## 1 Introduction  
Reinforced concrete structures constitute the backbone of modern civil infrastructure, from conventional buildings to critical protective facilities designed to withstand extreme dynamic loads [1, 2, 3]. Under impact, blast, or seismic loading conditions, these structures experience complex stress states at strain rates several orders of magnitude higher than quasi-static conditions [4, 5, 6]. The tensile response is particularly critical, as concrete's inherent brittleness and low tensile strength often govern structural failure modes under dynamic loading [7, 8]. Characterizing dynamic tensile behavior presents fundamental challenges due to limitations in conventional testing methodologies. Traditional approaches, including direct tension tests using split Hopkinson bar systems [9] and indirect methods such as Brazilian splitting tests [10, 11, 12], require quasi-static equilibrium during testing [13, 14]. This requirement constrains achievable strain rates to ranges often insufficient for simulating impact and blast scenarios [4, 15]. The spalling technique has emerged as a powerful alternative, capable of achieving strain rates exceeding 100 s\({}^{-1}\) without equilibrium constraints [16; 17; 18]. In this method, compressive stress waves reflect as tensile waves from free surfaces, creating superposition that induces tensile failure within specimens [17]. Three primary analysis methods have been established for interpreting spalling test results:  
Method A (Stress Field Reconstruction): Reconstructs elastic stress fields based on wave propagation theory and identifies stress levels at observed fracture locations [16; 17]. This approach assumes purely elastic behavior until maximum stress and requires accurate fracture localization. Method B (Fragment Velocity Analysis): Relates spall strength to ejection velocities of spalled fragments [16]. However, determining relevant velocities at failure instants is challenging, particularly with diffuse damage patterns. Method C (Pull-back Velocity Method): Based on [PERSON] et al. 's acoustic approximation [19], this method directly correlates spall strength with the \"pull-back\" velocity observed at the specimen's free surface [17; 20]. The method assumes elastic behavior between the spall plane and free surface, along with material homogeneity. Comparative studies have demonstrated that the pull-back method (Method C) provides the most robust results, particularly for complex fracture patterns [17]. While successfully validated for plain concrete [17; 20; 21], its application to unidirectional reinforced concrete (UDRC) introduces fundamental challenges that remain unaddressed in the literature. The theoretical foundation of the pull-back method relies on one-dimensional stress wave propagation and material homogeneity assumptions. However, in UDRC systems: (i) the steel reinforcement creates a significant impedance mismatch (\(Z_{\text{steel}}/Z_{\text{concrete}}\approx 15\)); (ii) multi-axial stress states develop near the steel-concrete interface; and (iii) material homogeneity is inherently violated. Additionally, accurate strain rate quantification--essential for establishing rate-dependent strength relationships--is complicated by the composite nature of UDRC. Traditional global measurement methods may underestimate local strain rates at fracture initiation sites. Furthermore, the influence of reinforcement type (plain versus deformed bars) on spall strength determination remains unexplored. While the pull-back method is well-validated for plain concrete, its application to UDRC remains a critical knowledge gap. This study, for the first time, systematically investigates the validity of the method's core assumptions in a composite system by quantifying the influence of reinforcement on internal stress states and macroscopic dynamic response combining experimental testing, numerical validation, and advanced measurement techniques. The research objectives are threefold:  
1.