Parameter Analysis for the Flexural Performance of Concrete Beams Using Near-Surface Mounted-Strengthening Application

Abstract

In this paper, a systematical study on the influence of strengthening parameters on the flexural performance of RC beams using the NSM application was carried out. Experimental results consist of two reference beams and 25 beams divided into two groups using NSM systems with various embedded bars and strengthening configurations were presented. Additionally, theoretical analysis was conducted to enrich the research on the parameters affecting the strength and failure mode of the beams. The accuracy of the theoretical formulas has been verified through experimental results, and the average value of the ratio between the theoretical and experimental values is approximately 0.9. Results indicated that NSM technology is an effective approach for strengthening RC structures. Compared with the control specimens, the maximum load-bearing capacity of the beams with the NSM system experiences a remarkable enhancement of nearly 140%. The flexural behavior of the beams strengthened by the NSM system are closely related to the material properties (steel bar, NSM bars, concrete, and filler), location of the cutoff points, external confinement, and prestress level. The NSM bars characterized by high strength and high elasticity prove to be far more advantageous in enhancing the strength of the strengthened specimens. The research findings can provide theoretical support for the practical engineering applications of the NSM technology in strengthening reinforced concrete structures.

1. Introduction

In the field of civil engineering, reinforced concrete (RC) structures have become the most widely used structural form globally. However, some RC structures that have been in service for many years are facing severe challenges, such as long-term environmental erosion coupled with the potential threat of natural disasters like earthquakes, leading to the continuous decrease in the safety and serviceability of the structures. Strengthening the existing RC structures proves to be a cost-effective and highly efficient approach to ensure that these structures can satisfy the current service requirements.

In recent decades, many strengthening methodologies have been proposed for restoring and improving the structural performance of deficient or damaged RC structures, such as externally bonded (EB) technology [1], near-surface mounted (NSM) technology [2,3], high-performance mortar [4,5,6], fiber-reinforced polymer (FRP) grid/sheet [7,8], etc. Among which, NSM technology has been acknowledged as one of the most available alternatives [3,9]. Prior investigations regarding NSM strengthening have primarily concentrated on the general responses of the strengthened structures/elements, including the flexural [2,10] and shear behavior [11] of beams, along with the bond behavior and bond mechanism of the NSM system since the bond behavior of the interface between NSM reinforcements, adhesive, and concrete is a crucial factor affecting the efficiency of this technique [12]. Currently, NSM technology began to be implemented in more complicated studies, such as the torsional behavior of RC beams [13], the seismic resistance of columns [14] and subassemblies [15], and the progressive collapse resistance of RC frames [16].

Regarding the bond behavior, pull-out tests and beams tests were carried out, and the factors such as concrete strength, filler, bond length, groove geometry, and surface treatment of NSM bars and groove have been meticulously examined [13,17]. Additionally, several analytical models have been proposed to predict the bond capacity of NSM-concrete joints [18]. At the structural member level, the factors affecting the global performance and bond behavior of the strengthened beams have also been explored. This mainly encompasses: (1) NSM materials, including various types of FRPs [8,19] and metallic tendons (such as steel bars [20], helical rib steel wires [21], steel strands [22], and shape-memory alloys [23]) with varying shapes (rectangular or round bar, strip, laminates, and ropes), lengths, diameters, and quantities; (2) filling materials, including cement-based mortar [24,25] and fibrous geopolymer paste [26] which have been employed in an attempt to substitute the typically epoxy resin; (3) anchoring method, including external mechanical anchorage, wrapped FRP sheets, and several improved anchored manners that have been proposed to prevent the premature debonding failure in the NSM system [17,27,28,29,30]; (4) strengthening construction, where different NSM-strengthening measures were investigated to improve the performance of the strengthened member [31,32]. Additionally, the prestressing device and prestress level applicable to NSM application have also been studied [33].

So far, extensive research has been performed regarding the flexural performance of concrete beams strengthened by means of NSM technology. A large number of research findings have been obtained to elucidate the work mechanism and enhancement effect of the NSM system in strengthening. However, due to the differences in test specimens accomplished by different researchers, such as specimen dimensions, concrete strength, reinforcement configuration, material properties of concrete or steel bars in experiments, as well as variations in strengthening treatment and loading systems, it remains arduous to conduct a comprehensive and systematic analysis of the effect of various parameters on the overall behavior of the strengthened members.

In addition, various reinforcements have been used and inserted in the NSM system for strengthening, which could generally be divided into brittle materials (such as FRPs having linear constitutive relation with poor elongation) and ductile materials (such as metallic materials which feature a nonlinear constitutive relation and a significantly higher fracture strain than FRPs). However, within the existing research, FRPs are predominantly utilized as NSM reinforcements [2], whereas the research on metallic materials remains relatively scarce, often amounting to merely an endeavor to superficially present the general response of the strengthened specimens [20,21,22]. Consequently, comparison research focusing on the influence of the sort and material characteristics of NSM reinforcement on the behavior of the strengthened members is still scarce, and there is thus an urgent need for an abundant and comprehensive investigation.

The author’s research team has conducted a series of experimental investigations on the flexural performance of RC beams strengthened using FRPs and metallic materials as NSM reinforcements, and several findings regarding them have been reported [34,35,36,37,38,39]. However, previous studies merely analyzed a single strengthening material or only a few parameters, failing to systematically examine the influence of parameters on the performance of strengthened beams, especially the characteristics of the strengthening materials. This paper presents a comprehensive analysis based on the experimental studies, in which the strengthening parameters, mainly including the material type and properties, reinforcement ratio of tensile steel bar and NSM tendons, prestress level, bonded length of NSM reinforcements, anchorage type, and filling materials type were comprehensively elaborated. In addition, to enrich the research and give a further understanding of the parameters affecting the failure mode and beam strength, several parameters related to the ultimate strength of the strengthened member were discussed based on ACI codes [40].

2. Experiment Program

2.1. Design of Test Specimens

To investigate the behavior and performance of RC structures rehabilitated and strengthened by NSM technology, two groups of experiments, with a total of 27 RC beam specimens had been conducted through four-point loading tests, and the effect of those parameters on the flexural behavior of the RC beams were comprehensive discussed in this paper. The first group consists of ten specimens, one reference beam, and nine beams using the NSM system with three different NSM reinforcements of different material properties [34,35]. And the second group contains seventeen specimens [36,37,38,39]. Note that most of the tested beams have been reported in the published literature, but there is a lack of a comprehensive comparative analysis in terms of the effects of inserted tendons with different physical properties as well as the affecting parameters. In this paper, experimental results of 27 specimens are presented to give a comprehensive understanding of the influence of parameters on the behavior of beams using the NSM system. Figure 1 illustrates the general configuration of the beams in Group 1 and Group 2.

Group 1: The beam dimensions are 2100 mm × 200 mm × 350 mm, as illustrated in Figure 1. The span of the beams between the two end supports is 1800 mm. The distance between the two load points is 600 mm. The variables of Group 1 are the types of NSM tendons (basalt FRP (BFRP), glass FRP (GFRP), and 6061 aluminum alloy (AA) bars), longitudinal reinforcement ratio (0.65% and 1.02%), and amount of NSM reinforcement (two or three NSM reinforcements).

Group 2: The beam dimensions are 3000 mm × 170 mm × 300 mm. The span of the beams between the two end supports is 2800 mm. The distance between the two load points is 600 mm. The variables concerned in Group 2 are listed as follows: (i) the types of NSM tendons (7075AA and prestressing screw-thread (PS) bars); (ii) the amount of NSM tendons (one or two NSM reinforcements); (iii) the anchorage type (CFRP sheet and mechanical anchorage, labeled as “U” and “MA”, respectively); (iv) the prestress level (40% and 80% of the yielding strength of the tendons); (v) the filling materials (common epoxy and engineering cementitious composites (ECC), labeled as “E” and “C”, respectively); (vi) the bonded length (48 d and 60 d, where d is the diameter of the tensile steel bar); (vii) the layer of CFRP sheet (“U2” or “U3” indicates 2 or 3 layers of the CFRP sheets applied and wrapped around the beam in U shape).

It is worthy of note that within the second group, considering the human labor and economic costs entailed in experimental implementation, this research has endeavored to reveal the influence mechanisms of diverse parameters while curtailing the number of specimens, rather than conducting a comprehensive orthogonal experiment. In the current investigation, the 17 specimens that have been completed incorporate the aforementioned seven parameters, and the research findings can, to a certain degree, achieve the expected research objectives.

2.2. NSM-Strengthening Program

The NSM technology for flexural beams involves cutting grooves on the concrete surface within the flexural region of the RC beam. Subsequently, strengthening tendons are inserted into the grooves, and then the adhesive agent is applied for bonding, thereby enabling the strengthening tendons and the beam to form an integral entity. In order to guarantee that the strengthening tendons can synergize efficiently with the beam in withstanding the imposed loads, an anchoring system is occasionally implemented at the distal ends of the strengthened beams. In the present experiment, the cut groves located at the bottom concrete cover have a square section of 25 mm × 25 mm in Group 1 and Group 2, greater than 1.5 times the size of the inserted bars, in line with the ACI specification [40]. The NSM-strengthening bars are inserted in the groves surrounded with epoxy resin except for beam BA-C-2-MA which was filled with ECC [39]. For beams strengthened with prestressed NSM tendons, a prestressing tension jack was used to apply the force for the NSM bars, and the mechanical anchorages consisting of a steel plate and rows of embedded bolts were used to fix the NSM bars at the cutoff point and to prevent prestress relaxation; detailed information for the prestress process can be found in the existing literature [37].

2.3. Material Characteristics

The NSM tendons embedded in the first group experiment are BFRP, GFRP, and 6061AA bars, and in the second group are 7075AA and PS bars. FRPs have linear elastic properties as the stress–strain relationship conforms to Hooke’s law, whereas the stress–strain relationship of metallic reinforcements shows an elasto-plastic behavior.

Table 1. Material properties of NSM reinforcement bars.

Materials	BFRP	GFRP	6061AA	7075AA	PS
Diameter/mm	14	14	14	16	15
Yield strength/MPa	-	-	371	528	407
Ultimate strength/MPa	1134	966	399	590	649
Modulus of elasticity/GPa	54	40	76.7	72.7	200

illustrates the material properties of these NSM materials used in the experiment, which will be utilized in the subsequent theoretical analysis in Section 4 and Section 5. The grade of concrete employed is C40, with a targeted compression strength of 40 Mpa [34,37]. The material properties of other materials, such as the epoxy resin and ECC can be found in the literature [39], as well as the material type, manufacturer, and mix proportion.

2.4. Experimental Setup

The beam specimens were subjected to four-point bending tests to investigate the flexural performance. Taking the second group of tests as an example, as depicted in Figure 2, a hydraulic servo actuator (Popwil Instrument Co., Ltd., Hangzhou, China) was used to impose a concentrated vertical load upon the distribution beam while automatically amassing the load data. The distribution beam transferred the load through the two supports to the beam. The displacement-controlled loading mode was adopted, with a loading speed of 0.3~0.6 mm/min, and the loading increment was set as 2 mm per stage [37]. While, the loading mode of the specimens in Group 1 was load-controlled loading, and the acceleration rate was 0.5 kN/min [34].

3. Experimental Results

The experimental results of specimens in Group 1 and Group 2 are summarized and listed in

Table 2. Experimental results of the test beam specimens.

Group	Specimen	NSM Materials	ρs/%	NSM Bars	Prestress Level/%	End Anchorage	Py /kN	ηy /%	Pmax/kN	ηmax /%	Δu /mm	μ	FM
Group 1	RB1	-	0.65	-	-	-	196	-	223	-	37.3	6.1	CC
	BCB-1	BFRP	0.65	2D14	-	-	210	7	422	85	39.4	5.6	CC-ICD
	BCB-2	BFRP	0.65	3D14	-	-	222	13	470	106	35.0	5.1	CC-ICD
	BCB-3	BFRP	1.02	2D14	-	-	254	30	470	106	33.5	5.0	CC-ICD
	GCB-1	GFRP	0.65	2D14	-	-	214	9	458	101	37.3	5.7	CC-ICD
	GCB-2	GFRP	0.65	3D14	-	-	234	19	522	128	34.1	5.1	ICD
	GCB-3	GFRP	1.02	2D14	-	-	258	32	534	133	32.3	4.6	CC-CCS
	ACB-1	6061AA	0.65	2D14	-	-	202	3	262	17	39.1	6.0	CC-DB
	ACB-2	6061AA	0.65	3D14	-	-	210	7	280	24	37.8	5.7	CC
	ACB-3	6061AA	1.02	2D14	-	-	298	52	338	49	37.7	4.9	CC
Group 2	RB2	-	0.71	-	-	-	67	-	82	-	80.2	6.7	CC
	BA-E-1	7075AA	0.71	1D16	-	-	77	15	110	34	50.1	4.5	ICD
	BA-E-2	7075AA	0.71	2D16	-	-	90	34	153	87	49.1	4.9	CCS
	BA-E-1-40	7075AA	0.71	1D16	40	MA	97	45	115	40	52.2	4.4	CC
	BA-E-1-80	7075AA	0.71	1D16	80	MA	90	34	100	22	60.0	5.0	CC
	BA-E-2-40	7075AA	0.71	2D16	40	MA	140	109	165	101	48.3	3.1	CC
	BA-E-2-80	7075AA	0.71	2D16	80	MA	144	115	165	101	45.0	3.1	CC
	BA-E-2(48d)	7075AA	0.71	2D16	-	-	89	33	146	78	57.1	5.7	CCS
	BA-E-2(60d)	7075AA	0.71	2D16	-	-	90	34	157	91	42.0	3.9	CCS
	BA-E-1-U2	7075AA	0.71	1D16	-	U-jacket	82	22	123	50	61.8	5.6	CC
	BA-E-2-U2	7075AA	0.71	2D16	-	U-jacket	86	28	163	99	47.2	4.6	CCS
	BA-E-2-U3	7075AA	0.71	2D16	-	U-jacket	88	31	164	100	51.0	5.0	CCS
	BA-E-2-MA	7075AA	0.71	2D16	-	MA	98	46	152	85	36.0	3.4	ICD
	BA-C-2-MA	7075AA	0.71	2D16	-	MA	92	37	112	37	55.0	5.1	DB
	BP-E-1	PS	0.71	1D15	-	-	86	28	91	11	68.9	5.2	CC-ICD
	BP-E-1-80	PS	0.71	1D15	80	MA	86	28	95	16	60.7	5.6	CC
	BP-E-2-80	PS	0.71	2D15	80	MA	124	85	139	70	60.8	4.4	CC

Note: ρ_s is the reinforcement ratio of tensile steel bar, expressed as ρ_s = A_s/A_c, ρ_e,N is the equivalent reinforcement ratio of NSM bar, defined as ρ_e,N = A_Nf_N/A_c f_sy, where A_s, A_N, A_c is the cross-sectional area of steel bar, NSM reinforcement, and concrete beam, respectively; f_sy and f_N is the effective strength of steel bar and NSM reinforcement, respectively. EA = external anchorage; MA= mechanical anchorage; U-jacket = U shape wrapping; FM = failure mode; CC-CCS = concrete crushing followed by concrete cover separation; η_y and η_max is the increase in yield and maximum load when compared to the reference beam, respectively.

. The failure mode, load-displacement curves, load-bearing capacity, and deformability of the strengthened beams using NSM technology were comprehensively analyzed. Moreover, a detailed discussion was conducted on the enhancement and effectiveness of the beam behavior in relation to the influence parameters investigated in the test study.

3.1. Failure Modes

First, to better understand the response of the strengthened beams, an analysis was conducted on the failure modes of the tested beams, along with an exploration of their failure mechanisms. Generally, when employing the NSM technology to strengthen beams, three typical failure modes can be observed: concrete crushing (CC), debonding failure of the NSM system, and fracture of NSM reinforcement. The failure process and mechanism were meticulously described and presented to elucidate each failure mode.

3.1.1. CC Failure Mode

The two non-strengthened beams (RB1 and RB2) presented typical flexural failure mode—steel reinforcements yielded followed by concrete crushing. Flexural vertical cracks sufficiently initiated in the pure-bending zone while oblique cracks germinated in the bending-shear zone. The beams finally failed due to the concrete crushing in the compression zone of the beam specimen along with the yield of longitudinal tensile steel bars.

More surprising is that the six prestressed strengthened beams with the mechanical anchorage at the ends also failed in flexural failure mode, whereas the other strengthened beams all failed in debonding failure of the NSM system. It can be inferred that the mechanical anchorage method installed at the NSM bar cutoff point has an effect on effectively preventing the debonding failure of NSM-strengthened beams.

3.1.2. Debonding Failure of NSM System

Figure 3 illustrates the schematic representation of beams installed with the NSM system. Evidently, within the system, there exist two bonding interfaces that can potentially serve as vulnerable zones, triggering interfacial debonding failure in the strengthened RC beams. Specifically, these are interface 4 (concrete–adhesive interface) and interface 5 (adhesive–NSM bar interface), as shown in Figure 3. In addition, breaking of the concrete cover (area 1) or adhesive cover (area 2) might also lead to debonding failure of the NSM system.

Classically, according to previous experimental observation, there are three types of debonding failure of NSM systems that happen in strengthened flexural RC beams, namely, intermediate crack-induced debonding (ICD), end concrete cover separation (CCS), and other interfacial debonding failures (DB) except ICD and CCS. In contrast to CC, the three modes are known as brittle failure modes. The beams failed by brittle modes commonly exhibit sudden failure characteristics, such as a sudden drop in the load without any obvious signal. The failure mechanism of the main debonding failure modes in the NSM system is demonstrated as follows.

(1)

Beams failed by ICD

Figure 4 depicts the failure mode of several beams due to ICD, in which the failure is caused by the dominant intermediate flexural crack (BA-E-1) or shear crack (BA-E-2-MA) adjacent to the loading points. These cracks extend and propagate toward the support points, ultimately resulting in the breaking and detaching of the concrete cover from the beam specimens. Within Group 1, the majority of the beams strengthened with GFRP and BFRP presented ICD failure, exemplified by specimens BCB-1, BCB-2, BCB-3, GCB-1, and GCB-2. Contrasting with the failure behavior of beams in Group 1 where the bottom concrete protective layer almost all fell off, the three beams in Group 2 (BA-E-1 and BP-E-1 strengthened with only one tendon, and BA-E-2-MA installed with mechanical anchorage) that failed by ICD manifested a more limited spalling of concrete cover. The reason behind the fact that the beams in Group 1 generally happened to ICD failure may be due to (1) the cutoff points of the embedded NSM reinforcements in Group 1 are located outside the support points which protected the specimens from end concrete cover separation. In contrast, for beams in Group 2, the cutoff points are positioned within the two support points, leading to the beams predominantly failing by CCS; and (2) the small shear span ratio (the ratio of the beam height to the distance from the support to the loading point) induces a relatively higher shear stress, which in turn gives rise to a more extensive debonding at the beam bottom.

(2)

Beams failed by CCS

Figure 5 illustrates the failure mode of several beams that experienced CCS failure. In this case, the failure is attributed to the diagonal cracks at the NSM bar cutoff points, which result in separation of the concrete cover. In Group 2, there are five specimens (BA-E-2, BA-E-2(48 d), BA-E-2(60 d), BA-E-2-U₂, and BA-E-2-U₃) were governed by typical CCS failure mode. In comparison with beam BA-E-1, the beam BA-E-2 strengthened with two AA bars had a higher load-bearing capacity, which caused higher stress in the cutoff points. Consequently, beam BA-E-2 ultimately failed in accordance with the CCS failure mode. It was observed that the other four specimens, which inserted with the same NSM AAs but strengthened with local bonded length (BA-E-2(48 d) and BA-E-2(60 d)) or wrapped with two or three sheets (BA-E-2-U₂ and BA-E-2-U₃), exhibited the same failure mode as BA-E-2. This may be attributed to the fact that these specimens have similar load-bearing capacities, which will be analyzed in Section 3.3.

(3)

Beams failed by DB

In addition to ICD and CCS failure modes, interfacial debonding failure can occur at the NSM bar–adhesive–concrete interfaces. Moreover, breaking of the concrete or adhesive cover, induced by high stress levels, can also result in the final failure of the strengthened beams. In this study, DB was observed in specimens ACB-1 and BA-C-2-MA. As depicted in Figure 6, extensive cracking in the concrete cover can be observed at the beam bottom, which caused debonding both between the adhesive–NSM bar interface and concrete–steel bar interface, as well as slippage of the NSM bar. The exposed NSM AA bars is a clear indication of the failure of the NSM system. Similar to ACB-1, beam BA-C-2-MA, which utilized ECC as a filler, also exhibited severe cracking in both the ECC cover and concrete cover at the beam bottom.

When comparing the failure modes, CC is the most preferable mode, in which case the concrete’s strength is fully exploited. Conversely, debonding failure modes are prematurely brittle failure and are highly undesirable, in which cases the strength of concrete and NSM tendons are not fully utilized. Also, Table 2 shows some specimens, like BCB-1 and ACB-1, experienced CC failure alongside ICD or CCS (namely, CC-ICD and CC-CCS). Here, the concrete compression zone of the beam was slightly crushed but could still carry a load, yet the strengthening system at the tension zone had already failed. This implies both the concrete and strengthening system in these specimens nearly maximally exerted their capabilities. Overall, for the NSM-strengthened beams, the debonding failure occurs prior to the CC failure. The former is contingent upon the quality of the strengthening system, such as the interfacial bond strength and the strength of adhesive. In contrast, the latter is predominantly governed by the compressive strength of the concrete.

In the present study, no fracture of the NSM bar was found, even for the beams only strengthened with one NSM tendon. This may be attributed to the high ultimate strength of FRPs and good elongation of AA bars. Overall, the results indicate that the material property, quantity of NSM reinforcements, end anchorage, and filling materials all are important parameters affecting the beam failure modes. Moreover, the length and location of the inserted NSM bar are significant factors that affect the possibility of CCS failure. Anyhow, the experimental results from Group 1 and Group 2 demonstrate that the beams strengthened by means of NSM technology are indeed susceptible to brittle failure modes. Intriguingly, installing end anchorages can mitigate or even eliminate the brittle failure characteristics of the strengthened beams. More information about the failure pattern of these beams can be found in the previous literature [39].

3.2. Load-Midspan Deflection Curves

Figure 7 depicts the load-midspan deflection curves of all the strengthened specimens. Evidently, with the exception of the specimens in Group 1, all specimens subjected to four-point bending loads have experienced four stages, namely, the pre-cracking stage, the yielding stage, the peak point stage, and the post-peak descending stage. Prior to specimen cracking, the initial stiffness of all specimens exhibits little disparity, and the curves manifest a linear relationship. Once the concrete cracks, the slope of the curves decreases slightly, and the load-midspan deflection curves retain an approximate linearity. Subsequent to specimen yielding, the curves demonstrate a pronounced non-linearity. In this stage, the magnitude of the load increment is governed by the type and quantity of the strengthening reinforcements. Upon reaching the peak point, the curves start to decline, and the degree of decline is affected by the failure mode. The specimens failed by brittle failure display a sudden drop in the loads. Given that the load-controlled loading mode was employed in Group 1, there is no descending stage in the load-midspan deflection curves. The following will present a detailed elucidation regarding the influence of the parameters on the development trend of the curves of the beams.

Figure 7a presents the load-midspan deflection curves of the beams obtained from the first group, including one unstrengthened beam, three BFRP-strengthened beams, three GFRP-strengthened beams, and three 6061 AA-strengthened beams. The loads were recorded by the MTS data-acquisition instrument and the deflection was obtained by the LVDTs which were vertically installed at the mid-span of the beam’s bottom. In this part, the influence of the NSM-strengthening application, as well as the type and reinforcement ratio of the NSM tendons, were analyzed. Generally, the load-bearing capacity of the concrete beams had been effectively improved after being strengthened by inserting the NSM reinforcements, and it increased significantly with the increase in the number of NSM tendons. However, it can be found that the three types of NSM reinforcements with different mechanical properties have different effects on the load-displacement curves. As seen, the 6061 AA tendons have a relatively low contribution to the beam behavior compared to FRPs, especially after the yielding of steel reinforcements, while the FRPs-strengthened beams still displayed a significant increasing tendency. Further analysis will be carried out in Section 5 to explain the relationship between the strength of NSM materials as well as the strengthening effect of material properties by means of theoretical analysis.

Figure 7b–d compare the load-midspan deflection response of the concrete beams in Group 2 with variable parameters. Similar to the behavior of test beams in Group 1, all strengthened beams exhibited improved bearing capacity when compared to the control specimen (RB2), and the bearing capacity increased with the NSM reinforcement ratio. However, it can be found that the post-yield response was different for specimens that failed by different failure modes. As shown, specimen RB2 exhibited typical ductile failure (CC) with excellent deformation property. However, after strengthening, the beams generally happened to debonding failure of the NSM system, manifested as a sudden drop in the load with poor deformability at the post-yield stage. After being installed with CFRP sheets, the beam strengthened with only one AA bar (BA-E-1-U₂) shows a better ductile behavior with good deformability compared to BA-E-1. While, beams strengthened by two AA bars still exhibit brittle sudden failure, but have experienced a relatively longer deformation process when compared to that without CFRP sheets. Results indicated that the U-jacket has an obvious effect on improving the ductility of the beams and delaying failure. The two partially bonded beams have a comparable load-displacement response to the fully bonded beams. Notice that all the beams with prestressed NSM tendons installed with mechanical anchorage exhibited ductile response as the curves have a relatively gentle descending branch after reaching the maximum loads with good deformation, as shown in Figure 7d. Although the two beams with non-prestressed NSM tendons installed with mechanical anchorage present a considerable decline in loads due to debonding failure, the specimens still had a certain bearing capacity and deformation capacity.

3.3. Load-Bearing Capacity

Table 2 lists the test results of all non-strengthened beams and strengthened beams with different NSM materials and constructions in Group 1 and Group 2. The yielding load P_y, maximum load P_max, and the corresponding mid-span displacements of these beam specimens were recorded. The ductility coefficient $\mu$ is defined as the ratio of displacement at failure state to that at yielding loads. Also, Figure 8 gives a visual representation of the P_y and P_max of the test specimens. As seen, the maximum bearing capacities of the specimens have been significantly improved after NSM strengthening. The percentage increase in load capacity shows significant variation when different reinforcement materials are used in NSM applications.

Compared with the reference beam in Group 1, the FRPs-strengthened beams presented an extremely high increase (about 89–139%) in the maximum loads, while the increase in 6061 AA-strengthened beams was about 17–52%. This is because the higher strength of FRPs compared to 6061 AA contributes more to the strength of strengthened beams. However, the percentage increases in yielding loads are modest: the FRPs-strengthened beams show a 7–32% increase, while the 6061 AA-strengthened beams increased by 3–52% compared to the reference beam. Generally, the yield and ultimate strength of the strengthened beams rise with the increase in the quantity of NSM bars. However, when the number of NSM bars reaches 3, the ultimate load-carrying capacity of beams strengthened with FRPs and AA bars show different growth trends. When the number of reinforcement bars increased from 2 to 3, the strength of the former undergoes negligible variation, potentially due to the fact that the performance of the strengthened beams is governed by the quality of the strengthening system. Conversely, the strength of the latter increases substantially, yet still remains considerably lower than that of the former.

In Group 2, as shown in Figure 8b, the parameters have a significant impact on the strength of concrete beams. Firstly, it is clearly observable that the yielding loads of the beams with two prestressed NSM bars are significantly higher than that of the control beam, with the increase of 124–144%. Compared to the strengthened beams with un-prestressed NSM bars, the yielding loads of the specimens strengthened with one and two prestressed NSM tendons increased by 16~25% and 55–59%, respectively. However, the prestress has little effect on the maximum load, as the percentage increase in the maximum load of the beams with prestress is only about 4~8% when compared to the beams without prestress. Once again, it is found that increasing the number of NSM bars leads to a significant increase in the strength of the strengthened beams. Except for BA-C-2-MA, the beams using two NSM bars presented a particularly high percentage increase in maximum load capacity (70–101%) than that using one bar (11–50%). In addition, it can be noticed that the beams with a CFRP-jacket presented an increase of 7–10% compared with the specimens without anchorage, while there is little increase in the yielding load. In contrast, the mechanical anchorage significantly improves the yielding load of the strengthened beam but has almost no effect on the ultimate load. For the beams strengthened with partial bonded length, their yield strength and ultimate strength are comparable to the beams strengthened with full bonding. In addition, compared with the PS bars, the AA bars contribute more to the ultimate strength of the beams.

3.4. Effect of Influencing Parameters on the Beam Performance

Based on the above test results and the existing literature, analysis was carried out regarding the influence of parameters, mainly including the material properties of the NSM reinforcements, the steel reinforcement ratio, end anchorage, filler, bonded length, and the prestress level, on the performance of the strengthened beams.

3.4.1. Effect of Material Properties of NSM Reinforcement

When the diameter and quantity of NSM bars are the same, the contribution of the 7075 AA bar to the beam strength is greater than that of the PS bar. However, an enhancement in strength typically entails a reduction in ductility [41]. As shown in Table 2, under the same conditions, the ultimate strength of the specimens strengthened with AA bars increases by 19–21% compared with that of the specimens strengthened with PS bars, whereas the ductility decreases by 11–30%. Similarly, the strength of 6065 AA is much lower than that of FRPs, resulting in a lower contribution to the beam’s bearing capacity. It seems that the strength of the NSM reinforcement is closely related to the bearing capacity of the strengthened beams. A detailed discussion will be carried out in the later section through theoretical analysis.

3.4.2. Effect of Reinforcement Ratio of the Tensile Bar

Similar to existing research [42], the bearing capacity of beam specimens is improved by increasing the tensile reinforcement ratio whether it is a steel or NSM bar. Define the total tensile reinforcement ratio as the sum of the ratio of longitudinal steel bars and NSM bars (${\rho }_T={\rho }_s+{\rho }_{e,N}$), and the relationships between the total tensile reinforcement ratio and the behavior of the strengthened beams discussed in the present study are illustrated in Figure 9. As seen, there is approximately a linear relationship between the beam strength and the reinforcement ratio of the tension bars, as well as the relationship between the displacement and the reinforcement ratio. It is worth noting that when the reinforcement ratio is too high, the curve no longer seems to follow a linear relationship. This is because the beam would fail due to concrete crushing when the tension bar is too much, thus the key to determining the beam strength is the strength of the concrete.

3.4.3. Effect of External Anchorage

Results show that the end anchorage can effectively improve the performance of RC-strengthened beams by avoiding or delaying the brittle failure of the beams. However, the strengthening bars in the NSM application cannot be completely embedded in the support points of a concrete beam due to space limitations in the actual project, thus the strengthened beams are prone to CCS failure. Therefore, it is necessary to implement external anchorage in the NSM application to avoid such brittle failure mode. If it is possible, anchorage can also be applied to the location where the beam sections bear the maximum loads such as the mid-span or the loading points to keep the beam from ICD failure, and further research can be conducted to verify this view.

3.4.4. Effect of Filler

Compared to the commonly used adhesive of epoxy resin, the mortar-based ECC [39] formulated in this study has a lower strength and poor bond performance between the NSM bar and the concrete substrate, resulting in DB failure of specimen BA-C-2-MA along with a lower bearing capacity. Usually, epoxy resin exhibits large brittleness after hardening, which would increase the risk of brittle failure. Since the interface bond characteristics in the NSM system have a great influence on the beam performance, future research can focus on the performance of filling materials.

3.4.5. Effect of Bonded Length

Based on the test results, it appears that the bonded length exerts a negligible influence on the flexural performance of the strengthened beams. Whereas, as per the experimental observations, the location of the cutoff point of the NSM bars has a pronounced impact on the failure mode of the beams. If the cutoff points are situated between the support points, the beam is prone to fail due to CCS failure. Although full-length strengthening of the beam can prevent the beam from CCS, it is challenging to accomplish in practical engineering, as previously stated. Therefore, implementing measures to effectively avert CCS and ICD failure of strengthened beams constitutes a crucial consideration for the NSM technology in the current applications.

3.4.6. Effect of Prestress Level

In NSM application, the embedded metallic materials with elastic-plastic characteristics would also yield during the test. Therefore, although it seems that applying to prestress has little enhancement on the ultimate strength, it indeed delays the concrete cracking and steel reinforcement yielding thus greatly increasing the cracking and yielding strength of the beams. In addition, due to the reverse arch effect caused by prestress force, the displacement of the specimen is greatly reduced compared to the beams without prestressing under the same load level. On the other hand, end anchorage was installed in the prestressed beams to avoid stress relaxation and provide confinement for the beams.

The effect of prestress and prestress level on FRPs-strengthened beams has been studied by several scholars [43], but the conclusions are not consistent. For example, El-Hacha and Gaafar [44] stated that prestressing the NSM bar has little effect on the ultimate strength of the specimen, while experimental results conducted by Obaydullah et al. [22] showed that the ultimate strength of the specimen increased with the prestressing level. Given this issue, this paper will perform a theoretical analysis in Section 5 to further clarify the influence of prestress and prestress level on the performance of specimens strengthened by NSM technology.

4. Theoretical Prediction of the Ultimate Strength of NSM Beams

4.1. Fundamental Principles

A limited number of test specimens cannot comprehensively elucidate the influence mechanism of the parameters for the NSM-strengthening system. Therefore, theoretical analysis will be conducted to expand on the influence parameters. ACI 440.2R-17 [40] has included a theoretical analytical approach for flexural beams strengthened with FRP plates/bars using the NSM system. The strain plane section assumption [45], which assumes the strains along the beam section are perpendicular to their distance to the compression concrete fiber, is used for analyzing the forces in concrete, steel bars, and NSM reinforcements. Note that the tensile stress of concrete and bond slip has not been taken into account in the beams.

Therefore, on the basis of the principle of strain compatibility and internal force equilibrium in the beam section [46], as illustrated in Figure 10, the following relationships between the strains at compression concrete edge ${\epsilon }_{\mathrm{c}}$, tensile steel bars ${\epsilon }_{\mathrm{s}}$, compressive steel bars ${{\epsilon }_{\mathrm{s}}}^{\prime }$, and NSM bar ${\epsilon }_{\mathrm{N}}$ can be found:

$$f_{\mathrm{s}}{A}_{\mathrm{s}}+f_{\mathrm{N}}{A}_{\mathrm{N}}-0.85{\beta }_1{f}_{\mathrm{c}}bc-{f_{\mathrm{s}}}^{\prime }{A_{\mathrm{s}}}^{\prime }=0$$

(1)

$${\epsilon }_{\mathrm{s}}={\epsilon }_{\mathrm{c}}{\displaystyle \frac{d_{\mathrm{s}}-c}{c}}$$

(2)

$${{\epsilon }_{\mathrm{s}}}^{\prime }={\epsilon }_{\mathrm{c}}{\displaystyle \frac{c-{d_{\mathrm{s}}}^{\prime }}{c}}$$

(3)

$${\epsilon }_{\mathrm{N}}={\epsilon }_{\mathrm{c}}{\displaystyle \frac{d_{\mathrm{N}}-c}{c}}$$

(4)

where c is the distance from concrete compression edge to the neutral axis; 0.85 and ${\beta }_1$ are the concrete stress block factors; ${A_{\mathrm{s}}}^{\prime }$ and ${f_{\mathrm{s}}}^{\prime }$ is the cross-sectional area and stress developed in the compressive steel bar, respectively.

And then, the flexural bearing capacity of RC beams inserted with NSM tendons is calculated, as shown below.

$$M_{\mathrm{u}}=f_{\mathrm{s}}{A}_{\mathrm{s}}(d_{\mathrm{s}}-{\beta }_{1}c/2)+{\psi }_{\mathrm{N}}{f}_{\mathrm{N}}{A}_{\mathrm{N}}(d_{\mathrm{N}}-{\beta }_{1}c/2)$$

(5)

$$P_{\mathrm{u}}=2M_{\mathrm{u}}/a$$

(6)

where ${\psi }_{\mathrm{N}}$ = 0.85 is a strength reduction factor for considering the effective contribution of the inserted NSM bar to the strengthened beam [47]; d_s and d_N is the distance from concrete compression edge to the longitudinal reinforcement and NSM reinforcement, respectively; a is the shear span of the beam.

4.2. The Ultimate Strength of Beams in Different Failure Modes

The conditions controlling the ultimate strength are different for the strengthened beams governed by different failure modes. To accurately calculate the strength of the NSM-strengthened beams, the failure modes of the beams should be taken into account. Figure 11 illustrates the calculation process for beams controlled by different failure modes.

4.2.1. CC Controlling

For the beams that failed with CC mode, it is considered that the concrete has reached its ultimate strain, which varies from 0.003 to 0.008 [47]. The design concrete strain is set as ${\epsilon }_{cu}$ = 0.0033 according to GB 50010-2010 [45] in this study. In this case, the maximum strength of the strengthened beam can be determined using Equations (1)–(6). Note that if the strains in FRPs exceed their design strain, the beam will govern by debonding failure of the NSM system; the calculation process for this case is described as below.

4.2.2. Debonding Controlling

For the beams that fail by debonding of the NSM system, it is considered that the strain in NSM FRP reaches its design strain, which varies from 0.6 to 0.9${\epsilon }_{fu}$ [40]. The design strain of FRPs is set as ${\epsilon }_{fd}=0.9{\epsilon }_{fu}$ and ${\epsilon }_{fd}=0.7{\epsilon }_{fu}$ for the NSM system with and without external anchorage, respectively, according to the ACI 44.2R-17 suggestion in this study. In this case, the strain of concrete may be less than its fracture strength, therefore, the concrete stress block factors may be changed and calculated using ACI 318 [47]. The calculation for the beams that failed due to debonding failure is also present in Figure 10.

Generally, the yield strain of metallic materials is close to that of ordinary steel reinforcements, so the NSM metallic materials could always yield unless there is excessive arrangement of the tensile bars. For the internal steel bar and NSM metallic bars, an ideal elasto-plastic property was employed to determine their stress, as presented in Equation (7).

$$f=\left\{\begin{array}{ll}{E}_{\epsilon }\hfill & 0\le \epsilon <{\epsilon }_{\mathrm{y}}\hfill \\ f_{\mathrm{y}}\hfill & {\epsilon }_{\mathrm{y}}\le \epsilon \le {\epsilon }_{\mathrm{u}}\hfill \end{array}\right.$$

(7)

4.2.3. Fracture of NSM Reinforcement Controlling

Fracture of NSM reinforcement usually occurs in the case of good bond performance between interfaces in the NSM system or good confinement is provided by external anchorage so that the beam would not fail by debonding failure and the NSM reinforcement can be fully utilized. If the strengthened beams are governed by the failure of fracture of NSM reinforcement, similar to the case of debonding failure, the strains of NSM reinforcements (${\epsilon }_{fd}=0.95{\epsilon }_{fu}$) would control the beam strength, and the strains of concrete may be less than its design strength.

4.2.4. Beam Strengthened with Prestressed NSM Reinforcement

Since the application of prestressing force will occupy part of the strain of the NSM reinforcement in advance, the available strength of the prestressed tendon under external load will reduce, resulting in the bar being more prone to fracture. In the strength calculation for the beams with NSM prestressed bars, an effective stress in the NSM reinforcement was defined and used to account for the prestress force, which is expressed in Equations (8)–(10).

$${\epsilon }_{\mathrm{eff},\mathrm{pre}}={\epsilon }_{\mathrm{pre}}-{\epsilon }_0$$

(8)

$${\epsilon }_{\mathrm{pre}}=P_{\mathrm{pre}}/E_{\mathrm{N}}{A}_{\mathrm{N}}$$

(9)

$${\epsilon }_0={\displaystyle \frac{P_{\mathrm{pre}}{e}^2}{E_{\mathrm{c}}I}}+{\displaystyle \frac{P_{\mathrm{pre}}}{E_{\mathrm{c}}bh}}$$

(10)

where P_res is the pre-applied force on the NSM bar, e = d_N−c; I is the moment of inertia, and E_N is the modulus of elasticity of NSM bar.

If CC counts for the beam failure, the concrete strain is equal to 0.0033, and the strength of the NSM reinforcement can be calculated using Equation (11) for NSM FRPs with elasto property and Equation (12) for metallic reinforcement with the elasto-plastic property.

$$f_{\mathrm{f}}=E_{\mathrm{f}}({\epsilon }_{\mathrm{eff},\mathrm{pre}}+{\displaystyle \frac{d_{\mathrm{f}}-c}{c}}{\epsilon }_{\mathrm{c}})\le f_{\mathrm{fd}}$$

(11)

$$f_{\mathrm{m}}=\left\{\begin{array}{l}{E}_{\mathrm{N}}({\epsilon }_{\mathrm{eff},\mathrm{pre}}+{\displaystyle \frac{d_{\mathrm{f}}-c}{c}}{\epsilon }_{\mathrm{c}})\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{f}_{\mathrm{m}}\le f_{\mathrm{my}}\hspace{1em}\hspace{1em}\\ f_{\mathrm{my}\hspace{1em}\hspace{1em}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{f}_{\mathrm{m}}>f_{\mathrm{my}}\end{array}\right.$$

(12)

If the strains of the NSM tendons exceeded its fracture stains, the available strength of the prestressed tendons (${\epsilon }_{\mathrm{N}}=0.95{\epsilon }_{\mathrm{fu}}-{\epsilon }_{\mathrm{eff},\mathrm{pre}}$) would control the beam failure, and the rest calculation process of the beam with prestressed NSM bar failed by fracture of NSM bar would be the same as the beams failed in debonding failure, as shown in Figure 10.

4.3. Verification

To verify the accuracy of the proposed formulas for beams strengthened with NSM bars, the calculated ultimate strength of the tested beams (except for EA-C-2-MA) strengthened with diverse NSM tendons in the presented experiment were compared to the experimental results, as tabulated in

Table 3. Prediction of the flexural strength of the test beams.

Specimen	NSM Materials	${\mathit{\epsilon }}_{\mathit{c}}$ (‰)	${\mathit{\epsilon }}_{\mathbf{Nf}}$ (‰)	$0.7{\mathit{\epsilon }}_{\mathbf{fu}}$ (‰)	Pu,th (kN)	Pu,exp (kN)	Pu,th /Pu,exp	Failure Mode
RB1	-	3.3	-	-	192.4	223.0	0.863	CC
GCB-1	GFRP bar	3.3	14.5	16.9	347.6	458.0	0.759	CC-ICD
GCB-2	GFRP bar	3.3	12.4	16.9	389.3	522.0	0.746	CC-ICD
GCB-3	GFRP bar	3.3	11.7	16.9	417.9	534.0	0.786	CC-ICD
BCB-1	BFRP bar	3.3	12.9	14.7	377.0	422.0	0.893	CC-ICD
BCB-2	BFRP bar	3.3	10.9	14.7	421.9	470.0	0.898	ICD
BCB-3	BFRP bar	3.3	10.6	14.7	445.0	470.0	0.947	CC-CCS
ACB-1	AA bar	3.3	17.9	-	243.8	262.0	0.930	CC-DB
ACB-2	AA bar	3.3	15.0	-	266.5	280.0	0.952	CC
ACB-3	AA bar	3.3	12.8	-	346.8	338.0	1.023	CC
RB2	-	3.3	-	-	62.0	81.7	0.759	CC
BA-E-1	AA bar	3.3	16.7	-	104.73	110.1	0.999	ICD
BA-E-1-U2	AA bar	3.3	16.7		104.7	123	0.851	CC
BA-E-2	AA bar	3.3	11.0	-	144.9	153	0.947	CCS
BA-E-2(48 d)	AA bar	3.3	11.0	-	144.9	146	0.993	CCS
BA-E-2(60 d)	AA bar	3.3	11.0	-	144.9	157	0.923	CCS
BA-E-2-MA	AA bar	3.3	11.0	-	144.9	152	0.953	ICD
BA-E-2-U2	AA bar	3.3	11.0	-	144.9	163	0.89	CC
BA-E-2-U3	AA bar	3.3	11.0	-	144.9	164	0.884	CCS
BP-E-1	PS bar	3.3	18.8	-	90.9	91	0.999	CC-ICD
BP-E-1-80	PS bar	3.3	20.3	-	90.9	95	0.957	CC
BP-E-2-80	PS bar	3.3	15.3	-	118.8	139	0.855	CC
BA-E-1-40	AA bar	3.3	19.6	-	104.7	115	0.911	CC
BA-E-1-80	AA bar	3.3	22.4	-	104.7	100	0.952	CC
BA-E-2-40	AA bar	3.3	13.8	-	144.9	165	0.878	CC
BA-E-2-80	AA bar	3.3	16.5	-	144.9	165	0.878	CC
Mean							0.899
Standard deviation							0.073
Coefficient of variation							0.081

. The ratio P_u,th/P_u,exp was used as the assessment index.

As evident from Table 3, the prediction results demonstrate a favorable agreement with the experimental responses. The mean value of P_u,th/P_u,exp for the 26 beams is approximately 0.9 and less than 1, with a standard deviation of 0.073, implying an accurate and safe estimation for the strengthened beams. Moreover, the calculated results of the beams with prestressed NSM bars also show good concordance with the experimental results, with an error ranging from 4.3% to 12.2%. Subsequently, these theoretical calculation formulas will be employed for parameter analysis in Section 5 to conduct a further analysis of the parameters affecting the strength and failure mode of NSM-strengthened beams.

5. Parameter Analysis

Notwithstanding the fact that over twenty specimens were experimentally investigated in the present paper, the impacts of prestress and material properties on the behavior and failure mode of specimens have not been comprehensively elucidated. Hence, in this section, the effects of parameters, mainly encompassing the material properties of NSM bars, NSM reinforcement ratio, concrete strength, and prestress level, on the flexural strength of the NSM-strengthened RC beams were further explored theoretically.

5.1. Material Property of NSM Tendons

In this section, the flexural strength of the beams strengthened by NSM tendons with different material properties was investigated. The test specimen RB2 in Group 2 was used as the analysis model, and the PS, BFRP, along with GFRP bar employed in the present experiment and a CFRP bar adopted in Badawi and Soudki’s research [43], were used as NSM reinforcement bars.

Suppose these NSM tendons have the same diameter (15 mm) and quantity, and the improvements in the maximum load of these strengthened beams with the same configuration are plotted in Figure 12a. Results demonstrate that the material strength of NSM bars is directly related to its contribution to the flexural strength of the strengthened beam. The CFRP bar with the highest strength has the highest contribution to the beam strength. A similar conclusion can be found in Hawileh’s finite element analysis [48] and experiment results conducted by Abdallah et al. [49]. When PS was used, the ultimate strength of the beam increased linearly with the number of PS bars. While, the FRP bars show a decreasing advantage over the PS as the quantity increases. This is because the PS can always yield before the beams fail due to its relatively low yielding strength, unless there are too many steel bars or NSM bars configured. However, the strength of FRPs can be fully utilized only at a small ratio of total tensile reinforcement, in this case, the strengthened beams governed by the fracture of NSM tendon. As the amount of the FRPs increases, the strain of FRPs decreases, resulting in lower utilization of the material strength. Therefore, a decreased slope in the increased percentage can be found in the curves.

The equivalent NSM reinforcement ratio ρ_e,N [50] is used to eliminate the effect of material strength. Assuming an identical value of ρ_e,N, signifying an equal maximum force the materials can provide in the NSM system, Figure 12b depicts the enhancements in the beam strength achieved using different NSM bars. Evidently, when ρ_e,N remains constant, PS exhibits a relatively higher contribution to the beam strength than FRPs. This stems from the full utilization of PS bars owing to their low yielding strain. For FRPs-strengthened beams, it is interesting to find that the ultimate strength of these beams is closely related to the ultimate strain of FRPs. GFRP, possessing the highest ultimate strain, contributes the least to beam strength, while CFRP with the lowest ultimate strain instead contributes the most. This is because the lower the ultimate strain of the material, the higher the utilization rate, resulting in a higher contribution to the beam strength.

Further, the material strength and elastic modulus of the NSM reinforcements were analyzed in detail. As shown in Figure 13a, usually, the PS bar can always reach its yield strength, and the strength of the specimen increases linearly with the equivalent reinforcement ratio. As a result, the type, strength, and elastic modulus of the NSM metallic materials have little effect on the ultimate strength of the strengthened beam when the equivalent reinforcement ratio is the same. However, if the yield strength of the PS is too high or the elastic modulus is too low, the PS bar does not yield when the beams fail, thus the contribution of the PS to the beam strength would be reduced. This situation is similar to that with FRPs that reduced increase in the strength can be found for beams with the lowest elastic modulus or the highest ultimate strength of CFRP bars, as seen in Figure 13b, in which the strength of the NSM bar was not fully utilized. Results display that when the available strength of the NSM bar can be completely used, the product of the available area and strength (A_N × f_u) of the NSM bars, i.e., the equivalent reinforcement ratio, is the main factor that counts for the bearing capacity of the beams. When the equivalent reinforcement ratio is the same, the available strain of the NSM bar is the key factor affecting the contribution to the strength of the strengthened beams.

5.2. Steel Reinforcements Ratio

Figure 14 shows the influence of the steel reinforcement ratio on the strength of beams strengthened by NSM application. PS and CFRP bars were used as NSM tendons for comparison, with a same equivalent reinforcement ratio. During the calculation process, it is assumed that the beams strengthened with PS bars all suffer from CC failure. While, the failure mode of the beams strengthened with CFRP bars is determined by the maximum strain the CFRP bars endure. Specifically, when the strain does not exceed 0.7 times the fracture strain, the beams experience CC failure; otherwise, debonding failure occurs. Therefore, as seen in Figure 14a, under the same reinforcement ratio, the load-bearing capacity of the PS bar-strengthened beams is consistently higher than that of the CFRP bar-strengthened beams. As the reinforcement ratio increases, the curve slope gradually decreases, especially for the beams strengthened with CFRP bars.

Figure 14b illustrates the strain variation of the strengthening bars under different reinforcement ratios. Evidently, as the reinforcement ratio increases, the strain borne by the strengthening bars decreases. Meanwhile, the disparity in the strain borne by PS bars and the CFRP bars gradually diminishes. For the CFRP bar-strengthened beams analyzed in this paper, the reinforcement ratio must attain 1% to avert debonding failure. In summary, increasing the steel reinforcement ratio will reduce the tensile force shared by the NSM bars, hence reducing the contribution of NSM tendons to the beam strength.

5.3. Concrete Strength

This section theoretically analyzes the influence of the concrete strength (ranging from 20.7 to 55.2 MPa) on the performance of the strengthened beams. Figure 15 plots the relationships between the concrete compressive strength and the flexural strength of the beam with PS and CFRP bars. Clearly, the beam strength increased with the concrete strength, yet the increases in strength were rather modest. Specifically, for unstrengthened beams, increasing the concrete strength has little impact on the beam strength. This is attributable to the fact that the strength of the flexural beams is predominantly governed by the strength and area of the longitudinal reinforcement. Regarding strengthened beams, when the concrete strength is comparatively low, increasing the concrete strength leads to a significant increase in the ultimate strength of the beams. Nevertheless, once the concrete strength exceeds 27.6 MPa, increasing the concrete strength scarcely affects the ultimate strength. In combination with Figure 15b, it can be observed that when the concrete strength is relatively low, the strengthened beams suffer from CC failure, and here the concrete strength is fully exploited. When the concrete strength is relatively high, the strength of the strengthening reinforcement in the tension zone is fully utilized, while the concrete may not be crushed. Results indicated that the concrete with a higher compressive strength is conducive to enhancing the utilization rate of NSM reinforcement.

5.4. Prestress Level

In NSM applications, prestressing the strengthening reinforcement can provide various advantages to structures/members, such as delaying the cracking of concrete and yielding of internal steel rebar, reducing the deflections and crack widths, as well as increasing the utilization of NSM materials [43]. Figure 16 presents the relationships between the prestress level and the enhancement on the strength of beams strengthened with one (${\rho }_{\mathrm{e},N}=0.36\%$) or two (${\rho }_{\mathrm{e},N}=0.73\%$) NSM tendons. Assume that the beams were adequately anchored by means of external anchorages, thus the beam specimens exhibited failure modes either as a result of CC or the fracture of the NSM reinforcement.

As expected, similar to the experiment results, the prestress level has little effect on the ultimate strength of the beams strengthened with PS, as shown in Figure 16a. For the CFRP-strengthened beams, when the equivalent reinforcement ratio is low, the specimen failure is triggered by fracture of the CFRP bar. As a result, the application of prestressing not only reduces the beam strength but also advances beam failure. This aligns with the experimental observation reported in ref. [44]. When two non-prestressed CFRP tendons were employed, increasing the prestress level enhances the utilization of CFRP strength until the beams started to fail owing to CFRP fracture. If the prestress level is further increased, a negative effect emerges, which is similar to that observed in beams strengthened with a single NSM bar. As demonstrated in Figure 16b, the higher the prestress level, the smaller the available strength of the CFRP bar. Given that the application of prestress force has occupied part of the strength of CFRP, increasing the prestress level would improve the utilization rate of NSM reinforcement, but there is an increasing risk of the fracture of the CFRP bar. This may explain the different experimental results regarding the effect of prestress level on specimen strength presented in the literature [22,44].

6. Conclusions

In this paper, experimental results of 27 RC flexural beams strengthened with various NSM bars were presented. A prediction approach for the ultimate strength of the flexurally NSM beams was proposed. The strengthening parameters consisting of the material type and material properties, reinforcement ratio of NSM bar and steel bar, concrete strength, filling materials, end anchorage, and prestress level on the beam behavior were theoretically and experimentally analyzed. The conclusions are as follows.

(1)

The RC flexural beams strengthened by the NSM technology are prone to premature brittle debonding failure. The application of wrapped CFRP sheets or mechanical anchorage at the beam ends can effectively delay or prevent the concrete cover separation failure.

(2)

Compared to FRPs, the metallic materials, characterized by superior elongation, contribute to a better ductility and deformability of the beams. Nevertheless, they offer a relatively more modest increase in the bearing capacity.

(3)

The maximum strength of the strengthened beam is intricately associated with the reinforcement ratio and steel and NSM bars, material properties of NSM tendons, and the bonding quality of the strengthening system. The application of prestress predominantly enhances the yield strength of the strengthened beams.

(4)

Increasing the concrete strength and the prestress level, using strengthening bars featuring high elastic modulus and low strain, and employing adhesives with good bonding performance can improve the utilization efficiency of the strengthening bars, but increase the risk of debonding failure of the NSM system or fracture of NSM bars.

(5)

The ultimate strengths of RC beams with different embedded strengthening bars were theoretically calculated in accordance with the ACI codes, which can effectively take into account the material properties and quantity of the strengthening bars, the prestress level, the concrete strength, as well as the failure modes, and it has been verified by the test results to possess a high accuracy.

The NSM technology is an effective method for strengthening concrete beams, columns, or bridge structures with insufficient flexural performance in practical engineering projects. Experimental results and theoretical analysis indicated that the type and quantity of NSM tendons, location of the cutoff points, external anchorage, and filling material, all of which influence the bond behavior at interfaces within the NSM system, are the main parameters determining the performance and failure mode of RC beams strengthened by NSM technology. In practical engineering, external anchorage should be adopted as much as possible. In the future, further analysis on the bond behavior, material properties of filler, the type and shape (rectangular or round bar, strip, laminate, and ropes) of NSM reinforcements can be carried out. Furthermore, the effect of the strengthening parameters on the shear performance and seismic performance of the strengthened components are also worthy of being intensively investigated.