**6. Conclusions**

This paper describes theoretical bases of the acoustoelastic method (AE) which is one of the methods of detecting stress in structures using NDT techniques. That method consists of the correlation between stress in the material and velocity of the wave propagation. It is commonly used in ultrasonic tensometry to determine own stresses usually in machine parts. Using that method for other materials has not been widely discussed in the literature so far. No results from tests and analyses in concrete, not mentioning masonry, are available. This lack of interest in using this method can only be explained by measuring difficulties (significant dispersion of measurement results) caused by inhomogeneity of that material. This work presents an attempt to use the AE method for autoclaved aerated concrete. It is a porous material with high homogeneity and repeatability of parameters due to the production of this material on an industrial scale. This work supplements comprehensive material tests for autoclaved aerated concrete [11]. The tests were divided into two stages: Stage I involved the suggestion of the procedure and the determination of acoustoelastic coefficient β<sup>113</sup> linking the propagation of the longitudinal ultrasonic wave cp with normal stress σ<sup>3</sup> acting towards the wave propagation. The standard cuboid specimens with the dimensions of 100 × 100 × 100 mm were used for calibration. The effect of density ρ and relative humidity w was included on the basis of testing AAC of different density using correlations presented in [11]. Those considerations resulted in formulating the relationship β<sup>113</sup> (ρ). The proposed procedure was verified in stage II, where destructive tests were conducted on small masonry walls made of autoclaved aerated concrete (AAC) with a nominal density of 600 kg/m3. The models were divided into three series differing in the location of head joints in the masonry. Velocity of the ultrasonic wave propagation was measured for one model of each series at different values of compressive stress. The following stress levels were analyzed: 0.25σ3max, 0.50σ3max and 0.70σ3max because the range of the applied method was only limited to the elastic range. The performed measurements were used to determine values of acoustoelastic coefficients β<sup>113</sup> = −0.0215–−0.0224, which were far lower than similarly determined acoustoelastic coefficients for metals. Mean stress values calculated with the proposed method using all measuring point for a given level (*n* = 308–315) were within the range of 93–96% of empirical values 0.25σ3max, 0.50σ3max. The highest underestimation of stress was found for the stress level of 0.75σ3max, for which the underestimation of mean stress values was equal to 24%. However, such a great number of measurements seem to be impractical for the applicable uses. Therefore, further analyses suggest determining stress values only on the basis of measurement results for central areas of each masonry unit. Then, the number of measuring points was significantly reduced to *n* = 45 and 44. As for all measuring points, the comparison indicated greater underestimation of the mean value of the order of 22–55%. It is not advantageous taking into account safety of the structure. Hence, it was decided to

estimate the confidence interval of the mean value associated with the quantile of the order of 95%. Such a procedure caused the stress values were underestimated at the level of 12–18% within the stress range of 0–0.50σ3max. In summary:


The formulation of explicit recommendations to diagnose in-situ structures requires additional tests on slender walls to evaluate the impact of stability and works on improving the selection of measuring points. The proposed procedure for selecting measuring points limited to central parts of masonry units can be inaccurate for slender walls. Tests are going to be performed on the acoustoelastic coefficient in the wall with a one-side access using transverse waves to determine the acoustoelastic coefficient β133.

**Funding:** The research was financed from the personal funds of the Department of Building Structures and Laboratory of Civil Engineering Faculty.

**Acknowledgments:** The author would like to express particular thanks to Solbet Company for valuable suggestions and the delivery of masonry units and mortar, which were used to prepare test models and perform tests.

**Conflicts of Interest:** The author declares no conflict of interest.
