Masonry structures subjected to a lateral load, such as earthquakes and wind, can be prone to out-of-plane failure. It is known that geometrical properties and boundary conditions have a large influence on the out-of-plane bending capacity of walls. In this thesis, a numerical study is performed to evaluate the influence of the bond pattern on the two-way out-of-plane bending capacity of unreinforced brick masonry walls. A nonlinear finite element analysis with a 3D block-based model has been adopted to simulate the texture of the wall in detail. The study builds on the work of Chang et al., which was validated against the experimental benchmarks by Griffith et al. The numerical model can accurately estimate the initial stiffness and out-of-plane bending capacity, but the model is less accurate post-peak.
It is assumed that the material properties of the mortar in the bed joints are the same as the one of the head and collar joints. The masonry wall was first subjected to self-weight and a vertical pre-compression of 0.1 MPa. Afterwards, a monotonic out-of-plane pressure placed on the face of the masonry wall is applied. The numerical model takes both physical and geometrical nonlinearity into account.
In the first phase, different modelling assumptions were checked and a sensitivity study was performed. Prior to the study must the compressive behaviour of the brick be determined, as the bricks are elastic without a limit, thus nonlinear effects like crushing are not modelled. The resulting check determined that the minimum principal stress did not exceed the compressive strength of the brick.
A mesh sensitivity study has also been performed as a change in mesh size was needed. In the model of Chang, the face of the brick was divided over its length into two parts called a halfbrick (Hbrick). The bond patterns require a division of the face into 4 parts, a quarterbrick (Qbrick) or an octogonalbrick (Obrick) which maintains the aspect ratio of the Hbrick. Eventually, the Qbrick mesh is the best option as convergence issues arose for the Obrick.
Additionally, experiments have shown that cracks can propagate through the bricks, while this is not possible with a smeared cracking model. To simulate this effect a discrete cracking model within the brick was introduced. The possible locations of the cracks can easily be assumed in a masonry wall, to be in line with a mortar joint in the course above or below it. The change to the discrete cracking model did not influence the out-of-plane two-way bending capacity, while convergence issues arose, and it was subsequently not used.
Finally, in the experiment by Griffith et al., clamps are installed over the height of the end of the return walls. These clamps prevent any horizontal translations and rotations in the horizontal plane. These clamps are represented by tyings in the numerical model. In this study are these tyings removed and is the length of the return wall parametrised. A masonry wall without any return walls is fully one-way bending and to a length of 360 mm does the masonry wall show a transition between one-way to two-way bending. A return wall of at least 480 mm long is sufficiently long to achieve two-way bending.
A parametric study was performed considering five single wythe and three double wythe bond patterns: stretcher bond, quarter bat bond, lateral bond, half Flemish bond, stack bond, chain bond, English bond and Flemish bond. The double wythe masonry wall has been assembled by adding an outer shell to the single wythe wall and by decreasing the pre-compression to 0.0478 MPa to maintain the same vertical force as the single wythe bonds.
The highest out-of-plane bending capacity for the single wythe bond patterns is the half Flemish bond with 4.9 kPa with a spread of 5.4% and for the double wythe bond patterns it is the Flemish bond with 18.7 kPa with 7.2%. The spread between the highest and lowest out-of-plane bending capacity is small. All the walls, except the one in stacked bonded masonry, show a crack pattern in the form of a cross. The slopes of the diagonal cracks with respect to the horizontal bed joint line have also been studied and relates as follows: a shallow slope in the crack pattern coincides with a higher two-way out-of-plane bending capacity. While a steeper slope or the absence of a cross-shaped pattern coincides with a lower out-of-plane bending capacity. On the contrary, the initial stiffness of the masonry wall does not relate to the out-of-plane bending capacity.
To further confirm these findings, research is needed concerning different masonry types, considering relative properties between bricks and mortar joints, different properties between bed, head and collar joints, and spatial variability of properties.