Bond stresses in post‐installed reinforcing bars derived via fiber optic sensors

A novel application of fiber optic sensing aimed at understanding the tensile behavior of post‐installed reinforcing bars in normal‐strength concrete is presented in this paper. To comply with established assumptions of cast‐in reinforcement, such as the uniform bond stress distribution, the design bond strength of post‐installed configurations is limited. In this study, pull‐out tests in confined conditions were conducted using two high‐performance mortars. Cast‐in‐place anchorages were tested for reference. The proposed fiber optic sensors and post‐processing techniques enable to continually measure and evaluate the bond stress distribution and monitor rebar deformation. Compared to cast‐in rebars, post‐installed rebars exhibit significantly higher bond resistance, particularly due to higher bond stresses at the beginning of the embedment length. These results highlight the potential for reducing the embedment length of post‐installed rebar. Moreover, variations in stiffness and bond stress distribution are found to significantly affect the slip and rebar deformation of both cast‐in‐place and post‐installed rebar.


| INTRODUCTION
Post-installed (PI) reinforcing bars (rebars) are commonly employed in concrete-to-concrete connections to rehabilitate, extend, and strengthen reinforced concrete (RC) structures or replace damaged or misplaced rebars.Unlike cast-in-place (CI) rebars that are embedded during concrete casting, PI rebars are installed after concrete has hardened and, typically, after years of service.The installation procedure involves drilling holes into the concrete member and fixing the bars using qualified mortar systems.In Europe, mortars are qualified by the assessment documents EAD 330087 and/or EAD 332402. 1,2nderstanding and quantifying the load transfer (bond) of CI or PI rebars is essential in designing and assessing the performance of RC structures, as it directly affects their bearing and deformation capacities, crack resistance, and overall durability.Figure 1a shows a sketch of a concrete-to-concrete connection.Bond is generated by mechanical interlock, chemical adhesion and frictional forces F, which are influenced by material properties, stress states, and load-time histories. 3or CI rebars, the bond strength comes primarily from the ribs around the rebar. 4As depicted in Figure 1b, concrete crushing, shearing planes, and radial cracks arise from the inclined bearing forces that interact between the materials.In PI rebars, the injection mortar layer between the reinforcement and the concrete increases the complexity of the load transfer mechanisms that govern bond.Despite the possible differences in load transfer between PI systems and CI rebars, the design currently relies mainly on provisions derived and provided for CI rebars, such as the EC2 5 in Europe.
In the literature, the experimental insight on the strain distribution of PI rebars is limited and mostly based on Spieth's 6 results.His measurements were performed with strain gauges installed every 60 to 75 mm.][9][10] This novel technique enables quasi-continuous strain measurements with minimal impact on the rebar behavior, as the geometry is barely altered by the sensors.Nevertheless, further research and innovative approaches are necessary to overcome the existing challenges 8 and fully exploit the capabilities of FOS in rebar applications.The rebar-to-concrete interaction is complex, and large strain gradients tend to arise near the ribs in rebars under tensile loads.Moreover, the installation of FOS in CI rebar and interpretation of strain data due to unavoidable anomalies can be challenging. 11Methods of instrumentation and post-processing of FOS data are required to compare the results with conventional approaches and gain new insights into the bond behavior. 12,13The instrumentation and interpretation of FOS becomes even more demanding when faced with the added complexities involved in PI rebars, for example, limitations due to drilling work, differences in mortars' performance, etcetera.
The developments of high-performance injection mortars and innovative cementitious composites offer a chance to enhance the performance of PI rebars.5][16] The design bond strength of PI rebar is limited to CI rebar provisions principally due to (i) assumption of an uniform bond stress approach, (ii) limitation of slip under service loads, and (iii) prevention of splitting cracks. 16Exploiting higher bond strengths in the design of PI rebars could be achieved with innovative measuring techniques that improve the knowledge of the bond-slip relation and the bond stress distribution.Moreover, as PI bars are going to be included in next-generation design codes and the development of both injection mortars and composite materials has markedly progressed in the last decades, improving the knowledge on bond in PI rebars is not only technically relevant, but also urgently requested.
The aim of this work is to investigate and develop the application of FOS toward a more accurate assessment of the bond stress and to foster the fundamental understanding of how PI rebars behave in concrete-to-concrete connections.To this end, pull-out tests in confined conditions under quasi-static tensile loading were performed according to the relevant European Assessment Document (EAD) qualification criteria. 1Two different high-performance mortars are investigated in conjunction with normal strength concrete.The embedment length related to the nominal rebar diameter d s was varied between 5 d s , and 10 d s to gain insight into the differences in stress distribution.CI anchorages with an embedment length of 7 d s were tested for reference.A proposal on the instrumentation and post-processing of FOS measurements is derived thereof.The bond-slip curves are determined and compared to that of CI bars and the provisions in fib Model Code 2010. 17 to the ones measured with conventional devices like strain gauges.Conclusions on special installation and evaluation needs of FOS are drawn.Their potential for gaining new insights in the bond behavior of PI rebars is discussed.

| Introduction
In structural health monitoring, FOS has developed significantly in the last few decades, proving to be a reliable and accurate measurement tool.FOS can be categorized based on gauge length and functional principle.In the first category, short and long gauge sensors facilitate either local or global structural monitoring (from 10 cm to several meters) utilizing Fiber Bragg-Grating Spectrometry, Extrinsic Fabry-Perot Interferometry, or Michelson and Mach Zehnder Interferometry.In the second category, distributed sensors enable one-dimensional quasi-continuous for simultaneous local and global strain monitoring (from less than 1 mm to 1 m) through Brillouin, Raman, or Rayleigh scattering. 18,19The interested reader is referred to the state of the art review. 20In recent studies, 8,9,[21][22][23] particularly the distributed FOS based on Rayleigh scattering has emerged as a promising method for achieving higher spatial resolution in the measurement of rebar strains.This innovative technique relies on the evaluation of the Rayleigh backscatter obtained from a signal emitted by a light source.The spectrometer enables the localization and interpretation of optical changes in independent virtual gauges that are distributed throughout the optic sensor.These changes provide crucial information, including accurate strain data, 7 with a spatial resolution otherwise unachievable with traditional gauges.This investigation highlights whether and how distributed FOS with Rayleigh scattering can help to understand the force transmission between concrete and reinforcement by measuring strains in CI and PI rebars in pull-out tests.Consequently, the forthcoming discussion will be dedicated exclusively to this specific type of FOS.

| Composition of sensors
The composition of FOS is crucial for ensuring efficient signal transmission while preventing modal dispersion and brittle breaking of the fiber.Each FOS consists of three layers: core, cladding, and coating.The core, with a diameter of 9 μm, is the medium for signal transmission.The cladding, with a diameter of 125 μm, confines the signal within the core.Externally, a coating provides protection to both the core and the cladding.Two commonly employed coatings include acrylate and polyamide, with the latter offering improved measurement sensitivity due to reduced slip between the coating and the cladding.However, it is important to note that polyamide coatings also tend to increase the fragility of the sensor. 12To facilitate connection with the spectrometer, a connector is spliced to one end of the FOS.At the opposite end, a termination is installed to refract the transmitted light.

| Derived quantities
Strains measured with FOS over the embedment length can be converted into the bond stress distribution and slip of the rebar.To such end, the load transfer mechanism on a differential element of a typical anchorage is depicted in Figure 2. The analysis considers the reinforcing bar area A s and perimeter U s in a concrete cylinder of cross-sectional area A c embedded concentrically over a length l b .The bar is subjected to a tensile load F s , which is transferred through bond to the concrete.The equilibrium at any differential element is given by where τ b ¼ τ b x ð Þ is the bond stress at the interface between steel rebar and surrounding medium at the generic position x along the rebar.
F I G U R E 2 Tensile load transfer through bond between rebar and surrounding concrete.
To solve the differential equation of bond, the derivatives can be approximated with finite differences.The continuum length of the rebar is discretized into a finite number of points where the virtual FOS gauges are located.Considering equilibrium of stresses, compatibility of deformation and constitutive equations in the noncracked elastic stage, the bond stress is derived from Equation (1): where is the difference between the strains measured at two consecutive gauges, Δx is the in-between distance, and E s is the Young's modulus of the steel rebar.
The compatibility of deformation between concrete and steel strains is characterized by the slip δ formation expressed in Equation (4).
If the concrete strains are small compared to the steel strains, the slip of the rebar can be calculated from the rebar elongation u s between the start x 0 and end x 1 of the embedment length.
In practice, Equation ( 5) can be numerically integrated using the virtual gauges of the FOS as discretization points.

| PULL-OUT EXPERIMENTS
The experimental campaign carried out as part of this study comprises 15 pull-out tests on individual bars embedded in fully-confined concrete.The main influence factors, the bond system (CI or PI rebar with two different injection mortars) and the embedment length are varied.Standard hot-rolled steel reinforcing bars type B500B of nominal diameter equal to 20 mm and normal strength concrete C20/25 are employed.

| Test setup
The experimental setup complies with the guidelines outlined by European Organization for Technical Assessment (EOTA) 1 for pull-out tests in confined conditions.Figure 3 illustrates the test configuration and depicts the specimen before being tested.The monotonic tensile load was applied to the rebars using a displacement-controlled method on a 1000 kN universal testing machine. 15,24The maximum bearing pressure under the steel plate, achieved when the rebar yielded, was 2.95 N/mm 2 .The displacement-controlled tests (stroke controlled, displacement rate = 0.5 mm/min) were conducted until either the pull-out of the bar from the concrete or the yielding of the bar occurred.In some cases, bar pull-out and yielding were roughly simultaneous (mixed failure).

| Embedment length and injection mortars
The bond characteristics of two different highperformance mortars, referred to as "A" and "B" throughout the manuscript, were investigated.Mortar A is a stiff organic epoxy-based material, while mortar B is a rather weak hybrid material consisting of two components (an inorganic and an organic binder).The components are stored separately in two connected cartridges and mixed upon use.The installation procedure for the PI rebar followed the Instructions for Use (IFU) provided in the respective technical assessment documents of the mortars, in accordance with the EOTA EAD 330087. 1 Both injection mortars were tested with embedment lengths of 100 mm (5 d s ), 140 mm (7 d s ), and 200 mm (10 d s ).A CI rebar with an embedment length of 140 mm (7 d s ) was tested for reference.In, 15 the authors have investigated the pull-out bond strength of PI rebars with the same mortar A and embedment lengths of 70, 100, and 140 mm.CI rebars with an embedment length of 140 mm were tested for reference.In this respect, the current campaign extends these basic findings and determines mortar B's bond strength.The largest embedment length of 200 mm is chosen since it aligns with the minimum anchorage length for rebars under tension, as specified by the EC2 5 and the required embedment length for pull-out tests to qualify the bond strength of mortars by EOTA. 1

| Concrete and formwork
Normal-strength concrete with a cement type CEM I 42,5 R and a maximum aggregate size of 16 mm was used for all specimens.The concrete was cast in two batches, both in agreement with the strength class C20/25.The uniaxial compressive strength of both mixtures was obtained from three standard cylinders with a height of 300 mm and a diameter of 150 mm.In addition, the splitting tensile strength and the Young's modulus of the second mixture were also measured with three cylinders.6][27] The splitting tensile strength was transformed into the direct tensile strength by applying a coefficient of 0.9.The cylinders were covered with foil and stored in a dry and closed room under the same conditions as the cylinders to be tested in pull-out.The average results from testing the mechanical properties of both concretes are listed in Table 1.
Steel pipes (S355) 250 mm long, 10 mm thick, and a nominal diameter of 300 mm were used as formwork to cast the concrete.The concrete cover of each rebar was approximately 7d s (140 mm).Considering that the transition between pull-out and splitting failure was found between 3d s and 5d s , 3 the provided passive confinement by concrete cover was sufficient to avoid splitting failure.The steel pipes were kept as part of the specimens during the test to provide extra confinement to the concrete around the rebar.

| Reinforcing bars
Ribbed steel reinforcing bars type B500B according to DIN 488-1 28 with a nominal diameter of d s = 20 mm were cast-in-place or embedded axially into the concrete with the injection mortars.The material properties of the bars presented in Table 2 were determined from three samples in a standard tensile test and evaluating the results according to EN ISO 6892-1. 29An average curve of the stress-strain data of the reinforcing steel is presented in Figure 4.
To facilitate FOS installation in the rebar, a cutting disc was employed to mill two longitudinal grooves on the opposite sides of the bar, in the regions where the ribs flatten.In this way, the ribs were nowhere intersected by the grooves, as depicted in Figure 5.Moreover, the extremity of the bar was smoothed, and a circular groove was created along the perimeter of a section in this region to join the opposite sides.The dimensions of the groove were designed to be approximately 1 Â 1.5 mm 2 .In order to assess the rib geometry and the dimensions of the milled grooves in the rebar, three samples were scanned using non-contact 3D scanners specifically manufactured for precise measurements (see Figure 5).
The average relative rib area of the four bars was determined to be 0.072, according to the calculation procedure in DIN EN ISO 15630-1. 30DIN EN 488-1 28 specifies a minimum relative rib area according to the type of rebar of 0.056 to guarantee bond stiffness and strength.
Following evidence on beam-end test results, in well confined concrete the bond strength increased only 10% from a relative rib area of 0.05 to 0.20. 31Therefore, no difference in bond strength is expected due to a higher relative rib area compared to the minimum specified by the norm.
A comparison and analysis at various sections of the rebar with and without grooves was conducted.Figure 5b shows part of the analysis along with some details on the FOS instrumentation.The scan evaluation revealed that the inclusion of two grooves on both sides resulted in a mere 0.71% reduction in the cross-sectional area of the rebar.Consequently, each groove was estimated to have an approximate area of 1.1 mm 2 .This reduction had minimal impact on the mechanical properties and bond performance of the bar.

| FOS configuration
The FOS utilized in all specimens were equipped with a polyamide coating and a connector (pigtail) at the beginning (see Figure 3).The sensors were strategically installed at locations within the embedment length of the rebars, where the bond with concrete occurs, and over a short length beyond the embedment length.The FOS were carefully positioned within the prepared groove in the rebar and securely fixed using a two-component acrylate-based adhesive named AC2411, which has been proven effective in analogous applications. 9he spectrometer employed for the tests was the ODiSI 6100, an optical distributed sensor interrogator manufactured by Luna Innovations Incorporated. 32his device measures strains within a range of ±12.000 με.Prior to conducting the tests, specific parameters including gauge spacing and length were determined.The distance between successive measuring points on  the gauge was set at 0.65 mm to achieve the maximum spatial resolution.Additionally, the spectrometer frequency was fixed at 4 Hz, which was deemed as more than sufficient for data acquisition during the quasistatic experiments.

| Additional measuring techniques
Two linear variable differential transformers (LVDTs) were employed to accurately measure the relative displacement between the rebar and the top surface of the concrete cylinder; in Section 4.1, this quantity is denoted as the slip at the loaded end, δ le .Elastic deformations of the rebar at the position of the LVDTs were subtracted using the constitutive equations of the material and the measured mechanical properties (see Table 2 and Figure 4).
To further validate the strain data obtained from the FOS, linear strain gauges with measuring grid length of 3 mm were utilized on four specimens.These strain gauges were positioned at two distinct locations (approximately at one and third quarter of the embedment length), enabling a direct comparison of the two measurement techniques.

| Failure mode and bond strength
Table 3 gives an overview of all specimen configurations along with data at which the loss of adhesion and the failure occurred.In total, 15 specimens were tested.The specimens are named using the following convention: the first part (two or three letters) indicates the bond system and the mortar (i.e., "PI" or "CI," and mortar "A" or "B"; e.g., PI-B denotes a post-installed rebar with mortar B).The second part corresponds to the embedment length (100, 140, or 200 mm), followed by the repetition number (1, 2, or 3).The 140 mm embedment length was tested three with three identical specimens per bond system.In contrast, shorter and longer embedment lengths were tested twice or once, respectively.
The test results comprise the maximum tensile load at failure F max , the bond stress at loss of adhesion τ b,adh , and at failure τ b, max , and the corresponding slip at the loaded end, δ le,adh and δ le,max .The maximum bond stress at failure τ b, max is converted to the nominal one τ b,max,nom regarding the cylinder compressive strength of concrete f cm,cyl and the characteristic compressive strength f ck ¼ 20 N/mm 2 as follows: In accordance with the EOTA EAD 330087, 1 the default value for the exponent m for pull-out failure is m = 0.3.The loss of adhesion, as defined in the EOTA EAD 330087 [1], refers to the load at which uncontrolled slip of the rebar and a significant stiffness loss occurs.To accurately determine the slip of the rebar at the loaded end, the elastic deformation between the position of the displacement transducer and the beginning of the embedment length was subtracted.
The failure modes are pull-out, steel yielding, or a combination of both.An illustration of the pulled-out rebar is shown in Figure 6.The failure of PI rebar predominantly occurs at the interface between the rebar and the mortar, with minimal areas of failure due to shearing planes between the concrete and mortar.In the case of CI bars, on the contrary, the primary failure mechanism involves shearing along the rib interface and localized crushing of the concrete.
Compared to the CI rebar, the nominal bond strength of mortar B is 1.6 times higher on average.Although mortar A reached yielding, the bond strength is at least 2.1 times higher than CI rebars.This disparity does not only highlight the difference between CI and PI rebars, but also variations among PI bars with different mortars.Interestingly, even for short anchorage lengths, such as 5 d s , PI rebars with mortar A reach steel yielding, meaning that a favorable behavior (highly ductile) is consistently observed, with maximum utilization of the steel.Similar trends are observed for the bond stresses at loss of adhesion, with mortars A and B showing increases of 105% and 40%, respectively, relative to CI rebar.7). Figure 7b shows the four model stages.
These branches are here evaluated on the assumption of "good" bond conditions.Consequently, the parameters are as follows: α ¼ 0:4, δ 1 ¼ 1:0 (mm), δ 2 ¼ 2:0 (mm).τ b,max ¼ 2:5 ffiffiffiffi f c p , s 3 ¼ c clear and τ bf ¼ 0:4 Á τ b,max .For CI rebars, the maximum bond strength, which largely determines the shape of the bond-slip curve, is calculated in three ways.Two curves are obtained from the fib Model Code 2010 [18]   outlined in Section 6.2. 1 Then, the maximum bond strength of the PI rebars is determined from the characteristic strength specified in the technical datasheet of the mortars for pull-out failure in non-cracked concrete C20/25, 50 years working life and good bond conditions.Since this document only specifies the characteristic strength to 14 and 12 N/mm 2 for mortars A and B, respectively, two out of five factors specified in EC 2 [1] were applied to calculate the mean strength.These account for the statistical distance between mean and 5% fractile (1/0.75) and for the length of embedment (0.8).
Comparing the experimentally obtained bond stressslip curves with the theoretical ones reveals a reasonable agreement.Notable differences only exist in terms of the slip at peak load regarding the PI bars.In particular, for PI bars, the slip rises from the loss of adhesion to maximum load at failure by a factor of 3.5 to 4.6.By contrast, CI rebars exhibit an increase of 2.2 times only.This shows that PI bars undergo greater deformations before reaching the peak load and show a favorable plastic (ductile) behavior, with an extended plateau where deformation increases while the maximum load is maintained.
The slip capacity is defined as the slip of the anchorage when the characteristic strength stress is applied. 1 For CI rebar, the average characteristic bond strength τ bk is 7.3 N/mm 2 .This value was calculated applying the two factors (1/0.75 and 0.8) to convert the measured maximum tensile load τ b,max (see Table 3) into a characteristic value.Similarly, the characteristic bond strength for mortars A and B is found to be 16.3 and 12.5 N/mm 2 , respectively.It is important to note that the slip capacity is 0.19 mm for CI rebars, whereas for both mortars, it is 0.40 mm and thus almost doubled.If the slip of the anchorages is critical to a design, the higher slip capacity of PI rebars must be considered.

| Post-processing
The objective of post-processing the FOS measurements is to identify the quasi-continuous strain variations along the embedment length of the rebars, removing the local effects due to the ribs, imperfections of the rebars, or the presence of cracks in the surrounding medium.Thus, the steps involve the complementary stages of (i) filtering and (ii) smoothing of the strain data.
Initially, the FOS measurements are filtered to extract the strains on the lengths of interest.The extremity of the rebar (unloaded end) and a 15 mm long part to both sides around it are disregarded due to the rounded profile that introduces excessive noise.Additionally, extreme values above 4000 μm/m resulting from discontinuities such as cracks or local effects are disregarded to ensure data integrity.Then, smoothing is performed applying a locally weighted linear regression technique to the data.This process effectively reduces noise and scatter, enabling clear observation of the overall strain distribution along the rebar.The post-processing steps are supported by insights in. 12Once this stage is completed for both sides S1 and S2 of the rebar, an average curve is computed to represent the entire length.Ideally, a straight reinforcing bar section under tensile stresses should exhibit the same strains along its circumference.However, imperfections, rib geometry, and stress localization can result in bending effects and varying strains across the section.The averaging procedure effectively mitigates any unwanted bending effects that may arise due to, for example, high or specific loading conditions, incorrect installation or deviations in the production.
Figure 8 exemplifies the outcome of post-processing the raw data.The distribution of steel strains measured by FOS on both sides of a single CI rebar (specimen no. 2) is shown on five load levels: 10%, 30%, 50%, 70%, and 90% of the maximum pull-out load (102.65 kN).The average curves of the measurements at both sides S1 and S2 are also presented for these load stages.The elastic strain of the bare rebar at the loaded end (ε s,e ) serves for comparison.It is calculated from the applied tensile load (F s ), the nominal cross-sectional area (A s ), and the Young's modulus of steel (E s ).The FOS raw data is displayed in gray.It is evident that noise and scatter in the strain measurements increase with the applied load.Consequently, post-processing of the data is strongly recommended to facilitate the interpretation of the results.

| Comparison with strain gauges
The strains obtained from FOS and gauges are examined at three tensile load levels over the entire embedment length.Figure 9 illustrates the strains over the embedment length in PI-200-A and PI-200-B specimens for three load levels.The design strength of this anchorage, as per EC2, corresponds to 44% of the yielding stress, that is, f y ¼ 544 N/mm 2 .The two load levels below (30%f y ) and above (σ sk = 68%f y ) are selected to analyze the behavior of the anchorage below and even beyond the design level.The strain gauge data is shown as a dotted line, while the post-processed measurements obtained from the FOS are drawn as solid lines.Strains from the two sides of the rebar are shown in gray, while the average is drawn in red.The dashed lines indicate the calculated elastic strains of the bare bars at the free/ pulling end.
At the loaded end, the FOS strains correspond to the applied force.They remain constant over the free length, then, they gradually decrease and nearly reach zero at the embedded end.The averaged curves of the three load levels share a similar trend.As expected, the higher the applied load, the higher the strains in the rebars.At the two selected positions, the FOS and gauge strains closely match, particularly on the side of the bar where the strain gauges are attached.
Differences between the strains on both sides are observed for mortar A, particularly between the loaded end and the first 80 mm of the embedment length (Figure 9a).This discrepancy is attributed to an unintentionally bent rebar.Consequently, the gauge data better correspond to the FOS strains on side S1, where the gauges are placed.

| Bond stress distribution
The bond stress distribution over the embedment length is obtained from FOS measurements using the procedure outlined in Section 3.3.This distribution is compared for a representative specimen of each length (100, 140, and 200 mm) for both mortars A and B to highlight the difference between CI and PI anchorages.To cover the entire range of strains, specific levels were chosen that represent the design σ sd , characteristic σ sk , and mean strength σ sm of rebar embedded in concrete of grade C20/25 according to EC2. 5 If the ultimate stress in the test σ su exceeded even the mean strength, the belonging results are reported, too.
As per EC2, the design strength of an anchorage with a CI rebar of diameter d s ¼ 20 mm is obtained from Equation (8).
In fully confined conditions, the coefficients α 2 and α 3 are both set to 0.70.The specimens' average compressive strength of concrete is f cm,cyl = 33.44 and 36.80N/ mm 2 , respectively (Table 3).Then, equation (8.2) in clause 8.4.2 of EC2 5 yields the design bond strength f bd for specimens with l b ¼ 140 mm (2.72 and 2.96 N/mm 2 ).Substituting f bd in Equation ( 8), the design strength σ sd for the three embedment lengths is obtained.Multiplication with the partial safety factor γ c ¼ 1:5 yields the characteristic strength σ sk .The mean strength σ sm is calculated according to Section 4.2.In Table 4 these quantities are related to the yielding stress of the rebar (f y ¼ 544 N/mm 2 , Table 2) and listed for the three embedment lengths.
Figure 10 shows strain and bond stress distributions of a CI rebar with 140 mm embedment length for the three reference levels defined above and the ultimate stress σ su reached in the test.Next to the post-processed strains, the bond stress distributions derived thereof are shown.Additionally, the average bond stresses τ b,FOS are calculated from integration of the area below the curve divided through the embedment length.
Over an initial length of 60 to 70 mm, the strain in the rebar decreases, while the bond stress increases.Then, the strain still decreases while the bond stress remains relatively constant on design and characteristic levels.However, under higher stresses, the strain distribution becomes increasingly non-linear.At ultimate stress, failure occurs at the location of maximum bond stress and the part of the rebar behind that location does not contribute anymore.Thus, a redistribution of bond stresses over the embedment length is observed with the stress increase.
Figure 11 compares the strain and bond stress distributions for PI rebar with mortars A (left) and B (right),  and for the three embedment lengths (100 mm at top, 200 mm at bottom).Among the six configurations, similarities but also significant differences are found.Across the load levels, the curves keep affine.
The above said still applies to the strain curves on the left side of these subfigures.A constant course over the free length is followed right from the beginning of the embedding by an initially nonlinear decrease of the strain with increasing depth.Depending on the embedment length, this decrease then turns linear up to the unloaded end.The profile of the bond stresses over the depth largely reflects this.As expected, only the mathematical order is one less, for example, if the strain varies linearly, the bond-stresses are constant.
This appears most clearly at the medium embedment length of 140 mm.At smaller embedment lengths, the bond stress plateau does not form completely, especially with mortar A. Also, the location of the maximum bond stress varies significantly between mortars A and B; more precisely, it is close to the unloaded end for mortar A and shifts to the middle of the embedment length for mortar B. Furthermore, in case of longer embedment lengths, two bond stress maxima tend to form under increasing loads.The bond stresses concentrate at these locations where inclined forces originating from the ribs could induce the formation of first splitting cracks.
These FOS results highlight how mortar stiffness affects strain and bond stress distributions and emphasize the role of mortar properties in bond performance assessment.Moreover, recognizing that a more efficient force transfer mechanism exists compared to conventional CI rebar represents a significant step forward in optimizing PI rebar anchorage design over a shortened embedment length.

| Rebar elongation
The rebar elongation u s can be obtained from FOS data by integrating the measured strains along the embedment length as per Equation (5).The calculated curves of CI and PI rebar anchorages for the reference embedment lengths and strength levels are shown in Figure 12.It should be noticed that the design, characteristic and average strength are different for each embedment length.The observed elongation over the length is notably nonlinear, contrasting the linear distribution assumption in most design standards. 5,17he elongations of CI rebars are slightly greater than that of PI rebars under the same applied stress.Moreover, mortar A exhibits smaller deformations compared to mortar B. These differences become more pronounced at higher stress levels.
The slip at the unloaded end δ ue provides valuable information for comparison of different anchorage configurations and an understanding of bond performances.However, measuring this value directly in experiments involving PI rebars is challenging due to the complex test setup required, particularly when embedding rebars in already hardened concrete.An alternative approach is to indirectly obtain the slip at the unloaded end by subtracting the rebar elongation u s deduced from FOS measurements from the measured slip at the loaded end δ le , which is recorded by displacement transducers.
In Table 5 the values of bar deformation and slip in both CI and PI bars are summarized at increasing load level.The outcomes are consistent with expectations, as the slip at the unloaded end increases proportionally with the applied stress.CI rebar presents minimal slip for design and characteristic strength, while on mean level slip of up to 0.5 mm is obtained.Mortar A shows less slip, even negligible for embedment lengths up to 140 mm and still small for embedment length of 200 mm.In contrast, mortar B exhibits notably higher slip than mortar A across all embedment lengths.Particularly, a high slip value is observed on the mean stress level for 200 mm embedment length, despite attaining the yielding stress without experiencing rebar pullout.

| CONCLUSIONS
The results of an experimental investigation on the bondstress profiles and on the performance of cast-in and post-installed rebars are presented in this paper, under quasi-static loading.Two high-performance injection mortars (a weak hybrid material, and the other a stiff organic material) are used in the test specimens provided with post-installed bars.Comparisons are made with the specimens provided with ordinary bonded cast-in bars, for different values of the bonded length/bar diameter ratio, always in confined conditions.The stress levels in the bars cover both the serviceability and the ultimate limit states.Special emphasis is paid on the instrumentation and post-processing of strains recorded with FOS.Data quality is verified against conventional techniques such as strain gauges.The plenty of information on the strains makes it possible to derive the bond stress profiles over the whole embedment length and allows measuring the slip at bar-concrete interface at both the loaded and unloaded ends.Finally, the strain-based bond stress distributions are compared to the models of fib Model Code 2010 and lead to the following conclusions: • The bond strength of post-installed rebars is significantly greater than that of cast-in rebars and depends on the stiffness of the mortar.With the stiff mortar, the bond strength of post-installed rebars was found to be at least 2.1 times higher than for cast-in rebars.
With the weak mortar, it is still 1.6 times higher.over the entire embedment length.Its distribution is similar to that of cast-in bars and agrees with the conventional assumption of recent design codes.However, the precise length at which the bond stresses increase depends on the bond system and the embedment length.• Post-installed rebars with embedment lengths of 200 mm (i.e., 10 d s ) show a completely different bond stress distribution.In particular, with stiff mortars, the bond stress appears to decrease at a distance close to 10d s from the loaded extremity of the anchored bar.• In contrast, in post-installed rebars with weak mortars, the bond stresses are uniformly distributed up to the extremity of the embedment length when stresses reach the design and characteristic levels.However, under high stresses, significant stress concentrations are observed in two locations of the embedment length.These findings suggest that in anchorages with stiff mortars, it is likely that not all parts of the embedment length are fully activated during the pull-out tests.On the other hand, anchorages with weak mortars show a more uniform bond stress distribution over the embedment length, resembling the stress distribution of cast-in rebars.However, stress concentrations are more likely to occur at loads close to pull-out failure.
Regarding the fiber optic sensor implementation to record strains and evaluate bond stresses along cast-in and post-installed rebars, the following conclusions are drawn: • With fiber optic sensors, noise and significant peaks arising from local phenomena are detected, particularly under conditions of high strain, indicating the initiation of cracking in the adjacent concrete and mortar.If the primary interest of the analysis lies in the bond characteristics over the entire length, the proposed post-processing method is able to provide basic  data instrumental in refining the design codes.It involves filtering and smoothing of raw data, facilitates the determination of the distribution of the strains in the bars and the quantification of bar-concrete slip that is closely related to crack width.• The grooves along opposite sides of the bars and the acrylate-based adhesive that protect the optic sensors inside the grooves showed no impact on the ultimate bond strength of the rebars.In case of an unintentionally bent rebar, as it is often the case in practice, a two-sided fiber optic sensor measurement is essential for capturing the average strain in the rebar over its whole length.
The valuable experience gained from implementing fiber optic sensor encourages further experimental analysis of post-installed rebar applications.In future, studies will be conducted to expand the evaluation of the bond stress distribution for post-installed rebars in less confined conditions and with a broader range of embedment lengths.
The bond stress distribution and rebar deformation of the PI and CI bars are derived from the strain distributions obtained with FOS.The strains recorded with FOS are compared F I G U R E 1 (a) Concreteto-concrete connection with PI rebars and (b) bond forces around ribs and failure initialization with radial cracks and shearing planes.

F I G U R E 4
Average tensile stress-strain curve of the steel rebar.F I G U R E 5 (a) Rebar during scanning, (b) characteristics of the FOS installation.

4. 2 |
Figure 7a illustrates the average bond-slip curves at the loaded end δ le of specimens PI-A-100 (1, 2), PI-B-100 (1, 2), and CI-140 (1, 2, 3), categorized by the bond system.For comparison, the values have been normalized to nominal values based on a strength class of C20/25 using Equation (6).For reference, the curves of the bond-slip model proposed in the fib Model Code 2010 17 are computed with Equation (7).Figure7bshows the four model stages.
using the average f cm or the characteristic f ck concrete compressive strength.The third curve employs the factors specified in EC2 as (a) (b) F I G U R E 7 (a) average curves of the pull-out specimens PI-A-100 (1,2), PI-B-100 (1,2), and CI-140 (1,2,3) compared with bond-slip models and (b) representation of the four model stages in fib Model Code 2010 (MC) (17).

F I G U R E 6
CI and PI rebars after being pulled out of the concrete.

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In general, the bond-slip model for cast-in rebar specified in the fib Model Code 2010 provides an appropriate approximation of the bond-slip behavior for post-installed rebars, too.However, the initial and final values of slip associated to the maximum bond strength are different for the two mortars and the castin configuration.Compared with cast-in bars, postinstalled bars show larger deformations before the bearing capacity is reached.They are more ductile.• Contrary to cast-in bars, bond stresses in post-installed bars increase close to the loaded extremity of the anchored bar.This allows for shorter anchorage length.• In post-installed rebars with (shorter) embedment lengths of 100 and 140 mm (i.e., 5 d s and 7 d s ), the bond stress increases linearly and remains relatively constant
Results of the pull-out tests (*converted from cube compressive strength).