## 5 Verification of the Numerical Model-Examples
### Simple Supported Concrete Slab  
To verify the developed model, a numerical simulation of the concrete slab presented in [32] was made. A detailed description of the experiment is given in [32], and only the most important data are repeated. The main geometrical characteristics of the tested slab are given in Figure 18. The reinforcement bars were made from steel with the declared strength of 560 MPa, the declared yield point of 500 MPa and modulus of elasticity Es = 200 GPa. The concrete was prepared with the classic Portland cement and the lime aggregate with the maximum grain size of 8 mm, without additives. The slab was concreted on a vibrating table. The concrete uniaxial compressive strength, the tensile strength and the modulus of elasticity were tested with the standard procedure, and the results were sorted in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time** & **t = 28 Days** & **t = 92 Days** & **t = 360 Days** \\ \hline Concrete uniaxial compressive & & & \\ strength (\(\mathrm{f_{cm}}\)) (tested on a & 55 MPa & 57 MPa & 60 MPa \\ cylinder 150/300 mm) & & & \\ \hline Concrete tensile strength (\(\mathrm{f_{cl}}\)) & 7.3 MPa & 7.6 MPa & 8.0 MPa \\ (tested by splitting the cylinder) & & & \\ \hline Concrete elastic modulus (\(\mathrm{E_{cm}}\)) & 36.7 GPa & 37.1 GPa & 37.7 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of concrete over the time. Figure 18: Basic data of the tested slab. After t = 90 days from the day concrete was placed, the slab was put on supports, exposed to self-weight and a total load of P = 10 kN. The load P was uniformly distributed over the central area of the slab 0.9 m \(\times\) 0.9 m and applied in five equal increments, 2.0 kN each (one row of concrete cubes--Figure 19). After the full load P = 10 kN had been applied, it stayed for 360 days. After 3, 7, 14, 28, 90, 180 and 360 days from applying the full load, the slab deflection, the concrete compressive strain and the reinforcement tensile strain were measured at selected points for each load increment. The picture of the fully loaded tested slab is shown in Figure 19.  
Numerical Analysis by Precon3D and the Comparison of the Obtained Results  
In Figure 20, the finite element mesh for the concrete slab is shown. The reinforcement is shown with thick red (x-direction) and thick blue (y-direction) lines. The properties of each material are chosen according to values from the experiment. Some results from the numerical model are shown in Figure 21.  
Figure 21: Slab deflections during loading. Figure 21a-c show the measured slab deflections during loading (90 days after concreting) and the comparison with the numerical results is made. In Figure 21a,b, the comparison of the numerical and the experimental results for measuring points MU-1 and MU-2 is shown and a good agreement of the results is visible. Figure 21c shows the comparison of the numerical and the experimental results for measuring point MU-3 and, unlike measuring points MU-1 and MU-2, it shows a slightly lower agreement of the results, especially in the region of the appearance of nonlinearity. At this measuring point, a lower load level causes the appearance of more significant nonlinearity than in measuring points MU-1 and MU-2. The most pronounced difference between the numerical and the experimental results are in this region. There are many reasons for this difference, but the most prominent reason is the high amount of reinforcement placed in the y-direction. This significantly prevents the development of shrinkage strain that causes the appearance of higher tensile stresses in concrete in the y-direction than in the x-direction. These tensile stresses cause an earlier appearance of cracks in concrete, i.e., nonlinearity. For the final load level, there is a good agreement between the numerical and the experimental results. A significant increase in time-dependent deflections of the slab after the full load P is applied can be observed in Figure 21d-f for the experimental and the numerical results.