*3.3. Failure Mechanism*

The failure mechanism of the specimens depended on the angle of the bed joints θ. In the case of samples with a load acting in the perpendicular direction to the bed joints (θ = 0◦), the failure was caused by vertical cracks. The first cracks appeared in the first and last rows of clay elements. At a load varying from 0.7 to 0.8 of the observed strength of the specimens, cracks appeared throughout the height of the specimens. After reaching the maximum stress, the width of the crack increased and local crush zones formed in the lower part of the samples (Figure 12a).

**Figure 12.** Failure mechanism of wall specimens θ = 0◦ (**a**) and θ = 90◦ (**b**).

For the angle θ = 90◦ (Figure 12b), the adhesion of the mortar and the brick was decisive. The failure occurred by breaking the contact zone between the brick and the mortar, which caused a loss of stability of the element. The first cracks were formed with a load of 10 to 20% of the wall strength. The initial crack length was 100–150 mm and its opening was 0.1 to 0.15 mm. With a load value of 40 to 60% of the breaking limit, the cracks passed through the entire height of the samples, dividing their surface into four columns. After reaching maximum load, there was a sharp increase in the width of all previously formed cracks. The collapse was caused by the loss of stability of the individual columns.

The failure mechanism of the samples loaded at an angle of θ = 22.5◦ (Figure 13a) was mixed. The main failure is caused by vertical cracks that pass through the bricks and the joins. The first cracks formed at stresses of 40 to 60% of the maximum stress values. After reaching the maximum stresses, the cracks passed through the contact zone of the clay elements and the mortar, and through the brick section. The collapse was accompanied by an increase in the width of the cracks and by crushing fragments of the samples.

**Figure 13.** Mechanism of failure of wall specimens θ = 22.5◦ (**a**), θ = 45◦ (**b**), and θ = 67.5◦ (**c**).

For angle θ = 45◦ (Figure 13b), mortar slip becomes a decisive cause of damage. The first cracks were formed under a load value from 25 to 35% of the observed strength of the wall samples. The initial length of the cracks did not exceed half of the height of the specimen. The width of the crack was 0.15 to 0.20 mm. With the increase in force to 80% of the tested strength, new cracks occurred, passing through the joints and the clay elements of the samples. After reaching maximum stress, the specimens collapsed as a result of cracks that ran through the entire height of the elements and chipping of the wall fragments.

The failure mechanism of the samples loaded at an angle θ = 67.5◦ (Figure 13c) mainly on the slip of the mortar in the adhesion plane with the clay elements. The first cracks appeared at loads ranging from 0.3 to 0.5 of the ultimate force. The length of the cracks ranged from 70 to 90% of the height of the specimen, and their width ranged from 0.15 to 0.20 mm. The cracks ran through both the supporting joints and the head joints. After reaching the maximum stress, all samples were damaged due to the sliding of the elements at the point of contact between the mortar and bricks, as shown in Figure 13c.

#### *3.4. General Discussion of the Results*

The results obtained were compared with the earlier studies on brick walls quoted in the review of the literature. The studies presented in the articles [18,31–34] do not provide results of load capacity that could be used as a comparison. Previous research of different types of clay bricks, hollowed, biaxially loaded walls [35] has shown different dependencies of strength anisotropy. This comparison is presented in Figure 14.

In the range of θ = 0◦ to 67.5◦, the course of the dependency curve for both types of ceramic walls shows some similarities. Coefficient *fc*,67.5/*fc*,0 (for θ = 67.5◦) reached a value of 8% for the biaxially compressed, hollowed blocks walls, and 24% for those tested in this research, uniaxially compressed brick walls. The load-bearing capacity for θ = 90◦ of the walls of clay blocks with hollows, in biaxial compression state of compression (*fc*,90/*fc*,0 = 14%) [35] is much lower than the research for uniaxially loaded brick walls (*fc*,90/*fc*,0 = 75%).

A comparison made between this study and studies [19,35] indicated that the most unfavorable loading angle is between θ = 45◦–67.5◦. The decrease in stiffness is also the highest in this direction, based on the research presented in this study.

The designed load-bearing capacity of masonry walls loaded at an angle to the bed joints should be significantly reduced. For estimating the strength of brick walls with differentiated load orientation, presented test results can be used. In the tests presented in this article, the reduction in strength in extreme cases of rotation was up to 24% of the initial value.

FEM structure modeling is often used for structural analysis of historic masonry buildings. The detailed micro-modeling or simplified micro-modeling is time consuming and requires a lot of calibration data from the existing structure. Very often, such detailed data are difficult or impossible to collect. To simplify these problems, masonry can be calculated as a homogenous composite with macro-modeling technics [11]. Experimental data provided by us could help to implement the change of stiffness of the model and the change of load-bearing capacity in the case of stresses trajectory direction towards the bed joints.

Future research should focus on the analysis of the degree of anisotropy of the masonry of the different types of wall elements. It is important to continue these types of analyses for a wider group of materials. Analyses that allow for the approximation of mechanical properties of the walls loaded in different directions in their surface plane allow, for example, for the proper calculation of the strength of the infilling walls interacting with building structures.

#### **4. Conclusions**

The study determined the degree of anisotropy for masonry samples made of solid bricks and cement mortar. The models were made on a 1:1 scale. Based on the research presented, the following conclusions were drawn.


**Author Contributions:** Conceptualization, R.N., R.O., V.D., T.K., A.H., E.E. and R.J.; methodology, R.N., R.O., V.D., T.K., A.H., E.E. and R.J.; validation, R.N. and R.O.; formal analysis, R.N., T.K. and R.O.; resources, R.N., R.O., V.D., A.H., T.K., E.E. and R.J.; writing—original draft preparation, R.O.; writing—review and editing, R.N. and T.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the privacy restrictions.

**Acknowledgments:** The works were carried out as part of the research project number 20201905, 2020–2021, in the field of design tests of the strength of walls made of brick materials.

**Conflicts of Interest:** The authors declare no conflict of interest.
