**1. Introduction**

Ultrasonic waves have been widely used in diagnostics of engineering structures. Significant scientists' interest has been focused on the nondestructive evaluation of concrete, which is one of the most popular construction materials used in the world. Its widespread use entails the need for the development of effective methods of damage detection in the early stage to prevent the development of significant defects, which would jeopardize the integrity and safety of the entire structure.

So far, a number of various approaches devoted to solving different problems have been proposed. Ultrasonic waves are most commonly used for crack detection [1–7], monitoring the hardening process [8–11], as well as for the quality assessment of the adhesive connection between concrete cover and reinforcement [12–16]. The method of scanning the surface opening cracks in reinforced concrete structures using transient elastic waves was developed by Liu et al. [1]. The effect of the depth of surface-breaking cracks in concrete plates on Lamb wave propagation was described by Yang et al. [2]. The influence of the width of partially closed surface-breaking cracks in concrete structures, the incident angle of waves with cracks, and the distance from the cracks on travel time and wave amplitude have been investigated by Pahlavan et al. [3]. Ultrasonic shear-wave tomography was used by Choi et al. [4] to identify horizontal cracks or delamination in concrete pavements, columns, and bridges. Surface wave propagation was used by Ham et al. [5] to assess the volume content of relatively small distributed defects and to characterize the microcrack networks in concrete. A combination of Rayleigh and longitudinal waves was employed by Aggelis and Shiotani [6] to evaluate the parameters of surface opening cracks in concrete before impregnation by the epoxy material, as well as to determine the final repair effectiveness. Quiviger et al. [7] conducted a simulation study of the influence of the depth and morphology of cracks in concrete on ultrasound diffusion.

Wave propagation was also effectively employed to monitor the concrete hardening process. The speed of propagation of ultrasound in various concrete samples varying in time of aging was investigated by del Rio et al. [8]. Piezoelectric transducers embedded in concrete structures were used by Dumoulin et al. [9] to monitor the setting and hardening phases of the early-age concrete. The hardening process of ultra-high-performance concrete was monitored by Lee et al. [10] using the characteristics of individual Lamb wave modes. The correlation between the shear wave velocity and penetration resistance for mortar mixtures was presented by Liu et al. [11].

Several scientific papers were devoted to guided waves for the detection of debonding occurring between concrete and internal or external reinforcement [12–15]. Monitoring of the interfacial debonding of a concrete-filled pultrusion-GFRP tubular column based on stress wave propagation was conducted by Yang et al. [12]. The wavelet packet-based energy index was proposed by Jiang et al. [13] to detect debonding between a steel beam and a carbon fiber-reinforced polymer plate. The time-reversal method was applied by Zhao et al. [14] to detect and localize the debonding along the steel–concrete interface. Giri et al. [15] employed the partial least-squares regression technique for detecting gaps in the steel–concrete composite specimens.

The above brief review of the literature indicates the multiplicity of investigation strands concerning wave-based concrete diagnostics carried out in the last decades. However, in the majority of reported cases, regardless of the considered problem, the diagnostic process requires some reference data collected for an intact structure, which would be compared to the data obtained for the damaged specimen. Due to obvious reasons, it is not always possible to make the baseline measurement for a pristine structure, and thus, the development of reference-free diagnostic procedures is of particular importance. The main idea of the recently developed reference-free methods is based on the comparison of the experimental measurement with the theoretical predictions [16]. The greater the difference between experimental and theoretical results, the greater the state of deterioration is expected. However, the discrepancies between experimental measurements and theoretical predictions were caused not only by the damage occurrence but also the simplification of the theoretical model of wave propagation in the concrete structure. The theoretical models were usually developed for homogeneous, isotropic materials characterized by the averaged macroscopic parameters, while the concrete is a multi-phase, strongly heterogeneous material. The complex mesostructure of the concrete led to inaccuracies in the wave propagation model. The theoretical predictions differed slightly from the actual results registered for experimental specimens, which, in consequence, led to inaccuracies in damage size assessment.

Although the papers published by Xu et al. [17], Abo-Quadis [18], and Ramaniraka et al. [19] deal with the impact of the concrete mesostructure on waves characteristics, the problem of wave propagation in heterogeneous materials is still not considered in detail, yet. The existence of aggregates varying in size, shape, and material parameters, and pores and cracks may lead to additional disturbing phenomena like scattering, diffractions, and wave attenuation affecting wave amplitude or propagation velocity, which were commonly used as indicative parameters in the above-mentioned studies. The wave propagation phenomenon may significantly differ for two different concrete specimens despite their identical macroscopic material parameters. Thus, the comprehensive analysis of wave propagation in concrete specimens taking into consideration their complex mesostructure is crucial for the further development of wave-based concrete diagnostic methods.

The main contribution of the paper is the analysis of the aggregate size and content on Lamb wave propagation. The algorithm of the generation of heterogeneous concrete models was developed and described step by step. Several numerical plate models differing in parameters of the internal mesostructure were developed using the Monte Carlo method. The averaged macroscopic parameters determined theoretically were compared to material parameters determined based on the shape of reconstructed dispersion curves for antisymmetric Lamb modes. The results obtained show that the concrete mesostructure has a significant influence on the wave propagation phenomenon. The wave velocity determined for the homogeneous concrete model differed from the velocity in

the heterogeneous concrete model, even if the averaged material parameters were the same, and according to the theoretical wave propagation model, differences in velocities should not be observed. The difficulties in exact wave velocity determination must be taken into account, especially if the developed diagnostic procedure involves monitoring of wave propagation velocity.

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