**1. Introduction**

It is fundamental to know the steel deformation in order to correctly calculate concrete structures. Although it deforms slightly before the concrete has not yet cracked, as shall be seen below, it acquires its greatest deformation when the concrete cracks, as it is not able to absorb traction. This article examines the appearance of the first cracks in reinforced concrete, embedding optic fiber sensors welded to the corrugated rebar steel, and it evaluates their deformation, comparing them with the values obtained from traditional material resistance calculation.

Although there is a lot of literature regarding crack detection in structural elements of reinforced concrete, the novelty of this article lies in the use of optic fiber sensors based on Bragg gratings (FBGs) welded to the corrugated steel rebars, which allows, on the one hand, determination of the precise moment when the crack appears, as the deformation of the steel shows a highly significant leap at the moment when it takes place, due to the concrete ceasing to collaborate in traction and the steel beginning to do so and, on the other hand, the deformation the steel suffers during the successive loading steps.

Diverse procedures have been used since methods have existed to detect cracks in reinforced concrete elements: infrared thermography [1–3], acoustic emission [4,5], fiber Bragg grating (FBG) [6–12], and digital image correlation [13,14]. One must emphasize the study of propagation and determination of the width of cracks in concrete, applying novel microwave sensors for crack detection in four reinforced concrete beam specimens [15]. By use of diffusing ultrasonic sensors, it has been possible to locate micro-cracks within the beam [16]. The stress wave technique with embedded smart aggregates in three samples of FRP reinforced concrete beams have provided satisfactory results in crack detection in the samples [17]. The use of plastic optical fibers to detect hairline cracks and ultimate failure crack in civil engineering structures has also obtained good results, even detecting the moment at which the structural element begins to crack and its evolution until the ultimate failure [18]. Carbon nanotube sensors embedded into concrete beams have also been used and were able to detect the initiation of cracks at an early stage of loads [19]. A novel sensing skin for monitoring cracks in concrete structures is capable of detecting, localizing and quantifying cracks in post-tensioned concrete specimens [20]. On the other hand, there are methods to determine cracks by images, such as the deep fully convolutional network (FCN). Images extracted from a video of a cyclic loading test on a concrete specimen is a reasonably method for crack detection [21], or use of a fully convolutional neural network [22]. A crack monitoring technique based on oblique fiber optic sensing network can accurately measure concrete cracks with a precision of 0.05 mm [23].

Fiber optic sensors based on Bragg gratings (FBGs) have been chosen for this study as they are more durable than conventional electric gages. They also provide long term signal stability and system stability, even under very unfavorable conditions, such as the vibration caused by roads. The cable length has no impact on the precision of the measurement. Multiplexing use allows different sensors to be placed on the same fiber optic cable, a much lighter cable than the conventional one of electric extensometric gages. The optic sensors are immune to electromagnetic and radiofrequency (EMI/RFI) interference, and resist hostile environments in the presence of water, salt, extreme temperatures, pressure (up to 400 bar), potentially explosive atmospheres and high voltage zones. Definitively, fiber optic sensors based on Bragg grating offer greater economic advantages, performance and precision than traditional electric gages [24].

FBG have been used both to detect cracks on the surface as well as by embedding them in the concrete. They have also been used to measure temperature and strain [25], biaxial-bending structural deformations [26], stress on the post-tensioned rod, detect moisture ingress in concrete based building structures [27].

In this study, we investigate the use of optic fiber sensors welded to the corrugated rebar to detect the moment at which the first crack takes place and the deformation the steel suffers from that moment onward during the whole process of loading the structural element. Section 2 analyses the materials used to perform the tests, the shape and dimensions of the beams studied. A tour is made through the characteristics of the equipment used and the software used. In Section 3, the test results are displayed and evaluated to determine the cracks and deformation of the steel in the two reinforced concrete beams, and conclusions are discussed in Section 4.

### **2. Materials and Methods**

There are different devices on the market to measure deformations. The sensors chosen, within the group of Bragg grating (FBG) sensors, are weldable sensors, as these are to be integrated with the structural steel of the reinforced concrete structural elements to be tested.

The fiber optic sensors are highly temperature sensitive, so in order to compensate these effects, a temperature sensor will be included within the array. An array is a chain of sensors linked by a fiber optic cable; custom made for the structural element that is to be tested. The array to be installed on our beams shall contain two weldable deformation sensors and a temperature sensor. Each one of the deformation sensors shall be welded to the two bars that reinforce the beam under flexion and are to

be stressed. As the temperature sensor only measures this, it will not be welded to the steel bars and will be located near to the deformation sensors.

Two beams of reinforced concrete are to be tested, with sections of 200 × 300 mm and 300 × 500 mm, and a length of 3000 mm. These sections have been chosen so they are sensitive to the loads to be applied.

#### *2.1. Fiber Optic Sensors*

The fiber optic deformation sensors used are weldable (Figure 1). These are welded to the corrugated steel bars that constitute the reinforcement of the beam. Their position is that of the maximum effort that it will receive according to the different loading steps applied. Measurement of the deformation is reliably obtained in micrometers per meter.

**Figure 1.** Weldable deformation sensor.

The sensor chain was custom manufactured for each beam. Each chain has a temperature sensor (Figure 2) to compensate the temperature effect on the deformation sensors. The sensor chains have two terminals to which the interrogator may be connected. That redundancy effect is important as if a part of the chain were to be damaged, the terminal could always be measured in the undamaged area of the array.

**Figure 2.** Temperature sensor.

#### *2.2. Reinforced Concrete Beams*

The first structural element we are going to test is a reinforced concrete beam with a section of 200 × 300 mm. Its reinforcement is of four rebars with a diameter of 12 mm, with stirrups with a diameter of 8 mm every 200 mm. The steel quality is B500S. The beam length between resting points is 3000 mm. The reinforcement scheme and placement of the fiber optic sensors is illustrated in Figures 3 and 4.

**Figure 3.** Reinforcement scheme of the 200 × 300 mm beam and application point of the loading steps.

**Figure 4.** Beam section 200 × 300 mm.

The choice of this beam with this section and reinforcement is due to the loads that are to be applied to it, so it is deformed significantly, and one may measure the deformations the steel suffers, as well as observe the cracks in the structural element, something that will be decisive in the section study.

The sensors are placed in the center of the beam, which is where the different loading steps are to be applied and where, as it is a beam that is simply resting on the support, there will be the maximum deformations in the structural element.

The temperature sensor has been placed attached to one of the corrugated steel bars, near the center zone, so it may compensate the effects the temperature has on the deformation sensors.

The second structural element we are going to test is a reinforced concrete beam with a section of 300 × 500 mm. It is reinforced by two rebars with a diameter of 25 mm on the lower face and 2 rebars with a diameter of 12 mm on the upper face. The frames are rebar with a diameter of 8 mm, every 20 mm. As with the 200 × 300 mm beam, the length between support points is 3000 mm. Figures 5 and 6 show schemes of the structural elements.

**Figure 5.** Reinforcement scheme of the 300 × 500 mm beam and application point of the loading steps.

**Figure 6.** Beam section 300 × 500 mm.

In this case, the sensors have only been placed on the lower bars, with a diameter of 25 mm, as the maximum deformation will take place on these and in the center of the span. As with the 200 × 300 mm beam, the temperature sensor has been placed near to the deformation sensors.

#### *2.3. Design of the Experiment*

In order to perform the experiment, the beams will be placed under different loading steps. The successive loads will be applied by a hydraulic press that will press on an RTN type loading cell of 10 Tn, with a ring torsion for the 200 × 300 mm beam. The device specifications are as follows: Nominal load: 10 t; Precision class: 0.05; Body measured: stainless steel; Protection class: IP68 to EN 60529; Cable type: shielded round cable, four wires in the case of the 200 × 300 mm beam, and for the 300 × 500 mm beam under RTN 100 Tn maximum ring torsion loading, Nominal load: 100 t; Precision class: 0.05; Body measured: stainless steel; Protection class: IP68 to EN 60529; Cable type: round shielded cable, four wires

Both loading cells are HBM brand (Hottinger Brüel & Kjaer Ibérica, S.L.U. San Sebastián de los Reyes, Madrid, Spain) with European Union Declaration of Conformity No. 238/2017-07 connected to an HBM QuantumX MX1615 data acquisition system with 16 channels, compatible with the following transducer technologies in all the channels:


In the process of successively loading the beam, the sag acquired by the structural elements will be measured by a linear potentiometer displacement transducer of 20 mm, 0.1% precision, compatible with MX1615B amplifier. The displacement transducer will also be connected to the QuantumX MX1615 data acquisition system.

The QuantumX MX1615 data acquisition system is connected to a computer in which software is installed to collect all the information, both from the loading cells as well as the displacement transducer. The software is Catman Easy, by the commercial brand HBM.

Figure 7 shows the loading cell device and displacement transducer installed to perform the test, as well as the loading bridge with the beam located in the position to commence testing.

(**a**) 200 × 300 beam (**b**) Loading cell and displacement transducer

**Figure 7.** Loading cell and displacement transducer on the 200 × 300 mm beam.

Data acquisition from the elements to measure applied force and deformation have been connected to the aforementioned QuantumX data acquisition system. Both the deformation as well as temperature sensors are connected to another device called interrogator. An optic interrogator is an optoelectrical instrument able to read fiber sensors with Bragg grating (FBG) in static and dynamic monitoring applications.

The same interrogator may obtain readings from an ample network of sensors of various types (deformation, temperature, displacement, acceleration, slope, etc.) connected through different fiber lines. All the data may be acquired simultaneously and with different sampling frequencies.

During the data acquisition, the interrogator measures the bandwidth associated with the light reflected by the optic sensors and converts it to technical units.

The interrogator model we are going to use is the FS22 (HBM), a device designed to interrogate Bragg grating based sensors. Its technology is continuous laser scan. This includes a reference to scannable bandwidth that provides continuous calibration and guarantees the long-term precision of the system. These interrogators are executed in an operating system in real time to acquire high quality data from a large number of sensors provided by the combination of broadband tuning range and simultaneous and parallel acquisition.

The interrogator is connected to the computer, which uses specific Catman Easy software, providing us the data on the deformations suffered by the beams in real time. The data acquisition system installed is shown in Figure 8.

**Figure 8.** Data acquisition system installed. QuantumX, Interrogator and computer with Catman Easy software.

#### **3. Experimental Results and Discussion**

The deformations we are going to measure are those of the steel, as that is the material the optic fiber is measuring. The cracking moment is a fundamental datum, as we know the moment at which the concrete ceases to absorb traction, in order for the steel to begin to work.

We must take into account, quoting Calavera [28] that "*Between the crack lips, the steel takes on the full traction strain on its own, but between the cracks, there is the anchorage of the reinforcement in the concrete and part of the traction force on the steel is transferred to it. If the traction on the concrete equals its resistance to traction, a new crack is formed*".

This means that there is, between cracks, part of the concrete that absorbs deformations. At the exact point where there is a crack, the concrete does not collaborate and the whole deformation is absorbed by the steel. That fact is fundamental to understand how the structural element works (Figure 9).

**Figure 9.** Variation in the tensions in concrete (σct) and steel (σs) between cracks. In CALAVERA, J. (2008), Proyecto y cálculo de estructuras de hormigón. Tomo II, p. 372. (Designing and calculating concrete Structures, Volume II, p. 372). Give as [28].

In the process of loading the structural elements, a visual inspection of the cracks that appear is carried out, to subsequently compare them with the theoretical calculations (Figure 10).

**Figure 10.** Visual inspection of cracks in 200 × 300 mm and 300 × 500 mm beams.

Laboratory test were carried out on the two beams studied, obtaining the following figures: For the 200 × 300 mm beam, the laboratory data is: Resistance to flexion-traction of concrete (fct): 5.4 MPa; Resistance to compression of the concrete (fck): 54.6 MPa; Concrete elasticity module (E): 33.400 MPa; and for the 300 × 500 mm beam: Resistance to flexion-traction of the concrete (fct): 8.9 MPa; Resistance to compression of the concrete (fck): 58.8 MPa; Elasticity module of the concrete (E): 33.053 MPa.

We used the values obtained in the laboratory for resistance of flexion-traction of the concrete (fct) to calculate the cracking moment. The cracking moments are calculated by applying the Equation (1), obtaining the following results:

$$\mathbf{M}\_{\rm fis} = \mathbf{f}\_{\rm ct} \, \text{\* (b } \text{\*} \, \text{h}^2\text{)}\% \, \tag{1}$$

For the 200 × 300 mm beam this gave Mfis = 16.2 mkN, and for the 300 × 500 mm beam: Mfis = 111.25 mkN. Once these values were known, the beams underwent different loading steps, applied in the center of the span, linking the loads applied to the deformations caused in the corrugated steel according to the tables included in the relevant sections. Visual inspections were performed to control the moment when the first cracks appear in these.

If we analyze the cracks in the section, and when they take place, we observe that these have taken place much before the cracking moment obtained by calculation. For the 200 × 300 mm beam, it is observed that the cracks nearest to the center of the span take place with a load of 10.4 kN, and a moment of 7.80 mkN, which is much further from the theoretical value obtained. The value of 10.4 kN has been obtained by visual inspection (Figure 11), but as we shall see, the real load for the beam to begin to crack is 8.5 kN.

**Figure 11.** Visual inspection of cracks on the 200 × 300 mm beam.

In the case of the beam of 300 × 500 mm, although the cracking moment obtained by calculation is 111.25 mkN, the real cracking moment is 40.5 mkN, that corresponds to a load of 58 kN, as we may see below (Figure 12).

**Figure 12.** Visual inspection of cracks on the 300 × 500 mm beam.
