# Numerical Analysis of the Impact of Thermal Spray Insulation Solutions on Floor Loading
## Materials and Methods  
### Laboratory Tests  
The present study uses the results of in situ tests carried out in order to determine the value of the stiffness subgrade of an insulation layer made of closed-cell polyurethane spray foam. The subject of the tests was polyurethane foam used for insulating surfaces particularly exposed to mechanical impact with the following parameters: thermal conductivity coefficient \(\lambda=0.022\) W/(mK), density in the range of 34-37 kg/m\({}^{2}\), closed cell content approximately 95%, water absorption \(\leq 0.20\) kg/m\({}^{2}\). The tested material was taken from the construction site; the sheets were \(60\times 120\) cm, from which \(20\times 20\) cm test samples were made. The temperature in the laboratory where the samples were stored was 24\({}^{\circ}\) and they were stored for 6 h prior to testing. The tests cited in the paper was carried out with the use of 40 samples, 7 cm to 16 cm thick, according to [21; 22]. Figure 2 shows the measuring stand for conducting compressive strength tests of polyurethane foam samples and configuration of the universal testing machine prepared to perform the test (b). The force reading with an accuracy of 0.5 kN was carried out when the tested sample obtained 10% relative strain [21]. Figure 3 shows a sample made of polyurethane foam during the test (a) and the straight edge with a measuring accuracy of 1 mm used for measuring the deflection of the samples (b), while Figure 3c illustrates the universal testing machine with a visible straight edge prior to testing. We determined the average compressive stresses at 10% relative strain for a given thickness [21]. Formula (1) provided the basis to determine the subgrade stiffness for a given thickness, which was followed by determination of the average subgrade stiffness calculated from 40 tests. To carry out the  
Figure 2: Measuring stand for compressive strength tests (**a**) and measuring disc of the universal testing machine with configuration of the clock (**b**). tests, 40 samples were used in the following configuration: for 16 mm thickness, 2 samples; 14.5 mm, 1 sample; 14 mm, 3 samples; 13.5 mm, 1 sample; 13 mm, 5 samples; 12.5 mm, 1 sample; 12 mm, 2 samples; 10.5 mm, 2 samples; 9.5 mm, 3 samples; 9 mm, 3 samples; 8.5 mm, 3 samples; 8 mm, 10 samples; 7.5 mm, 1 sample; and 7 mm, 3 samples. The average compressive stress at 10% relative strain was determined for each of the thicknesses listed above, as provided in Table 1. Table 1 sets out the average compressive stress at 10% relative strain for a given thickness [23] and the determined average subgrade stiffness reaction for each sample thickness, followed by the average subgrade stiffness reaction obtained from all performed tests. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Thickness of the Sample [cm]**} & **Average Compressive** & **Average Subgrade** & **Average Subgrade** \\  & **Stresses at 10\% Relative** & **Stiffness Reaction for a** & **Stiffness Reaction** \\  & **Strain for a Given** & **Given Thickness** & **K [kN/m3]** \\  & **Thickness [kPa]** & **K [kN/m3]** & \\ \hline
16 & 300.0 & 18,750 & \\
14.5 & 305.0 & 21034 & \\
14 & 320.0 & 22,857 & \\
13.5 & 320.0 & 23,704 & \\
13 & 320.5 & 24,654 & \\
12.5 & 325.0 & 26,000 & \\
12 & 327.5 & 27,292 & \\
10.5 & 336.3 & 32,024 & \\
9.5 & 338.3 & 35,614 & \\
9 & 340.0 & 37,778 & \\
8.5 & 357.7 & 41,372 & \\
8 & 357.8 & 44,719 & \\
7.5 & 312.5 & 41,667 & \\
7 & 360.8 & 51,548 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average compressive stress values at 10% relative strain and average subgrade stiffness reaction for a given thickness along with average subgrade stiffness reaction. Figure 3: Polyurethane foam sample during compression in the testing machine (**a**), straight edge used for measuring deflections of samples (**b**), universal testing machine with a visible straight edge prior testing (**c**). With the use of Formula (3) for each point of the division mesh, a displacement equation was written.