**1. Introduction**

Engineering structures are subjected to various loads, e.g., dead loads, live loads, environmental loads, and other, over the entire service life. In many situations, it may be necessary to increase the load capacity. The main reasons are planned changes in the way a structure is used and carrying out rehabilitation and retrofitting works due to degradation of a structure or its natural aging. To achieve higher load capacity, strengthening is commonly used. Various reinforcement systems such as steel elements (plates, rods, and flat bars) or composite elements (carbon tapes, carbon mats, and other fiber reinforcement polymers) are increasingly used [1–3]. Such externally bonded reinforcement (EBR) is very often connected to a strengthened structure by adhesive bonding [4]. It is worth noticing, that the technical condition of the connection between joined elements has a great influence on the behavior of the whole structure and, if not properly evaluated, may cause an unexpected collapse.

The existing literature presents many examples of the use of adhesives in connections between concrete and steel [4–8] as well as between concrete and fiber reinforced polymeric (FRP) composites [9–17]. Czaderski and Meier [4] proved that the condition of concrete elements strengthened using the EBR technique can be good even after several dozen years of exploitation. However, the monitoring of such structures is crucial because of the possibility of debonding between the substrate and overlay, which is the most common damage type in this type of connections. It should be also noted that debonding is a dangerous defect due to the lack of its visibility, thus the problem of detection of such damage is not a trivial task. The strength of elements reinforced with EBR technique is usually considered as the bond strength between joined elements [15], thus the condition of the adhesive layer is of great importance. Debonding in externally reinforced concrete elements, which is initiated by crack grows, is the aim of the work of many researchers. The reinforcement in the form of steel plates was considered as the protection of concrete beams against failure induced by flexural [6] or shear cracking [5,7,8]. Typical peel-off tests were conducted for concrete beams strengthened with glass fiber reinforced polyester to determine their strength [9]. The influence of carbon fiber reinforced polymers (CFRP) [10], steel reinforced polymers (SRP), and steel reinforced grouts (SRG) [12] on the failure induced by flexural cracking in concrete beams during bending load was also considered. Pre-stressing of CFRP laminates was shown to be the effective method of reduction of debonding in strengthened concrete beams under flexural load [13]. A number of works were conducted based on the shear tests for concrete beams reinforced with SRG [16] and CFRP [17]. The influence of additional CFRP anchorages on the shear strength was also analyzed [14]. The combined influence of normal and shear stresses was investigated for U-shaped CFRP reinforcement covering the bottom and the sides of the beams [11,15].

With the increasing use of adhesive connections to reinforced structures, there is a need to develop efficient techniques of non-destructive detection and imaging of debonding between a substrate and overlay, as for example active thermography [18–22]. A group of the most effective techniques to evaluate the interfacial adhesion consists of the methods utilizing elastic wave propagation. Existing papers have presented numerous successful applications of wave propagation phenomenon for damage identification in civil engineering structures [23–27]. The impact-echo (IE) method, based on the use of low-frequency vibrations, supported with the frequency spectrum analysis and wavelet analysis, was efficiently utilized for the assessment of adhesion in concrete structures [28,29]. Another promising approach, applicable also for the evaluation of adhesive joints, is based on the analysis of wave energy distribution supported with weighted root mean square (WRMS) calculation, e.g., in aluminum [30] and steel connections [31,32]. Recently, ultrasonic waves have also been increasingly used to inspect and evaluate adhesive bonding between concrete elements and externally bonded reinforcement. Castaings et al. [33] analyzed the propagation of a pseudo-Rayleigh wave mode to evaluate the adhesion level between concrete block and glass-epoxy composite plate joined by the epoxy resin, based on the numerical dispersion calculations and experimental measurements. Shen et al. [34] investigated a concrete block strengthened with steel plate joined by epoxy adhesive. Dispersion properties for a three-layer medium were determined by analytical, experimental, and numerical approaches, giving comparable results. Propagation of shear waves was used by Zeng et al. [35] to detect bond slip at the steel–concrete interface in concrete encased I-shape beam under tensile test. Song and Popovics [36] studied the influence of different bonding conditions on dispersion characteristics of fundamental A0 and S0 wave modes propagating in the steel-clad concrete beams. They observed that attenuation characteristics of guided waves are sensitive to adhesion level at the steel–concrete interface. Li et al. [37] applied the time-reversal method and continuous wavelet transform to evaluate debonding in the CFRP-reinforced concrete blocks. The analysis of strain distribution of wave propagation in numerical models was used as an attempt to imaging of damaged areas; however the exact size and position of defects were not determined. Zima and Rucka [38] presented experimental and numerical results of condition assessment of adhesive joint between concrete beam and steel plate with various states of degradation. The correlation between the amplitude of peak values in wave signals and bonding quality was observed. The numerical guided wave field represented by acceleration magnitudes was used to visualize debonding areas. Mechanical degradation of adhesive connection in concrete–steel specimens during push-out tests was monitored ultrasonically by Rucka [39]. Changes in the interface slip between adherends were treated as an indicator of

approaching failure. Chen et al. [40] proposed detecting interfacial debonding in concrete-filled steel tubes using the transient multichannel analysis of surface waves. The differences in dispersion characteristics allowed determining the presence of defects. Liu et al. [41] monitored debonding between CFRP sheet and concrete beam during three-point bending using the pitch-catch wave-based method. The decrease of signal amplitude was observed in the case of damaged connection compared with an intact one. Experimental strain distribution at different loading levels was used to illustrate the development of damaged areas. Interfacial debonding in steel–concrete and steel-epoxy-concrete plates was quantitatively evaluated by Ke et al. [42]. Comparison of signal spectrograms obtained by the short time Fourier transformation of signals obtained allowed determining the debonding range between joined parts. Yan et al. [43] investigated steel–concrete–steel sandwich beams under bending test. Acoustic emission and electromechanical impedance methods were used to evaluate the cracking process and the structural state of analyzed specimens. Giri et al. [44] analyzed the prediction of a gap in concrete–steel and concrete–aluminum connections using partial least squared regression technique based on the Lamb wave propagation phenomenon. Nonlinear Rayleigh waves were used by Ng et al. [45] for debonding detection in CFRP-retrofitted reinforced concrete blocks. Short time Fourier transformation of wave signals allowed preparing location images of defects with different size. Wang et al. [46] detected the severity and type of damage in concrete columns with CFRP sheeting using Fourier transform and wavelet packet energy analysis. Damage and health indices were used to evaluate concrete cracking and debonding initiation. Huo et al. [47] made a review on monitoring of bond-slip in steel–concrete structures presenting well-known wave-based approaches, including active and passive sensing methods. The reported works present an extensive analysis of debonding detection in steel–concrete composite structures. However, the issue of damage imaging was not deeply considered, except some above-mentioned attempts based on the analysis of the guided wave field represented by the wave acceleration or stress distribution. It should be noted, that the determination of actual location, size, and shape of damaged areas has not been performed, notwithstanding these features have a great impact on the actual strength of adhesive connections.

This paper deals with the condition assessment of concrete beams strengthened with steel plates. The novelty of the study is connected with comprehensive theoretical-numerical-experimental analysis of wave propagation in steel–concrete adhesively bonded specimens and the possibility of debonding imaging using WRMS-based ultrasonic diagnostics. The conducted research was divided into two stages. The initial analysis focused on the characterization of the guided wave propagation in a single-layer and a three-layer media. The main part of the study was directed at the damage identification and imaging in adhesive joints of composite beams with different levels of debonding. The guided waves were sensed and recorded in a number of points on the surface of the steel plate using both contact and non-contact measurement techniques. The signal processing technique based on the WRMS calculation allowed detecting and imaging of the damaged areas. The obtained results indicated that the quality of damage maps strongly depended on the location of excitation.
