Introduction

The historical reinforced concrete buildings constructed between 1912 and 1949 were critical carriers for the integration of Chinese construction techniques and Western engineering technologies. They witnessed China’s socio-economic transformation, from the early stage of industrialization to post-war reconstruction, and possess significant historical, artistic, scientific, and social value. Meanwhile, these structures are widely distributed across core urbanized areas, including Shanghai, Guangzhou, Nanjing, Wuhan, Tianjin, and other major cities. Their targeted conservation is therefore essential to preserving the integrity of architectural heritage. However, historical reinforced concrete differs from the reinforced concrete (RC) commonly adopted in engineering nowadays1,2. It is not appropriate to directly apply the current engineering guides or codes on its conservation, otherwise, it could induce adverse impact on historical reinforced concrete architectural heritage. Except for the differences in steel rebars’ features, historical reinforced concrete exhibits lower concrete cover strength which is around 20 MPa or even lower3. And, the strength compatibility in terms of rebars and concrete is not rational from modern perspective. Targeted investigation into its mechanical features is meaningful for its conservation.

The historical steel rebars have diverse rib and shape features4. In contrast, the steel rebars used in modern society mainly commonly present a monolithic apparent feature. These diverse features in historical steel rebars could post effect on the mechanical properties of historical reinforced concrete. Firstly, the tensile behaviors of these historical rebars differ from those of modern steel rebars due to variations in manufacturing techniques and material composition4,5,6. Furthermore, targeted experimental research on bond-slip behavior is essential, and the key rationale lies in the following: the rib features of steel rebars directly affect the mechanical interlocking between rebars and concrete. When the concrete cover in historical reinforced concrete structures exhibits relatively low strength, this mechanical interlocking becomes the dominant force maintaining the interfacial bond performance between rebars and concrete. Thus, only through targeted experiments can the influence law of rib features on bond-slip behavior be accurately revealed, providing a reliable basis for subsequent studies7,8,9,10.

Current investigations of bond-slip behavior predominantly employ static loading protocols11,12,13. However, in practical engineering applications, the loading rate is not invariably constant. Existing research indicates that bond-slip behavior exerts a notable influence on both the ultimate strength and rebar pull-out length; specifically, elevated loading rates may substantially increase the ultimate strength while concurrently reducing the rebar pull-out length7,10,14,15,16. Due to the complex rib features and diminished concrete cover strength common in historical reinforced concrete, experimental conclusions may not align with those from modern materials. Therefore, establishing a targeted analytical model is a valuable approach for facilitating further research in this area.

Current analytical models predominantly rely on a semi-empirical methodology, incorporating a diverse range of parameters, including, but not limited to, concrete compressive strength, reinforcing bar diameter, and external environmental conditions6,17,18,19,20,21,22,23. However, existing analytical models developed for modern reinforced concrete may not adequately represent the behavior of historical reinforced concrete structures due to the distinct material properties and construction techniques employed in their creation. Consequently, targeted modifications to these existing models, informed by experimental observations, are essential to enhance their predictive accuracy when applied to historical reinforced concrete.

Addressing the previously outlined knowledge gaps, this research undertakes a comprehensive investigation of the tensile and dynamic bond-slip characteristics of historical reinforcing steel. The experimental program includes uniaxial tensile tests to characterize ultimate tensile strength and fracture elongation, and dynamic pull-out tests on reinforced concrete specimens to quantify slip and ultimate bond-slip strength with varying loading rates. Based on both theoretical considerations and empirical observations, a simplified analytical bond-slip model is formulated. The results provide a refined understanding of the parameters influencing the performance and durability of historical reinforced concrete structures.

Methods

Raw materials

The steel rebars (Fig. 1) used in this study are sourced from real historical scenarios, specifically collected as identical batches of original rebars from historical reinforced concrete structures dating to the 1912–1949 period. Their origin is directly linked to actual heritage buildings, ensuring the historical authenticity and engineering representativeness of the research objects. At the sample classification stage, the overall geometric shape of the rebars serves as the core macro-level classification criterion. Through this process, a total of 6 different types of historical steel rebars were sorted out. The six types of historical steel rebars were selected as they are the most commonly used ones found in practical engineering of China’s historical building heritage from 1912 to 1949, covering the mainstream forms and specifications of the period with representativeness. According to experiment from research group, the common chemical composition of historical steel rebar is listed4,24: Carbon (C) 0.03–0.16%, Silica (Si) 0.017–0.061%, Manganese (Mn) 0.27–0.45%, Phosphorus (P) 0.035–0.106%, Sulfur (S) 0.047–0.072%. While the chemical composition of the HRB 400, which is commonly used nowadays, is: Carbon (C) ≤ 0.025%, Silica (Si) ≤ 0.80%, Manganese (Mn) ≤ 1.60%, Phosphorus (P) ≤ 0.045%, Sulfur (S) ≤ 0.045%24. Concrete used has the same mix proportion adopted during 1912 to 1949, which is obtained by experimental results and literature investigation in the research group’s previous study1,2,3, the specific mix proportion is shown in Table 1.

Fig. 1
figure 1

Historical steel rebars with different shape features.

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Table 1 Historical concrete mix proportion
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The historical steel rebars were subdivided and denoted based on shape features, rib details, and size parameters of the rebars as listed in Table 2. Rebar dimensions were established by measuring the rebars, and the validity of the measurements was confirmed using the average values derived from three specimens per batch of historical steel rebars.

Table 2 Historical steel rebar details
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Test setup

A universal loading machine, two Linear Variable Differential Transformers (LVDTs), and a Laser Extensometer are adopted. Reflection stickers are applied as reference spots for Laser Extensometer. And the LVTDs are installed above the upper surface of the pull-out specimens to measure the relative slip. These setups make sure the actual slip recording data will not be influenced by the slip of upper loading end or lower fixing end. The specific test setup is shown in Fig. 2.

Fig. 2: Test setup.
figure 2

a Tensile test. b Uniaxial pull-out test. c Setup details. (①: Reflection plastic plate②: Reflection sticker③: Laser light from laser extensometer).

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Test method

Tensile and bond-slip behavior were evaluated using a universal testing machine. In the tensile tests, a constant loading rate of 2 mm/min was applied according to GB/T 228.1-201025. To investigate the influence of loading rate on bond-slip behavior, pull-out tests were conducted at varying displacement rates: 2 mm/min, 5 mm/min, and 10 mm/min. For each loading rate, a set of three nominally identical specimens was tested, resulting in nine specimens per test group.

Tensile test specimens were uniformly prepared with a total length of 500 mm. Bond-slip test specimens were fabricated in accordance with the guidelines outlined in GB/T 228.1-2010 as shown in ref. 25. For bond-slip specimen preparation, custom wooden molds are first used to cast concrete cubes (mold inner diameter matches target size), with ±0.5 mm-tolerance rebar holes pre-drilled at the centers of opposite mold panels to ensure rebar alignment with the cube center and avoid additional test bending stress. Next, as shown in Fig. 3, a 2 mm-thick smooth PVC sleeve is sheathed on the rebar’s non-bonded section, leaving only the exposed section (e.g., 5 times rebar diameter) as the bonded length according to Chinese Standard GB/T 50152-201226; the sleeve isolates rebar from concrete to limit bond stress to the target section. Subsequently, well-mixed concrete is poured in 3 layers, each compacted for 30 s via a 50 Hz/0.5 mm vibrating table to eliminate voids, with the top surface leveled. After casting, the mold is covered with plastic film and placed indoors at 20 ± 2 °C, demolded after 24 h, then transferred to an outdoor ambient environment (15–25 °C) for 28-day curing. Water is sprayed at 9:00/17:00 daily to keep specimens moist, simulating real engineering conditions. The initial gauge length for tensile specimens was defined as five times a characteristic dimension of the steel rebar25. For square and spiral rebars, this dimension was taken as five times the side length, while for oblate steel rebars, it was five times the major axis length. The elongation rate was then calculated using Eq. 1.

$$A=\left(\frac{L-{L}_{0}}{{L}_{0}}\right)\times 100 \%$$
(1)

where A is the elongation at break, L0 is the original gauge length (mm), and L is the length after elongation (mm).

Fig. 3
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Bond-slip test specimen.

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The ultimate tensile strength and fracture strength were calculated in accordance with Eqs. 2 and 3, respectively. The yield strength was defined as the stress corresponding to a plastic strain of 0.2% of the initial gauge length according to ISO 6892-1:201925.

$${f}_{t,u}=\frac{{P}_{t,u}}{A}$$
(2)
$${f}_{t,b}=\frac{{P}_{t,b}}{A}$$
(3)

where f is the strength of steel rebar at certain stage, P is the applied load, subscript t,u represents the ultimate tensile stage(maximum load reached), t,b represents tensile stage at break. A is the cross-section area of the tested steel rebar.

Bond-slip behavior was determined following the procedures outlined in Chinese Standard GB/T 50152-201226. The bonded length was specified as five times a characteristic dimension of the steel rebar. For square and spiral steel rebars, this dimension was defined as five times the side length. For oblate (elliptical) rebars, it was conservatively specified as five times the major axis length to ensure adequate anchorage. The constitutive relationship for ribbed steel rebars is represented by Eqs. 4–8 and illustrated in Fig. 4.

$$\tau ={k}_{1}s\,0\le s\le {s}_{\mathrm{cr}}$$
(4)
$$\tau ={\tau }_{\mathrm{cr}}+{k}_{2}(s-{s}_{\mathrm{cr}})\,{s}_{\mathrm{cr}} < s\le {s}_{u}$$
(5)
$$\tau ={\tau }_{u}+{k}_{3}(s-{s}_{u})\,{s}_{u} < s\le {s}_{r}$$
(6)
$$\tau ={\tau }_{{\rm{r}}}\,s > {s}_{r}$$
(7)
$$\tau ={\tau }_{an}+{k}_{1}(s-{s}_{un})$$
(8)

where τ is bonding stress between concrete and ribbed steel rebars (MPa), s is the relative displacement between concrete cover and steel rebar(mm), k1 is the slope of linear segment, k2 is the slope of split section, k3 is the slope of descent stage, Sun is the relative displacement at unloading point(mm).

Fig. 4
figure 4

Bond-slip constitutive model.

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In addition, metallographic analysis was performed, with specimens prepared in accordance with GB/T 13298-201525 as shown in Fig. 5. The metallographic microstructures were then observed at magnifications of 100x, 200x, 500x, and 1000x.

Fig. 5
figure 5

Metallographic specimens.

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Results

Tensile behavior

The tensile strength results are detailed in Table 3. sq-22 group may be attributed to stress concentrations at the rib edges, leading to premature fracture without observable yielding or necking (Fig. 7). Typically, spiral rebars did not exhibit a distinct yielding stage as shown in Fig. 6. In the spiral rebar groups, the absence of a clear yielding plateau is likely due to the complex stress state induced by their helical geometry. Compared to the other rebar types tested, the spiral shape introduces a combination of tensile, flexural, and torsional stresses. Furthermore, the curvature of the helix generates stress concentrations, potentially causing localized yielding at lower overall stress levels. The heterogeneous stress distribution, with differing stress magnitudes in the curved and straight segments of the rebar, contributes to non-uniform deformation. Additionally, small, localized stress concentration zones may be difficult to observed in the overall stress-strain curve, effectively masking any localized yielding behavior.

Fig. 6: Typical stress-strain curves (spiral rebars).
figure 6

a sp-15. b sp-22.

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Table 3 Tensile strength details
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In contrast to this behavior, the inherent shape characteristics of helical steel rebars render them susceptible to significant necking during tensile loading. This susceptibility is primarily attributed to: (1) intensified stress concentrations, particularly in the bent regions; (2) non-uniform loading, causing preferential yielding in the bent segments; (3) local geometric weakening, further exacerbating stress concentrations; (4) a reduction in effective length, elevating stress levels in the necking region; and (5) the Poisson’s effect, promoting the development of necking. These factors collectively induce a highly localized concentration of plastic deformation, ultimately leading to pronounced necking and subsequent fracture, as illustrated in Fig. 7.

Fig. 7
figure 7

Steel rebar fracture.

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In comparison, modern HRB400 steel rebar typically exhibits an elongation exceeding 16%. This study revealed an inverse relationship between the cross-sectional area of the historical steel rebars and their elongation properties; rebars with smaller cross-sections demonstrated greater elongation and a more pronounced necking phenomenon prior to fracture, as listed in Table 3.

Bond-slip curves

Bonding strength is influenced by rib characteristics, with the tested steel rebar specimens exhibiting variations in rib width, rib spacing, rib shape, and rib area. The combined effect of these parameters on bonding strength is complex. Therefore, to establish a comprehensive correlation, a representative index – the Relative Rib Area Ratio (ρ) – is introduced. This index integrates the aforementioned parameters and is defined as:

$${\rho }={s}_{rib}/{s}_{cs}$$
(9)
$${\rho }=(\pi \cdot \,{{\rm{d}}}^{2\,}\,\cdot {\rm{ns}})\,/\,({{\rm{D}}}^{2\,}\,\cdot {\rm{p}})$$
(10)

where Srib is the projected area of rib calculated by multiplying rib height and width (mm) and rib width(mm), Scs is the cross-section area of steel rebars, d is the side length of the spiral steel rebar, ns is the spiral circle within the longitudinal length(mm), D is the effective bonding diameter, which is half side length of the concrete cube. p is the packing coefficient, which is between 0 and 1; it is chosen to be 1 in this research. The ρ values corresponding to each type of specimen are listed in Table 4.

Table 4 Historical steel rebar details
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The maximum bonding strength is related to the Relative Rib Area Ratio (ρ), with the increase of ρ, the bonding strength is generally increased as shown in Fig. 8.

Fig. 8: Maximum bonding stress to ρ.
figure 8

a Maximum bonding strength. b Average bonding strength to ρ.

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Since the bond-slip curves show similar patterns across all groups, sq-10 serves as a representative example, as shown in Fig. 9. Minor variations in bond-slip behavior across the test groups are likely attributable to inherent material heterogeneity among the original steel rebars. This heterogeneity persisted even among the short rebar specimens extracted from nominally identical sources. However, the bond-slip curves obtained from the three replicate specimens within each group consistently exhibited comparable characteristics. Increasing the loading rate resulted in a more rapid development of bond-slip stress, both during the ascending phase of the curve and in the descending region following the attainment of peak bonding strength. Furthermore, a slight, yet observable, increase in the maximum achievable bonding strength was generally observed with higher loading rates.

Fig. 9
figure 9

Typical bond-slip curves(sq-10).

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The maximum increase in bonding strength attributable to variations in loading rate was 8.11%, as illustrated in Fig. 10. Increasing the loading rate from 2 mm/min to 5 mm/min generally resulted in an elevation of the bond stress prior to reaching the peak. However, at a loading rate of 10 mm/min, this trend was not consistently observed, potentially due to premature anchorage failure induced by the limited strength of the surrounding concrete matrix. While it is reported that HRB 400 rebars in 30 MPa and 60 MPa concrete show a constant bonding stress increase when loading rate increased from 0.1 mm/s to 100 mm/s, indicating a stronger bond connection compared to historical ones27. However, constrained by the core research focus of this study, an in-depth investigation into the dynamic behavior of bond-slip in historical reinforced concrete has not been conducted herein. Supplementary research on this dimension is planned to be further advanced and refined in our subsequent related work.

Fig. 10
figure 10

Effect of loading rates on bonding stress.

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Using existing bond-slip calculation models (Eqs. 4–8), initial bond-slip curves were generated for the historical reinforced concrete. Representative bond-slip curves for each test group were then established by minimizing the Euclidean geometric distance and identifying characteristic segmentation points as shown in Fig. 11, in accordance with the methodology prescribed in GB/T 50010-201028. The average coefficient of determination (R²) for these representative curves exceeded 0.93. For clarity, characteristic points of representative bond-slip fitting curves are listed in Table 5.

Fig. 11
figure 11

Representative fitting of bond-slip curve (sq-10).

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Table 5 Characteristic points details of representative bond-slip fitting curves
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Bond-slip model

A simplified bond-slip model is proposed, accounting for the dominant influence of mechanical interlocking on the bond-slip behavior of historical reinforcing steel. The model is based on existing static and dynamic pull-out constitutive models developed for modern ribbed steel rebars (e.g., HRB400). But considering the specific scenario in historical reinforced concrete. This model focuses on mechanical interlocking (Fig. 12), a phenomenon predominantly governed by rebar rib features, which are quantified by the relative rib area ratio, ρ = Srib / Scs (as discussed in Section 3.2.1). The rib area ratio serves to normalize the effective bonding area. Specifically, assuming that the total bond force (Fmec) arises primarily from the interaction of the rebar ribs with the surrounding concrete, then Fmec is directly proportional to the effective contact area, Srib. To account for variations in rebar size, Srib is normalized by the rebar’s cross-sectional area (Scs), resulting in the dimensionless rib area ratio, ρ. The model then introduces a mechanical interlocking index (μ), relating the mechanical bond stress (τmec) to the concrete compressive strength (fc) through the experimentally validated relationship τmec = μ * fc * ρ. The mechanical interlocking contribution is subsequently calculated using Eq. 11, which formally expresses this relationship.

$${\tau }_{mec}=\mu * {f}_{c}* ({S}_{rib}/{S}_{cs})=\mu * {f}_{c}* \rho$$
(11)

where μ is mechanical interlocking index(dimensionless) is derived from experimental data through a regression analysis (one specimen from each test group), which is 1.91, Srib is the projected area of rib which is calculated by multiply the rib height(mm) and rib width(mm), Scs is the cross-section area of steel rebars.

Fig. 12
figure 12

Simplified bond-slip model illustration.

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By integrating Eq.11 within the range from 0 to Lb, the bonding force can be expressed as:

$${F}_{mec}={\int }_{0}^{{L}_{b}}\pi * d* {t}_{mec}(x){d}_{x})$$
(12)

where Fmec is the bonding force(kN), Lb is the effective bonding length(mm), d is the diameter of steel rebar(mm).

To validate the analytical bond-slip model, the experimentally obtained bond strengths and corresponding slip values were compared with the values predicted by the analytical bond-slip model, as summarized in Table 6. The average bonding strength for each bond-slip specimen group was used in the comparison, given the relatively close agreement in bonding strengths among the specimens within each group. The average error between the experimental and predicted results was 6.87%.

Table 6 Validation of analytical bond slip model
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To provide a more comprehensive assessment of model performance, three Normalized Root Mean Squared Error (NRMSE) metrics were calculated. The physical meaning of NRMSE is to quantify the average error magnitude between the model’s predicted values and actual measured values; normalization eliminates the influence of the original data’s units, enabling error comparison across scenarios. Different normalization methods correspond to different reference benchmarks: the mean-based NRMSE is 0.105 (mean = 6.79), indicating that the Root Mean Squared Error (RMSE) accounts for approximately 10.5% of the dataset’s average value; the standard deviation-based NRMSE is 0.235 (standard deviation = 3.03), suggesting a reasonably good fit of the model to the data’s variability; the Interquartile Range (IQR, i.e., the difference between the 75th and 25th percentiles of the measured data, 4.96 here)-based NRMSE is 0.144. This method focuses on the representative central 50% of the data, is less affected by extreme outliers, and more truly reflects the model’s error under regular data—its result also confirms that the model exhibits relatively stable and accurate predictive performance across the observed data range. The consistency of these low NRMSE values indicates that, in the context of this dataset, the model provides a reasonable approximation of the true values.

This study reveals significant differences in bond-slip behavior between historical and modern steel rebars through comparative analysis; specifically, typical historical rebars generally undergo substantial slip deformation before reaching the ultimate bond strength (Fig. 9), while in contrast, modern rebars tend to exhibit a shorter slip stage and attain their ultimate bond strength at a relatively smaller slip value6, and although numerous bond-slip models have been established for modern rebars, the aforementioned differences confirm that the bond-slip behavior of historical rebars is inherently distinct from that of modern ones. To obtain more detailed and scientific comparison results, additional experimental comparisons and model comparisons need to be conducted, which will be reflected in our subsequent potential work.

Metallographic result

Metallographic analysis revealed no observable non-metallic inclusions in the cross-sections examined. However, variations in the relative proportions of pearlite and ferrite were observed. Specifically, spiral and oblate steel rebars exhibited a higher pearlite content compared to square steel rebars, as illustrated in Fig. 13.

Fig. 13
figure 13

Metallographic analysis results.

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The pearlite and ferrite content for the cross-sections of the steel rebars are summarized in Table 7. As documented in the literature, an increase in pearlite content typically results in higher tensile strength but lower ductility. This relationship provides further explanation for the absence of distinct yielding stages observed in the sp-15 and sp-22 test groups, as shown in Fig. 7a. A notable difference in microstructure is evident between the spiral steel rebars (sp-15 and sp-22) and the other steel rebar types (sq-10, sq-15, sq-22, and ob-10). Specimen sp-22 exhibits a markedly higher pearlite content and a significantly lower ferrite-to-pearlite (F/P) ratio compared to all other specimens, suggesting a potentially different manufacturing process or alloy composition. The remaining specimens demonstrate relatively low and consistent pearlite content, resulting in substantially higher F/P ratios.

Table 7 Pearlite and ferrite content
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It is confirmed that all historical rebars used in this study adopted hot-rolled process4, so the differences in pearlite content observed at the metallographic interface are not caused by process distinctions between cold-drawing and hot-rolling. Instead, these differences are preliminarily attributed to variations in annealing temperatures during the hot-rolling post-treatment stage. The content and morphological distribution of pearlite serve as key references for analyzing the annealing process of hot-rolled rebars: during the annealing process, the cooling rate (determined by annealing temperature control) directly regulates the phase transformation of austenite. When the annealing temperature is moderately reduced (within the range between the Ac1 line ~727 °C and Ar1 line ~677 °C) and maintained for an appropriate duration, it slows down the diffusion rate of carbon atoms. This slower diffusion inhibits the excessive precipitation of soft ferrite—since ferrite (with extremely low carbon solubility) tends to precipitate first at higher temperatures—while promoting the sufficient transformation of remaining austenite (enriched with carbon) into pearlite. As a result, the proportion of hard pearlite in the microstructure increases29, and its distribution becomes more uniform. The unusually high pearlite content observed in “sp-22” shown in Fig. 13 further supports the inference of annealing temperature differences. Based on existing test results, supplementary inferential conclusions have been provided; in subsequent studies, we will integrate historical archives of steel production techniques from the corresponding period, and by comparing the microstructures of rebars with clear annealing process records (focusing on both pearlite morphology and volume fraction), further verify the quantitative relationship between annealing temperature and pearlite content, and clarify the specific annealing temperature parameters applied in the manufacturing of historical hot-rolled rebars.

Discussion

The primary objective of this study was to investigate the mechanical behavior of historical steel rebars used in China between 1912 and 1949, and to develop a simplified bond-slip model. Through the implementation of uniaxial tensile tests and pull-out tests on relevant specimens, the key findings and main discussions are presented as follows:

Spiral steel rebars did not exhibit a distinct yielding stage during tensile testing. Specimen sp-22 had a drastically higher pearlite content (48.77%), suggesting a different manufacturing process or alloy composition. Generally, no apparent non-metallic inclusions were found in any of the historical steel rebars.

Variations in loading rates were found to influence bond-slip behavior. Higher loading rates contributed to a slight increase in the linear stage, resulting in relatively higher bonding strength (up to 8.11%). However, higher loading rates could also induce earlier bond failure.

The bond-slip behavior of all tested steel rebars conformed to the pattern described in GB/T 50010-2010. Specifically, optimized bond-slip models with characteristic segmentation points have been proposed for these six types of historical steel rebars using Euclidean geometric distance fitting, resulting in an average R-squared value exceeding 0.93.

A simplified analytical bond-slip model is proposed, exhibiting an average error below 6.87%. Low and consistent values for the NRMSE metrics (NRMSE_mean = 0.105, NRMSE_std = 0.235, NRMSE_IQR = 0.144) indicate that the model provides a relatively accurate and stable approximation of the true values within the observed dataset.

Understanding the mechanical properties and bond-slip behaviors of historical steel rebars used between 1912 and 1949 provides critical technical support for the conservation of historical reinforced concrete buildings. The core value of the derived test data and models lies in two key aspects for such conservation projects: first, they offer targeted, real-world data on the tensile properties and bond-slip behaviors of historical reinforced concrete. This data serves to refine and validate material parameters in numerical simulations, ensuring the simulations accurately reflect the actual performance of the historical structure; second, they provide realistic, application-specific bond-slip constitutive models. These models effectively enhance the precision of numerical simulations, enabling more reliable predictions of structural responses during the conservation process and thus underpinning the scientific rigor of conservation design.

Notably, the bond-slip model constructed in this study exhibits excellent general applicability for historical reinforced concrete structures in China from 1912 to 1949. The model is established based on test data of historical steel rebars sourced from real engineering surveys during the past decades; these rebars are not random samples but effectively represent the most mainstream and widely used rebar types of this historical era. Such a data foundation ensures the model can accurately capture the interfacial bond-slip behavior between rebars and corresponding concrete of the period, making it highly reliable for guiding the conservation of reinforced concrete architectural heritage from 1912 to 1949.

It should be noted that the model’s current application scope is tailored to the aforementioned historical period, as it has not yet been applied to rebars from other eras/regions or non-concrete substrate scenarios. Future research will further supplement test data of rebars from multiple batches with different sources and periods, clarify the model’s applicable boundaries under diverse material combinations and stress environments via parameter sensitivity analysis, and explore ways to expand its application scope (e.g., introducing correction coefficients) to provide more comprehensive technical support for the conservation of a broader range of historical buildings.