## 3 Model Calibration  
To mimic the behavior of fiber-reinforced concrete specimens, we initially calibrated the LDPM by fitting macroscopic numerical results with the available experimental data [10]. The compressive and splitting tensile strengths of the concrete were determined based on experiments on six cubes with an edge length of 15 cm [10]. The geometrical sizes of the simulations were designed to be in accordance with the experiment.  
LDPM has a double parameter set consisting of the mixing design parameters that are directly involved in the experimental concrete mixture design: cement consumption 400 kg/m\({}^{3}\), water demand 132 kg/m\({}^{3}\), and the aggregates consisting of 0/2 mm sand 39%, 2/8 mm gravel 25%, and 8/16 mm gravel 36%. The mechanical parameters form the second set of parameters calibrated against the experimental uniaxial compression data by fitting the compressive strength to 90 MPa. The full details of the mix design and mechanical parameters are listed in Tables 1 and 2. The geometry of the specimen for the uniaxial compressive test is shown in Figure 2. To ensure numerical stability and quasi-static conditions, we calibrated the maximum time step based on the minimum aggregate size, the smallest finite element, and the material density to prevent instability, i.e., an uncontrollable increase in kinetic energy. The platen movement was assigned with a velocity rate, having a constant acceleration step especially adjusted to match the quasi-static conditions under which kinetic energy is significantly lower than internal work but yet gives acceptable computational efficiency. Also, to make sure that there were no undesirable dynamic effects, we verified that the stress in the top and bottom platens remained constant during the simulation.  
Having determined the mechanical concrete parameters by calibration to plain concrete, we next calibrated the fiber parameters with the uniaxial compression experiment of 20 kg/m\({}^{3}\) fiber content cubes. The curve-fitted experimental data from the calibration yielded a compressive strength of 90.826 MPa; the experiments had a standard deviation of \(\pm\)4.150 MPa. The calibrated LDPM concrete and fiber parameters are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**C [kg/m\({}^{3}\)]** & **w/c** & **a/c** & **\(d_{o}\)** & **\(d_{a}\)** & **\(n_{f}\)** \\ \hline
400 & 0.33 & 2.679 & 4.75 & 16 & 0.424 \\ \hline \end{tabular}
\end{table}
Table 1: Mix design parameters controlling the formation of concrete meso-structure.  
\begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **LDPM Parameters** & **Units** & **Set 1** \\ \hline
1 & \(E_{0}\) & MPa & 78,529 \\
2 & \(\alpha\) & - & 0.25 \\
3 & \(\sigma_{t}\) & MPa & 5.6 \\
4 & \(l_{t}\) & mm & 300 \\
5 & \(\sigma_{\text{CO}}\) & MPa & 200 \\
6 & \(E_{d}/E_{0}\) & - & 2.5 \\
7 & \(H_{\text{CO}}/E_{0}\) & - & 0.4 \\
8 & \(k_{\text{C0}}\) & - & 4 \\
9 & \(k_{\text{C1}}\) & - & 1 \\
10 & \(k_{\text{C2}}\) & - & 5 \\
11 & \(m_{0}\) & - & 0.4 \\
12 & \(m_{\infty}\) & - & 0 \\
13 & \(\sigma_{N0}\) & MPa & 300 \\
14 & \(n_{t}\) & - & 0.05 \\
15 & \(\sigma_{s}/\sigma_{t}\) & - & 2.7 \\
16 & \(k_{c}\) & - & 0.8 \\
17 & \(k_{t}\) & - & 0.8 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters controlling the formation of concrete meso-structure.  
Figure 2: Geometry and aggregate size distribution for uniaxial compression test.