*4.2. Stage II—Test Results for Small Masonry Models*

Stage II consisted of verifying empirical relationships developed in stage I. Small masonry walls made of AAC of nominal type of 600 kg/m3, with thin joints laid in the ready-mixed mortar and with the strength *f* <sup>m</sup> equal to 6.10 N/mm2 [49] were used for that purpose. Nine test elements in total were prepared and divided into three series marked as I, II, and III. All elements had the same external dimensions: the length of 500 mm, the height of 724 mm, and the thickness of 180 mm. The presence of the head joint or its lack differentiated the models. This was required to highlight potential effects in changes of ultrasound wave velocity in the real wall near head joints. All models of series I were made from three masonry units without the head joint. The models of series II had the head joint in the central layer at the mid-length of the masonry units, and those of series III had the head joint at 1/4 of the masonry length. The view, shape, and dimensions of tests elements of series I, II, and III are shown in Figure 7.

**Figure 7.** Geometry of models made of AAC tested in stage II (dimensions in mm): (**a**) models of series I without head joint, (**b**) models of series II with head joint at the mid-length of the element, (**c**) models of series III with head joint at 1/4 length; *1*—masonry units, *2*—bed joints, *3*—head joints.

Test models were placed in the strength testing machine with an operating range of 1000 kN (class 1). The applied load was perpendicular to the plane of bed joints and the machine piston displacement was monotonically increasing at a rate of 1 mm/min. The value of the applied load *F* was read from the dynamometer of the testing machine. Stress applied to top and bottom parts of the bed surface of the model was calculated from the equation σ<sup>3</sup> = *F*/*A* (where *A*—area of bed surface of the element *<sup>A</sup>* <sup>=</sup> <sup>180</sup> <sup>×</sup> <sup>500</sup> <sup>=</sup> 90,000 mm2). During the tests, displacements and deformations were measured for two models of each series with the Digital Image Correlation (DIC) using the ARAMIS 6M system by GOM GmbH Braunschweig, Germany (the class of reading accuracy for displacements was 1%) [50–52]. To determine values of forces and stresses causing cracks (σ3cr) and failure (σ3max), some models of each series (I-3, II-3, III-3) were tested without measuring the velocity of ultrasonic wave propagation. Wave velocity cp was measured in two other models at the following values: 0, 0.25σ3max, 0.50σ3max, 0.75σ3max. The transmission method was used to measure waves. Hence, the precise arrangement of ultrasonic transducers vis-à-vis each other was necessary. For that purpose, two plastic templates were used with holes having a diameter of 5 mm, made at the regular spacing adjusted to the model geometry—Figure 8a,b. Holes in the template (Figure 8b) were placed in horizontal and vertical configuration within a distance of ~30 mm. Before testing, apparent density ρ<sup>0</sup> in air-dry conditions, relative moisture content in the material used for preparing the models were calculated, and additionally the maximum moisture content wmax was calculated from the following relationship (39). Basic results for properties of the models and test results in the form of stresses causing cracks σ3cr, and maximum stresses σ3max are presented in Table 3, whereas relationships between compressive stress and deformation σ-ε are illustrated in Figure 9. All models were characterized by minor differences in obtained parameters. Density of models varied from 587 to 597 kg/m3, and relative moisture content was within the range of 4.5–6.0%. At determined values of loading, the procedure of loading was stopped to measure passing time *t*p of the ultrasonic wave, and then the propagation velocity was calculated from the relationship *c*<sup>p</sup> = *L*/*t*<sup>p</sup> (*L* = 180 mm). The tests were performed only on one model of each series (highlighted rows in Table 3). No measurements were made when the measuring points overlapped with bed or head joints.

**Figure 8.** Testing methodology for models made of AAC used in stage II: (**a**) measurement of velocity of ultrasonic wave propagation at different stress values σ3, (**b**) template geometry used for symmetric arrangement of ultrasonic transducers, (**c**) models during tests, (**d**) failure of selected models *1*—masonry units, *2*—ultrasonic transducers, *3*—cables connecting transducers with recording equipment, *4*—templates for symmetric location of ultrasonic transducers.



\*—models, for which the propagation of ultrasonic waves cp was measured.

Nearly proportional increase in deformations was observed in all models exposed to increasing loading. Clear breaking of graphs illustrating stress–deformation relationships was only observed at the time preceding maximum stress that was reached under mean stress within the range of 2.96–3.01 N/mm2. Cracks on external surfaces of masonry units were not observed until maximum stress that was reached in the weakening phase under mean stress within the range of 2.89–2.95 N/mm2.

The transmission method was used to measure passing time of ultrasonic wave at stress levels (0, 0.25σ3max, 0.50σ3max, 0.75σ3max) shown in Figure 9. Results in the form of maps showing passing time of the wave tp are illustrated in Figures 10–13.

**Figure 9.** Relationships between stress and strain σ-ε for all tested models.

**Figure 10.** Results from measuring passing time of the ultrasonic wave under the load σ<sup>3</sup> = 0: (**a**) model I-1, (**b**) model II-1, (**c**) model III-1.

Basic results in the form of mean time of wave propagation for all points are compared in Table 4.

**Table 4.** Results from measuring propagation of ultrasonic waves.


**Figure 11.** Results from measuring passing time of the ultrasonic wave under the load σ<sup>3</sup> = 0.25σ3max: (**a**) model I-1, (**b**) model II-1, (**c**) model III-1.

**Figure 12.** Results from measuring passing time of the ultrasonic wave under the load σ<sup>3</sup> = 0.50σ3max: (**a**) model I-1, (**b**) model II-1, (**c**) model III-1.

**Figure 13.** Results from measuring passing time of the ultrasonic wave under the load σ<sup>3</sup> = 0.75σ3max: (**a**) model I-1, (**b**) model II-1, (**c**) model III-1.

The conducted tests indicated passing times of the ultrasonic wave in walls under zero loads were not constant, some fluctuations were observed—Figure 10. Usually, waves in central parts of the elements had the longest passing time. Clear disturbances at vertical edges and near bed joints were observed. However, the calculated coefficient of variation for all measurements, and from disturbed areas, was relatively low in the order of 1.4–1.6% due to a great number of performed measurements. An increase in loads to 0.25σ3max—Figure 11 caused an evident increase in passing time of the ultrasonic wave for all models. The effect of previous original disturbances was found on nearly whole surfaces of the units. The greatest difference in results was observed near edges of masonry units. As in the primary phase, the coefficient of variation was minor and ranged from 1.0–1.3%. An increase in loads to 0.50σ3max and 0.25σ3max—Figures 12 and 13 produced a gradual increase in mean time of propagation, but did not cause apparent qualitative changes in maps presenting passing times. Similarly, coefficients of passing time of waves did not dramatically changes as the maximum value they reached was 1.4%.
