Masonry with poor mortar strength refers to structures where the unit/mortar interface governs the formation of cracks and collapse mechanism. Masonry with poor unit strength concerns structures where the strength of unit dominates mechanical behaviour. Tuff blocks are a prime example of this case. In the third case, the strength of mortar and unit are considered comparable and both have a major effect on failure mode. The type of material and bond strength affect the mechanical performance of the overall masonry structure . Different experimental work was carried out in various studies to explore the effect of bond between masonry and plastering and concluded the high importance of bond in the strength of masonry . Masonry walls are considered to be strong in resisting of vertical axial load , but there is often a need to improve their resistance when subjected to lateral load  such as wind and earthquake. Evaluation of the safety of masonry structures under seismic loading is a complex problem, and both linear and nonlinear methods have been used in different studies .
The finite element method is the most well-known analysis technique for elements subjected to static or dynamic loading. For a numerical model to effectively represent the behaviour of a real structure, both the constitutive model and the input material properties must be selected carefully. For this study, the computational software TNO DIANA was used for the application of the finite element method. For a masonry structure, FEM analysis can be performed using various modelling approaches. These include macro-element and micro-modelling approaches . The most refined approach used by other researchers is micro-modelling . Here different mechanical parameters and constitutive laws are used for different component parts. It allows for local failure of the units and of any bonding, so they can be modelled separately. In addition, it is possible to model the units with or without interfaces. Furthermore, to study structural failure cracking behaviour should be modelled accurately. Two types of cracking model are available to simulate behaviour numerically, which include the discrete crack and smeared crack models. The former introduces the crack to FE models manually by means of a separation between element edges . The smeared crack approach does not track individual cracks but smears their effect over the FE by modifying its mechanical properties, as shown in Fig. 1 . This approach is considered better than its discrete crack counterpart, which requires the mesh configuration to be updated as the cracks develop in the FE model. The smeared crack approach is further divided into two types: fixed smeared cracking and rotating smeared cracking approaches. With the former, the orientation of cracks remains fixed, which leads to an unrealistic and distorted crack pattern. With the rotating smeared crack approach, the orientation of the crack follows any change in the direction of principal tensile stresses. This gives results closer to the realistic value accepted by other studies .
In light of the outcome of previous studies micro-modelling, rotating smeared crack finite element modelling was chosen in this study to predict the lateral failure load of interlocked masonry. FE modelling of mortar-free interlocked block was also identified as a knowledge gap in the literature. The proposed FE modelling was validated by comparing peak load with the experimental lateral failure load, as explained in Sect. 3. These validated NLFE models are used to carry out the parametric study of different parameters including block and plaster compressive strength and plaster thickness rather than constructing various experimental columns/walls.
For block material properties, constitutive models proposed by another researcher  were used, based on a smeared-crack approach, assuming exponential strain softening in tension and plasticity in compression. Parabolic curve formulations, based on tensile and compressive fracture energy, are shown in Fig. 5.
In this section, the results of the comparison between the finite element model output and the experimental work are presented. The comparative study was undertaken to determine the validity of the finite element models in predicting the nonlinear behaviour of the unplastered, plain-plastered and fibrous-plastered columns. Failure load, maximum displacement, stiffness and cracking patterns are compared in Sects. 3.1, 3.2 and 3.3, respectively. The results of the comparative study between FE models and experimental works are presented with the help of graphs and tables.
The experimental results of failure load Fexp and the FE predicted values FDiana for all specimens are presented in Table 9. The FE predicted value is the maximum force which can be calculated as the sum of the reactions at the point of application of loading. The FE prediction values were in good agreement with the experimental results for all cases within 13% difference. The proposed FE models for all cases underestimated failure load with a maximum mean experimental/FE ratio of 1.07 for plain-plastered models. The rotating crack model assumes that cracking always occurs within principal planes, and it does not consider internal shear contribution across the crack plane. Therefore, it was expected to obtain a lower value of failure load from FE models than the experimental value. The only exception was found for the 8-mm rice straw plastered model where the experimental/FE ratio was 0.98. The reason for this is due to assumed values of block interface properties due to a lack of experimental data. Figure 8 shows the comparison of the results for both experimental and FE analysis. The ranges at the top of bars represent variability in the experimental result.
FE analysis has the capacity to show the development of cracks which is considered as one of the merits of using such analysis. Figure 10 shows the comparison between experimental and FE model crack patterns at failure for unplastered, plain-plastered and fibrous-plastered samples. The FE models crack pattern is presented by the crack contour plots. It can be seen that the FE model adequately projected the failure cracks of unplastered sample, which showed the stress concentration with red contours at the base and the opening of interlock at tension face, as shown in experimental results.
Similarly, for plain and fibrous samples, FE predicted the cracks within block and plaster interface showing resemblance to the experimental results. The difference between the plain-plastered and fibrous-plastered samples can be observed with showing fewer cracks in the plain-plastered FE model as shown in Fig. 10b, whereas the fibrous-plastered sample showed more cracks as is visible in Fig. 10c. This ties in well with the outcome of the experimental work as fibrous plastered samples showed more ductility due to the presence of the fibres.
This resulted in the ductile failure of the fibrous plastered samples as compared to the brittle failure for all other samples. It can also be observed that failure of plain- and fibrous-plastered samples occurred due to cracking in the interface between the block and plaster rather than within the block. Similar behaviour was noted in FE models where cracks were initiated within the interface between block and plaster.
From experimental and numerical analysis, it was found that addition of fibrous plastering to the tension face of columns enhanced the peak lateral load and other mechanical properties such as elastic stiffness, pre- and post-crack energy absorption and toughness. However, addition of plaster and fibres to one face will increase the overall construction cost. In order to reduce the construction cost of the wall in practical application, the thickness of the wall (i.e. thickness of blocks) could be reduced. Finite element sensitivity analysis was carried out to find the equivalent thickness of fibrous plastered column to an unplastered column having similar or better lateral resistance. An unplastered unmortared column of 150 mm thickness was taken as datum. Plain- and fibrous-plastered walls with mortar and interlock were compared to find this equivalent thickness. The following variations were considered as detailed below:
The aim of this numerical work was to develop NLFE predictive tools to firstly identify a likely failure mechanism (e.g. bond failure) compatible with the experimental work and secondly to do parametric studies more cheaply than via constructing many walls. 3D nonlinear FE models of unplastered, plain-plastered and fibrous-plastered columns made of mortar-free interlocked blocks were developed. The FE models were validated using the experimental results of this study. The FE model represented the block and plaster with eight-node isoparametric solid brick elements. For the interface between block and plaster, eight-node interface elements were used. The adopted geometrical and material properties were either obtained from the experimental work as a part of this study or calculated based on well-used models. The solution method was adopted based on an incremental iterative procedure using displacement increments of 0.1 mm for 20 steps. Failure behaviour was verified by comparing the FE models failure load, load displacement curves and crack patterns to the experimental results. Based on the comparative results between FE models and experimental results, the following conclusions were obtained.
The FE models crack patterns have a good agreement with the crack patterns observed in the experimental tests, e.g. the opening of joints for unplastered columns and cracking in the interface between plaster and block for plastered ones. This showed most emphasis is required to increase the strength of interface for an overall increase in lateral resistance.
Parametric studies suggest that increasing the strength of plaster does not change the failure load. This is because failure is initiated by cracks in the interface between plaster and block. Also plaster contribution is expected in the tensile zone rather than compressive. 2b1af7f3a8