withstand extreme loading, such as aircraft engine impact as well as internal and external missile impact [1, 2, 3]. Under projectile penetration, attaching a relative thin steel plate onto the concrete wall rear (protected) face would better protect the inner inhabitants and vulnerable instruments by preventing rear face ejected fragmentation, which might occur even if the concrete panel is not breached. In practice, steel plate reinforced concrete (SC) walls have been effectively used as primary and secondary shelters in protective structures. It is important to develop a simple but robust analytical model for projectile perforation on SC walls. SC walls have superior performance in terms of resisting impact loading, since the rear steel plate induces a considerable effect on limiting crater development and preventing the pulverized pieces from flying away. Concerning the impact resistance of the SC walls, experimental studies have compared and analyzed projectile impact tests on concrete slabs with and without the rear steel plate. [PERSON] et al. [4, 5] investigated the static and impact performance of SC walls in which no shear connectors were utilized to connect the steel faceplates and the concrete core. Owing to the specially designed connection details, the tested panels exhibited tensile membrane resistance at large deformations. Armour-piercing projectiles impacting high-strength concrete backed by armoured steel were studied by [PERSON] et al. [6], showing spaced composite targets had larger residual penetration depth than segmented ones. [PERSON] [7] concluded that the rear attached steel plate has little effect on enhancing the impact resistance of SC walls, while it can efficiently restrain scabbing and spalling fragments. Aiming at identifying the influence of the steel plate on local damage of SC walls, [PERSON] et al. [8] performed a series of impact tests in which the steel plate was placed on the rear, front and both faces of a concrete panel, respectively. The rear steel plate attached to reinforced concrete (RC) plate could prevent local damage caused by perforation, while the front steel plate attached to the impacted face had a relatively slight effect. [PERSON] and [PERSON] [9] showed that the steel plate placed on the rear face had better impact performance than the front one, which further validated the above conclusion. [PERSON] et al. [10] also showed that a thicker steel plate would result in less local damage under low-velocity impact. [PERSON] et al. [11] found that SC panels have better impact resistant performance than RC panels, which enabled reduction of panel thickness by almost 30%. [PERSON] et al. [12] developed an analytical and empirical model of SC walls under rigid projectile impact and proposed a three-step method for designing SC walls against missile impact which can be used to evaluate the ballistic limit of SC walls. For rigid projectile perforation, [PERSON] and [PERSON] [13] investigated the thickness of the SC composite barrier with respect to energy absorption. [PERSON] et al. [14] performed projectile perforation tests on monolithic and segmented RC panels with a rear steel plate. The ballistic performances of layered RC and SC targets were analyzed quantitatively, which further validated the equivalent approach in Ref. [13]. To assess the core concrete thickness and steel ratios effect on failure modes, [PERSON] and [PERSON] [15] numerically evaluated the impact resistance of SC and RC panels via a LS-DYNA solver, suggesting SC walls can better resist impacting loads than RC panels. Although extensive studies on SC structures have been conducted both experimentally and numerically, analytical models of hard projectile perforation on SC walls need to be further explored.