**1. Introduction**

To tackle the challenges that are in front of civil engineering—such as reduction in carbon footprint with optimized design, proper allocation of scarce resources through the use of engineered structural materials or extension of service duration thanks to deeper understanding of performance of structures—up-to-date methods should be used.

From the construction material point of view, such a developing technology is the Ultra High Performance Fiber Reinforced Cementitious composite (UHPFRC). It allows for design of refined and more slender structures as well as reinforcing and upgrading existing ones. To fully master its performance on both micro- and macroscopic levels, new measurement techniques are needed.

Such a possibility is given through the development of Distributed Fiber Optics (DFO) sensing techniques. The DFOs, used mostly in the automotive and mechanical industry, have recently found place in the civil engineering field. During the last decade, Fiber Optics (FO) sensors became increasingly popular in Structural Health Monitoring (SHM), and now, they are the second most used

sensing technology in this field [1]. These sensors are small-sized, lightweight and resistant to both chemical degradation and electromagnetic interference. In the past few years, it was demonstrated by numerous researchers that DFOs can be used for measurements of strain and crack opening in ordinary reinforced concrete [2–5] and fiber reinforced concrete [6]. Still, the verification of usefulness of this SHM for UHPFRC is missing, especially considering the unique behavior of this material under tensile action.

For UHPFRC structures, the photogrammetry with digital image correlation (DIC) is now a well-established technique to track and measure cracks [7–9]. However, there were not any attempts to monitor crack propagation and measure crack opening using the DFO sensing techniques in UHPFRC structural elements. Schramm and Fischer [10] tested a slab element and a prestressed beam. For the slab without rebars, the externally glued DFOs were able to detect the apparent strain peaks due to microcracking. However, no estimation of crack opening was done. In cases of beam elements under shear action, the pattern of fictitious cracks was observed using DIC. The DFOs were glued on the steel rebars and used to detect the stress peaks in the reinforcement (stirrups) near these fictitious cracks. Similar instrumentation, with DFOs on the rebars and DIC on the surface, was used for investigation of the stress transfer between UHPFRC and reinforcement by others [11]. The DFOs sensors were employed for SHM of a UHPFRC bridge [12] but without attempt to detect discontinuities.

This paper presents results of an experimental validation of the use of DFOs to detect and measure discontinuities in UHPFRC structures. The full-scale beam is instrumented with DFOs, DIC and extensometers in order to compare their crack monitoring features. The results are discussed from structural and material points of view, with an outlook for the possible use of DFOs for Structural Health Monitoring of UHPFRC structures.

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

#### *2.1. Distributed Fiber Optics Sensing for Discontinuity Monitoring*

Recently, DFO sensors were especially used where an urgent need of high number of sensing points appeared. The difference between these systems and traditional long gauge or point sensors is their ability to provide distributed measurements, and thus, simultaneously local and global information [13]. Measurement systems are composed of an interrogator and an optical fiber playing the role of a sensor. These sensors are either embedded into new concrete structures or bonded to the surface of existing ones. Different interrogation units available nowadays are based on the analysis of the Brillouin and Rayleigh backscattered light over the silica optical fiber. The Rayleigh-based systems can perform distributed strain measurements with higher spatial resolutions (<1 cm) than Brillouin-based systems which, on the other hand, can interrogate larger distances (>100 km).

The DFOs techniques can be used not only to measure strains but also to detect, localize and measure cracks of small openings. DFO sensors allow achieving of an accurate, reliable and quasi real-time crack detection and characterization in concrete structures. They contributed to the detection and localization of cracks in the massive structures, showing supremacy over the short and long gauge sensors (Figure 1a). Actually, any type of discontinuity in the host material, like a crack, can cause a strain localization propagating through the optical fiber layers up to the core of the optical fiber (Figure 1b).

There are numerous studies on the use of DOFs for detection of crack formation. The sensors, based on measuring losses with Optical Time Domain Reflectometry technique [3–5,14–16], were very limited in practical applications. Similarly, those based on Brillouin backscattering [6,17–20] were limited due to their low spatial resolution, affecting their strain sensing accuracy around a crack in the concrete material [21,22]. In fact, the complicated strain distribution and its rapid variation within the spatial resolution decreases the strain measurement accuracy [23]. Later on, Optical Backscattering Reflectometry (OBR), based on the Optical Frequency Domain Reflectometry (OFDR) technique, emerged. This technique, characterized by high spatial resolution, is proven to be capable of detecting and localizing tiny microcracks in reinforced concrete structures [24]. Different methods were also

proposed to quantify crack openings from the strain profiles, either based on a combination with finite element models of the structure [25,26] or on the calculation of the optical fiber elongation by summing distributed strain gradients [27,28].

**Figure 1.** Crack detection in concrete using Distributed Fiber Optics sensing techniques; (**a**) comparison to traditional sensors, (**b**) strain transferring between layers.

#### *2.2. Analytical Models Based on Strain Transfer Theories*

A distributed optical fiber sensor is an optical fiber surrounded by various protective and adhesive layers, forming a multilayered strain transfer system. The existence of these intermediate layers leads to differences in the strain of host material and the strain measured by an optical fiber due to the shear lag effect in intermediate layers. The problem of strain transfer through an optical fiber sensor has been studied in the field of short dimensional sensors like Bragg grating or interferometric sensors [29–35]. Indeed, many research works focused on designing discrete sensors with improved strain transfer efficiency [36] and performing parametric studies of different mechanical and geometrical properties of multilayered sensors [37].

Since 2012, different analytical and numerical models were proposed [38] to describe the strain transfer from a discontinuous (cracked) host material. Imai et al. [6] introduced the effect of crack discontinuity in host material as a Gaussian distribution at the interface with protective coating. Later, it was assumed that the strain at the discontinuity location is equal to the crack opening over the spatial resolution of the measurement instrument [39]. Finally, the Crack Opening Displacement (COD) was introduced as an additional term provoked by the local discontinuity in the host material deformation field. Feng et al. [18] deduced a mechanical transfer equation, showing that the strain measured by the optical fiber ε*f(z)* consists of a crack-induced strain ε*crack(z)* part added to the strain in host material ε*m(z)*. Recently, Bassil et al. [40,41] deduced a similar strain transfer equation for a multilayer system with imperfect bonding between layers:

$$
\varepsilon\_f(z) = \varepsilon\_{crack}(z) + \varepsilon\_m(z) = \lambda \frac{\text{COD}}{2} e^{-\lambda|z|} + \varepsilon\_m(z) \tag{1}
$$

$$\lambda^2 = \frac{2}{E\_f r\_f^2 \left[ \frac{1}{G\_1} \ln \left( \frac{r\_1}{r\_f} \right) + \sum\_{i=1}^N \ln \left( \frac{r\_i}{r\_{i-1}} \right) + \sum\_{i=1}^N \frac{1}{k\_i r\_i} \right]} \tag{2}$$

where λ is the strain lag parameter that includes mechanical (*G* and *E*, shear and Young's moduli, respectively) and geometrical properties (*r*) of the different *i* layers and *z* is the position of discontinuity along the optical cable. It also includes coefficients *k* depicting the level of interfacial adhesion between two consecutive layers.

The strain lag parameter λ is crucial for the sensing of cracks. As this value increases, the crack-induced strains ε*crack(z)* figure higher peaks at the crack location, and thus, the exponential part covers a narrower zone over the optical fiber length, as shown in Figure 2. Thanks to this, the capacity of detecting and localizing discontinuities increases.

**Figure 2.** The spatial distribution form of the crack-induced strains ε*crack(z)* for different strain lag parameter λ values.

The authors also demonstrated the validity of the model for different types of optical cables through an experimental testing campaign on concrete specimens. The estimated CODs proved to be accurate, reaching relative errors of 1–10% for a dynamic range [CODmin, CODmax], with a strain repeatability of ±20 μm/m for the interrogator unit. In this range, the layers behave in an elastic manner and sufficient, stable bonding between them exists. CODmax varied widely from 80 to 1500 μm for different types of optical cable assemblies. On the other hand, the authors fixed the CODmin to 50 μm, below which other parameters prevail, i.e., the nature of cracking of concrete material (in the fracture process zone) or the strain accuracy and repeatability of interrogator.

In terms of crack detection, Bassil et al. [42] demonstrated that an OBR system with a strain repeatability of <sup>±</sup> 2 <sup>μ</sup>m/m and an optical cable with <sup>λ</sup> = 20 m−<sup>1</sup> can detect concrete discontinuities of less than 1 μm.

#### *2.3. Ultra High Performance Fiber Reinforced Cementitious Composite*

UHPFRC is a composite fiber reinforced cementitious building material with a high content (>3% vol.) of short (*lf* < 20 mm) and slender steel fibers. Its behavior under tensile stress comprises three stages, as shown in Figure 3.

The first stage is an elastic stage. The cementitious matrix is continuous and the behavior of UHPFRC is simply linear. The strain of the material can be directly measured.

After the elasticity limit (*fe,* ε*e*) is reached, discontinuities in the matrix start to appear and the material enters the strain-hardening phase. The openings of these fine, distributed microcracks (hairline cracks) are smaller than 50 μm and their spacing can vary from 2 to 30 mm [43–45]. They are not detrimental from a durability point of view [46,47] and are impossible to see with the naked eye. These microcracks can be, however, measured using appropriate instrumentation. From the macroscopic point of view, the material can be considered as continuous, with strain-hardening quasi-linear behavior and reduced stiffness [48]. However, after unloading, the residual strain remains in the material.

When the maximum tensile resistance *fu* is reached, the material enters the softening phase. One or more neighboring microcracks start rapidly growing, eventually reaching openings above 50 μm. This localized discontinuity is bridged by multiple fibers carrying the tensile stress. It is called a fictitious crack, contrary to the real crack which cannot transfer the stress [49]. Since the stress transfer capability in this critical zone is reduced, the overall stress in the area decreases. The localized fictitious crack is growing, while the strain and stress around it decrease. The location of the fictitious crack depends on the distribution of fibers [44,45,50,51]. Since this fictitious crack leads eventually to the

failure of structural elements, it is called the critical crack as well. With the gradual opening of the fictitious crack, the measured deformation increases, leading to fast growth of the apparent strain. Importantly, it is not the real strain of the material anymore due to the fictitious crack localized between the reference measurement points.

**Figure 3.** UHPFRC behavior under tension.

The fictitious crack grows until opening of half of the steel fiber length, in the present case *lf*/2 = 6.5 mm [44] and the resistance of the material decreases. After the fibers are pulled out, no more stress transfer is possible and the real crack is formed.

In the case of a structural R-UHPFRC (Reinforced UHPFRC) element under bending action, the tensile behavior of UHPFRC has important influence on the overall response. Each of the three stages are present under the maximum bending moment in the critical section, where the fictitious crack forms. Under the assumption that the cross-sections remain plain, the distribution of stress along the height of the beam is nonlinear due to nonlinearity of the constitutive law of UHPFRC, as presented schematically in Figure 4. The proportion between parts in elastic, strain-hardening and softening regimes depends on geometry of the element [44].

**Figure 4.** Schematic distribution of stresses and strains in UHPFRC at the critical section of R-UHPFRC beam under the ultimate bending moment.

#### **3. Test Set-Up and Specimen**

The tested beam has a T-shaped cross-section and dimensions according to Figure 5. This kind of design refers to the use of UHPFRC for waffle deck or unidirectional ribbed slab designs. An example of such a structure is the railway bridge in Switzerland described in reference [52].

**Figure 5.** Scheme of test setup and instrumentation: (**a**) beam dimensions and reinforcement, (**b**) instrumentation on the front side and (**c**) instrumentation on the back side; dimensions in mm; the critical fictitious cracks 1 and 2 are marked.

Commercially available UHPFRC premix Holcim710® was used, with 3.8% vol. of 13 mm long straight steel fibers with an aspect ratio of 65. Its mechanical properties as obtained by material testing were compressive strength *fc* = 149 MPa; elastic limit stress *fe* = 6.3 MPa; tensile strength *fu* = 12.0 MPa; strain at *fu* − ε*<sup>u</sup>* = 3.5‰; modulus of elasticity *E* = 41.9 GPa. Steel reinforcement bars B500B (with *fsk* = 500 MPa) were used for both stirrups and longitudinal rebars.

To observe the behavior of UHPFRC at the three stages of its performance, the beam was designed with a reinforcement bar of 34 mm diameter at a height of 187 mm from the bottom, thus, the distance between the bottom face of the beam and bottom of the reinforcement was 170 mm at midspan (Figure 5), allowing for observation of unreinforced UHPFRC. To impose bending failure rather than shear failure under four-point bending, Ω shaped stirrups, Ø 6 mm, were placed outside the constant bending moment zone. Additionally, L-shaped Ø 34 mm reinforcement bars were used on the bottom of the beam, outside of the constant bending zone, to increase the lever arm of longitudinal reinforcement in shear.

The beam of 2 m span was tested in displacement-controlled four point bending. The displacement of the servo-hydraulic actuator was transmitted with the use of hinges and a steel beam. The application points were symmetrically positioned at ±0.25 m from the midspan of the R-UHPFRC beam. The course of the actuator was done with velocity of 0.01 mm/s during the first loading, and 0.02 mm/s in unloading and re-loading phases. Several unloadings were performed to obtain the residual deflection of beams at each loading stage.

The beam was instrumented with extensometers; photogrammetry DIC by means of two 20 MP cameras; DFO sensors (Figure 5). The fiber optics sensors for distributed strain sensing were installed in three lines at each face of the beam—40, 90 and 190 mm from the bottom of the beam. As shown in Figure 6, the DFO sensors were glued in a 2 × 2 mm groove on the UHPFRC surface using a bicomponent epoxy adhesive (Araldite 2014-2). On the front side of the beam, the SMF-28 Thorlabs® fiber was glued, with an external diameter of Ø 900 μm and elastomer tubing. On the back side of the beam, the Luna® High-Definition Polyimide fiber was used, with an external diameter of Ø 155 μm. The DIC measurement zone spanned 35 cm from the midspan symmetrically, and over the whole height of the beam on the front side. The extensometers of 100 mm measurement base were glued on the back side of the beam, at the level of each DFO measurement line. Additionally, three LVDTs with the common measurement base were vertically installed on the back side of the beam, at midspan and over the supports. The mean vertical displacement over the supports is subtracted from the vertical displacement at midspan to obtain the deflection of the beam. The resistance force was measured by the load cell of the actuator.

**Figure 6.** Scheme of installation method of DFO sensors in UHPFRC; dimensions in mm.

#### **4. Test Results**

#### *4.1. Global Response of the Beam*

The force–midspan deflection curve is presented in Figure 7. Several loading–unloading cycles were executed at different stages of the test. The goal was to visualize the influence of residual strain of the UHPFRC in the strain-hardening domain after unloading on the global response of the beam. Thanks to this, a gradual degradation of material can easily be observed. The load steps (LS) were chosen arbitrarily to discuss the state of material in detail.

The first linear part of the curve is very short. This is due to the material at the bottom of the beam entering the strain-hardening regime relatively soon. As the zone where UHPFRC is in the strain-hardening regime is growing, gradual reduction in material stiffness, and thus, beam rigidity occurs, effecting nonlinearity of the force–deflection curve. The residual deflection in the unloading cycle comes from the fact that this part of cross-section contains discontinuities (microcracks < 50 μm) or, in the further stages, the fictitious crack (> 50 μm) is present. Both types of discontinuities transmit the tensile stresses thanks to fibers, but do not close completely while unloaded. Finally, when the beam resistance is maximum with the force of 313 kN, gradual degradation with a rise in deflection continues as the localized fictitious cracks propagate and the longitudinal rebar is yielding.

**Figure 7.** Load–deflection curve of the R-UHPFRC beam during quasi-static test, total jack force presented with consecutive load steps (LS) marked.
