## 3 Database Development
### Finite-Element Modelling of the Benchmark URM Building
#### 3.1.2 Development of the Simplified Numerical Model  
A simplified 3D model of the benchmark URM building developed in SAP2000 v.22 with nonlinear layered shell elements was used in the present study to obtain the seismic response of the building. This is a macro-modelling technique, in which the masonry is modelled as a homogeneous material with equivalent mechanical properties. This technique is suitable for studying the overall behaviour of the masonry with reduced computational time. In this layered-element approach, various layers in the thickness direction with different associated constitutive laws can be used [32]. In the present study, masonry was considered as a nonlinear isotropic material and the material angle in each layer was taken as zero. The orthotropic behaviour of the masonry was not considered due to the lack of availability of experimental data for suitable calibration of the required parameters. Two stress-strain curves, corresponding to normal stress (compression and tension) and shear stress, were used in the model to represent the nonlinear behaviour of the masonry, using two layers of quadrilateral shell elements in the model [33]. The bottom nodes of the URM building were constrained in all three degrees of freedom. The RC lintels and roof were modelled using linear elastic elements, and the total weight of the 0.25 m thick sand layer was applied on the roof of the building as distributed mass. A rigid diaphragm constraint was applied at the roof level to constrain the nodes. The optimal mesh size (equal to 0.114 m) for the model was identified through detailed sensitivity analysis, for which 5184 shell elements were ultimately used. The FE model of the URM building is shown in Figure 4a. Readers can refer to [2; 31; 34] for additional insights as to the advantages and reproducibility of this simplified numerical model. The basic motivation behind the use of this simplified numerical modelling approach is to reduce the computational time. Since a considerable amount of data is required to develop ML models, this numerical model can aid in the procurement of data satisfactorily. Further, the application of this simplified numerical modelling approach for the seismic response and fragility analyses of base-isolated URM buildings in the Himalayan regions highlights the suitability of the model for the real-world applications [2; 33]. Additionally, it is also important to note that experimental data on non-engineered masonry buildings are scarce in the literature, and insufficient for the development of ML models. Hence, this attempt by the authors to develop the seismic damage prediction models along with data development is unique. Figure 3: Plan of the benchmark URM building [30; 31]. In this simplified modelling approach, the model parameters were defined through the direct implementation of stress-strain points. Hence, existing models in the literature were used to develop the stress-strain curves, using the available masonry strength parameters from the experiments. The constitutive models used in the study are shown in Figure 4b,c, with the material properties obtained from [PERSON] et al. [30]. The analytical model developed by [PERSON] et al. [35] was used to define the uniaxial compressive behaviour of the masonry. The uniaxial tensile behaviour of the masonry was defined by the relationship proposed by [PERSON] and [PERSON] [36]. The trilinear stress-strain curve was used to reduce the convergence issues that arise during the early stages of the analysis. The FE model was calibrated through a series of push-over analyses by applying incremental horizontal displacement at the control node in the roof level of the building. According to the experimental study, the masonry building reached its peak lateral resistance of 99.5 kN at a lateral displacement equal to 7.89 mm (corresponding to an inter-storey drift of 0.23%).