Assessment of RC elements strengthened with NSM FRP rods by experimental tests

Near surface mounted (NSM) technique of strengthening with FRP rods inserted in grooves on the concrete cover of damaged RC beams has been improved in recent years. The aim of this paper is the examination of the static and dynamic behaviour of undamaged and damaged reinforced concrete (RC) beams with free-free ends. RC beams strengthened with NSM Glass and Carbon fiber reinforced polymer (GCFRP) rods have been experimentally analysed. The damage of the RC beam model was obtained by the cracking of concrete under bending tests. The detection of damage and monitoring of RC beams with and without strengthening were carried out by vibration tests assuming free-free ends at different degree of damage. Envelope diagrams of Frequency Response Functions (FRFs) obtained by the dynamic experimental tests are shown and the changes of natural frequency values are correlated to the damage degree of beam elements. Experimental results are discussed with particular emphasis on the aspect of the loss of bond.


Introduction
The strengthening of damaged reinforced concrete (RC) beams is a relevant topic of civil engineering. In fact, many causes, such as environmental conditions that result in the corrosion of steel reinforcement and static not foreseen high loads, or more simply errors of design may usually damage reinforced concrete elements. The use of fiber-reinforced composites has increased in recent years and the near surface method (NSM) with FRP rods inserted inside grooves on the concrete cover appears useful to in order to solve many problems [1][2][3][4]. Examples of NSM using steel rods for strengthening RC structures go back to the early 1950s; the advantages of FRP rods compared to steel is that they are easier and quicker to assemble due to the lightness of the strengthening materials, the slimness of the grooves attributable to the higher traction resistance and, FRPs' improved corrosion resistance. Furthermore, the NSM strengthening appears capable of solving the susceptibility of FRP sheets or externally bonded FRP reinforcements to damage deriving from collision, high temperature and fire.
The availability of strengthening with NSM FRP strips or rods depends on maintaining the bond between NSM rods and concrete. Many factors affect the bond performance: bonded length, diameter of the FRP rod, type of FRP material, surface configuration of the rod, size of the groove [5][6][7].
Bond behaviour has an influence on the ultimate capacity of reinforced elements as well as on serviceability aspects such as crack width and spacing. NSM FRP rods are prone to show greater slips than steel reinforcement due to potentially lower bond shear stress of FRP materials [8,9], to the presence of surrounding adhesive layers and local cracking in the cover concrete [9,10].
Investigations and theoretical studies addressing the bond behaviour of FRP rods in RC elements [9,11,12] and describing most of the fundamental aspects of the NSM technique have been developed: an experimental program involving pull-out and bending tests was carried out to evaluate local bond stress-slip relationship by controlling numerically developed strategies [13][14].
Although these methods are destructive in character, direct pull-out tests and bending tests may be adequate for describing bond mechanism and failure modes in NSM strengthening. In addition, an analysis of dynamic responses may be adopted as a nondestructive testing method (NDTM) for investigating the behaviour of RC beams strengthened with NSM FRP rods [12,15]. The basic concept behind vibration monitoring is that dynamic characteristics are functions of structures' physical properties. Therefore any change caused by damage results in a change in dynamic response [15,16]. In the strengthening method, actual bond-slip may be influenced by the cracking of concrete and loss of adhesion of rods which can modify frequency values and beams' modes of vibration.
The aim of this paper is to analyze the static and dynamic behaviour of RC beams damaged and strengthened by both carbon and glass fiber reinforced polymer (C-GFRP) rods utilizing near surface method.
A large investigation concerning both specimens subjected to pull-out tests with NSM FRP rods and bending tests of RC beams with strengthening [13,14] allows to analyze the response of RC elements and define the reliability of the theoretical model. Furthermore, the nondestructive method based on vibration tests adopted during the experiments enables the control of the RC beams at different damage steps due to the cracking of concrete; experimental static and vibration results are discussed and comments on the strengthening of the bond of NSM C-GFRP rods were developed.

Analysis of bond and results of pull-out tests
Bond in NSM strengthening has influence on the ultimate capacity of the strengthened RC beams as well as on serviceability aspects of cracking on the surface of concrete, width and spacing. The mechanics of bond are linked to bond stress and slip at the failed interfaces of material. The relative displacement between FRP rod and concrete is the sum of rod-toepoxy and epoxy-to-concrete slips. If failure occurs at the epoxy-concrete interface, the average bond strength is that at the failed interface [9,14]: where: Pmax is the peak load; dg is the perimeter of groove size and lb the bonded length. When a failure mechanism emerges at the interface between rod and groove-filled material, the average bond strength may be computed as: where: db is the diameter of the FRP rod.
In general, the most dangerous failure mechanism is the loss of bond around the rod at the rod-epoxy interface. An analytical model was developed [14] through an energy approach which allows to obtain bond stress-slip laws and to evaluate the fracture energy value Gf. It assumes failure occurs at the interface between the rod and groove-filling material ( Fig. 1): the w(z) function represents the displacement of the point of rod along its axis under applied load. The total energy of the system may be written as the sum of internal energy of deformation and external energy due to load P: where: P is the tensile load; EFRP is the Young's modulus of FRP; AFRP is the cross section of FRP rod; is the stiffness of resin surrounding the FRP rod ( Fig. 1 , respectively, the shear strain and stress; GEP the shear modulus of resin. Minimizing the total energy with respect to the w(z) function, the following 2 nd order differential equation is obtained: with the coefficient: AMCM 2020 With the following boundary conditions: By the Eq. (5), the strain distribution along the rod may be evaluated: Assuming a simplified theoretical bi-linear model of the bond with a softening branch after the maximum shear stress value, the fracture energy Gf is given by: where: Ȉb ideal perimeter of the groove. For a sufficiently long bond length, having , from the maximum normal stress for the NSM FRP rod is obtained: We may note that if tension max σ is lower than the resistance of the FRP bar, the total capacity of the strengthening cannot be developed independently from the length of the rod anchorage; when max σ exceeds the tensile strength of the rod, the total capacity of the strengthening can be developed with infinite values of energy fracture [8] as

Pull-out tests
Experimental investigation foresaw direct pull-out tests on RC elements with one FRP rod inserted into the groove. Dimensions of RC specimens were: length 400mmÂ150mmÂ150mm. An epoxy resin characterized by tensile strength fEPOX 8N/mm 2 and Young's modulus equal to EEPOX= 9.5Â10 3 kN/mm 2 was adopted. Specimens were built with different geometry of the section of the FRP and different characteristics evaluated experimentally in laboratory as well; main properties of CFRP rods: tensile strength fCFRP =1704.82N/mm 2 ; Young's modulus ECFRP=1.24Â10 5 N/mm 2 ; and diameter db=8mm; main parameters of the GFRP rod: db = 9.53mm fGFRP=1040 N/mm 2 EGFRP=33.6Â10 3 N/mm 2 . Pullout tests were carried out with different bond length of FRP rods: lb=200mm -250mm and 300mm and the position of strain gauges with an interval of 50mm to measure strain under pull-out tests-are shown. LVDT was used to measure the displacement at the free end of the rod during loading. In Figure 2, a general view of the location of strain gauges and the setup of direct pull-out test is shown.
In Figures 3(a), (b) and (c) the experimental diagrams load versus strain for four strain gauges no. 1, …, 4 on CFRP rods are shown. It may be noted that for a bond length lb 250mm the strain value measured on strain gauge no. 1, εCFRP , is below 4Â10 -3 . For a greater bond length equal to 300mm, the maximum strain value recorded on strain gauge no. 1 is approximately 7.05Â10 -3 . The experimental laws shear stress, Ĳ, versus slip, w, were calculated by a numerical procedure considering the measured data of strains; in Figure 4 the experimental law obtained for the specimen with bond length equal to 300mm is compared with the theoretical curve proposed in literature [2,9]. Experimental results of the pull-out test with GFRP rods lead to lower values of fracture energy with higher maximum slip. In this case, the experimental shear stress versus slip diagrams are substantially linear. It appears that the bond between GFRP rods-resinconcrete is maintained up to the failure of the rod with bond shear stress values about 11.0 N/mm 2 ; fracture energy values vary between Gf = 1.37÷1.56 N/mm. By comparing the results obtained on pull-out tests, we can conclude that the failure due to the loss of bond seems a relevant mechanism of damage, in particular utilizing the NSM GFRP rod.

Static and vibration tests on RC beams
Static tests were planned in laboratory in different phases utilising RC beams with the geometric and mechanical characteristics described below. The dimensions of the beam's sections are 150mm·220mm and measure 1700mm in length (Fig. 5). The steel reinforcement used was 4 bars measuring10mm and stirrups at the interval of 60mm having a diameter of 6mm. Several beams were damaged by bending tests and, successively, strengthened with CFRP circular rods into rectangular grooves measuring 20mm·20mm in section. Other RC beams without damage due to cracking were strengthened with GFRP rods and subjected to bending path and at each step of loading analysed by free vibration tests.
Below, experimental results are discussed for one RC beam strengthened with the CFRP rod without the initial damage degree. The failure of the strengthened RC beam was reached at the load value equal to P=115.0 kN; the failure was due to the crash of the compressive edge of concrete. The strength of the RC beam with NSM CFRP rods compared with an analogous beam without strengthening is more than double.
The experimental measures of strain İCFRP on CFRP rods at the midspan of the beam confirm that the recorded values reached values equal to İCFRP § 4.0x10 -3 without any damage due to the loss of bond of CFRP rods (Fig. 6). Finally, experimental free vibration tests were carried out on beams in order to evaluate the influence on the dynamic response of beams of cracking and/or the loss of bond of CFRP rods. The experimental dynamic test was carried out using a specific impact hammer (Fig. 7) using the well-known technique where a mobile accelerometer measures the acceleration of the structural element triggered using a hammer in a fixed point. It was determined that the specimens would be tested dynamically in free-free edge condition. In Figure 7, the setup of vibration tests with the location of measuring instruments is shown. In Figure 8, experimental results are shown with the envelope of FRFs at different damage degrees Di, i=1,…,6 due to bending tests. The transition of the diagram to the left along with the increase in the level of load is evident. In the second phase of the investigation, the static and dynamic response of the RC beam damaged by bending loading with and without the NSM GFRP rod strengthening was analysed. The RC beam of 2.20m length and the rectangular section of 120mmÂ160mm was reinforced with similar steel bars and only one GFRP circular rod, inserted after static tests without strengthening, into the rectangular groove of the 20mmÂ20mm section.
The RC beam was firstly subjected to the bending test without the GFRP strengthening, according to the setup of a simply supported beam with hinge restraints. The instrumentation used was as follows: one vertical jack and one load cell to evaluate the vertical load value during the bending test; three LVDTs to measure deflections at midspan and close to restraints; LVDTs to record strains at the midspan of beams at the top and bottom on the midspan section (Fig. 9). Fig. 9. Setup of static bending tests for simply supported RC beam with and without the GFRP rod.
The RC beam was subjected to three loading and unloading cycles: D1-P1=4kN, D2-P2=8kN, D3-P3=18kN. The choice of these load cycles permitted to damage the beam with cracks on concrete reaching the maximum experimental value of steel strain equal to İs؆ 3.35Â10 -3 for damage degree D3, higher than the yield strain value of steel. After D3 damage degree, the RC beam was strengthened with a GFRP circular rod inserted in the groove by adhesive epoxy resin and subjected to a similar loading path for the load step D1, D2 and D3. Successively, the beam was subjected to increasing load until failure.
The collapse, reached at a load value equal to P=33 kN, occurred with the crushing of the compressed concrete and successively the expulsion of the concrete cover at the intrados with the detachment of the GFRP rod. The evolution of the strain on the GFRP rod was monitored through a strain gauge glued on the rod's surface at the midspan section of beam. The experimental measures of strain İGFRP on GFRP rods highlight that the recorded values reached a maximum equal to İGFRP §6.0x10 -3 before the collapse (Fig. 10). Finally, experimental free vibration tests were carried out on the beam in order to evaluate the influence on the dynamic response of beams of cracking and/or the loss of bond of GFRP rods. The dynamic responses were obtained using, once again, the same methodology described above with the impact by hammer and an accelerometer at 9 nine measurement points connected to an acquisition system working in a range of frequencies between 0 and 1500 Hz. The signals were recorded and elaborated in the frequency domain through the FFT technique and FRFs obtained using Pulse software. The un-strengthened and GFRP strengthened beam was dynamically tested in free-free ends condition. The FRF envelope recorded during free vibration tests for each step of damage degree is shown in Figure 11 for both configurations. As seen from the envelope diagrams of FRFs, there was a progressive lowering of frequency values from the undamaged degree D0 up to the damage degree D3. The comparison of frequency variations for the response of GFRP strengthened beam shows that the difference between the peak frequency for different damage degrees is rather small. In fact, the application of the NSM GFRP strengthening contributes to reducing the width of the cracks undergoing even heavy loads.

Conclusions
A large investigation on specimens with NSM C-GFRP rods and subjected to pull-out tests, bending tests and vibration tests allowed to analyze the structural response of strengthened RC elements. Experimental static and vibration results are discussed and comments on the strengthening bond of NSM C-GFRP rods were developed. Main conclusions of investigations can be summarized as follows: the failure due to the loss of bond seems a relevant mechanism of damage, in particular utilizing the NSM GFRP rod; combined static and dynamic experimental measures confirm that beams strengthened with the NSM C-GFRP rod under service loads present an adequate response without relevant capacity decrease; frequency variations are relatively low in strengthened RC beams with the NSM C-GFRP rod while the variations are high when the RC beams are strengthened only with steel reinforcement, due to the FRP capacity to limit the cracking damage state under bending conditions. This experimental research was supported by research funds provided by Università Politecnica delle Marche. The authors would like to express their gratitude to all the technicians and students who collaborated to develop the experimental research.