## 3 DEM Simulations  
This work introduces a 2D DEM of a mortar specimen. The 2D DEM corresponds to the cross-section of a cylindrical mortar specimen. The width and height of the model cross-section correspond to the diameter and the height of the mortar cylinder. 2D DEMs of cylindrical specimens have been used to model triaxial tests in granular and brittle materials [43; 44]. The solver software used in this work was the Particle Flow Code 2D (PFC2D 5.0) by Itasca Consulting Group [35]. The computational system processor was an Intel(r) Xeon(r) Gold 6248 CPU @2.50 GHz (four processors) and 768 GB RAM memory. Following the process from Potypody and Cundall [14] and the PFC2D material generation process [35], the simulation process was divided into five stages. Particle generation: A rectangular material vessel is created that contains the particles at half their final size and placed randomly within the vessel bounded with frictionless walls. The generated particles have a linear contact model (linear behavior) at this stage, and the properties are specified in Table 2. The friction coefficient was manually calibrated from the experimental value. The number of particles was calculated with respect to the overall porosity of the sample and the particle radius. Porosity was re-calculated from Equation (8). This equation is suggested by [PERSON] et al. [45] as a correction for modeling in two dimensions in the DEM. \[n_{2D}=0.42\times n_{lab}^{2}+0.25\times n_{lab} \tag{8}\]  
where \(n_{2D}\) is the initial 2D porosity and \(n_{lab}\) is the experimental porosity. The damping ratio is selected to ensure quasi-static conditions [14]. The particles are allowed to re-arrange under a low friction coefficient while the particles' radius is increased to their final size. A low isotropic stress is applied by modifying the diameters of all particles simultaneously. Once static equilibrium was reached, the facets/walls were deleted. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Value** & **Unit** & **Source** & **Type** \\ \hline \(q_{u}\) & 2.75 & MPa & [36] & Experimental \\ \(\sigma_{t}\) & 0.30 & MPa & [37] & Experimental \\ \(E\) & 7994 & MPa & [36] & Experimental \\ \(k_{n}/k_{s}\) & 25 & Unitless & [38] & Experimental \\ \(\phi\) & 34 & Degree & [39] & Experimental \\ \(\mu\) & 0.3 & Unitless & [37] & Experimental \\ \(\rho\) & 1624 & kg/m\({}^{3}\) & [40; 41] & Experimental \\ \(n\%\) & 22 & \% & [42] & Experimental \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mortar properties. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Symbol** & **Value** & **Unit** \\ \hline Density & \(\rho\) & 1624 & kg/m\({}^{3}\) \\ Diameter & \(D_{max}\)–\(D_{min}\) & 4.48–0.54 & mm \\ Young’s modulus & \(E\) & 8.00 & GPa \\ Stiffness ratio & \((k_{n}/k_{s})\) & 2.5 & Unitless \\ Friction coefficient & \(\mu\) & 0.10 & Unitless \\ Porosity & \(n\%\) & 10 & \% \\ Damping ratio & \(\beta\) & 0.70 & Unitless \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model particle generation—linear contact material properties. Bond creation: flat joint material properties were assigned through the specimen between the particles that satisfy the installation gap (particles-particle separation less than or equal to \(2\times 10^{-4}\) m). [PERSON], [PERSON], and [PERSON] [20] used a 0.4 installation gap ratio (\(\overline{g}/\mathrm{d_{min}}\)) for their model. In this work, it was used a 0.24 installation gap ratio since it created adequate particle connectivity to reproduce the mortar's behavior. The remaining particle-particle contacts and contacts formed during the simulation process were assigned the linear contact model with properties derived from the linear contact group of the flat jointed material properties [24]. The top and bottom facets were created after the forces and moments were set to 0 after the bond creation.