**1. Introduction**

Clay (or mud) has been used in the building industry since ancient times [1,2]. Claybased building materials can be classified in many categories in terms of the preparation process and use, such as mud bricks, clay plasters, cob, and rammed earth [2,3]. Most typical clay brick structures work mainly in compression perpendicular to the bed (horizontal) joints. Therefore, their compressive strength is determined in this particular direction, according to the methodology presented in the standard [4]. It is less common for masonry to work in compression at a different angle from the joints [5–10].

An example of masonry loaded at different angles to the bed joints are walls subjected to seismic actions. The evaluation of the shear behavior of masonry walls is a fundamental step for the assessment of masonry in seismic zones [11,12]. Under lateral forces, the low tensile strength generally leads to local or global failure modes, the latter related to shear or flexural mechanisms [13]. The latest works in the field of research and modeling of masonry structures concern the influence of the value of the modulus of elasticity and Poisson ratio outside the range of 33% of the ultimate stress on the shear behavior of masonry

**Citation:** Nowak, R.; Kania, T.; Derkach, V.; Orłowicz, R.; Halaliuk, A.; Ekiert, E.; Jaworski, R. Strength Parameters of Clay Brick Walls with Various Directions of Force. *Materials* **2021**, *14*, 6461. https://doi.org/ 10.3390/ma14216461

Academic Editor: Dinesh Agrawal

Received: 28 September 2021 Accepted: 23 October 2021 Published: 28 October 2021

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walls. Nonlinear static analyses are commonly adopted for the evaluation of seismic performance [11–17]. Research on that subject has been presented by Laurenco et al. [14] with a yield criterion that includes different strengths along each material axis. The criterion includes two different fracture energies in tension and two different fracture energies in compression. This model is validated with uniform biaxial loading conditions [11,14]. Celano et al. in [15] presented research on the in-plane resistance of masonry walls by means of two modeling approaches: a finite element model and a discrete macro-element model with the use of non-linear analyses. Beconcini et al. in [12] presented a combined test procedure for the experimental characterization of masonry mechanical parameters and the assessment of the shear behavior of masonry walls.

Another example of masonry with load (P) at an angle to the bed joints is visible in arched lintels (Figure 1a), commonly found in historic buildings. The angle of inclination of the pressure line in the support zones depends on its shape and the span-to-bow ratio. It can range from θ = 10◦ to 40◦. As compression is applied to the wall at a lower angle of load capacity, stone blocks were sometimes required to be used as supports [18–20]. (Figure 1b).

**Figure 1.** Examples of arched lintels (**a**) diagram with load (P) acting at an angle to the joints; (**b**) image of an arched lintel with stone blocks in support zones.

The supports of masonry vaults also transfer the point load towards the wall at a different angle to the joints. In the case of historical buildings, vault support zones are susceptible to damage and repairs, as they transfer the most stresses (Figure 2).

**Figure 2.** Arched lintels support zones in masonry (**a**) diagram; (**b**) example of failure mechanism.

In most scientific research on design procedures, only the strength perpendicular to the bed joints is usually considered. The anisotropy of the masonry is described as the

ratio of the wall strength at the angle *fc*,<sup>θ</sup> and perpendicular to the bed joints (*fc*,0). The rate depends on the material used, number of hollows, thickness, and type of the joint. The influence of masonry anisotropy is usually neglected and not analyzed. According to [21], with a more precise calibration of the calculation models, a shear test is also performed. Rarely is the strength of the masonry parallel to the bed joints tested, which may be much weaker than perpendicular [22–30]. Tests show that the strength parallel to the bed joints usually differs from the perpendicular strength within the limits *fc*,90/*fc*,0 = 0.2–1.2. In the study [23] obtained value was *fc*,90/*fc*,0 = 1.2, however, the models in this direction had a much lower height dimension than in the perpendicular direction—which could have influenced the results.

Even less frequently, the parameters of the wall are tested at different angles. In the studies [31–34], masonry elements were tested on a 1:2 scale for compression and tension at the following angles θ = 0◦, 22.5◦, 45◦, 67.5◦, 90◦ at load in both planes σ<sup>1</sup> and σ2. For the purpose of that study, the authors used cement and lime mortar with a compressive strength of 5.55 MPa and 15.41 MPa clay bricks. The described research allowed to create calculation criteria for later different FEM (Finite Element Method) models. A different study [19] tested sand plast bricks (calcium silicate form) with a compressive strength of 23.4 MPa and 10.2 MPa cement and lime mortar with joints of approximately 5 mm. The study considered elements of the 1:2 scale in compression and tension at the same angles. The influence of the wall angle on the achieved wall strength, i.e., the degree of anisotropy, was highlighted in that study. In study [35], a failure criterion for biaxially loaded hollow blocks masonry has been researched. 1:1 scale samples of hollow clay blocks were tested, with angles as in previous studies for models with different geometries depending on the size of blocks. Similarly in study [18], but for angles θ = 0◦, 15◦, 30◦, 45◦, 60◦, 75◦, 90◦, the tests were carried out on concrete blocks with 20% and 40% hollows, silicate blocks with 20% hollows, and clay blocks with 20% and 40% hollows. This research considered a typical cement–lime mortar. Studies allowed to estimate the degree of anisotropy of masonry for concrete and silicate blocks *fc*,90/*fc*,0 = 0.71 and for hollow clay blocks *fc*,90/*fc*,0 = 0.37.

Other structures that work in a state of compressive stress, in a different direction than indicated in the standard [4], are stiffening walls, infilling walls or elements subjected to uneven settlement of the ground. The different direction of the force action results in a complex stress state within the masonry construction, where the main axes are not parallel to the plane of the bed joints. In the case of this type of structure, its damage usually occurs as a result of exceeding its tensile strength. In residential buildings constructed in the last year in Poland, more than 95% of infilling walls were made with masonry technology [36]. Furthermore, 27.5% of the walls were made of clay elements, indicating the essence of the cracking problem that was solved in the presented research.

One of the most common calculation methods for stiffening walls in skeleton buildings is to assume a strut model. In this method, it is assumed that due to the interaction of the reinforced concrete skeleton with the walls, for the purpose of the calculation, compressed equivalent pinned strut masonry elements are being assumed. The elements with width *w* and length *Ld* (Figure 3) play the role of stiffeners for the building [37,38]. The width of the element depends on the length of contact between the filling wall and the building skeleton [39–45]. Due to the masonry anisotropy discussed in the article, the actual strength of the wall will change depending on the slope of stress in relation to the plane of the bed joints of the wall. This effect will be particularly visible in walls with a low *H*/*L* ratio or in walls made of elements with vertical hollows.

In the analysis of these building elements, it is important to take into account the anisotropy of the strength parameters of the walls in relation to the direction of the compressive forces. As there are not many studies showing the mechanical properties of ceramic walls subjected to angular loads, the authors undertook this task. The novelty state of this study is the determination of the degree of anisotropy, compressive strength, the change of Young's modulus and Poisson's coefficient of 1:1 scale ceramic wall samples made of <sup>25</sup> × <sup>12</sup> × 6.5 cm<sup>3</sup> solid bricks with compressive strength *fb* = 44.1 MPa.

**Figure 3.** Strut model for the masonry infill wall based on [6] *L, H, H*1*, H*2*, H*3—wall geometry, 1—infill wall; 2—equivalent pinned strut; 3—stress distribution in the equivalent pinned strut; 4—contact stresses at corners; *w*—width of the strut; *Ld*—length of the strut; *fm* –compressive strength of the masonry.

#### **2. Materials and Methods**

*2.1. Materials*

The tested samples presented in this research were built using clay brick (FCP, Brest, Republic of Belarus), class 40. These are elements used for bricklaying the stiffening and infilling walls in the authors' countries. The dimensions of the bricks are <sup>25</sup> × <sup>12</sup> × 6.5 cm3. For the preparation of joints, cement mortar (FCP, Brest, Republic of Belarus) with compressive strength *fm* = 10.9 MPa has been used. For the preparation of masonry mortars, a factory-made dry mortar mixture was used (FCP, Brest, Republic of Belarus). The thickness of the joint was about 1 cm. To determine the properties of the materials used, initial tests were conducted for bricks and mortar. Tests were performed in accordance with current standards [46–48]. The results are presented in Table 1.


