**5. Analysis of Test Results**

On the basis of empirical relationships and those developed in the testing stage, an attempt was made to determine normal stresses in the tested models. The comprehensive approach based on all test results or the approach using a limited number of points was implemented for each model. In the first case, there were 315 (the model of series I) or 308 (the models of series II or III) measurement results for each step of loading. The calculations also included results for edges of the masonry units that demonstrated clear disturbances. The approach based on a limited number of points for determining stress involved only points located in the central area of the masonry units. That significantly limited the number of analyzed measuring points to 45 for model I, and 44 for models of series II and III. For successive levels of loading, the difference in passing time of the ultrasonic wave was calculated, and then acoustoelastic coefficient β<sup>113</sup> was calculated from Equation (38). Finally, stress σ<sup>3</sup> from the transformed relationship (36) was calculated. The obtained values of stress are presented in Table 5.


**Table 5.** Results from calculating normal stress in the wall using all measuring points.

The obtained coefficients depended on apparent density of AAC of the order <sup>−</sup>0.0215–−0.0224 mm2/N. The values obtained for autoclaved aerated concrete aerated were many times greater than similarly determined acoustoelastic effect for metals [40] (β<sup>113</sup> <sup>=</sup> <sup>−</sup>0.99 <sup>×</sup> <sup>10</sup><sup>−</sup>5–−2.06 <sup>×</sup> <sup>10</sup>−<sup>5</sup> mm2/N—steel, <sup>β</sup><sup>113</sup> <sup>=</sup> <sup>−</sup>7.75 <sup>×</sup> <sup>10</sup>−<sup>5</sup> mm2/N—aluminium, <sup>β</sup><sup>113</sup> <sup>=</sup> <sup>−</sup>1.88 <sup>×</sup> <sup>10</sup>−<sup>5</sup> mm2/N—copper). The determined stress values were similar only at relatively low stress values equal to 0.25σ3max and 0.50σ3max. Maximum differences in stress determined using the EA method did not exceed 11% (model II-1). For stress values of the order of 0.75σ3max, the estimated values of non -destructive stress were considerably lower than those determined from destructive testing. Stress values were underrated by no more than 28%.

In the second approach based on the limited number of results for central areas of all masonry units, the procedure was similar to the first one. The location of measuring points in the central part of the masonry units was determined by analysing the maps of passing times illustrated in Figures 10–13. Firstly, differentiation in passing time of ultrasonic waves was smaller in the central areas. Secondly, stress states in that area of masonry units was the most similar to stress states in the specimens

100 × 100 × 100 mm used to validate the AE method in stage I. In addition, the final aspect was purely practical because it was the easiest to determine centers of masonry units, apart from edge areas. For successive levels of loading, the difference in passing time of the ultrasonic wave was calculated. Then, acoustoelastic coefficient β<sup>113</sup> was calculated from Equation (38), and finally stress values σ<sup>3</sup> were calculated from the relationship (36). The obtained values of stress are presented in Table 6.


**Table 6.** Results from calculating normal stress in the wall using a limited number of measuring points.

Using the approach of considerably decreased number of measuring points limited to central areas of the masonry units, much lower stress values were obtained. For the lowest level of stress of the order of 0.25 σ3max, stress calculated for the model II-1 with the AE method was lower by 60% than in destructive tests. Stress underestimation for other models I-1 and III-1 was at the level of 36–43%. At the stress level of 0.50σ3max, the underestimation of stress was at the lowest level of 16–21%. As in the case of a greater number of points, stress values determined by the EA method at the stress level of 0.75σ3max were the least accurate. Calculated compressive stress differed by 49–62% from experimentally obtained values. Compared results from destructive testing and calculated results are shown in Figures 14–16.

**Figure 14.** Measurement results of stress in the model I-1.

**Figure 15.** Measurement results of stress in the model II-1.

**Figure 16.** Measurement results of stress in the model III-1.

In conclusion, the most favorable results from measuring stress with the calibrated acoustoelastic method were obtained when all measuring points were used at stress levels within the range of 0–0.5σ3max. The determined stress values were lower than those from destructive testing small wall models. Considering the approach based on the limited number of points, underestimation of compressive stress was considerably greater. The greatest differences in both methods were found at the stress level of 0.75 σ3max, which resulted from an increase in effects of ultrasonic wave scattering, developing microcracks in AAC structure (invisible on the external surface of the models).
