Eccentric Compression Behavior of High-Performance Fiber-Reinforced Cementitious Composite-Strengthened Concrete Hollow Block Masonry Walls with Simulated Material Property Degradation

Abstract

High-performance fiber-reinforced cementitious composite (HPFRCC) has shown considerable potential as a strengthening material for improving the crack resistance, integrity, and deformation capacity of masonry structures. In aging concrete hollow block masonry walls subjected to long-term eccentric compression, material degradation may lead to premature cracking, local crushing, stiffness deterioration, and reduced safety margins, thereby adversely affecting structural reliability and service performance. However, studies on the eccentric compression behavior of HPFRCC-strengthened concrete hollow block masonry walls with simulated material degradation remain limited. In this study, experimental, finite element, and theoretical analyses were conducted on three HPFRCC-strengthened specimens with an eccentricity ratio of 0.5y, namely a 30 mm double-sided strengthened specimen, a 45 mm double-sided strengthened specimen, and a 30 mm single-sided strengthened specimen. The failure modes, load–displacement responses, lateral deformation, strain development, and DIC strain distribution characteristics were investigated. The results showed that, under the test conditions considered in this study, the double-sided strengthened specimens exhibited higher load-bearing capacity, greater stiffness, and better structural integrity than the single-sided strengthened specimen. Among them, the 45 mm double-sided strengthened specimen reached the highest peak load of 1643 kN, whereas the 30 mm double-sided strengthened specimen exhibited a gentler post-peak response, more dispersed crack development, and better deformation compatibility. The finite element results were generally consistent with the experimental results; the ratios of the experimental to numerical peak loads ranged from 0.96 to 1.01, while the corresponding peak displacement ratios ranged from 1.02 to 1.09. Within the parameter range considered in the numerical analysis, increasing the strengthening thickness was generally beneficial to the eccentric compression capacity. The proposed preliminary sectional bearing capacity model showed acceptable agreement with the test results for the specimens considered in this study; however, its broader applicability requires further validation using additional specimens.

1. Introduction

Masonry structures are widely used in civil and industrial buildings because of their convenience in construction, relatively low cost, and satisfactory fire resistance and durability. Among them, concrete hollow block masonry has been extensively adopted in residential and industrial buildings owing to its resource efficiency, construction convenience, and favorable overall performance. However, in aging concrete hollow block masonry walls, long-term service may gradually lead to cracking, local crushing, stiffness deterioration, and reduced load-bearing capacity because of material degradation, environmental action, and inadequate structural detailing. In practical buildings, the vertical loads transmitted from slabs, beams, and upper walls are often accompanied by a certain degree of eccentricity. As a result, many masonry walls remain under long-term eccentric compression, under which the stress distribution becomes markedly non-uniform: the tension zone is prone to cracking, whereas the compression zone is susceptible to local crushing. This may further reduce the safety margin, serviceability, and structural reliability of existing walls.

To improve the performance of existing masonry structures, various strengthening techniques have been studied, including welded wire mesh-mortar overlays, fiber-reinforced composite strengthening, prestressed strengthening, and high-ductility cementitious composite overlays [1,2,3]. Among these methods, high-performance fiber-reinforced cementitious composites (HPFRCC) have shown considerable potential in the repair and strengthening of existing structures because of their tensile strain-hardening behavior, multiple cracking characteristics, excellent crack resistance, and high damage tolerance [4,5,6,7,8]. Compared with conventional mortar or ordinary concrete overlays, HPFRCC can not only improve the bearing capacity and integrity of structural members, but can also more effectively suppress crack localization, thereby enhancing post-peak behavior and deformation compatibility [9,10,11,12,13]. Therefore, HPFRCC is particularly suitable for strengthening masonry structures characterized by relatively high brittleness and insufficient ductility.

Existing studies on concrete hollow block masonry can be broadly grouped into two categories. The first category focuses on the compressive behavior and constitutive characteristics of hollow concrete block masonry, including prism strength, elastic modulus, and stress–strain response under compression [14,15,16,17,18,19]. These studies have provided an important basis for understanding the material-level and prism-level mechanical behavior of hollow concrete masonry. The second category focuses on strength prediction and performance evaluation methods, including empirical formulations and, more recently, data-driven or artificial-intelligence-based approaches such as artificial neural networks, adaptive neuro-fuzzy inference systems, explainable artificial intelligence, and hybrid machine-learning models [20,21,22,23,24,25]. Recent studies have shown that machine-learning-based approaches can improve the prediction efficiency and accuracy of the compressive strength of hollow concrete prisms or hollow block masonry and can also provide a supplementary perspective for identifying the key material and geometric variables affecting compressive strength [21,22,23,24,25]. Meanwhile, recent experimental and analytical studies have continued to improve the understanding of the compressive behavior of hollow concrete masonry prisms and grouted concrete masonry in a broader sense [18,19,26,27]. In addition, recent structural studies have also examined the enhancement of weak concrete hollow block masonry systems through reinforcement-based measures, highlighting the continued need to relate material-level strength evaluation to system-level structural performance [28]. However, these studies remain mainly concerned with material-, prism-, or general structural-level assessment and do not directly address the structural response, failure evolution, or strengthening effectiveness of hollow concrete block masonry walls strengthened with HPFRCC under eccentric compression.

Research on HPFRCC- or ECC-strengthened masonry members has also developed along a relatively clear line. Existing studies have mainly examined the seismic, in-plane shear, cyclic, and lateral behavior of masonry walls strengthened with HPFRCC or ECC overlays [9,10,11,12,13,29,30,31,32,33,34,35,36]. A general consensus from these studies is that overlay strengthening can significantly improve the bearing capacity, integrity, crack control performance, and deformation capacity of masonry members, and that double-sided strengthening is usually more effective than single-sided strengthening [9,10,11,12,13,29,30,31,32,33,34,35,36]. In addition, related studies and recent review papers on HPFRCC, ECC, and other high-ductility cementitious composites applied to the repair and strengthening of structural members have further demonstrated their advantages in suppressing crack localization, improving deformation compatibility, enhancing damage tolerance, and strengthening different reinforced concrete components and repair layers [37,38,39,40,41,42]. These broader applications indicate that cementitious overlay-based strengthening materials with crack-control capability are not limited to masonry walls alone, but can also be extended to other structural members and retrofitting scenarios. Nevertheless, the available studies have mainly focused on seismic or shear-related actions, while the eccentric compression behavior of HPFRCC-strengthened concrete hollow block masonry walls, especially under simulated material degradation conditions, remains insufficiently studied. As a result, the effects of strengthening scheme and strengthening thickness on failure evolution, post-peak response, and sectional bearing capacity under eccentric compression have not yet been systematically clarified.

Another issue that deserves attention is the deterioration state of existing masonry structures. In practice, aging walls are often affected by strength reduction, cracking, bond deterioration, and environmental damage. In the present study, the deterioration condition is simulated primarily from the perspective of material strength reduction by adopting relatively low-strength blocks and masonry mortar. This treatment does not reproduce all service-related deterioration mechanisms, but it provides a simplified and controllable way to investigate how strength-degraded hollow block masonry walls respond to HPFRCC strengthening under eccentric compression. Therefore, although previous studies have established the strengthening advantages of HPFRCC overlays and improved the understanding of hollow concrete masonry behavior, the coupled influence of eccentric compression, simulated material degradation, and strengthening configuration on the structural response of concrete hollow block masonry walls still lacks systematic experimental, numerical, and analytical clarification.

Based on the above review, the scientific problem addressed in this study is that the coupled effects of strengthening configuration, strengthening thickness, and simulated material degradation on the failure evolution, post-peak response, and sectional resistance of HPFRCC-strengthened concrete hollow block masonry walls under eccentric compression have not yet been clarified. From an engineering perspective, a clearer basis is needed for evaluating whether HPFRCC strengthening can effectively improve the eccentric compression resistance, deformation performance, and damage tolerance of aging hollow block masonry walls, and how different strengthening schemes may influence both peak capacity and post-peak stability. Therefore, the purpose of this study is to investigate the eccentric compression behavior of HPFRCC-strengthened concrete hollow block masonry walls with simulated material degradation through a combination of experimental testing, finite element analysis, and theoretical analysis. To achieve this purpose, three strengthened specimens with an eccentricity ratio of 0.5y were designed, including a 30 mm double-sided strengthened specimen, a 45 mm double-sided strengthened specimen, and a 30 mm single-sided strengthened specimen. The specific objectives of this study are as follows: (1) to compare the effects of double-sided and single-sided HPFRCC strengthening schemes under the same eccentric compression condition; (2) to examine the influence of strengthening thickness on failure modes, load–displacement response, strain development, and deformation characteristics; (3) to analyze the strain evolution and localization characteristics of the strengthened specimens with the aid of DIC observations; (4) to establish a finite element model for reproducing the overall structural response and conducting parametric analysis; and (5) to propose a preliminary sectional bearing capacity model for HPFRCC-strengthened concrete hollow block masonry walls under eccentric compression. The overall research framework and experimental–analytical program of the present study are shown in Figure 1.

2. Experimental Program

2.1. Specimen Design

To investigate the mechanical behavior of HPFRCC-strengthened concrete hollow block masonry walls with simulated aging-induced material degradation under eccentric compression, three wall specimens were designed. The original walls were constructed using concrete hollow blocks with dimensions of 390 mm × 190 mm × 190 mm, and the designed wall dimensions were 1000 mm × 720 mm × 190 mm. To simulate the degraded material condition of aging walls, both the blocks and the masonry mortar were selected to have relatively low strength grades. This simplified treatment was intended to represent the strength degradation aspect of aging masonry walls, while other service-related deterioration effects, such as cracking, bond degradation, and environmental damage, were not explicitly simulated in the present test program. The eccentricity ratio of all specimens was taken as 0.5y.

The specimens were designated as KXW-30, KXW-45, and SKXW-30. Among them, KXW-30 and KXW-45 were double-sided strengthened specimens, with strengthening thicknesses of 30 mm and 45 mm, respectively, whereas SKXW-30 was a single-sided strengthened specimen with a strengthening thickness of 30 mm. For the double-sided strengthened specimens, HPFRCC layers were applied to both faces of the wall and along the peripheral edges, whereas for the single-sided strengthened specimen, the HPFRCC layer was applied only to one face of the wall and along the peripheral edges. Before strengthening, the wall surfaces were roughened and the mortar joints were treated. In addition, a 10 mm thick cement mortar leveling layer was provided at both the top and bottom of each specimen. The dimensions of the strengthened specimens were 1060 mm × 780 mm × 250 mm, 1090 mm × 810 mm × 280 mm, and 1060 mm × 780 mm × 220 mm, respectively. The detailed parameters are listed in

Table 1. Specimen design parameters.

Specimen ID	Strengthening Scheme	Strengthening Thickness (mm)	Measured Dimensions (H × W × T) (mm)	Mortar Strength Grade	Eccentricity Ratio
KXW-30	Double-sided strengthening	30	1060 × 780 × 250	Mb5.0	0.5y
KXW-45	Double-sided strengthening	45	1090 × 810 × 280	Mb5.0	0.5y
SKXW-30	Single-sided strengthening	30	1060 × 780 × 220	Mb5.0	0.5y

Note: y represents the distance from the section centroid to the edge.

. The specimen configuration and fabrication process are shown in Figure 2 and Figure 3, respectively.

All strengthening layers were reinforced with 6 mm diameter steel wire mesh, with vertical bars arranged as C6@200 and horizontal bars arranged as C6@180. In the double-sided strengthened specimens, the steel meshes on both sides were connected by tie bars, and U-shaped reinforcing bars were used at the side edges and corners for strengthening. The single-sided strengthened specimen adopted similar detailing on the strengthened side and in the edge regions.

Owing to the limitations of the experimental conditions, only three strengthened specimens with an eccentricity ratio of 0.5y were included in the present test program, and no unstrengthened original wall was incorporated as a control specimen. Accordingly, the experimental program was designed primarily to compare the relative mechanical responses of different HPFRCC strengthening configurations under the same eccentric compression condition, rather than to directly quantify the absolute strengthening effectiveness relative to an unstrengthened wall. Such direct quantification was beyond the scope of the present study and should be investigated in future work.

2.2. Mechanical Properties of Materials

The reinforcing bars used in the tests were 6 mm-diameter HRB400 steel bars. Their measured yield strength and ultimate tensile strength were 468.99 MPa and 575.23 MPa, respectively, as listed in

Table 2. Measured mechanical properties of reinforcing bars.

Steel Grade	Diameter (mm)	Yield Strength (MPa)	Ultimate Tensile Strength (MPa)
HRB400	6	468.99	575.23

.

The masonry units were MU5.0 concrete hollow blocks, with an average compressive strength of 3.69 MPa. The masonry mortar had a design strength grade of Mb5.0 and an average compressive strength of 6.35 MPa, as listed in

Table 3. Measured mechanical properties of concrete hollow blocks and masonry mortar.

Material	Grade	Specimen Size (mm)	Number of Specimens	Strength Index	Measured Values (MPa)	Average Value (MPa)
Concrete hollow block	MU5.0	390 × 190 × 190	5	Compressive strength	4.15, 4.45, 2.88, 3.65, 3.34	3.69
Masonry mortar	Mb5.0	70.7 × 70.7 × 70.7	4	Cube compressive strength	4.60, 6.90, 7.30, 6.60	6.35

.

The strengthening material was HPFRCC incorporating polyvinyl alcohol (PVA) fibers. The properties of the PVA fibers are listed in

Table 4. Properties of PVA fibers.

Fiber Type	Length (mm)	Diameter (μm)	Aspect Ratio	Elongation (%)	Tensile Strength (MPa)	Density (g/cm3)	Elastic Modulus (GPa)
PVA	12	39	308	7	1600	1.3	40

.

The average tensile strength and compressive strength of HPFRCC, obtained from direct tensile tests and cube compression tests, were 2.40 MPa and 24.16 MPa, respectively, as listed in

Table 5. Measured mechanical properties of HPFRCC.

Property	Test Method	Number of Specimens	Measured Values (MPa)	Average Value (MPa)
TENSILE strength	Dog-bone tensile test	6	2.87, 3.21, 2.73, 1.52, 2.44, 1.67	2.40
COMPRESSIVE strength	Cube compression test	6	25.60, 25.48, 24.55, 24.25, 23.23, 21.83	24.16

. It should be noted that the material tests in this study were primarily intended to provide the strength parameters required for structural analysis, rather than to systematically determine a complete set of tensile constitutive parameters, such as the full tensile stress–strain curve, ultimate tensile strain, and the slope of the strain-hardening branch. Given the scatter in the direct tensile test results, the tensile strain-hardening behavior of HPFRCC was represented using an equivalent simplified approach based on the measured strength values for structural-level analysis rather than detailed material-level constitutive characterization.

2.3. Test Setup and Loading Procedure

The eccentric compression test was carried out using a 10,000 kN electro-hydraulic servo universal testing machine. A spherical hinge was installed above the loading beam to minimize unintended secondary bending moments caused by slight installation eccentricities or contact imperfections. The eccentric load was applied by intentionally offsetting the vertical load line from the section centroid of the specimen at the top loading position. In this study, the eccentricity ratio was taken as 0.5y, where y denotes the distance from the section centroid to the edge of the section. During loading, the prescribed eccentricity was maintained through the relative position between the loading plate and the specimen section, while a cement mortar leveling layer was used at the top and bottom of the specimen to improve the uniformity of contact stress. The overall test setup and the eccentric load application scheme are illustrated in Figure 4.

The tests were conducted using a combination of load control and displacement control. Before formal loading, a preload of 20 kN was applied. During the initial loading stage, the load was increased by 10 kN per increment and held for 5 min at each level. After the appearance of the first crack, the load increment was increased to 20 kN, with a holding time of 5 min for each level. As crack development progressed further, the load increment was increased to 50 kN, again with a holding time of 5 min at each level. After the peak load was reached and the descending branch was entered, the loading mode was changed to displacement control at a rate of 0.1 mm/min. The test was terminated when the load dropped to 85% of the peak load.

2.4. Measurement Scheme

The test adopted a combined measurement scheme consisting of local sensor measurements and digital image correlation (DIC) full-field measurements. Strain gauges were attached to the surfaces of the longitudinal reinforcing bars to monitor the development of steel strain. Surface strain gauges were installed at critical locations on the wall to monitor the strain in the compression zone and other key regions. Displacement transducers were arranged at the top and mid-height of the wall to measure vertical displacement, lateral deflection, and overall rotation. The layouts of the strain gauges and displacement transducers are shown in Figure 5 and Figure 6, respectively.

To obtain the full-field displacement and strain distributions on the wall surface, a random speckle pattern was sprayed onto the observation surface of the specimens, and the DIC technique was employed for measurement. Owing to the poor surface condition on the unstrengthened side of the single-sided strengthened specimen, DIC measurement was mainly carried out for the double-sided strengthened specimens. The corresponding measurement setup is shown in Figure 7.

2.5. Failure Criteria

A specimen was considered to have reached its ultimate state when a marked reduction in load-bearing capacity occurred after the peak load, accompanied by obvious crushing or spalling in the compression zone, rapid propagation of major cracks, significant stiffness degradation with a sharp increase in deformation, or evident bending and instability. In this study, the loading was terminated when the load decreased to 85% of the peak load.

3. Test Results and Analysis

3.1. Failure Process and Failure Modes

Under eccentric compression, all specimens experienced the elastic stage, cracking stage, nonlinear deformation stage, and final failure stage. The final failure of all specimens was characterized by local crushing in the compression zone, through-crack formation, and local debonding of the strengthening layer; however, the failure characteristics differed significantly depending on the strengthening scheme. In specimen KXW-30, cracks were more widely distributed, and a certain load-bearing capacity was still retained after the peak load. In specimen KXW-45, crushing in the upper region on the near-load side was more pronounced, and debonding occurred in the strengthening layer along the side surface, indicating the most concentrated failure pattern among the three specimens. In specimen SKXW-30, cracks were mainly concentrated on one side, while block crushing and spalling on the far-load side were more evident, accompanied by more pronounced overall bending and top rotation.

Overall, the double-sided strengthened specimens exhibited better integrity and more uniform stress distribution than the single-sided strengthened specimen. Among them, the 45 mm double-sided strengthened specimen showed a higher peak load but a more concentrated local failure pattern. By contrast, the 30 mm double-sided strengthened specimen exhibited a more dispersed crack distribution and a gentler post-peak response, indicating better stability during the failure development process. These results suggest that increasing the thickness of double-sided strengthening can improve the compressive stiffness and load-bearing capacity of the section, but may also intensify local restraint and stress concentration in the compression zone, thereby leading to a more concentrated post-peak failure pattern. In contrast, the thinner double-sided strengthening layer resulted in more dispersed crack development and better deformation compatibility, which is consistent with the superior crack-dispersing capacity of the HPFRCC overlay. The typical final failure modes of the specimens are shown in Figure 8. To provide more direct visual evidence of local failure characteristics, close-up views of the typical local damage zones are presented in Figure 9. These images further illustrate the differences in crack concentration, local crushing, and strengthening-layer damage among the three strengthening configurations.

3.2. Load–Displacement Curves and Analysis of Characteristic Parameters

The load–displacement curves of all specimens can be divided into three stages: the elastic stage, the nonlinear development stage, and the post-peak descending stage. Significant differences were observed in both the curve shapes and the characteristic parameters under different strengthening schemes. Specimen KXW-45 exhibited the highest initial stiffness and peak load, indicating that increasing the thickness of double-sided strengthening can significantly improve the eccentric compression capacity and overall stiffness of the wall. Specimen KXW-30 showed a gentler post-peak descending branch, suggesting a relatively stable post-peak load-carrying process. In contrast, specimen SKXW-30 entered the nonlinear stage earlier and exhibited the lowest peak load, indicating that single-sided strengthening had a limited effect on improving the overall mechanical performance. The load–displacement curves of the specimens are shown in Figure 10.

The characteristic loads and stiffness values of the specimens are listed in

Table 6. Characteristic loads.

Specimen	Cracking Load (kN)	Yield Load (kN)	Peak Load (kN)	Ultimate Load (kN)	Initial Stiffness (kN/mm)	Equivalent Stiffness (kN/mm)
KXW-30	90	810	985.1	837.3	135	67.8
KXW-45	50	1412.8	1643	1396.1	153	109.9
SKXW-30	30	438.5	565.8	477.5	32	52.1

. The peak loads of KXW-30, KXW-45, and SKXW-30 were 985.1 kN, 1643.0 kN, and 565.8 kN, respectively, while the corresponding initial stiffness values were 135.0 kN/mm, 153.0 kN/mm, and 32.0 kN/mm, respectively. Overall, under the test conditions considered in this study, double-sided strengthening was more effective than single-sided strengthening in improving both load-bearing capacity and stiffness. Among the double-sided strengthened specimens, the 45 mm strengthening thickness was more beneficial for enhancing the ultimate load-bearing capacity, whereas the 30 mm strengthening thickness showed better performance in terms of post-peak stability and deformation compatibility.

It should be noted that the cracking load of KXW-45 was lower than that of KXW-30. Considering the sensitivity of the specimen to local defects in the compression zone, the timing of first-crack identification, and the non-uniform stress distribution under eccentric compression, this difference is more likely to reflect the sensitivity of the initial cracking stage to local weak regions and crack identification criteria, rather than indicating that the overall mechanical performance of the thicker double-sided strengthening was inferior to that of the 30 mm double-sided strengthening. In fact, KXW-45 still exhibited significantly higher yield load, peak load, and overall stiffness than KXW-30.

From the perspective of post-peak response, the differences between KXW-30 and KXW-45 can be attributed to the different balance between sectional strengthening efficiency and post-peak strain redistribution capacity. The thicker double-sided strengthening layer in KXW-45 significantly enhanced the sectional stiffness and peak load-bearing capacity, but also led to a stronger local restraint effect in the compression zone. Once the specimen approached the peak load, the compressive damage and crack development were more likely to concentrate within a narrower dominant region, resulting in faster strain localization, more concentrated local crushing, and a steeper post-peak descending branch. By contrast, although KXW-30 exhibited a lower peak load, its thinner double-sided strengthening layer allowed a relatively more dispersed development of cracks and strains, so that a certain degree of stress redistribution could still be maintained after the peak load. As a result, the post-peak load-carrying process of KXW-30 was relatively gentler, indicating better deformation compatibility and failure stability. Therefore, the post-peak behavior of the double-sided strengthened specimens was governed not only by the increase in sectional resistance provided by the HPFRCC layer, but also by the ability of the strengthened section to maintain distributed cracking and strain redistribution after the peak load.

To improve the reproducibility of the parameter definitions, the initial stiffness in this study was defined as the secant slope of the approximately linear initial stage of the load–displacement curve, while the equivalent stiffness was defined as the ratio of the yield load to the yield displacement, i.e., $K_e={\displaystyle \frac{P_y}{{\mathsf{\Delta }}_y}}$. For specimen SKXW-30, the apparent stiffness in the initial loading stage was relatively low, possibly because of factors such as compaction of the leveling layer, contact adjustment, and local micro-slip. After entering the stable loading stage, the mechanical compatibility of the composite section was gradually established, and the slope of the curve increased accordingly, resulting in an equivalent stiffness greater than the initial stiffness. This phenomenon essentially indicates that the single-sided strengthened specimen was more sensitive to contact conditions and local deformation during the initial loading stage. It also indirectly suggests that its overall composite action was weaker than that of the double-sided strengthened specimens. However, this does not alter the basic conclusion that its overall load-bearing capacity and mechanical stability were inferior to those of the double-sided strengthened specimens.

3.3. Analysis of Ductility and Lateral Deformation

The ductility parameter was defined as the ratio of the ultimate displacement to the yield displacement, as listed in

Table 7. Ductility factors.

Specimen	Yield Displacement (mm)	Ultimate Displacement (mm)	Ductility Factor
KXW-30	11.95	17.253	1.444
KXW-45	12.85	14.828	1.098
SKXW-30	8.42	12.088	1.436

. The ductility factors of KXW-30, KXW-45, and SKXW-30 were 1.444, 1.098, and 1.436, respectively, indicating that KXW-30 and SKXW-30 had similar ductility levels, both of which were higher than that of KXW-45. This suggests that although a thicker double-sided strengthening layer can significantly increase the peak load-bearing capacity, its effect on improving the post-peak plastic deformation capacity is not pronounced. The load-deflection curves of the specimens and the lateral deflections corresponding to the peak loads are shown in Figure 11. Overall, the double-sided strengthened specimens exhibited a lower rate of deflection development than the single-sided strengthened specimen. Among them, specimen KXW-30 showed the smallest lateral deflection at the peak load, with a value of only 0.7 mm. Specimen KXW-45 reached the highest peak load, but its corresponding lateral deflection increased to approximately 1.8 mm. In contrast, specimen SKXW-30 exhibited a lower load-bearing capacity and relatively weaker overall stability. These results indicate that different strengthening schemes have distinct characteristics in terms of enhancing load-bearing capacity and controlling deformation: the 45 mm double-sided strengthening scheme was more effective in improving the ultimate load-bearing capacity, whereas the 30 mm double-sided strengthening scheme showed a more balanced performance in controlling lateral deformation and maintaining post-peak deformation compatibility.

3.4. Analysis of Load-Strain Relationships

The load-strain curves of the specimens are shown in Figure 12. At the initial loading stage, the strain in the reinforcing bars at each measurement point increased approximately linearly with increasing load. As the load increased further, the curves gradually became nonlinear, indicating the onset of crack development and internal force redistribution. The reinforcing bar strains in the double-sided strengthened specimens, KXW-30 and KXW-45, were generally lower than those in the single-sided strengthened specimen, indicating that double-sided strengthening was beneficial for improving the sectional stress condition. In KXW-30, the strain developed relatively steadily, whereas in KXW-45, the strains in the reinforcing bars on the near-load side and at the bottom increased more rapidly, indicating a more pronounced local strain concentration under the thicker double-sided strengthening condition. In SKXW-30, the strain in the reinforcing bars near the mid-height on the near-load side increased most significantly and approached yielding near the peak load. In addition, the bottom reinforcing bars gradually changed from tension to compression, reflecting a more pronounced non-uniform sectional stress distribution under the single-sided strengthening condition. Overall, double-sided strengthening was more effective in suppressing strain concentration, and the 30 mm double-sided strengthening scheme exhibited a more balanced strain development.

3.5. DIC-Based Validation Analysis

The DIC results showed that the strain distributions of the double-sided strengthened specimens were relatively dispersed during the cracking stage. As the load increased, the strain gradually concentrated in the vicinity of the major cracks. The transverse strain contours indicated that KXW-45 developed more continuous and concentrated high-strain bands at the peak and ultimate stages, suggesting that crack propagation and localized tensile deformation were more likely to concentrate within a single dominant region. In contrast, KXW-30 still retained several dispersed high-strain bands at the ultimate stage, indicating that it maintained a certain capacity for strain redistribution after the peak load. The vertical strain contours further showed that the compression zone near the top of KXW-45 was more likely to form a continuous high-strain concentration region, whereas the high-strain region in KXW-30 remained relatively narrow, with a certain transition zone still preserved around it. The transverse strain contours of KXW-45 and KXW-30 are shown in Figure 13 and Figure 14, respectively. The vertical strain contours of KXW-45 and KXW-30 are shown in Figure 15 and Figure 16, respectively.

These observations are consistent with the more concentrated local crushing of KXW-45 described in Section 3.1 and the gentler post-peak descending response of KXW-30 discussed in Section 3.2. This indicates that the DIC results not only provide visual evidence of the failure patterns, but also support, from the perspective of strain evolution, the conclusion that the 45 mm double-sided strengthening scheme achieved higher load-bearing capacity but was more prone to post-peak localization, whereas the 30 mm double-sided strengthening scheme exhibited better post-peak deformation compatibility.

To further quantify the strain localization characteristics revealed by the DIC results, representative strain values and the area proportions of high-strain zones were extracted from the transverse and vertical strain fields of the two double-sided strengthened specimens at the peak and ultimate stages. The quantitative results are listed in

Table 8. Quantitative DIC indicators of the double-sided strengthened specimens at the peak and ultimate stages.

Specimen	Load Stage	Transverse Representative Strain	High Transverse Strain Zone Ratio (%)	Vertical Representative Strain Magnitude	High Vertical Strain Zone Ratio (%)
KXW-45	Peak	0.011	12.36	0.016	11.52
KXW-45	Ultimate	0.023	21.15	0.046	8.42
KXW-30	Peak	0.009	8.69	0.012	7.73
KXW-30	Ultimate	0.016	14.55	0.031	12.29

Note: The representative strain values were extracted under the same processing settings for both specimens, and the area ratios were calculated with respect to the effective DIC measurement area.

. At the peak stage, KXW-45 exhibited higher transverse and vertical representative strain values, as well as larger high-strain zone area ratios, than KXW-30. At the ultimate stage, the transverse representative strain and high transverse strain zone ratio of KXW-45 increased to 0.023 and 21.15%, respectively, compared with 0.016 and 14.55% for KXW-30, indicating a more pronounced tensile strain localization in KXW-45. For the vertical strain field, the representative strain magnitude of KXW-45 also remained higher than that of KXW-30 at the ultimate stage (0.046 versus 0.031), whereas its high vertical strain zone ratio was lower (8.42% versus 12.29%). This indicates that the compressive strain in KXW-45 was concentrated within a narrower but more intense dominant zone, while KXW-30 retained a relatively wider but less intense compressive high-strain region. Therefore, the quantitative DIC analysis further supports the conclusion that KXW-45 was more prone to localized strain concentration, whereas KXW-30 showed a more dispersed strain distribution and better post-peak deformation compatibility.

4. Finite Element Analysis

4.1. Establishment of the Finite Element Model

To further investigate the mechanical response of HPFRCC-strengthened concrete hollow block masonry walls with simulated aging-induced material degradation under eccentric compression, and to provide a basis for the parametric analysis, a finite element model of the specimens was established in ABAQUS. The model was built at a 1:1 scale according to the actual specimen dimensions and mainly consisted of the original masonry wall, the HPFRCC strengthening layer, vertical reinforcing bars, horizontal distributed reinforcing bars, tie bars, end reinforcing bars, and the loading plate. The main components of the finite element model are illustrated in Figure 17.

In terms of element selection, the original masonry wall and the HPFRCC strengthening layer were both modeled using the three-dimensional solid element C3D8R to simulate the continuum mechanical behavior of the wall and strengthening layer. The reinforcing bars were modeled using the three-dimensional truss element T3D2 to simulate the mechanical response of the vertical bars, horizontal bars, and connecting reinforcement. Considering that the focus of this study is on the overall mechanical behavior of the wall and the response differences under different strengthening schemes, all constituent materials in the model were assembled according to the actual detailing configuration to ensure that the numerical results were comparable with the experimental observations. The original masonry wall and the HPFRCC strengthening layer were discretized using structured solid meshes, with characteristic mesh sizes of 25 mm and 50 mm, respectively. The reinforcing bars were modeled using truss elements with a characteristic discretization interval of 20 mm, and were embedded in the HPFRCC strengthening layer to establish coordinated action.

In terms of constitutive modeling, the original masonry under compression was described using a nonlinear compressive constitutive relationship, while its tensile behavior was neglected. This assumption is commonly adopted in simplified masonry modeling because the tensile capacity of masonry is relatively low and crack development under eccentric compression is mainly governed by the behavior of the compression zone and the strengthened section. Nevertheless, neglecting the tensile behavior of the original masonry may affect the prediction of the initial cracking stage, the stiffness transition before significant nonlinear development, and the stress redistribution in the tension zone. Therefore, the present numerical model is more suitable for capturing the overall response trend and relative differences between strengthening configurations than for precisely reproducing the onset of cracking and the detailed tensile response of the unstrengthened masonry. The reinforcing bars were modeled using a bilinear constitutive model. For HPFRCC, a bilinear constitutive model was adopted in tension and a piecewise constitutive model was used in compression. It should be noted that the cracking strength and peak tensile stress of HPFRCC were determined mainly from the average measured strengths obtained from the direct tensile tests, while the post-cracking strain-hardening branch was represented in a simplified manner by an equivalent slope [4,5,6,7,8]. Since a complete tensile stress–strain curve was not systematically obtained in this study, the bilinear tensile constitutive relationship was mainly used as an equivalent representation for the overall structural analysis. The material parameters were determined on the basis of the experimental results. Specifically, the strength parameters of the reinforcing bars were taken from Table 2, those of the blocks and mortar were taken from Table 3, and those of HPFRCC were taken from Table 5. The plasticity-related material parameters adopted for the masonry and HPFRCC materials in the finite element model are summarized in

Table 9. Plasticity-related material parameters adopted in the finite element model.

Material	Poisson’s Ratio	Dilation Angle	Eccentricity	${\mathit{f}}_{\mathit{b}\mathbf{0}}\mathbf{/}{\mathit{f}}_{\mathit{c}\mathbf{0}}$	K	$\mathbf{Viscosity} \mathbf{Parameter} \mathsf{\mu }$
MASONRY	0.3	30	0.1	1.16	0.667	0.02
HPFRCC	0.2	30	0.1	1.16	0.667	0.008

.

With regard to the interaction relationships and boundary treatment, the original masonry wall was modeled as an equivalent homogeneous continuum, and the block–mortar joints were not explicitly discretized in the present finite element model. This simplified treatment was adopted to focus on the overall eccentric compression response of the strengthened walls rather than on the local interaction between individual blocks and mortar joints. The reinforcing bars were connected to the HPFRCC strengthening layer using the Embedded Region constraint to simulate their coordinated action, while the HPFRCC strengthening layer was connected to the original masonry wall using a Tie constraint to ensure compatible deformation during loading. In addition, the loading plate was tied to the top surface of the wall, and the vertical load was applied through a reference point coupled to the loading plate. The bottom of the model was fully restrained according to the support conditions in the tests. Further details of the reference point coupling, eccentric loading scheme, boundary conditions, and mesh discretization are presented in Figure 18.

It should be noted that this idealized interaction treatment can reasonably reproduce the overall response of the specimens, but local phenomena such as interface slip, bond degradation, joint opening or sliding, initial defects, and non-ideal contact were not explicitly considered. This is also one of the main reasons why the initial stiffness predicted by the numerical simulation was slightly higher than that measured in the tests.

Overall, the established model provided a reliable basis for comparison with the test results and for the subsequent parametric analysis.

4.2. Comparison Between Numerical and Experimental Results

The tensile damage contours of the specimens are shown in Figure 19. The comparison between the experimental and numerical load–displacement curves is shown in Figure 20. The comparison of numerical and experimental peak loads and corresponding displacements is summarized in

Table 10. Comparison of numerical results for walls under eccentric compression.

Specimen	Peak Load (kN)			Vertical Displacement at Peak Load (mm)
	Experimental	Numerical	Experimental/Numerical	Experimental	Numerical	Experimental/Numerical
KXW-30	985.1	1023	0.96	14.63	14	1.04
KXW-45	1643	1622.46	1.01	13.41	13.05	1.02
SKXW-30	565.8	584.3	0.97	10.42	9.5	1.09

. The finite element results indicate that the developed model can reasonably capture the overall mechanical response of HPFRCC-strengthened concrete hollow block masonry walls with simulated aging-induced material degradation under eccentric compression. The simulated load–displacement curves were generally consistent with the experimental curves in terms of their overall pre-peak evolution, and the predicted peak loads and corresponding displacements were close to the experimental results. For KXW-30, KXW-45, and SKXW-30, the ratios of the experimental values to the numerical values were 0.96, 1.01, and 0.97 for the peak load, and 1.04, 1.02, and 1.09 for the corresponding peak displacement, respectively. These results indicate that the model provided reasonably accurate predictions of both the load-bearing capacity and the displacement response.

Compared with the experimental results, the simulated curves exhibited slightly higher initial stiffness. This discrepancy is mainly attributable to the idealization of the material constitutive models, the neglect of interface slip and bond degradation, and the omission of initial defects and local non-ideal contact conditions. Therefore, the model is more suitable for reflecting the overall mechanical response trend of the specimens and the relative influence of parameter variations, whereas it still has limitations in describing the initial contact stage, nonlinear transition points, and local damage details in the post-peak stage.

In terms of damage distribution, the double-sided strengthened specimens showed relatively uniform damage development, whereas the single-sided strengthened specimen exhibited a higher degree of damage concentration. Among the double-sided strengthened specimens, local damage in KXW-45 was more concentrated, while the damage distribution in KXW-30 was more dispersed. These results are generally consistent with the experimentally observed failure patterns and curve evolution characteristics, indicating that the model can reasonably reflect the damage development features under different strengthening schemes.

4.3. Parametric Analysis of Strengthening Thickness Based on the Finite Element Model

Based on the experimentally validated finite element model, a controlled-variable approach was adopted to investigate the effect of strengthening thickness on the eccentric compression behavior of the walls. It should be noted that the conclusions in this section are mainly derived from an idealized numerical model validated against only three specimens and should therefore be interpreted as trend-based findings within the scope of the present model and parameter range. The numerical results show that, under a constant eccentricity ratio, as the HPFRCC strengthening thickness increased, the peak loads of both the single-sided and double-sided strengthened specimens generally increased, while the peak displacements generally decreased. The increase in load-bearing capacity was more pronounced for the double-sided strengthening scheme. These results indicate that an appropriate increase in strengthening thickness is beneficial for improving the overall stiffness and eccentric compression capacity of the member. The load–displacement curves for different strengthening thicknesses are shown in Figure 21.

The corresponding peak loads, peak displacements, and variations in peak load are listed in

Table 11. Comparison of peak results for different parameters.

Parameter Type	Condition	Variable Value	Peak Load (kN)	Peak Displacement (mm)	Variation in Peak Load (%)
Strengthening thickness	Double-sided	10	712.30	18.10	-
		20	861.32	16.40	21.13
		30	1023.28	14.00	18.95
		45	1622.46	13.05	58.60
		55	1981.62	11.80	22.04
	Single-sided	10	431.15	12.50	-
		20	505.72	11.40	17.44
		30	584.30	9.50	15.64
		45	781.56	8.80	33.56
		55	879.60	8.20	12.82

. At the same time, combined with the local crushing and strain concentration observed in specimen KXW-45 during the tests, it can be inferred that a thicker double-sided strengthening layer, while improving the load-bearing capacity, may also intensify local restraint and stress concentration in the compression zone, thereby leading to a more concentrated post-peak failure pattern. It should also be noted that when the thickness of the double-sided strengthening layer increased from 30 mm to 45 mm, the increase in peak load was significantly greater than that in the preceding stages. This may be related to the simultaneous enhancement of flexural stiffness and core confinement after the thickness of the composite section increased. Considering that the model did not explicitly account for factors such as interface slip, bond degradation, and initial defects, this increase should be understood as a stage-specific response characteristic under the present modeling conditions, rather than being directly extrapolated as a general engineering rule.

5. Theoretical Analysis and Bearing Capacity Calculation

5.1. Basic Assumptions and Calculation Approach

To analyze the eccentric compression bearing capacity of HPFRCC-strengthened concrete hollow block masonry walls with simulated aging-induced material degradation, a preliminary simplified sectional bearing capacity model for this type of member was proposed in this study based on the experimental observations and sectional mechanical characteristics. The following basic assumptions were adopted in the calculation: plane sections remain plane after deformation; the hollow block section is treated as an equivalent continuous medium; the HPFRCC strengthening layer, longitudinal reinforcing bars, and core masonry act in a coordinated manner before the ultimate state; and the tensile resistance of the original masonry in the tension zone is neglected. It should be noted that this model is a preliminary analytical method developed on the basis of limited experimental results, and its parameter values and applicability still require further verification through additional tests.

5.2. Calculation Method for Sectional Bearing Capacity

Based on the above assumptions, an equivalent analysis was carried out for the eccentrically compressed section by considering the mechanical characteristics of the original masonry, the HPFRCC strengthening layer, and the reinforcing bars. To facilitate calculation, an equivalent rectangular stress block was adopted to simplify the nonlinear stress distribution in the compression zone. In addition, utilization factors for the compressive and tensile strengths of HPFRCC and a confinement-modified equivalent compressive strength of the core masonry were introduced.

The utilization factors for the compressive and tensile strengths of HPFRCC were determined mainly based on the measured material strengths and the degree of stress development at the ultimate state. These factors were introduced to account for the fact that the strength of the strengthening layer cannot be fully mobilized according to the nominal material strength under the present sectional assumptions. Therefore, they should be understood as experiment-informed and condition-dependent parameters within the framework of the present simplified model, rather than as universally applicable design parameters. The confinement-modified equivalent compressive strength of the core masonry was determined based on Richart’s confinement concept and the lateral static equilibrium relationship [43], and was used to reflect the enhancement in compressive resistance of the core masonry subjected to lateral confinement under the double-sided strengthening condition.

The above parameters were introduced so that the theoretical model, while remaining simplified, could approximately reflect the influences of the constituent materials and detailing characteristics on the eccentric compression bearing capacity. It should be emphasized that the utilization factors and equivalent strength parameters adopted in the present model were established mainly on the basis of measured material strengths and simplified sectional assumptions under the present test conditions. Although these parameters enable the model to reasonably reflect the sectional response of the tested specimens, they should not be interpreted as universally applicable design parameters. Their values remain condition-dependent and may vary with the strengthening configuration, material properties, eccentricity level, and modeling assumptions. Therefore, the present calculation method should be regarded as a preliminary analytical approach for specimens similar to those considered in this study. For a wider range of structural configurations and parameter values, further verification through additional tests and sensitivity analyses is still required. The sectional calculation model and the corresponding strain and stress distributions are illustrated in Figure 22.

(1) Calculation of key coefficients

To account for the actual strength mobilization of the HPFRCC strengthening layer at the ultimate state, the compressive strength utilization factor α_c and the tensile strength utilization factor α_t are defined as follows:

$${\alpha }_c={\displaystyle \frac{{\sigma }_{hc}}{f_{hc}}}$$

(1)

$${\alpha }_t={\displaystyle \frac{{\sigma }_{ht}}{f_{ht}}}$$

(2)

where ${\sigma }_{hc}$ is the actual compressive stress in the HPFRCC strengthening layer in the compression zone when the specimen reaches its ultimate bearing capacity; $f_{hc}$ is the measured compressive strength of HPFRCC; ${\sigma }_{ht}$ is the actual tensile stress in the HPFRCC strengthening layer in the tension zone when the specimen reaches its ultimate bearing capacity; and $f_{ht}$ is the measured tensile strength of HPFRCC.

Under the double-sided strengthening condition, the core masonry is subjected to passive lateral confinement provided by the HPFRCC overlays on both sides. According to Richart’s confinement model, the equivalent compressive strength of the confined core masonry can be expressed as:

$$f_{mc}=f_m+4.1f_l$$

(3)

From lateral static equilibrium, it follows that:

$$f_l{h}_m=2f_{ht}{t}_h$$

(4)

Rearranging gives:

$$f_{mc}=f_m+4.1{\displaystyle \frac{2f_{ht}{t}_h}{h_m}}$$

(5)

where $f_{mc}$ is the confinement-modified equivalent compressive strength of the core masonry; $f_m$ is the compressive strength of the unconfined core masonry; $f_l$ is the effective lateral confining stress exerted on the core masonry by the double-sided HPFRCC strengthening layers; and $h_m$ is the thickness of the inner core hollow block masonry wall.

(2) Calculation of the eccentric compression bearing capacity for the double-sided strengthening scheme

When $x\le {\xi }_b{h}_0$, the tensile reinforcing bars yield, and the following relation is adopted:

$$T_s=f_y{A}_s$$

(6)

For the large-eccentricity compression case, the axial force equilibrium equation is written as follows:

$$N={\alpha }_c{f}_{hc}b{t}_h+f_{mc}\gamma b(x-t_h)+f_y’A_s’-f_y{A}_s-{\alpha }_t{f}_{ht}b{t}_h$$

(7)

For the small-eccentricity compression case, the axial force equilibrium equation is written as follows:

$$Ne={\alpha }_c{f}_{hc}b{t}_h\left(h_0-{\displaystyle \frac{t_h}{2}}\right)+f_{mc}b(x-t_h)\left(h_0-{\displaystyle \frac{x+t_h}{2}}\right)+f_y’A_s’(h_0-a_s’)+{\alpha }_t{f}_{ht}b{t}_h\left(a_s-{\displaystyle \frac{t_h}{2}}\right)$$

(8)

When $x>{\xi }_b{h}_0$, the tensile reinforcing bars do not yield, and their stress is:

$${\sigma }_s=E_s{\epsilon }_u\left({\displaystyle \frac{{\beta }_1{h}_0-x}{x}}\right)$$

(9)

The axial force equilibrium equation is:

$$N={\alpha }_c{f}_{hc}b{t}_h+f_{mc}b(x-t_h)+f_y’A_s’-{\sigma }_s{A}_s-{\alpha }_t{f}_{ht}b{t}_h$$

(10)

The moment equilibrium equation is:

$$Ne={\alpha }_c{f}_{hc}b{t}_h\left(h_0-{\displaystyle \frac{t_h}{2}}\right)+f_{mc}b(x-t_h)\left(h_0-{\displaystyle \frac{x+t_h}{2}}\right)+f_y’A_s’(h_0-a_s’)+{\alpha }_t{f}_{ht}b{t}_h\left(a_s-{\displaystyle \frac{t_h}{2}}\right)$$

(11)

where $N$s the ultimate axial bearing capacity of the composite section; e is the distance from the line of action of the axial load to the resultant force point of the longitudinal tensile reinforcement; $e_0$ is the initial eccentricity; b is the width of the wall section; $h$ is the total height of the section; $t_h$ is the thickness of the HPFRCC strengthening overlay on one side; $h_0$ is the effective depth of the section; $A_s$ and $A_s’$ are the cross-sectional areas of the longitudinal reinforcement in the tension zone and compression zone, respectively; as and as’ are the distances from the resultant force points of the longitudinal reinforcement in the tension zone and compression zone, respectively, to the nearest edge of the section; $f_y$ and $f_y’$ are the tensile and compressive yield strengths of the longitudinal reinforcement, respectively; $f_{hc}$ and $f_{ht}$ are the compressive strength and tensile strength of HPFRCC, respectively; $f_m$ is the compressive strength of the unconfined masonry; $f_{mc}$ is the confinement-modified equivalent compressive strength of the core masonry; and ${\sigma }_s$ is the stress in the tensile reinforcement under small-eccentricity compression.

When the eccentricity is small and the iterative results indicate that the section is fully in compression, the tensile terms in the above equations are taken as zero, and the reinforcing bars are included in the calculation as compression reinforcement.

(3) Calculation of the eccentric compression bearing capacity for the single-sided strengthening scheme

For the single-sided strengthened specimen, the HPFRCC strengthening overlay was provided only on the compression side, whereas the tension side remained as the original masonry. Consequently, the section exhibited a pronounced asymmetry in mechanical behavior. Therefore, the bearing capacity was calculated using an asymmetric composite section model under actual eccentric loading. In the calculation, only the contributions of the HPFRCC strengthening overlay on the compression side, the masonry in the compression zone, and the compression reinforcement were taken into account, while the contribution of the tension zone was neglected.

For the single-sided strengthening scheme, the total thickness of the composite section is expressed as

$$h=h_m+t_h$$

(12)

where $h$ is the total thickness of the composite section after single-sided strengthening, $h_m$ is the thickness of the original masonry wall, and $t_h$ is the thickness of the HPFRCC strengthening overlay on one side.

The distance from the line of action of the axial load to the compression edge is expressed as

$$e_c={\displaystyle \frac{h}{2}}-e_0-e_a$$

(13)

where $e_c$ is the distance from the line of action of the axial load to the compression edge, $e_0$ is the initial eccentricity, and $e_a$ is the additional eccentricity.

Accordingly, the axial force equilibrium equation can be written as

$$N={\alpha }_c{f}_{hc}b{t}_h+f_{m}b(x-t_h)+{\sigma }_s’A_s’$$

(14)

and the moment equilibrium equation can be written as

$$N{e}_c={\alpha }_c{f}_{hc}b{t}_h\left({\displaystyle \frac{t_h}{2}}\right)+f_{m}b(x-t_h)\left({\displaystyle \frac{x+t_h}{2}}\right)+{\sigma }_s’A_s’a_s’$$

(15)

The stress in the compression reinforcement is taken as

$${\sigma }_s’=\left\{\begin{array}{ll}{E}_s{\epsilon }_s’,& {\epsilon }_s’\le {\epsilon }_y\\ f_y’,& {\epsilon }_s’>{\epsilon }_y\end{array}\right.$$

(16)

with

$${\epsilon }_s’={\epsilon }_u\left(1-{\displaystyle \frac{a_s’}{x_n}}\right)$$

(17)

$${\epsilon }_y={\displaystyle \frac{f_y’}{E_s}}$$

(18)

where ${\epsilon }_s’$ is the strain in the compression reinforcement, ${\epsilon }_u$ is the ultimate compressive strain at the compression edge, $a_s’$ is the distance from the resultant force point of the compression reinforcement to the compression edge, $x_n$ is the actual neutral axis depth, ${\epsilon }_y$ is the yield strain of the compression reinforcement, $f_y’$ is the yield strength of the compression reinforcement, and $E_s$ is the elastic modulus of the reinforcing steel.

5.3. Comparison Between Theoretical and Experimental Results

To verify the rationality of the proposed preliminary sectional bearing capacity model, the theoretical predictions were compared with the experimental results, as listed in

Table 12. Comparison between experimental and calculated values.

Specimen	Experimental Value	Calculated Value	Relative Error
KXW-30	985.1	1000.91	0.02
KXW-45	1643	1429.86	0.13
SKXW-30	565.8	583.46	0.03

. The relative errors between the experimental and theoretical values were 2%, 13%, and 3% for KXW-30, KXW-45, and SKXW-30, respectively. Overall, the theoretical results showed acceptable agreement with the experimental results, indicating that the model can provide a preliminary estimation of the eccentric compression bearing capacity under the specimen conditions considered in this study. Among the three specimens, KXW-45 exhibited a relatively larger deviation, suggesting that, for thick double-sided strengthened specimens, the current model does not yet fully account for the effects of enhanced local confinement, strain localization, and stress redistribution. Therefore, the proposed theoretical model should be regarded as a preliminary calculation method for this type of member. It may be used for preliminary bearing capacity estimation and comparative analysis under conditions similar to those considered in this study; however, its parameter values and scope of applicability still require further refinement and validation through additional tests involving more specimens, a wider range of eccentricities, and different structural configurations.

5.4. Discussion, Engineering Implications, and Limitations

The experimental results obtained in this study are generally consistent with the trends reported in previous studies on HPFRCC- or ECC-strengthened masonry members under seismic, in-plane shear, cyclic, or lateral loading conditions, in which overlay strengthening was found to improve the bearing capacity, integrity, crack control performance, and deformation capacity of masonry members, and double-sided strengthening was generally more effective than single-sided strengthening. In the present study, under eccentric compression, the double-sided strengthened specimens also exhibited higher load-bearing capacity, greater stiffness, and better overall integrity than the single-sided strengthened specimen, which is in agreement with the strengthening tendency reported in the existing literature.

At the same time, the present results further indicate that, under eccentric compression, the influence of strengthening thickness is not limited to the enhancement of peak load-bearing capacity. Although the 45 mm double-sided strengthening scheme achieved the highest peak load, it also showed a more concentrated local failure pattern and more pronounced post-peak strain localization. By contrast, the 30 mm double-sided strengthening scheme exhibited a gentler post-peak response, more dispersed crack development, and better deformation compatibility. This observation supplements the existing body of research by highlighting the interaction between strengthening thickness, sectional resistance, and post-peak localization under eccentric compression.

From an engineering perspective, HPFRCC overlay strengthening can effectively improve the integrity, stiffness, and eccentric compression resistance of degraded concrete hollow block masonry walls, especially when a double-sided strengthening scheme is adopted. However, the present findings should be interpreted within the limitations of the study, since only three strengthened specimens with a single eccentricity ratio of 0.5y were considered, no unstrengthened control wall was included, the degradation condition was simulated primarily through reduced material strength, and the finite element and theoretical models still contain simplified assumptions. Therefore, the present conclusions are more suitable for comparative interpretation under representative eccentric compression conditions than for direct extrapolation to all masonry structures in practice. Future work should include additional specimens with wider eccentricity ranges, unstrengthened control walls, more detailed deterioration characterization, and further validation of the theoretical model.

6. Conclusions

This study investigated the eccentric compression behavior of high-performance fiber-reinforced cementitious composite (HPFRCC)-strengthened concrete hollow block masonry walls with simulated material degradation through a combination of experimental testing, finite element analysis, and theoretical analysis. Based on the results obtained under the present test conditions and parameter range, the conclusions can be summarized as follows.

(a) Scientific findings

(1) Under the test conditions considered in this study, the double-sided strengthened specimens exhibited better integrity, higher load-bearing capacity, and greater stiffness than the single-sided strengthened specimen. In contrast, the single-sided strengthened specimen was more prone to crack concentration and showed more pronounced lateral deformation.

(2) Among the three strengthened specimens, KXW-45 reached the highest peak load of 1643.0 kN, whereas KXW-30 exhibited a gentler post-peak descending response, more dispersed crack development, and better deformation compatibility. This indicates that increasing the thickness of the double-sided HPFRCC strengthening layer can significantly improve the peak load-bearing capacity, but may also intensify post-peak localization.

(3) The strain, deflection, and DIC results consistently showed that double-sided strengthening was more effective in suppressing lateral deformation and strain concentration. Compared with KXW-45, specimen KXW-30 retained a more dispersed strain field and better post-peak strain redistribution capacity, which was more favorable for gradual post-peak softening and failure stability.

(4) The finite element model could reasonably reproduce the overall mechanical response of the strengthened walls under eccentric compression. Within the numerical parameter range considered in this study, increasing the HPFRCC strengthening thickness generally led to an increase in peak load and a decrease in peak displacement for both the single-sided and double-sided strengthening schemes.

(5) The proposed preliminary sectional bearing-capacity model showed acceptable agreement with the experimental results. The relative errors between the experimental and theoretical values for KXW-30, KXW-45, and SKXW-30 were 2%, 13%, and 3%, respectively, indicating that the model can provide a preliminary estimation of the eccentric compression bearing capacity for specimens similar to those considered in this study.

(b) Engineering implications

(6) From an engineering perspective, HPFRCC overlay strengthening can effectively improve the eccentric compression resistance and structural integrity of degraded concrete hollow block masonry walls, especially when a double-sided strengthening scheme is adopted. For strengthening scenarios in which improving peak load-bearing capacity is the primary objective, a thicker double-sided strengthening layer is advantageous.

(7) However, when post-peak stability, deformation compatibility, and failure controllability are also important design considerations, a relatively thinner double-sided strengthening layer may provide a more balanced strengthening effect. Therefore, the practical selection of strengthening scheme and strengthening thickness should depend not only on the target bearing capacity, but also on the expected deformation performance and failure characteristics of the strengthened wall.

(c) Limitations and future work

It should be noted that this study considered only three strengthened specimens with an eccentricity ratio of 0.5y and did not include an unstrengthened control wall. In addition, the degradation condition was simulated primarily through reduced material strength, the DIC measurements were mainly conducted on the double-sided strengthened specimens, the finite element parametric analysis focused primarily on strengthening thickness, and the theoretical model still contains equivalent and simplified assumptions. Therefore, the present conclusions should be interpreted mainly as comparative findings on the relative mechanical responses of different HPFRCC strengthening configurations under a representative eccentric compression condition. Future work should include additional specimens with wider eccentricity ranges, unstrengthened control walls, more detailed deterioration characterization, and further validation and refinement of the theoretical model for broader engineering application.